Source code for empymod.filters

r"""

:mod:`filters` -- Digital Linear Filters
========================================

Filters for the *Digital Linear Filter* (DLF) method for the Hankel
[Ghos70]_) and the Fourier ([Ande75]_) transforms.

To calculate the ``dlf.factor`` I used

.. code-block:: python

    np.around(np.average(dlf.base[1:]/dlf.base[:-1]), 15)


The filters ``kong_61_2007`` and ``kong_241_2007`` from [Kong07]_, and
``key_101_2009``, ``key_201_2009``, ``key_401_2009``, ``key_81_CosSin_2009``,
``key_241_CosSin_2009``, and ``key_601_CosSin_2009`` from [Key09]_ are taken
from *DIPOLE1D*, [Key09]_, which can be downloaded at
http://marineemlab.ucsd.edu/Projects/Occam/1DCSEM (1DCSEM_). *DIPOLE1D* is
distributed under the license GNU GPL version 3 or later. Kerry Key gave his
written permission to re-distribute the filters under the Apache License,
Version 2.0 (email from Kerry Key to Dieter Werthmüller, 21 November 2016).

The filters ``anderson_801_1982`` from [Ande82]_ and ``key_51_2012``,
``key_101_2012``, ``key_201_2012``, ``key_101_CosSin_2012``, and
``key_201_CosSin_2012``, all from [Key12]_, are taken from the software
distributed with [Key12]_ and available at http://software.seg.org/2012/0003
(SEG-2012-003_). These filters are distributed under the SEG license.

The filter ``wer_201_2018`` was designed with the add-on ``fdesign``, see
https://github.com/empymod/article-fdesign.

.. _1DCSEM: http://marineemlab.ucsd.edu/Projects/Occam/1DCSEM
.. _SEG-2012-003: http://software.seg.org/2012/0003

"""
# Copyright 2016-2019 Dieter Werthmüller
#
# This file is part of empymod.
#
# Licensed under the Apache License, Version 2.0 (the "License"); you may not
# use this file except in compliance with the License.  You may obtain a copy
# of the License at
#
#     http://www.apache.org/licenses/LICENSE-2.0
#
# Unless required by applicable law or agreed to in writing, software
# distributed under the License is distributed on an "AS IS" BASIS, WITHOUT
# WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.  See the
# License for the specific language governing permissions and limitations under
# the License.


import os
import numpy as np

__all__ = ['DigitalFilter', 'kong_61_2007', 'kong_241_2007', 'key_101_2009',
           'key_201_2009', 'key_401_2009', 'anderson_801_1982', 'key_51_2012',
           'key_101_2012', 'key_201_2012', 'wer_201_2018',
           'key_81_CosSin_2009', 'key_241_CosSin_2009', 'key_601_CosSin_2009',
           'key_101_CosSin_2012', 'key_201_CosSin_2012']


# 0. Filter Class and saving/loading routines

[docs]class DigitalFilter: r"""Simple Class for Digital Linear Filters. Parameters ---------- name : str Name of the DFL. savename = str Name with which the filter is saved. If None (default) it is set to the same value as ``name``. filter_coeff = list of str By default, the following filter coefficients are checked: ``filter_coeff = ['j0', 'j1', 'sin', 'cos']`` This accounts for the standard Hankel and Fourier DLF in CSEM modelling. However, additional coefficient names can be provided via this parameter (in list format). """ def __init__(self, name, savename=None, filter_coeff=None): r"""Add filter name.""" self.name = name if savename is None: self.savename = name else: self.savename = savename # Define coefficient names. self.filter_coeff = ['j0', 'j1', 'sin', 'cos'] if filter_coeff is not None: # Additional, user provided. self.filter_coeff.extend(filter_coeff)
[docs] def tofile(self, path='filters'): r"""Save filter values to ascii-files. Store the filter base and the filter coefficients in separate files in the directory `path`; `path` can be a relative or absolute path. Examples -------- >>> import empymod >>> # Load a filter >>> filt = empymod.filters.wer_201_2018() >>> # Save it to pure ascii-files >>> filt.tofile() >>> # This will save the following three files: >>> # ./filters/wer_201_2018_base.txt >>> # ./filters/wer_201_2018_j0.txt >>> # ./filters/wer_201_2018_j1.txt """ # Get name of filter name = self.savename # Get absolute path, create if it doesn't exist path = os.path.abspath(path) os.makedirs(path, exist_ok=True) # Save filter base basefile = os.path.join(path, name + '_base.txt') with open(basefile, 'w') as f: self.base.tofile(f, sep="\n") # Save filter coefficients for val in self.filter_coeff: if hasattr(self, val): attrfile = os.path.join(path, name + '_' + val + '.txt') with open(attrfile, 'w') as f: getattr(self, val).tofile(f, sep="\n")
[docs] def fromfile(self, path='filters'): r"""Load filter values from ascii-files. Load filter base and filter coefficients from ascii files in the directory `path`; `path` can be a relative or absolute path. Examples -------- >>> import empymod >>> # Create an empty filter; >>> # Name has to be the base of the text files >>> filt = empymod.filters.DigitalFilter('my-filter') >>> # Load the ascii-files >>> filt.fromfile() >>> # This will load the following three files: >>> # ./filters/my-filter_base.txt >>> # ./filters/my-filter_j0.txt >>> # ./filters/my-filter_j1.txt >>> # and store them in filt.base, filt.j0, and filt.j1. """ # Get name of filter name = self.savename # Get absolute path path = os.path.abspath(path) # Get filter base basefile = os.path.join(path, name + '_base.txt') with open(basefile, 'r') as f: self.base = np.fromfile(f, sep="\n") # Get filter coefficients for val in self.filter_coeff: attrfile = os.path.join(path, name + '_' + val + '.txt') if os.path.isfile(attrfile): with open(attrfile, 'r') as f: setattr(self, val, np.fromfile(f, sep="\n")) # Add factor self.factor = np.around(np.average(self.base[1:]/self.base[:-1]), 15)
# 1. Hankel DLF
[docs]def kong_61_2007(): r"""Kong 61 pt Hankel filter, as published in [Kong07]_. Taken from file ``FilterModules.f90`` provided with 1DCSEM_. License: `Apache License, Version 2.0, <http://www.apache.org/licenses/LICENSE-2.0>`_. """ dlf = DigitalFilter('Kong 61', 'kong_61_2007') dlf.base = np.array([ 2.3517745856009100e-02, 2.6649097336355482e-02, 3.0197383422318501e-02, 3.4218118311666032e-02, 3.8774207831722009e-02, 4.3936933623407420e-02, 4.9787068367863938e-02, 5.6416139503777350e-02, 6.3927861206707570e-02, 7.2439757034251456e-02, 8.2084998623898800e-02, 9.3014489210663506e-02, 1.0539922456186430e-01, 1.1943296826671961e-01, 1.3533528323661270e-01, 1.5335496684492850e-01, 1.7377394345044520e-01, 1.9691167520419400e-01, 2.2313016014842979e-01, 2.5283959580474641e-01, 2.8650479686019009e-01, 3.2465246735834979e-01, 3.6787944117144239e-01, 4.1686201967850839e-01, 4.7236655274101469e-01, 5.3526142851899028e-01, 6.0653065971263342e-01, 6.8728927879097224e-01, 7.7880078307140488e-01, 8.8249690258459546e-01, 1.0000000000000000e+00, 1.1331484530668261e+00, 1.2840254166877421e+00, 1.4549914146182010e+00, 1.6487212707001280e+00, 1.8682459574322221e+00, 2.1170000166126748e+00, 2.3988752939670981e+00, 2.7182818284590451e+00, 3.0802168489180310e+00, 3.4903429574618419e+00, 3.9550767229205772e+00, 4.4816890703380636e+00, 5.0784190371800806e+00, 5.7546026760057307e+00, 6.5208191203301116e+00, 7.3890560989306504e+00, 8.3728974881272649e+00, 9.4877358363585262e+00, 1.0751013186076360e+01, 1.2182493960703470e+01, 1.3804574186067100e+01, 1.5642631884188170e+01, 1.7725424121461639e+01, 2.0085536923187671e+01, 2.2759895093526730e+01, 2.5790339917193059e+01, 2.9224283781234941e+01, 3.3115451958692312e+01, 3.7524723159601002e+01, 4.2521082000062783e+01]) dlf.factor = np.array([1.1331484530668261]) dlf.j0 = np.array([ 1.4463210615326699e+02, -1.1066222143752420e+03, 3.7030010025325978e+03, -6.8968188464424520e+03, 7.1663544112656937e+03, -2.4507884783377681e+03, -4.0166567754046082e+03, 6.8623845298546094e+03, -5.0013321011775661e+03, 2.1291291365196648e+03, -1.3845222435542289e+03, 2.1661554291595580e+03, -2.2260393789657141e+03, 8.0317156013986391e+02, 1.0142221718890841e+03, -1.9350455051432630e+03, 1.6601169447226580e+03, -7.5159684285420133e+02, -9.0315984178183285e+01, 5.0705574889546148e+02, -5.1207646422722519e+02, 2.9722959494490038e+02, -5.0248319908072993e+01, -1.2290725861955920e+02, 1.9695244755899429e+02, -1.9175679966946601e+02, 1.4211755630338590e+02, -7.7463216543224149e+01, 1.7638009334931201e+01, 2.8855056499202671e+01, -5.9225643887809561e+01, 7.5987941373668960e+01, -8.1687962781233580e+01, 8.0599209238447102e+01, -7.4895905328771619e+01, 6.7516291538794434e+01, -5.9325033647358048e+01, 5.1617042242841528e+01, -4.4664967446820263e+01, 3.8366152052928278e+01, -3.3308787868993100e+01, 2.8278671651033459e+01, -2.4505863388620480e+01, 2.0469632532079750e+01, -1.7074034940700429e+01, 1.4206119215530070e+01, -1.0904435643084650e+01, 8.7518389425802283e+00, -6.7721665239085622e+00, 4.5096884588095891e+00, -3.2704247166629590e+00, 2.6827195063720430e+00, -1.8406031821386459e+00, 9.1586697140412443e-01, -3.2436011485890798e-01, 8.0675176189581893e-02, -1.2881307195759690e-02, 7.0489137468452920e-04, 2.3846917590855061e-04, -6.9102205995825531e-05, 6.7792635718095777e-06]) dlf.j1 = np.array([ 4.6440396425864918e+01, -4.5034239857914162e+02, 1.7723440076223640e+03, -3.7559735516994660e+03, 4.4736494009764137e+03, -2.2476603569606068e+03, -1.5219842155931799e+03, 3.4904608559273802e+03, -2.4814243247472318e+03, 5.7328164634108396e+02, 5.3132044837659631e-01, 6.8895205008006235e+02, -1.2012013872160269e+03, 7.9679138423597340e+02, 4.9874460187939818e+01, -5.6367338332457007e+02, 4.7971936503711203e+02, -5.8979702298044558e+01, -3.1935800954986922e+02, 4.5762551999442371e+02, -3.7239927283248380e+02, 1.8255852885279569e+02, -2.3504740340815669e-01, -1.1588151583545380e+02, 1.5740956677133170e+02, -1.4334746114883359e+02, 9.9857411013284818e+01, -4.8246322019171487e+01, 2.0371404343057380e+00, 3.3003938094974323e+01, -5.5476151884197712e+01, 6.7354852323852583e+01, -7.0735403363284121e+01, 6.8872932663164747e+01, -6.3272750944993042e+01, 5.6501568721817442e+01, -4.8706577819918110e+01, 4.1737211284663481e+01, -3.4776621242200903e+01, 2.9161717578906430e+01, -2.3886749056000909e+01, 1.9554007583544220e+01, -1.5966397353366460e+01, 1.2429310210239199e+01, -1.0139180791868180e+01, 7.4716493393871861e+00, -5.5509479014742613e+00, 4.3380799768234208e+00, -2.5911516181746550e+00, 1.6300524630626780e+00, -1.4041567266387460e+00, 7.5225141726873213e-01, 4.6808777208492733e-02, -3.6630197849601159e-01, 2.8948389902792782e-01, -1.3705521898064801e-01, 4.6292091649913013e-02, -1.1721281347435180e-02, 2.2002397354029149e-03, -2.8146036357227600e-04, 1.8788896009128770e-05]) return dlf
[docs]def kong_241_2007(): r"""Kong 241 pt Hankel filter, as published in [Kong07]_. Taken from file ``FilterModules.f90`` provided with 1DCSEM_. License: `Apache License, Version 2.0, <http://www.apache.org/licenses/LICENSE-2.0>`_. """ dlf = DigitalFilter('Kong 241', 'kong_241_2007') dlf.base = np.array([ 4.0973497897978643e-04, 4.3725238042414673e-04, 4.6661782370309847e-04, 4.9795542150327349e-04, 5.3139762179825294e-04, 5.6708576763830356e-04, 6.0517069453505309e-04, 6.4581336796593124e-04, 6.8918556369279311e-04, 7.3547059377007120e-04, 7.8486408131093165e-04, 8.3757478728596971e-04, 8.9382549284889267e-04, 9.5385394091834482e-04, 1.0179138409954376e-03, 1.0862759414638579e-03, 1.1592291739045914e-03, 1.2370818742617167e-03, 1.3201630860205026e-03, 1.4088239509056637e-03, 1.5034391929775724e-03, 1.6044087023989032e-03, 1.7121592255655228e-03, 1.8271461687448972e-03, 1.9498555228451206e-03, 2.0808059174495293e-03, 2.2205508127982939e-03, 2.3696808389813539e-03, 2.5288262922292556e-03, 2.6986597988524685e-03, 2.8798991580882404e-03, 3.0733103758703055e-03, 3.2797109023435700e-03, 3.4999730868071656e-03, 3.7350278646880674e-03, 3.9858686921282905e-03, 4.2535557448151254e-03, 4.5392203988006852e-03, 4.8440700122489664e-03, 5.1693930283203291e-03, 5.5165644207607716e-03, 5.8870515052116155e-03, 6.2824201408011177e-03, 6.7043413482289257e-03, 7.1545983723145792e-03, 7.6350942188599617e-03, 8.1478596976799818e-03, 8.6950620057954561e-03, 9.2790138870647437e-03, 9.9021834069673818e-03, 1.0567204383852655e-02, 1.1276887520740558e-02, 1.2034232284723775e-02, 1.2842439584178571e-02, 1.3704925297364945e-02, 1.4625334709594208e-02, 1.5607557919982831e-02, 1.6655746282908664e-02, 1.7774329953659442e-02, 1.8968036612429941e-02, 2.0241911445804381e-02, 2.1601338470175833e-02, 2.3052063287225571e-02, 2.4600217367638302e-02, 2.6252343965687961e-02, 2.8015425774221808e-02, 2.9896914436926308e-02, 3.1904762042607962e-02, 3.4047454734599344e-02, 3.6334048577339996e-02, 3.8774207831722009e-02, 4.1378245800970381e-02, 4.4157168419692860e-02, 4.7122720770327912e-02, 5.0287436723591865e-02, 5.3664691912730114e-02, 5.7268760265467331e-02, 6.1114874332588359e-02, 6.5219289668127525e-02, 6.9599353533269015e-02, 7.4273578214333877e-02, 7.9261719264731550e-02, 8.4584859001564691e-02, 9.0265495609784266e-02, 9.6327638230493035e-02, 1.0279690843528640e-01, 1.0970064851551141e-01, 1.1706803704412637e-01, 1.2493021219858241e-01, 1.3332040336594936e-01, 1.4227407158651356e-01, 1.5182905942943059e-01, 1.6202575093388075e-01, 1.7290724229171636e-01, 1.8451952399298926e-01, 1.9691167520419406e-01, 2.1013607120076472e-01, 2.2424860473053532e-01, 2.3930892224375450e-01, 2.5538067598807768e-01, 2.7253179303401259e-01, 2.9083476236785155e-01, 3.1036694126548503e-01, 3.3121088224198103e-01, 3.5345468195878016e-01, 3.7719235356315689e-01, 4.0252422403363597e-01, 4.2955735821073915e-01, 4.5840601130522352e-01, 4.8919211179633149e-01, 5.2204577676101604e-01, 5.5710586181217392e-01, 5.9452054797019427e-01, 6.3444796794822822e-01, 6.7705687449816465e-01, 7.2252735364207221e-01, 7.7105158580356625e-01, 8.2283465805601841e-01, 8.7809543092056130e-01, 9.3706746337740343e-01, 1.0000000000000000e+00, 1.0671590243841926e+00, 1.1388283833246218e+00, 1.2153109864897309e+00, 1.2969300866657718e+00, 1.3840306459807514e+00, 1.4769807938826425e+00, 1.5761733830339912e+00, 1.6820276496988864e+00, 1.7949909856399000e+00, 1.9155408290138962e+00, 2.0441866822585570e+00, 2.1814722654982011e+00, 2.3279778145702346e+00, 2.4843225333848169e+00, 2.6511672109826070e+00, 2.8292170143515598e+00, 3.0192244688065686e+00, 3.2219926385284996e+00, 3.4383785207051250e+00, 3.6692966676192444e+00, 3.9157230519927220e+00, 4.1786991919232470e+00, 4.4593365528478257e+00, 4.7588212451378542e+00, 5.0784190371800815e+00, 5.4194807051312059e+00, 5.7834477419567749e+00, 6.1718584498835538e+00, 6.5863544420150681e+00, 7.0286875805892945e+00, 7.5007273812029629e+00, 8.0044689142963534e+00, 8.5420412372940930e+00, 9.1157163930403051e+00, 9.7279190125598838e+00, 1.0381236562731843e+01, 1.1078430282186428e+01, 1.1822446851646363e+01, 1.2616430848036902e+01, 1.3463738035001692e+01, 1.4367949545996751e+01, 1.5332887019907195e+01, 1.6362628753157214e+01, 1.7461526936579997e+01, 1.8634226049899006e+01, 1.9885682491564729e+01, 2.1221185526912038e+01, 2.2646379643175401e+01, 2.4167288405845099e+01, 2.5790339917193062e+01, 2.7522393984568446e+01, 2.9370771113289432e+01, 3.1343283446669389e+01, 3.3448267783944921e+01, 3.5694620815655881e+01, 3.8091836725399020e+01, 4.0650047316878776e+01, 4.3380064835851620e+01, 4.6293427667950432e+01, 4.9402449105530195e+01, 5.2720269389647328e+01, 5.6260911247127851e+01, 6.0039339157450577e+01, 6.4071522599936642e+01, 6.8374503548558152e+01, 7.2966468499632811e+01, 7.7866825336828100e+01, 8.3096285358343764e+01, 8.8676950812960627e+01, 9.4632408314924064e+01, 1.0098782853248096e+02, 1.0777007257140046e+02, 1.1500780550310940e+02, 1.2273161751726525e+02, 1.3097415321081860e+02, 1.3977024956000301e+02, 1.4915708315838788e+02, 1.5917432734329714e+02, 1.6986431987468302e+02, 1.8127224187515122e+02, 1.9344630878742183e+02, 2.0643797415630826e+02, 2.2030214709649516e+02, 2.3509742436523857e+02, 2.5088633802084459e+02, 2.6773561971364717e+02, 2.8571648272651305e+02, 3.0490492295690876e+02, 3.2538204011263201e+02, 3.4723438047873475e+02, 3.7055430270433595e+02, 3.9544036815532411e+02, 4.2199775748276141e+02, 4.5033871516762099e+02, 4.8058302392070897e+02, 5.1285851094282907e+02, 5.4730158818487951e+02, 5.8405782889129489e+02, 6.2328258286358414e+02, 6.6514163304436181e+02, 7.0981189619693009e+02, 7.5748217064180938e+02, 8.0835393421053413e+02, 8.6264219578923701e+02, 9.2057640405108020e+02, 9.8240141721825944e+02, 1.0483785379522853e+03, 1.1187866177464875e+03, 1.1939232354884318e+03, 1.2741059551734540e+03, 1.3596736680849924e+03, 1.4509880251144575e+03, 1.5484349652742915e+03, 1.6524263468644833e+03, 1.7634016881866382e+03, 1.8818300251626902e+03, 2.0082118937094979e+03, 2.1430814452477584e+03, 2.2870087042864643e+03, 2.4406019776245007e+03]) dlf.factor = np.array([1.0671590243841931]) dlf.j0 = np.array([ 2.0521734894828349e+01, -1.8902686822627982e+02, 7.3615711333621391e+02, -1.5743636401162100e+03, 1.9044172285355407e+03, -9.3177949828687565e+02, -8.4756674787751410e+02, 1.8896580243120454e+03, -1.4364973619770130e+03, 3.9999475225222255e+02, -1.3542454844021287e+02, 9.2532241451272546e+02, -1.9710056537324476e+03, 2.4446279171484089e+03, -2.1906123203102729e+03, 1.5850478978775775e+03, -1.0505328230896389e+03, 7.6984613632493506e+02, -7.0040976495766233e+02, 7.1606276337453505e+02, -7.1676220487815579e+02, 6.6234563164374151e+02, -5.5792724680287802e+02, 4.2758743543890813e+02, -2.9556591300691770e+02, 1.7825665706981184e+02, -8.3414675513698882e+01, 1.2417017098470755e+01, 3.7033552727335611e+01, -6.8808606022416711e+01, 8.7059849275066583e+01, -9.5546538383371242e+01, 9.7381161313521631e+01, -9.4989208296887298e+01, 9.0188673544147917e+01, -8.4292718636942382e+01, 7.8226832173348868e+01, -7.2614408878060885e+01, 6.7859682477117360e+01, -6.4196278592205076e+01, 6.1741547025682522e+01, -6.0519141387284385e+01, 6.0491769334480402e+01, -6.1560425911383518e+01, 6.3581206383691445e+01, -6.6354594873531482e+01, 6.9646829420226268e+01, -7.3188103112902326e+01, 7.6708283429767803e+01, -7.9940731778724427e+01, 8.2660409124105158e+01, -8.4678217919647295e+01, 8.5870333056460041e+01, -8.6157409171557106e+01, 8.5526114160418373e+01, -8.3997300873449348e+01, 8.1646015415233720e+01, -7.8563495286564020e+01, 7.4879819626555161e+01, -7.0721125046688840e+01, 6.6236029868394425e+01, -6.1547931592552032e+01, 5.6787391190038285e+01, -5.2042250889790630e+01, 4.7401124144337359e+01, -4.2904131591225969e+01, 3.8598898252452933e+01, -3.4488213955995406e+01, 3.0594494176351635e+01, -2.6898802810010366e+01, 2.3412439481509015e+01, -2.0106495314306827e+01, 1.6993408313817032e+01, -1.4047029053019282e+01, 1.1294767677459204e+01, -8.7239710357940154e+00, 6.3824509509500222e+00, -4.2667780201601095e+00, 2.4325051404370148e+00, -8.6492951505166771e-01, -3.9467042614078562e-01, 1.3928518582065126e+00, -2.1151897072040806e+00, 2.6442660480353983e+00, -2.9851029846728716e+00, 3.2414793692894390e+00, -3.4159478759422446e+00, 3.6114813897567299e+00, -3.8065481471148583e+00, 4.0881401855578137e+00, -4.3995650940379534e+00, 4.8090112941999275e+00, -5.2256078193681690e+00, 5.7072204037420695e+00, -6.1390449324831593e+00, 6.5839615678399346e+00, -6.9164266653291033e+00, 7.2188877597238257e+00, -7.3636288680068356e+00, 7.4607479507817942e+00, -7.3815887701068963e+00, 7.2656732754121194e+00, -6.9791586417386533e+00, 6.6886849969172548e+00, -6.2474308336775373e+00, 5.8445619106015023e+00, -5.3113072582819267e+00, 4.8557012512460096e+00, -4.2807487698944051e+00, 3.8139742889863348e+00, -3.2285888930306363e+00, 2.7762320886023009e+00, -2.2014921362632469e+00, 1.7852627321359549e+00, -1.2441166658179819e+00, 8.9066883548526044e-01, -4.1204139236605647e-01, 1.5134230126345752e-01, 2.3623794557833316e-01, -3.8120367816755335e-01, 6.6106381680388782e-01, -6.8548466976773659e-01, 8.6073950596627435e-01, -7.8244282877711779e-01, 8.7517842089752496e-01, -7.3021880955390983e-01, 7.7262232832472633e-01, -6.0480748494904057e-01, 6.2658579242671697e-01, -4.7604045939428874e-01, 4.9376650403683020e-01, -3.8947933764667242e-01, 4.0212565692397595e-01, -3.6042458247357878e-01, 3.5204231781815948e-01, -3.7930843668720610e-01, 3.2733689195982146e-01, -4.2315508593901219e-01, 3.0989441332277490e-01, -4.6647831068082313e-01, 2.9127018318261688e-01, -4.8705387071535239e-01, 2.7698618486052751e-01, -4.6732646495222491e-01, 2.8247063840665948e-01, -3.9734195755492102e-01, 3.2057830222839734e-01, -2.8520009926766782e-01, 3.8137726386396886e-01, -1.7293887127458049e-01, 4.1451464616516831e-01, -1.3721835010891198e-01, 3.4710931937928907e-01, -2.3427502149669574e-01, 1.7531537381430198e-01, -3.8202053727848895e-01, 6.9544164681199228e-02, -3.4148035441124835e-01, 2.2691549707658903e-01, -7.7194405672412439e-02, 3.9072641204282460e-01, -8.3147250278941501e-02, 9.2847198484461116e-02, -3.6217207710792204e-01, 1.0822725873639430e-02, 5.1804674714713058e-03, 3.1786543576503390e-01, -7.5374320952788773e-02, -1.9068492965240180e-01, -8.3243368421653877e-02, 2.8203125407893237e-01, -1.6118506235275606e-02, -2.6963245268577724e-01, 1.9777266987246947e-01, 8.3472930934463230e-02, -2.7664291725690993e-01, 2.8131050087465398e-01, -1.7190500226396740e-01, 4.7929281626787730e-02, 4.0609103740114338e-02, -8.8052363812875192e-02, 1.0655635530077956e-01, -1.0911039889769197e-01, 1.0429389492393636e-01, -9.6633502650203901e-02, 8.8193660973234708e-02, -7.9818272272792340e-02, 7.1826372817129266e-02, -6.4338746209327960e-02, 5.7410843811670373e-02, -5.1077264811879450e-02, 4.5360450730759908e-02, -4.0267658416644959e-02, 3.5786523769444523e-02, -3.1883184387833892e-02, 2.8503987928848736e-02, -2.5580391582215669e-02, 2.3035937972928848e-02, -2.0793869607217731e-02, 1.8783956187539304e-02, -1.6947463041594817e-02, 1.5239810059902827e-02, -1.3631136080120022e-02, 1.2105408954537602e-02, -1.0658744979296539e-02, 9.2973012802827770e-03, -8.0347421903655229e-03, 6.8891191289946248e-03, -5.8791440085348362e-03, 5.0201744968206546e-03, -4.3205477515280673e-03, 3.7790104974130003e-03, -3.3838316346466528e-03, 3.1138040173687830e-03, -2.9408759849158255e-03, 2.8337622799129800e-03, -2.7617063348841968e-03, 2.6976528553792770e-03, -2.6203758209448719e-03, 2.5154519816519300e-03, -2.3752432671978732e-03, 2.1981931889228849e-03, -1.9877598903184075e-03, 1.7512378319139862e-03, -1.4986007967920582e-03, 1.2413783399553321e-03, -9.9151066433110242e-04, 7.6014790547529541e-04, -5.5645455379022023e-04, 3.8658922048399793e-04, -2.5308541294203246e-04, 1.5481736123335846e-04, -8.7598356988947244e-05, 4.5276882194925013e-05, -2.1044884609057091e-05, 8.6194148443616213e-06, -3.0265483432492266e-06, 8.7586378588036060e-07, -1.9631579670478718e-07, 3.0405955678339503e-08, -2.4535953018971818e-09]) dlf.j1 = np.array([ -6.8036776043707992e+00, 1.2311367914708828e+02, -6.0393880274694629e+02, 1.4366739793969700e+03, -1.8485584122626103e+03, 1.0200389392810666e+03, 5.5616172944428206e+02, -1.3603216652028611e+03, 7.0167261135195611e+02, 5.3402931472384910e+02, -1.1429297666385887e+03, 9.0089651035093164e+02, -4.1234322841018411e+02, 2.0384051761852257e+02, -2.8956552394430940e+02, 4.0377046372586426e+02, -3.6323786432883537e+02, 1.8298774315085831e+02, 1.9289907486739775e+01, -1.4580899521803201e+02, 1.6824962609150825e+02, -1.1236235241859872e+02, 2.2347944322515357e+01, 6.4941329832499832e+01, -1.2923900641568204e+02, 1.6503157425386775e+02, -1.7577683834104877e+02, 1.6854431620724952e+02, -1.5058653072004714e+02, 1.2774003008692418e+02, -1.0402698302316379e+02, 8.1858707646356891e+01, -6.2444337865410809e+01, 4.6197726342228336e+01, -3.3061362052896769e+01, 2.2733224772330665e+01, -1.4810952273048434e+01, 8.8755599393231179e+00, -4.5352205696513836e+00, 1.4449219838043461e+00, 6.8743711356557613e-01, -2.1019399621163908e+00, 2.9910240715100782e+00, -3.5052807631070255e+00, 3.7597471619400826e+00, -3.8399078959004260e+00, 3.8072695188293357e+00, -3.7042465619688505e+00, 3.5586759844836791e+00, -3.3877703451391699e+00, 3.2017608368233237e+00, -3.0067309393330288e+00, 2.8068645418014970e+00, -2.6056123347708602e+00, 2.4063835683466084e+00, -2.2124155853618990e+00, 2.0267333591783983e+00, -1.8516694378892813e+00, 1.6889204130272601e+00, -1.5392291077389748e+00, 1.4027911155907105e+00, -1.2791049665324250e+00, 1.1676349053464947e+00, -1.0675953584302726e+00, 9.7863461730665857e-01, -9.0027354444851670e-01, 8.3249709182475107e-01, -7.7482174407455295e-01, 7.2701622202684046e-01, -6.8800213341352723e-01, 6.5698937864345264e-01, -6.3225165202126643e-01, 6.1273246350052379e-01, -5.9649977526660647e-01, 5.8279442137494575e-01, -5.6994253522747218e-01, 5.5790401373575793e-01, -5.4545052833277607e-01, 5.3336442347695479e-01, -5.2069797861987954e-01, 5.0887851227988856e-01, -4.9685712521558462e-01, 4.8646743314063406e-01, -4.7619096686921952e-01, 4.6816529269778301e-01, -4.6015156373071614e-01, 4.5466141540832178e-01, -4.4857363825706975e-01, 4.4499201335812283e-01, -4.3980181069680696e-01, 4.3704907382079500e-01, -4.3150722634129624e-01, 4.2859194645669874e-01, -4.2173773973311074e-01, 4.1817784119266610e-01, -4.0960162465920091e-01, 4.0553804034464430e-01, -3.9532815510851277e-01, 3.9136208758411489e-01, -3.7983009113722693e-01, 3.7671762005172676e-01, -3.6406330003120191e-01, 3.6244935256730459e-01, -3.4854450330689657e-01, 3.4888232036420985e-01, -3.3325449310423266e-01, 3.3591600342224537e-01, -3.1786716813473143e-01, 3.2333450491673743e-01, -3.0206709086775535e-01, 3.1108664637173294e-01, -2.8574426655786522e-01, 2.9938562076378405e-01, -2.6899179718067823e-01, 2.8862849386853856e-01, -2.5197407940080729e-01, 2.7924443578937680e-01, -2.3479292380166417e-01, 2.7158086404171844e-01, -2.1743177724854762e-01, 2.6585734716833231e-01, -1.9977886402875333e-01, 2.6215186968647208e-01, -1.8169913895160320e-01, 2.6037686710257568e-01, -1.6314391449016330e-01, 2.6022362236599678e-01, -1.4430969552882361e-01, 2.6106112640293244e-01, -1.2585051878275111e-01, 2.6176557155826263e-01, -1.0912157374630198e-01, 2.6047541087804182e-01, -9.6410349758274366e-02, 2.5434822704405619e-01, -9.1058907636613021e-02, 2.3952590152331843e-01, -9.7233907394681532e-02, 2.1169127037476246e-01, -1.1886530901829440e-01, 1.6780342130647322e-01, -1.5708700322500274e-01, 1.0962587924131692e-01, -2.0578176345887339e-01, 4.8885661268589009e-02, -2.4642892106977957e-01, 1.1194065592765716e-02, -2.4747581882772479e-01, 3.0611266302904498e-02, -1.7906330306689583e-01, 1.2284053143305627e-01, -5.2283741701101033e-02, 2.3805370442772930e-01, 3.8699307341758679e-02, 2.4690725918834208e-01, -3.8424035688006668e-02, 7.1201119703791560e-02, -2.3889263981505893e-01, -7.7114690286621504e-02, -2.1836754494419724e-01, 1.2315414896678636e-01, 7.5338270471735747e-02, 2.7696240054976468e-01, -6.8197423407317256e-02, -9.2154357023181005e-02, -2.7364306064385413e-01, 1.4776915895856893e-01, 1.5391397605873250e-01, 1.1202666775507018e-01, -3.3501468763636766e-01, 5.3448876160720617e-02, 1.8824613952112992e-01, -4.6814043305072224e-03, -3.0449707752313021e-01, 3.7651614016005935e-01, -2.0743158205566595e-01, -1.1420479303107758e-02, 1.4728687125987736e-01, -1.8431611574819040e-01, 1.6270659034524407e-01, -1.2222143749935742e-01, 8.4181157909789264e-02, -5.5281360387327068e-02, 3.5292561498256686e-02, -2.1995586173467183e-02, 1.3230592337602392e-02, -7.4157047320195287e-03, 3.5088522519723777e-03, -8.5018538826118518e-04, -9.7550322159493529e-04, 2.2326305963338822e-03, -3.0933635050624424e-03, 3.6729552029512069e-03, -4.0509173928643906e-03, 4.2837535729585508e-03, -4.4126872566431202e-03, 4.4684173716055568e-03, -4.4741053242745125e-03, 4.4473069057176040e-03, -4.4012645981419867e-03, 4.3457940693551285e-03, -4.2878952176510369e-03, 4.2321726027587606e-03, -4.1811395672186466e-03, 4.1354762911556932e-03, -4.0942937154137878e-03, 4.0554223224550864e-03, -4.0157136359124266e-03, 3.9713297394453244e-03, -3.9180044788809047e-03, 3.8512768724064841e-03, -3.7667091650295829e-03, 3.6601079883520934e-03, -3.5277760443730628e-03, 3.3668346001750932e-03, -3.1756548702066185e-03, 2.9543911277564146e-03, -2.7055140265840505e-03, 2.4341413354852411e-03, -2.1479350621587340e-03, 1.8564376110443456e-03, -1.5699285271508928e-03, 1.2980859369581127e-03, -1.0488156933979571e-03, 8.2752974192331252e-04, -6.3697315746016306e-04, 4.7751718968428873e-04, -3.4772734444372060e-04, 2.4499928240303252e-04, -1.6610663484386119e-04, 1.0758513633705277e-04, -6.5954676827986505e-05, 3.7834534141493396e-05, -2.0025414475625305e-05, 9.6121169858568779e-06, -4.0939692455506115e-06, 1.5034842918522733e-06, -4.5718370169166360e-07, 1.0805490301555136e-07, -1.7684735514194769e-08, 1.5081394131412287e-09]) return dlf
[docs]def key_101_2009(): r"""Key 101 pt Hankel filter, as published in [Key09]_. Taken from file ``FilterModules.f90`` provided with 1DCSEM_. License: `Apache License, Version 2.0, <http://www.apache.org/licenses/LICENSE-2.0>`_. """ dlf = DigitalFilter('Key 101 (2009)', 'key_101_2009') dlf.base = np.array([ 3.182780796509667e-03, 3.570677233218250e-03, 4.005847942090417e-03, 4.494054401183452e-03, 5.041760259690979e-03, 5.656216913953108e-03, 6.345559512909110e-03, 7.118914664064660e-03, 7.986521265955502e-03, 8.959866066878890e-03, 1.005183574463358e-02, 1.127688752074056e-02, 1.265124056800531e-02, 1.419309074557768e-02, 1.592285150451168e-02, 1.786342415331403e-02, 2.004050106168401e-02, 2.248290581673552e-02, 2.522297483522721e-02, 2.829698548418685e-02, 3.174563637806794e-02, 3.561458621137186e-02, 3.995505826065390e-02, 4.482451855926687e-02, 5.028743672359186e-02, 5.641613950377735e-02, 6.329176835964070e-02, 7.100535373963698e-02, 7.965902028589801e-02, 8.936733892175319e-02, 1.002588437228037e-01, 1.124777336542896e-01, 1.261857817050387e-01, 1.415644766941340e-01, 1.588174261069207e-01, 1.781730517728984e-01, 1.998876140751445e-01, 2.242486047305353e-01, 2.515785530597565e-01, 2.822392961405233e-01, 3.166367693790532e-01, 3.552263809249515e-01, 3.985190410845142e-01, 4.470879265593564e-01, 5.015760690660555e-01, 5.627048688069557e-01, 6.312836455069260e-01, 7.082203534678000e-01, 7.945336025033340e-01, 8.913661439068313e-01, 1.000000000000000e+00, 1.121873437571938e+00, 1.258600009929478e+00, 1.411989919667659e+00, 1.584073984994482e+00, 1.777130526914038e+00, 1.993715533243082e+00, 2.236696498819987e+00, 2.509290389936297e+00, 2.815106235624064e+00, 3.158192909689768e+00, 3.543092736108982e+00, 3.974901627494749e+00, 4.459336552847826e+00, 5.002811227833588e+00, 5.612521029693157e+00, 6.296538261026657e+00, 7.063919023701211e+00, 7.924823117849490e+00, 8.890648553371371e+00, 9.974182454814724e+00, 1.118977035755271e+01, 1.255350613666823e+01, 1.408344508312441e+01, 1.579984294826040e+01, 1.772542412146164e+01, 1.988568249156473e+01, 2.230921897527583e+01, 2.502812018133782e+01, 2.807838322380105e+01, 3.150039230874794e+01, 3.533945340427969e+01, 3.964639407257260e+01, 4.447823640552875e+01, 4.989895197340787e+01, 5.598030878164415e+01, 6.280282144920171e+01, 7.045681718843254e+01, 7.904363169956446e+01, 8.867695081296063e+01, 9.948431564193386e+01, 1.116088111737080e+02, 1.252109606547652e+02, 1.404708508514462e+02, 1.575905163233670e+02, 1.767966142764323e+02, 1.983434254093812e+02, 2.225162204838159e+02, 2.496350371896939e+02, 2.800589173104007e+02, 3.141906602856942e+02]) dlf.factor = np.array([1.1218734375719379]) dlf.j0 = np.array([ 1.761499629714979e+00, -1.261104080802587e+01, 4.589440735380221e+01, -1.137201615271146e+02, 2.171373845748458e+02, -3.427418757004401e+02, 4.682970092296048e+02, -5.721810218704758e+02, 6.404705872914975e+02, -6.689903305418517e+02, 6.614840943418809e+02, -6.261458042620394e+02, 5.724742839763362e+02, -5.091188391804840e+02, 4.429121852279642e+02, -3.786064826795332e+02, 3.191588258655895e+02, -2.660734942256455e+02, 2.198909349916423e+02, -1.804655347160418e+02, 1.473251045730838e+02, -1.197617622162473e+02, 9.706708172663220e+01, -7.848237715099181e+01, 6.337970122621439e+01, -5.112377096515730e+01, 4.125319165745542e+01, -3.328022871692455e+01, 2.690546850964645e+01, -2.176077775919447e+01, 1.767900438275361e+01, -1.437298500741315e+01, 1.177821110514306e+01, -9.653214292533669e+00, 8.014188621856462e+00, -6.636716121370467e+00, 5.605112419659892e+00, -4.690136885102554e+00, 4.040369173672801e+00, -3.404103887583860e+00, 2.995747642598741e+00, -2.524176278751386e+00, 2.274303867444810e+00, -1.898578152750098e+00, 1.759903177266298e+00, -1.438255316175359e+00, 1.383718859899911e+00, -1.090411693791455e+00, 1.103187499775871e+00, -8.232645366851894e-01, 8.897253309567960e-01, -6.181710614766990e-01, 7.214321035775552e-01, -4.660523646863802e-01, 5.784691305884657e-01, -3.658095952962029e-01, 4.407748104824833e-01, -3.217298446491200e-01, 2.909042759264825e-01, -3.338253349563184e-01, 1.293953529828388e-01, -3.718639185374572e-01, 8.698186744359777e-03, -3.389828291018994e-01, 4.963953772877858e-02, -1.147290346722791e-01, 2.818501136331604e-01, 1.360129862128020e-01, 2.683528605579231e-01, -1.505769588191184e-01, -2.031064772010313e-01, -2.437687529694006e-01, 2.876770799753536e-01, 2.011329588874316e-01, -2.275463527816749e-01, -1.749917271598988e-01, 4.306671898041470e-01, -3.992878212851492e-01, 2.550550974806911e-01, -1.336748872779371e-01, 6.423008702535922e-02, -3.108808914792973e-02, 1.639821648563433e-02, -9.842274279418138e-03, 6.685502920904526e-03, -4.955006305606947e-03, 3.851240446211632e-03, -3.047184325211406e-03, 2.405935290382968e-03, -1.869259018281964e-03, 1.412821020240033e-03, -1.027340635931714e-03, 7.099124273512882e-04, -4.593396038963651e-04, 2.731571829548821e-04, -1.457155899557221e-04, 6.748422483369748e-05, -2.590402870915282e-05, 7.676168023731497e-06, -1.549433571510781e-06, 1.584912057504873e-07]) dlf.j1 = np.array([ 3.382421751388876e-04, -2.080089427136974e-03, 6.616516890510206e-03, -1.444442106541980e-02, 2.445603365138576e-02, -3.439020151920317e-02, 4.205277853503258e-02, -4.616883971957859e-02, 4.665044563723574e-02, -4.417942425707860e-02, 3.983124989286448e-02, -3.456241855974430e-02, 2.919015247012813e-02, -2.413480064473489e-02, 1.973163931127073e-02, -1.595784764119277e-02, 1.292753867241687e-02, -1.040069021237603e-02, 8.496859564365926e-03, -6.857608112687733e-03, 5.734515396281575e-03, -4.635710275375116e-03, 4.034369992101164e-03, -3.217728935403965e-03, 2.990802607299357e-03, -2.269398404454681e-03, 2.363714769044985e-03, -1.583785021876379e-03, 2.025371816097564e-03, -1.027952174606392e-03, 1.922153595502174e-03, -5.043945522132147e-04, 2.054567905217619e-03, 7.633835394740574e-05, 2.471902278652444e-03, 8.190345324336234e-04, 3.277371965548541e-03, 1.870779100759767e-03, 4.642867014031185e-03, 3.454727180711420e-03, 6.839165720545689e-03, 5.911273173907802e-03, 1.028566504388743e-02, 9.752018620581887e-03, 1.561636209584471e-02, 1.572789508971819e-02, 2.375132082749520e-02, 2.489168113861482e-02, 3.593610268802203e-02, 3.858602166700044e-02, 5.363612015669736e-02, 5.817318184012853e-02, 7.800216974165830e-02, 8.408281670359681e-02, 1.083042686943279e-01, 1.133712057428050e-01, 1.383564865699443e-01, 1.348125772346644e-01, 1.504073961323417e-01, 1.224262032649067e-01, 1.106446266767018e-01, 3.772825296930285e-02, -1.353204196275998e-02, -1.266046406313744e-01, -1.730074119319237e-01, -2.327661941998823e-01, -1.312677137162940e-01, -1.104509755532312e-02, 2.294237929047981e-01, 2.327988918717147e-01, 9.149367519642598e-02, -3.004964869169849e-01, -1.797040516746428e-01, 1.817308988818578e-01, 2.935346562382805e-01, -4.502465801331593e-01, 2.151483212376926e-01, 4.924585434461976e-02, -1.679842097056792e-01, 1.754997616383300e-01, -1.428351980172456e-01, 1.076274808049898e-01, -8.030885482867917e-02, 6.079630210587774e-02, -4.687267027003955e-02, 3.664115351116358e-02, -2.884253032421485e-02, 2.269535305564210e-02, -1.772060472957579e-02, 1.362455706705945e-02, -1.022825775681532e-02, 7.424720522409015e-03, -5.150709666353805e-03, 3.365543012321504e-03, -2.033399376196629e-03, 1.108895838202336e-03, -5.283266194475448e-04, 2.099779511098949e-04, -6.484566005000160e-05, 1.372984806560325e-05, -1.482645851470641e-06]) return dlf
[docs]def key_201_2009(): r"""Key 201 pt Hankel filter, as published in [Key09]_. Taken from file ``FilterModules.f90`` provided with 1DCSEM_. License: `Apache License, Version 2.0, <http://www.apache.org/licenses/LICENSE-2.0>`_. """ dlf = DigitalFilter('Key 201 (2009)', 'key_201_2009') dlf.base = np.array([ 6.112527611295728e-04, 6.582011330626792e-04, 7.087554594672159e-04, 7.631927021868981e-04, 8.218110956199024e-04, 8.849317805958155e-04, 9.529005637454616e-04, 1.026089812002297e-03, 1.104900492614410e-03, 1.189764369843323e-03, 1.281146370384213e-03, 1.379547130466501e-03, 1.485505738589109e-03, 1.599602688916441e-03, 1.722463061515276e-03, 1.854759946855503e-03, 1.997218133335814e-03, 2.150618078036461e-03, 2.315800182452862e-03, 2.493669396634629e-03, 2.685200176953821e-03, 2.891441824663527e-03, 3.113524234494096e-03, 3.352664084780651e-03, 3.610171503034560e-03, 3.887457243476130e-03, 4.186040415850672e-03, 4.507556807870229e-03, 4.853767846875483e-03, 5.226570249814254e-03, 5.628006414404065e-03, 6.060275608406676e-03, 6.525746018315052e-03, 7.026967723461506e-03, 7.566686666625634e-03, 8.147859697679989e-03, 8.773670772690183e-03, 9.447548397216066e-03, 1.017318440937716e-02, 1.095455420558538e-02, 1.179593851975157e-02, 1.270194687528350e-02, 1.367754283835671e-02, 1.472807121080859e-02, 1.585928731163164e-02, 1.707738850748481e-02, 1.838904816496257e-02, 1.980145221062947e-02, 2.132233849911398e-02, 2.296003920493998e-02, 2.472352647033940e-02, 2.662246155912740e-02, 2.866724778592989e-02, 3.086908751073575e-02, 3.324004351101861e-02, 3.579310506765532e-02, 3.854225912669247e-02, 4.150256692682124e-02, 4.469024651236346e-02, 4.812276158381668e-02, 5.181891717272583e-02, 5.579896266503613e-02, 6.008470273734039e-02, 6.469961681378547e-02, 6.966898769808187e-02, 7.502004008532698e-02, 8.078208971247929e-02, 8.698670396460390e-02, 9.366787481677047e-02, 1.008622050590664e-01, 1.086091088249580e-01, 1.169510275215943e-01, 1.259336623450285e-01, 1.356062246541897e-01, 1.460217055752807e-01, 1.572371663136276e-01, 1.693140507634552e-01, 1.823185221282210e-01, 1.963218253956815e-01, 2.114006776535105e-01, 2.276376883838127e-01, 2.451218120391174e-01, 2.639488353792869e-01, 2.842219022392174e-01, 3.060520786022707e-01, 3.295589610751891e-01, 3.548713320980274e-01, 3.821278654786651e-01, 4.114778861171706e-01, 4.430821880821678e-01, 4.771139155210344e-01, 5.137595112299984e-01, 5.532197380808739e-01, 5.957107789003212e-01, 6.414654208273198e-01, 6.907343306373547e-01, 7.437874280201796e-01, 8.009153643346592e-01, 8.624311149420454e-01, 9.286716938412872e-01, 1.000000000000000e+00, 1.076806805496220e+00, 1.159512896362974e+00, 1.248571377864284e+00, 1.344470156832053e+00, 1.447734614663324e+00, 1.558930485621915e+00, 1.678666956213205e+00, 1.807600002612004e+00, 1.946435984427591e+00, 2.095935514494364e+00, 2.256917625888753e+00, 2.430264259001381e+00, 2.616925093246914e+00, 2.817922749882108e+00, 3.034358394435675e+00, 3.267417769442918e+00, 3.518377690535413e+00, 3.788613041474606e+00, 4.079604306451588e+00, 4.392945680918757e+00, 4.730353805388542e+00, 5.093677170047323e+00, 5.484906241707685e+00, 5.906184368579528e+00, 6.359819522601831e+00, 6.848296943665372e+00, 7.374292754997836e+00, 7.940688624303139e+00, 8.550587550976035e+00, 9.207330865882248e+00, 9.914516536837411e+00, 1.067601888007134e+01, 1.149600978566695e+01, 1.237898157325731e+01, 1.332977160319577e+01, 1.435358877803146e+01, 1.545604207947845e+01, 1.664317129721834e+01, 1.792148011788406e+01, 1.929797175550276e+01, 2.078018731859920e+01, 2.237624712415386e+01, 2.409489518475410e+01, 2.594554711266131e+01, 2.793834170323650e+01, 3.008419648032392e+01, 3.239486750789821e+01, 3.488301379565316e+01, 3.756226665137786e+01, 4.044730436006738e+01, 4.355393259889750e+01, 4.689917102861648e+01, 5.050134653574537e+01, 5.438019363641357e+01, 5.855696259189233e+01, 6.305453582813728e+01, 6.789755329714343e+01, 7.311254746690634e+01, 7.872808867953015e+01, 8.477494167382795e+01, 9.128623412992303e+01, 9.829763815922249e+01, 1.058475657340557e+02, 1.139773791276396e+02, 1.227316175172651e+02, 1.321582409921502e+02, 1.423088933027569e+02, 1.532391847910440e+02, 1.650089970516890e+02, 1.776828109933644e+02, 1.913300600973533e+02, 2.060255108088307e+02, 2.218496721447841e+02, 2.388892367626087e+02, 2.572375559057747e+02, 2.769951508285525e+02, 2.982702635016372e+02, 3.211794496157137e+02, 3.458482171317310e+02, 3.724117138761822e+02, 4.010154679483840e+02, 4.318161849960710e+02, 4.649826067271839e+02, 5.006964353612040e+02, 5.391533290846429e+02, 5.805639739642864e+02, 6.251552381906738e+02, 6.731714149753277e+02, 7.248755609109528e+02, 7.805509371268035e+02, 8.405025611345947e+02, 9.050588778667341e+02, 9.745735590616712e+02, 1.049427440854279e+03, 1.130030610186370e+03, 1.216824651467729e+03, 1.310285065796017e+03, 1.410923875989213e+03, 1.519292431702289e+03, 1.635984429995926e+03]) dlf.factor = np.array([1.0768068054962201]) dlf.j0 = np.array([ 1.104702818216325e-01, -3.002860174042879e-01, 0.000000000000000e+00, 9.304611998317738e-01, -1.237989456789895e+00, 0.000000000000000e+00, 1.522782496923861e+00, -1.481262207187227e+00, 0.000000000000000e+00, 1.200938682543965e+00, -1.042356281617017e+00, 0.000000000000000e+00, 8.186482154233182e-01, -7.837979439107681e-01, 0.000000000000000e+00, 1.072087935017888e+00, -2.017973482744253e+00, 2.638551914228436e+00, -2.916973810417140e+00, 2.932547717791041e+00, -2.782030176901836e+00, 2.548634287940637e+00, -2.286132540834447e+00, 2.028668029433413e+00, -1.790466549754032e+00, 1.579778206432123e+00, -1.395100794535786e+00, 1.236899777150533e+00, -1.099633354001948e+00, 9.829180606149369e-01, -8.808127495830721e-01, 7.939417322911940e-01, -7.166399975760631e-01, 6.508052453577512e-01, -5.909087763650980e-01, 5.400346833052113e-01, -4.925062292020488e-01, 4.525012829058494e-01, -4.139282151279450e-01, 3.820303825432799e-01, -3.500694920581675e-01, 3.243907465091445e-01, -2.973991010648227e-01, 2.766317890637754e-01, -2.534315625567141e-01, 2.366617712595763e-01, -2.163875214294563e-01, 2.029716420595088e-01, -1.849663778885546e-01, 1.744470283910267e-01, -1.581901786171230e-01, 1.502386381629129e-01, -1.352956168139171e-01, 1.296732438173242e-01, -1.156619860385481e-01, 1.121981827706036e-01, -9.877037098650596e-02, 9.735307747326948e-02, -8.418324552747586e-02, 8.475347956447533e-02, -7.152829800825916e-02, 7.407480907190452e-02, -6.048336872780390e-02, 6.504162604072715e-02, -5.077074526100943e-02, 5.742706238192050e-02, -4.215804851336973e-02, 5.105276831205472e-02, -3.445402816016690e-02, 4.578139059809960e-02, -2.749842403920171e-02, 4.150734318146184e-02, -2.115449634951816e-02, 3.815224456264026e-02, -1.530500719575409e-02, 3.566006962242232e-02, -9.844572094042197e-03, 3.398735588004622e-02, -4.669634342048067e-03, 3.309505748308261e-02, 3.248775057265341e-04, 3.294860285661111e-02, 5.240451270870069e-03, 3.352191931272241e-02, 1.016839266998432e-02, 3.479748010810809e-02, 1.518640694860538e-02, 3.675989077470884e-02, 2.035623099573585e-02, 3.938537294158406e-02, 2.571720552065411e-02, 4.262879025301092e-02, 3.127265047233792e-02, 4.640586621922704e-02, 3.696789312241264e-02, 5.056664152720505e-02, 4.265736230160079e-02, 5.485681544583107e-02, 4.805697373905592e-02, 5.886326726197704e-02, 5.267934237797620e-02, 6.194081754102766e-02, 5.575263672089661e-02, 6.312348308951768e-02, 5.613171205140025e-02, 6.103877063939782e-02, 5.223073389072554e-02, 5.387340754058757e-02, 4.205003959253396e-02, 3.949537291826706e-02, 2.344464896766128e-02, 1.592975900866907e-02, -5.112454956546657e-03, -1.750424757311479e-02, -4.293028583599693e-02, -5.806536835195215e-02, -8.443837687273714e-02, -9.651641994648259e-02, -1.160353562902818e-01, -1.145716151033802e-01, -1.152746912280352e-01, -8.753115163764941e-02, -5.917367601312370e-02, -6.660378399098311e-04, 4.966494483361900e-02, 1.157206357429209e-01, 1.448966611107768e-01, 1.588998330585965e-01, 1.031590212340854e-01, 2.389465737393602e-02, -1.007600802615937e-01, -1.701081679147513e-01, -1.806596339730873e-01, -5.044220811489127e-02, 1.067558829070489e-01, 2.243843205181916e-01, 1.124861192136151e-01, -1.060750025290042e-01, -2.494689576049384e-01, -2.532563907981785e-02, 2.313093162590108e-01, 1.265041517428334e-01, -2.716895564501260e-01, -5.741673301698751e-02, 2.828355798553848e-01, -1.151529184187685e-01, -1.895238214387882e-01, 3.498981818372285e-01, -3.283594487966644e-01, 2.228689935519562e-01, -1.191882703384384e-01, 4.914136861200422e-02, -1.085046330669215e-02, -6.989673166059397e-03, 1.396225098602933e-02, -1.583247654053119e-02, 1.553798887482501e-02, -1.443534141636538e-02, 1.310934487425667e-02, -1.179562561923210e-02, 1.057909167982074e-02, -9.482129155265809e-03, 8.502636346417821e-03, -7.630076138978968e-03, 6.852043148244981e-03, -6.156761038065365e-03, 5.533849408416496e-03, -4.974383010461074e-03, 4.470699747473056e-03, -4.016161870832697e-03, 3.604955260613827e-03, -3.231951863754572e-03, 2.892630190613161e-03, -2.583034645430386e-03, 2.299750969077188e-03, -2.039879838855092e-03, 1.801000017171617e-03, -1.581121784044337e-03, 1.378637896797070e-03, -1.192281463551114e-03, 1.021096380613436e-03, -8.644169540225837e-04, 7.218438967094129e-04, -5.932006323351060e-04, 4.784596555937276e-04, -3.776406369869407e-04, 2.906937486164167e-04, -2.173880970439557e-04, 1.572247021446439e-04, -1.093880480994978e-04, 7.274278828090175e-05, -4.587508579334320e-05, 2.717284254234203e-05, -1.493569664311702e-05, 7.502072444202401e-06, -3.374980009202976e-06, 1.323028566570774e-06, -4.342813347631881e-07, 1.120529389225740e-07, -2.023679217396607e-08, 1.923133952677995e-09]) dlf.j1 = np.array([ 1.289633927144360e-05, -4.692852957012775e-05, 5.712407500240781e-05, 0.000000000000000e+00, -5.401898356504400e-05, 0.000000000000000e+00, 1.163813605855986e-04, -1.341585158986474e-04, 0.000000000000000e+00, 1.563529882751311e-04, -1.701932285008713e-04, 0.000000000000000e+00, 2.685212722282496e-04, -5.148623386148907e-04, 6.653519984942213e-04, -7.072232255490351e-04, 6.684047762347991e-04, -5.847964888682289e-04, 4.877023048974497e-04, -3.939313465485314e-04, 3.136345180982827e-04, -2.470064062519923e-04, 1.953997902093073e-04, -1.539602296158165e-04, 1.234529832565310e-04, -9.817008106125012e-05, 8.058804362211881e-05, -6.451459975546781e-05, 5.456430430893415e-05, -4.344419043404446e-05, 3.815523049837875e-05, -2.949393655677912e-05, 2.732187176767718e-05, -1.959842972127203e-05, 1.982911726363689e-05, -1.200904791302960e-05, 1.443251606646564e-05, -5.683761857979987e-06, 1.043594555177340e-05, 4.513240229146117e-08, 7.457609318727016e-06, 5.653216751529018e-06, 5.308688404222969e-06, 1.152796570665543e-05, 3.932961600888582e-06, 1.803352844385906e-05, 3.380683574927984e-06, 2.555716029426899e-05, 3.803729181402945e-06, 3.454895491783953e-05, 5.466139820523614e-06, 4.556234770039426e-05, 8.768101084525483e-06, 5.930097379335330e-05, 1.428416302046287e-05, 7.667672615961499e-05, 2.281866040881824e-05, 9.888436530447273e-05, 3.548288867698162e-05, 1.274995405373852e-04, 5.380041779170104e-05, 1.646090070216299e-04, 7.984956415148433e-05, 2.129842798716441e-04, 1.164554629053559e-04, 2.763133928114338e-04, 1.674485387417859e-04, 3.595100112861982e-04, 2.380118276339850e-04, 4.691253417077570e-04, 3.351463657538389e-04, 6.138970952511212e-04, 4.682919161509869e-04, 8.054805703670692e-04, 6.501519986304682e-04, 1.059417913885959e-03, 8.977881651498095e-04, 1.396414494631849e-03, 1.234064772364374e-03, 1.844009097024346e-03, 1.689538327387063e-03, 2.438744274863229e-03, 2.304895516259244e-03, 3.228952488337877e-03, 3.134049181497694e-03, 4.278260457055239e-03, 4.247981356211152e-03, 5.669864127830826e-03, 5.739341687299852e-03, 7.511500876566557e-03, 7.727614768189288e-03, 9.940768446104526e-03, 1.036426807004136e-02, 1.312987922331795e-02, 1.383652144093020e-02, 1.728788292640136e-02, 1.836695924406547e-02, 2.265651442167874e-02, 2.420372071766719e-02, 2.949262366900291e-02, 3.159191631258840e-02, 3.802499854417571e-02, 4.071065391868849e-02, 4.836588871048378e-02, 5.155150426795294e-02, 6.034835565661112e-02, 6.370530818484274e-02, 7.325374787602650e-02, 7.602246037354336e-02, 8.540182884134039e-02, 8.613756797984258e-02, 9.363045212001810e-02, 8.994780552031496e-02, 9.285438346694046e-02, 8.138538169597652e-02, 7.625701418518774e-02, 5.331840281941071e-02, 3.728410637826844e-02, 1.088918303862871e-03, -2.482185562667677e-02, -6.966985038573692e-02, -9.508370436510773e-02, -1.320457796877950e-01, -1.333188913518803e-01, -1.345679831656020e-01, -8.403605511993056e-02, -3.270153309655380e-02, 6.374700977990792e-02, 1.243720031600276e-01, 1.818967705583269e-01, 1.375740652175917e-01, 5.811873304105276e-02, -1.043087758627017e-01, -1.815595823147628e-01, -1.819917129979687e-01, 1.631402693428312e-02, 1.752375632474410e-01, 2.152308945759099e-01, -6.135834728025826e-02, -2.260012732339317e-01, -1.058818826360049e-01, 2.751720328057493e-01, 7.282078436121274e-02, -2.453904197631155e-01, -2.981552944151773e-02, 3.295321158355015e-01, -3.395688755289581e-01, 1.437347757121746e-01, 5.569137331864311e-02, -1.618975349034848e-01, 1.840881618330268e-01, -1.638475650685530e-01, 1.323098979187242e-01, -1.035844311836129e-01, 8.132823321716304e-02, -6.502108525281801e-02, 5.316632459343718e-02, -4.441483689628730e-02, 3.779017256454915e-02, -3.263631595413427e-02, 2.852104339616387e-02, -2.515785440611284e-02, 2.235339482483744e-02, -1.997416046894760e-02, 1.792574037444691e-02, -1.613980618851269e-02, 1.456582802493779e-02, -1.316569266298338e-02, 1.191013283575226e-02, -1.077631048875747e-02, 9.746151537603939e-03, -8.805179856684300e-03, 7.941688885035929e-03, -7.146145811536250e-03, 6.410759357461669e-03, -5.729165010828318e-03, 5.096195694120956e-03, -4.507714364593528e-03, 3.960490050623528e-03, -3.452101711144719e-03, 2.980856037463172e-03, -2.545706551739226e-03, 2.146162475389078e-03, -1.782177147988815e-03, 1.454007747414243e-03, -1.162041366288416e-03, 9.065878213110874e-04, -6.876473801626548e-04, 5.046718335603190e-04, -3.563489117729183e-04, 2.404501739881472e-04, -1.537865721775565e-04, 9.230834105005988e-05, -5.136252914208434e-05, 2.608318212185880e-05, -1.184499677743133e-05, 4.678587718668116e-06, -1.544064223784288e-06, 3.995921803021977e-07, -7.219416019819105e-08, 6.844864105885603e-09]) return dlf
[docs]def key_401_2009(): r"""Key 401 pt Hankel filter, as published in [Key09]_. Taken from file ``FilterModules.f90`` provided with 1DCSEM_. License: `Apache License, Version 2.0, <http://www.apache.org/licenses/LICENSE-2.0>`_. """ dlf = DigitalFilter('Key 401 (2009)', 'key_401_2009') dlf.base = np.array([ 6.825603376334870e-08, 7.375625734276621e-08, 7.969970121723440e-08, 8.612208106759941e-08, 9.306199062400369e-08, 1.005611335855232e-07, 1.086645742284082e-07, 1.174210082088922e-07, 1.268830551878997e-07, 1.371075750361032e-07, 1.481560095194920e-07, 1.600947515187244e-07, 1.729955440010014e-07, 1.869359111419852e-07, 2.019996241884814e-07, 2.182772048613791e-07, 2.358664693239236e-07, 2.548731159841640e-07, 2.754113606638370e-07, 2.976046229505788e-07, 3.215862678579245e-07, 3.475004072499321e-07, 3.755027658463905e-07, 4.057616170126568e-07, 4.384587939575313e-07, 4.737907824157171e-07, 5.119699013810637e-07, 5.532255789859379e-07, 5.978057311938045e-07, 6.459782515899233e-07, 6.980326212227157e-07, 7.542816481697429e-07, 8.150633472817832e-07, 8.807429714008947e-07, 9.517152062585649e-07, 1.028406542243639e-06, 1.111277837292621e-06, 1.200827086303379e-06, 1.297592413714413e-06, 1.402155307232813e-06, 1.515144112143249e-06, 1.637237807196195e-06, 1.769170084765623e-06, 1.911733759794935e-06, 2.065785534025608e-06, 2.232251144137991e-06, 2.412130924740802e-06, 2.606505819638747e-06, 2.816543877501467e-06, 3.043507270968020e-06, 3.288759881366484e-06, 3.553775494627146e-06, 3.840146657640719e-06, 4.149594248281688e-06, 4.483977816605428e-06, 4.845306759362147e-06, 5.235752394978102e-06, 5.657661011565692e-06, 6.113567966371402e-06, 6.606212921388751e-06, 7.138556306690845e-06, 7.713797110415130e-06, 8.335392102304759e-06, 9.007076606325931e-06, 9.732886947188948e-06, 1.051718470566020e-05, 1.136468292842132e-05, 1.228047444997721e-05, 1.327006249680666e-05, 1.433939375766396e-05, 1.549489411875887e-05, 1.674350727855744e-05, 1.809273647424976e-05, 1.955068957062923e-05, 2.112612778233479e-05, 2.282851832224015e-05, 2.466809129236741e-05, 2.665590115919790e-05, 2.880389318280080e-05, 3.112497519896879e-05, 3.363309518571897e-05, 3.634332508027547e-05, 3.927195135021125e-05, 4.243657286301518e-05, 4.585620664220731e-05, 4.955140214551744e-05, 5.354436475185514e-05, 5.785908919913498e-05, 6.252150377482026e-05, 6.755962612566159e-05, 7.300373162293296e-05, 7.888653529491450e-05, 8.524338841989974e-05, 9.211249096110730e-05, 9.953512112007229e-05, 1.075558833879609e-04, 1.162229765854152e-04, 1.255884835016470e-04, 1.357086838732945e-04, 1.466443925838176e-04, 1.584613251157513e-04, 1.712304924519203e-04, 1.850286277986747e-04, 1.999386476954356e-04, 2.160501502814794e-04, 2.334599537141681e-04, 2.522726779741279e-04, 2.726013735535827e-04, 2.945682008058004e-04, 3.183051640380327e-04, 3.439549047593057e-04, 3.716715588498817e-04, 4.016216828033581e-04, 4.339852546074165e-04, 4.689567552777785e-04, 5.067463375445843e-04, 5.475810887141261e-04, 5.917063952947988e-04, 6.393874175876612e-04, 6.909106831027882e-04, 7.465858083766792e-04, 8.067473595375511e-04, 8.717568627991351e-04, 9.420049769645596e-04, 1.017913840995439e-03, 1.099939610753318e-03, 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9.835675748306749e-05, -9.173298412621861e-05, 8.539584183369774e-05, -7.932647157887555e-05, 7.350799507002284e-05, -6.792579804522193e-05, 6.256766460994959e-05, -5.742369885284320e-05, 5.248607676312167e-05, -4.774876610278635e-05, 4.320737034558452e-05, -3.885918466176108e-05, 3.470344555454732e-05, -3.074167696093530e-05, 2.697802016509551e-05, -2.341946443717172e-05, 2.007591620962982e-05, -1.696002345446848e-05, 1.408663272782194e-05, -1.147175200077509e-05, 9.130950853154427e-06, -7.077245367140833e-06, 5.318671603956403e-06, -3.855913768030704e-06, 2.680452779662483e-06, -1.773679649172923e-06, 1.107284379526082e-06, -6.450375038180866e-07, 3.458519700889004e-07, -1.677370250259620e-07, 7.195813987460663e-08, -2.650936383269536e-08, 8.053026529021296e-09, -1.901548822685746e-09, 3.176144531356312e-10, -3.147399480514734e-11, 1.181734681811153e-12]) dlf.j1 = np.array([ 0.000000000000000e+00, 0.000000000000000e+00, 0.000000000000000e+00, -1.761153377678605e-10, 0.000000000000000e+00, 0.000000000000000e+00, 0.000000000000000e+00, 0.000000000000000e+00, 0.000000000000000e+00, 0.000000000000000e+00, 3.440216255617151e-10, 0.000000000000000e+00, 0.000000000000000e+00, 0.000000000000000e+00, -5.012130889133619e-10, 0.000000000000000e+00, 0.000000000000000e+00, 5.096249946359556e-10, 0.000000000000000e+00, 0.000000000000000e+00, -5.137927435894773e-10, 0.000000000000000e+00, 4.901252024472790e-10, 0.000000000000000e+00, -3.412499448385044e-10, 0.000000000000000e+00, 2.331695173457025e-10, 0.000000000000000e+00, -2.490134046395816e-10, 1.954047749927753e-10, 0.000000000000000e+00, -8.103005437723991e-11, 0.000000000000000e+00, 1.279088845538237e-10, -1.851480627564174e-10, 1.332990147779435e-10, 0.000000000000000e+00, -1.624963592448070e-10, 3.098241711700410e-10, -4.149316491270542e-10, 4.685626300171698e-10, -4.712327624043219e-10, 4.305062986549322e-10, -3.542442130313303e-10, 2.522911525991727e-10, -1.313966839434664e-10, 0.000000000000000e+00, 1.374783013515889e-10, -2.736921677833286e-10, 4.061582817302266e-10, -5.279722941941932e-10, 6.386355968571155e-10, -7.315427954629247e-10, 8.087932062353638e-10, -8.640922282673907e-10, 9.028429079409167e-10, -9.186974584267662e-10, 9.208119531836431e-10, -9.017596435374981e-10, 8.746151932449153e-10, -8.291880695503223e-10, 7.826366656707373e-10, -7.199240415978938e-10, 6.630127031117425e-10, -5.898849811863955e-10, 5.290634200040055e-10, -4.493240826470479e-10, 3.886261259968761e-10, -3.037437366057724e-10, 2.460094930171363e-10, -1.562353890563393e-10, 1.042595244297130e-10, -9.277742086714826e-12, -3.359801793948191e-11, 1.346759112142224e-10, -1.644581113778544e-10, 2.735615970185790e-10, -2.856750577185324e-10, 4.064174138388151e-10, -3.956626260990240e-10, 5.339967379460912e-10, -4.942289770979441e-10, 6.590721699414525e-10, -5.825238873978475e-10, 7.864186241426929e-10, -6.626363292105279e-10, 9.225771435176782e-10, -7.369977848939469e-10, 1.075704953982971e-09, -8.079491312165849e-10, 1.255853770105183e-09, -8.775982413533787e-10, 1.475677833588153e-09, -9.478165158795805e-10, 1.751454564451092e-09, -1.020150878388706e-09, 2.104270247990516e-09, -1.095430340362651e-09, 2.561356147221457e-09, -1.172968828002544e-09, 3.157686036019299e-09, -1.249340900707534e-09, 3.938151654389299e-09, -1.316804538118081e-09, 4.960584143866221e-09, -1.361050365193285e-09, 6.299594474808514e-09, -1.357732636276717e-09, 8.051372567815041e-09, -1.267357938643338e-09, 1.034000380570114e-08, -1.028333203364199e-09, 1.332639788605693e-08, -5.481128505786461e-10, 1.722132657425943e-08, 3.079572462647345e-10, 2.230389235352557e-08, 1.731612035551629e-09, 2.894640331467214e-08, 3.992876253106220e-09, 3.764713519770196e-08, 7.470342606008511e-09, 4.907355253852564e-08, 1.269390990642245e-08, 6.411984689966026e-08, 2.040424455749986e-08, 8.398456134765634e-08, 3.163423793932673e-08, 1.102763405195791e-07, 4.782016944498328e-08, 1.451576997806275e-07, 7.095396726449770e-08, 1.915405053682995e-07, 1.037907010433357e-07, 2.533530424909100e-07, 1.501316966404849e-07, 3.359015461416407e-07, 2.152163676698347e-07, 4.463548364795692e-07, 3.062649070955455e-07, 5.943990986479385e-07, 4.332201278554725e-07, 7.931323845043337e-07, 6.097551748617194e-07, 1.060288415924516e-06, 8.546425300312143e-07, 1.419911983644722e-06, 1.193611725125921e-06, 1.904650353313021e-06, 1.661883236417129e-06, 2.558861699766762e-06, 2.307654632812588e-06, 3.442811157821135e-06, 3.196895656510743e-06, 4.638358992076794e-06, 4.419902312928682e-06, 6.256715142637839e-06, 6.100218940817017e-06, 8.449032402277294e-06, 8.406776377975507e-06, 1.142087099410692e-05, 1.157042201253195e-05, 1.545191683298927e-05, 1.590647868284089e-05, 2.092279678518197e-05, 2.184558773386808e-05, 2.835151124366015e-05, 2.997585693259872e-05, 3.844299184771377e-05, 4.110034139799833e-05, 5.215663114685968e-05, 5.631528820209043e-05, 7.079837414439344e-05, 7.711659421807641e-05, 9.614618225427727e-05, 1.055447661767286e-04, 1.306206751127902e-04, 1.443823581310115e-04, 1.775170452103382e-04, 1.974225796898412e-04, 2.413201291349723e-04, 2.698342899158978e-04, 3.281318482161766e-04, 3.686575352518240e-04, 4.462498902719190e-04, 5.034750551777089e-04, 6.069499176331384e-04, 6.873187128242988e-04, 8.255410973454176e-04, 9.378875323431232e-04, 1.122784104067260e-03, 1.279178262961256e-03, 1.526781204453462e-03, 1.743655859738250e-03, 2.075473273444583e-03, 2.375110960283700e-03, 2.819903510936917e-03, 3.232361399449634e-03, 3.828410021593598e-03, 4.393943043291972e-03, 5.191863182780206e-03, 5.963857250198409e-03, 7.029925656135096e-03, 8.078221794986575e-03, 9.497983356558860e-03, 1.091218414985025e-02, 1.279369144280816e-02, 1.468546702846075e-02, 1.716070017133079e-02, 1.966301954392782e-02, 2.288457156694697e-02, 2.614381914454830e-02, 3.027139461924632e-02, 3.442503605732608e-02, 3.959217858802792e-02, 4.471956265829849e-02, 5.096501947760914e-02, 5.699213341078931e-02, 6.413328819589428e-02, 7.066611680136001e-02, 7.808858155732867e-02, 8.415253392588408e-02, 9.050430770970036e-02, 9.420119432022898e-02, 9.704525747507635e-02, 9.525207334318243e-02, 9.091107970583592e-02, 7.941214687854993e-02, 6.360896948482617e-02, 3.851999787085855e-02, 8.930119389229475e-03, -2.931232114631221e-02, -6.745472857764939e-02, -1.071387129122266e-01, -1.337787672525563e-01, -1.467487065654186e-01, -1.280178925639679e-01, -8.266114319901335e-02, -1.829018947010989e-03, 8.538653035086596e-02, 1.634948424549636e-01, 1.768283682900049e-01, 1.165478617534897e-01, -2.909864536607605e-02, -1.650763395456089e-01, -2.108189429067250e-01, -6.548403763878953e-02, 1.474231756411919e-01, 2.387075880611132e-01, 8.364392500807047e-03, -2.375301184090862e-01, -1.324045834042435e-01, 2.623684401711879e-01, 9.558257428232823e-02, -2.795911533969242e-01, 4.155824322494574e-02, 2.715606356255319e-01, -3.742520323983440e-01, 2.853293391721109e-01, -1.417457299548064e-01, 3.117732200130105e-02, 2.889458199693983e-02, -5.278084724642508e-02, 5.771601780075224e-02, -5.477531833561626e-02, 4.939546060797920e-02, -4.378947822887341e-02, 3.869238569366965e-02, -3.425716943762586e-02, 3.044093551672354e-02, -2.715226194815648e-02, 2.430080341386173e-02, -2.181052920166688e-02, 1.962073026812987e-02, -1.768361271316385e-02, 1.596144663779621e-02, -1.442412760579961e-02, 1.304729403368628e-02, -1.181093160074335e-02, 1.069835428430446e-02, -9.695462302234538e-03, 8.790199228345667e-03, -7.972150985921739e-03, 7.232245468946166e-03, -6.562523603657329e-03, 5.955961653845067e-03, -5.406331000039078e-03, 4.908085823543291e-03, -4.456271717308975e-03, 4.046450048794231e-03, -3.674634444757500e-03, 3.337237040467819e-03, -3.031022902436713e-03, 2.753071298464685e-03, -2.500742536477930e-03, 2.271649199484839e-03, -2.063630842184971e-03, 1.874731507609227e-03, -1.703179664969160e-03, 1.547370305159833e-03, -1.405848965175527e-03, 1.277297436350464e-03, -1.160520897100170e-03, 1.054436232968270e-03, -9.580613717996333e-04, 8.705055444165467e-04, -7.909604401097324e-04, 7.186922398324291e-04, -6.530344915884751e-04, 5.933817682686722e-04, -5.391840290971849e-04, 4.899415886335732e-04, -4.452005847911536e-04, 4.045488440443307e-04, -3.676120749678280e-04, 3.340503647933679e-04, -3.035549812866991e-04, 2.758454813737592e-04, -2.506671088369273e-04, 2.277884460323346e-04, -2.069992810457240e-04, 1.881086606885530e-04, -1.709431124465889e-04, 1.553450267830473e-04, -1.411711924592810e-04, 1.282914747613330e-04, -1.165876238497402e-04, 1.059521991589964e-04, -9.628759515338238e-05, 8.750515384295626e-05, -7.952435126636077e-05, 7.227204913633232e-05, -6.568180805443277e-05, 5.969326263717584e-05, -5.425155895475095e-05, 4.930685077009869e-05, -4.481384639404849e-05, 4.073139627769274e-05, -3.702211350786090e-05, 3.365202295484529e-05, -3.059023779502484e-05, 2.780866410092890e-05, -2.528173545505838e-05, 2.298617982129317e-05, -2.090081950209839e-05, 1.900640153317426e-05, -1.728545097076178e-05, 1.572213560023288e-05, -1.430213090870262e-05, 1.301247986370528e-05, -1.184145017024185e-05, 1.077839734116676e-05, -9.813642618247219e-06, 8.938371729153144e-06, -8.144555804633981e-06, 7.424890780058305e-06, -6.772748023670692e-06, 6.182129388552279e-06, -5.647624656180153e-06, 5.164374046764935e-06, -4.728037195336446e-06, 4.334761689817321e-06, -3.981136442356169e-06, 3.664118637205433e-06, -3.380939384592361e-06, 3.129009529723152e-06, -2.905847492954934e-06, 2.709034327844308e-06, -2.536183084429876e-06, 2.384905895111026e-06, -2.252772087223033e-06, 2.137259365710216e-06, -2.035698487395405e-06, 1.945208220753021e-06, -1.862627051737732e-06, 1.784472814922380e-06, -1.706983978589542e-06, 1.626297101583022e-06, -1.538789746921996e-06, 1.441575114294373e-06, -1.333077139855850e-06, 1.213536734497111e-06, -1.085223736705093e-06, 9.521451230126823e-07, -8.192296419664399e-07, 6.912547372495382e-07, -5.719422069867315e-07, 4.635461014353267e-07, -3.669835113430816e-07, 2.823229600705464e-07, -2.093541854410099e-07, 1.479865821668501e-07, -9.831343971854163e-08, 6.033173947686275e-08, -3.349527235750482e-08, 1.640107598073682e-08, -6.856420858188184e-09, 2.340536901536035e-09, -6.097093750212437e-10, 1.074334228952679e-10, -9.576603341064843e-12]) return dlf
[docs]def anderson_801_1982(): r"""Anderson 801 pt Hankel filter, as published in [Ande82]_. Taken from file ``wa801Hankel.txt`` provided with SEG-2012-003_. License: http://software.seg.org/disclaimer.txt. """ dlf = DigitalFilter('Anderson 801', 'anderson_801_1982') dlf.base = np.array([ 8.9170998013276122e-14, 9.8549193740053558e-14, 1.0891370292131004e-13, 1.2036825704856271e-13, 1.3302749714952577e-13, 1.4701812115404721e-13, 1.6248015192957424e-13, 1.7956833867707853e-13, 1.9845370571306597e-13, 2.1932526413842384e-13, 2.4239190352504611e-13, 2.6788448255287750e-13, 2.9605813952118386e-13, 3.2719484585839544e-13, 3.6160622818694338e-13, 3.9963668718723693e-13, 4.4166684447542651e-13, 4.8811735199248203e-13, 5.3945310203018623e-13, 5.9618788002945774e-13, 6.5888950671773090e-13, 7.2818552104964630e-13, 8.0476946082782683e-13, 8.8940780386233457e-13, 9.8294763913818316e-13, 1.0863251447666380e-12, 1.2005749575704075e-12, 1.3268405280767117e-12, 1.4663855645545188e-12, 1.6206066806315963e-12, 1.7910473730731519e-12, 1.9794134696162351e-12, 2.1875902014670651e-12, 2.4176610713286508e-12, 2.6719287057960420e-12, 2.9529379008172930e-12, 3.2635010908666289e-12, 3.6067264967339290e-12, 3.9860492336432057e-12, 4.4052656910401999e-12, 4.8685715281340575e-12, 5.3806036654648819e-12, 5.9464866927629836e-12, 6.5718841575654989e-12, 7.2630552479034764e-12, 8.0269174363596475e-12, 8.8711157124590269e-12, 9.8040990962935900e-12, 1.0835205199155430e-11, 1.1974753677488654e-11, 1.3234149515479892e-11, 1.4625997169973320e-11, 1.6164226720111148e-11, 1.7864233284248175e-11, 1.9743031099470126e-11, 2.1819423805797495e-11, 2.4114192639334892e-11, 2.6650304417866614e-11, 2.9453141400489177e-11, 3.2550755321790535e-11, 3.5974148143039067e-11, 3.9757582330231898e-11, 4.3938923764370285e-11, 4.8560020715925063e-11, 5.3667122676391448e-11, 5.9311343238746032e-11, 6.5549171659464899e-11, 7.2443038221988632e-11, 8.0061939059984521e-11, 8.8482126693839770e-11, 9.7787873191516816e-11, 1.0807231359173380e-10, 1.1943837803073504e-10, 1.3199982190169390e-10, 1.4588236435691723e-10, 1.6122494654738060e-10, 1.7818112219246607e-10, 1.9692059439719579e-10, 2.1763091409795137e-10, 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-0.13398787953334260281E-25, 0.11796045820480120133E-25, -0.10407147490908270710E-25, 0.92071944889040744035E-26, -0.81731249295591442672E-26, 0.72825159703487444195E-26, -0.65131006447129183541E-26, 0.58430301262485386924E-26, -0.52513930081011199285E-26, 0.47187919679302219783E-26, -0.42284069142292412393E-26, 0.37676954747502728537E-26, -0.33299134001135826479E-26, 0.29143004338630110718E-26, -0.25243668234065648260E-26, 0.21646903157623978348E-26, -0.18376734028052161580E-26, 0.15423017366879009263E-26, -0.12758944190588119779E-26, 0.10371662830395429178E-26, -0.82748173500706471962E-27, 0.64909427840638429032E-27, -0.50234666376562531025E-27, 0.38452110973130778698E-27, -0.29091636205058451455E-27, 0.21678009467166822096E-27, -0.15874578619111640200E-27, 0.11537394235020309101E-27, -0.86900364189788941857E-28, 0.74355723662636970071E-28, -0.78471428315427385396E-28, 0.98949852128730596091E-28, -0.13427202805922251023E-27, 0.18174242734021449278E-27, -0.23763619609508699858E-27, 0.29778198107110528091E-27, -0.35868369680655068529E-27, 0.41844766665021181973E-27, -0.47660851066880372752E-27, 0.53287774452581460041E-27, -0.58588249858342115784E-27, 0.63294098597067369917E-27, -0.67092689718604759703E-27, 0.69754161721794173542E-27, -0.71229292612293631973E-27, 0.71678213553979546309E-27, -0.71422093211775989035E-27, 0.70847857438160299782E-27, -0.70324864718393631473E-27, 0.70176504791510964044E-27, -0.70696084721646144402E-27, 0.72149205056137611593E-27]) return dlf
[docs]def key_51_2012(): r"""Key 51 pt Hankel filter, as published in [Key12]_. Taken from file ``kk51Hankel.txt`` provided with SEG-2012-003_. License: http://software.seg.org/disclaimer.txt. """ dlf = DigitalFilter('Key 51 (2012)', 'key_51_2012') dlf.base = np.array([ 4.9915939069102170e-03, 6.1703482511978082e-03, 7.6274629409160176e-03, 9.4286721829279947e-03, 1.1655233178024955e-02, 1.4407591843112350e-02, 1.7809914185937643e-02, 2.2015687754376449e-02, 2.7214645856121149e-02, 3.3641326918204623e-02, 4.1585655121173182e-02, 5.1406019627642255e-02, 6.3545442443014022e-02, 7.8551564282309541e-02, 9.7101350057185065e-02, 1.2003162851145673e-01, 1.4837684372696586e-01, 1.8341572156771246e-01, 2.2672895630607542e-01, 2.8027051982381157e-01, 3.4645581033005746e-01, 4.2827061721265969e-01, 5.2940581770869455e-01, 6.5442388190885858e-01, 8.0896469756649991e-01, 1.0000000000000000e+00, 1.2361478850785035e+00, 1.5280615937840571e+00, 1.8889101074258496e+00, 2.3349722343978727e+00, 2.8863709892679585e+00, 3.5679813939355345e+00, 4.4105526541128617e+00, 5.4520953354089947e+00, 6.7395961181122024e+00, 8.3311374876876929e+00, 1.0298517985703377e+01, 1.2730491227470161e+01, 1.5736769806847677e+01, 1.9452974714702009e+01, 2.4046753552064487e+01, 2.9725343546388515e+01, 3.6744920558100112e+01, 4.5422155835273074e+01, 5.6148501871478999e+01, 6.9407851838755207e+01, 8.5798369258319340e+01, 1.0605947270185592e+02, 1.3110519287294045e+02, 1.6206540689269471e+02, 2.0033680997479166e+02]) dlf.factor = np.array([1.2361478850785039]) dlf.j0 = np.array([ 6.5314496156480717e-02, -2.2265895125268051e-01, 4.2794928430042073e-01, -5.8890658905204007e-01, 6.7897324897038758e-01, -6.8296549495756353e-01, 6.4702210424566342e-01, -5.6843090153083187e-01, 4.9960500362966542e-01, -4.0923517268678855e-01, 3.5487831784012780e-01, -2.7408257835871558e-01, 2.4668368971888163e-01, -1.7348161774657314e-01, 1.7509173908347012e-01, -1.0007796678766585e-01, 1.3297302593795621e-01, -4.3822390117083297e-02, 1.1415804492335258e-01, 4.2584271963990363e-03, 1.1496183925974515e-01, 5.1313336759457658e-02, 1.3312389010285514e-01, 1.0111673764393908e-01, 1.6331446488042209e-01, 1.4704406144951229e-01, 1.8341391219815678e-01, 1.5073655145087875e-01, 1.2356364992866918e-01, 1.1529465836107913e-02, -1.2852626053530605e-01, -2.9874216118407571e-01, -3.1330553036684633e-01, -3.2332453606385231e-02, 4.2056051544727674e-01, 1.3883637369942961e-01, -5.0223684329542873e-01, 3.7996073748731690e-01, -1.7984404170109178e-01, 7.0557286965350657e-02, -2.7522277139686569e-02, 1.1909130661901874e-02, -5.8977428045126450e-03, 3.2648420034561555e-03, -1.9304039780209286e-03, 1.1594138315987755e-03, -6.7050941490060716e-04, 3.5089803807606258e-04, -1.5287051174029577e-04, 4.8238483411813232e-05, -8.0433917146487977e-06]) dlf.j1 = np.array([ 3.8409924166118657e-05, -9.4382633059055269e-05, 1.6377612356675232e-04, -1.7853487610334151e-04, 1.9759569268356316e-04, -1.2796247718553291e-04, 1.3163370416771999e-04, 1.7066927559149181e-05, 4.1368007808198310e-05, 2.3582259002758631e-04, -1.9929745662753875e-05, 5.8196110748926486e-04, 1.1164151202379049e-05, 1.2053942009238238e-03, 2.8328713800714110e-04, 2.4375075610646724e-03, 1.1709289200267103e-03, 5.0080095645252103e-03, 3.5856849047131551e-03, 1.0536604059335859e-02, 9.6674718436839564e-03, 2.2583365267100426e-02, 2.4201911801947001e-02, 4.8602551164692191e-02, 5.6856974938076565e-02, 1.0202078096072606e-01, 1.2202639829343022e-01, 1.9561985197118459e-01, 2.1570853920674185e-01, 2.8552388758852060e-01, 2.0559964796530625e-01, 1.1666011451374350e-01, -2.3636714743601936e-01, -3.4036030266164258e-01, -1.9475364255836261e-01, 5.7608115965662166e-01, -2.1471464584834585e-01, -1.2611070492338947e-01, 2.0019703515125831e-01, -1.6147664664730754e-01, 1.1398023016900673e-01, -7.9924455203352035e-02, 5.7024556382799692e-02, -4.1006636508593382e-02, 2.9192063091319696e-02, -2.0089573135329029e-02, 1.2965400526524978e-02, -7.5154910983038946e-03, 3.6269079130258285e-03, -1.2668720233377250e-03, 2.3403502580547994e-04]) return dlf
[docs]def key_101_2012(): r"""Key 101 pt Hankel filter, as published in [Key12]_. Taken from file ``kk101Hankel.txt`` provided with SEG-2012-003_. License: http://software.seg.org/disclaimer.txt. """ dlf = DigitalFilter('Key 101 (2012)', 'key_101_2012') dlf.base = np.array([ 5.5308437014783363e-04, 6.4259236035555788e-04, 7.4658580837667996e-04, 8.6740895730700251e-04, 1.0077854290485113e-03, 1.1708796207911744e-03, 1.3603680375478939e-03, 1.5805221687362171e-03, 1.8363047770289071e-03, 2.1334817700377098e-03, 2.4787521766663585e-03, 2.8798991580882430e-03, 3.3459654574712720e-03, 3.8874572434761303e-03, 4.5165809426126703e-03, 5.2475183991813838e-03, 6.0967465655156379e-03, 7.0834089290521185e-03, 8.2297470490200302e-03, 9.5616019305435132e-03, 1.1108996538242306e-02, 1.2906812580479873e-02, 1.4995576820477703e-02, 1.7422374639493515e-02, 2.0241911445804391e-02, 2.3517745856009110e-02, 2.7323722447292573e-02, 3.1745636378067953e-02, 3.6883167401240015e-02, 4.2852126867040180e-02, 4.9787068367863944e-02, 5.7844320874838456e-02, 6.7205512739749784e-02, 7.8081666001153169e-02, 9.0717953289412512e-02, 1.0539922456186433e-01, 1.2245642825298191e-01, 1.4227407158651359e-01, 1.6529888822158656e-01, 1.9204990862075413e-01, 2.2313016014842982e-01, 2.5924026064589156e-01, 3.0119421191220208e-01, 3.4993774911115533e-01, 4.0656965974059917e-01, 4.7236655274101469e-01, 5.4881163609402650e-01, 6.3762815162177333e-01, 7.4081822068171788e-01, 8.6070797642505781e-01, 1.0000000000000000e+00, 1.1618342427282831e+00, 1.3498588075760032e+00, 1.5683121854901687e+00, 1.8221188003905089e+00, 2.1170000166126748e+00, 2.4596031111569494e+00, 2.8576511180631639e+00, 3.3201169227365472e+00, 3.8574255306969740e+00, 4.4816890703380645e+00, 5.2069798271798486e+00, 6.0496474644129448e+00, 7.0286875805892928e+00, 8.1661699125676499e+00, 9.4877358363585262e+00, 1.1023176380641601e+01, 1.2807103782663029e+01, 1.4879731724872830e+01, 1.7287781840567639e+01, 2.0085536923187668e+01, 2.3336064580942711e+01, 2.7112638920657883e+01, 3.1500392308747923e+01, 3.6598234443677974e+01, 4.2521082000062783e+01, 4.9402449105530167e+01, 5.7397457045446188e+01, 6.6686331040925154e+01, 7.7478462925260828e+01, 9.0017131300521811e+01, 1.0458498557711414e+02, 1.2151041751873485e+02, 1.4117496392147686e+02, 1.6402190729990167e+02, 1.9056626845862999e+02, 2.2140641620418697e+02, 2.5723755590577474e+02, 2.9886740096706029e+02, 3.4723438047873447e+02, 4.0342879349273511e+02, 4.6871738678241655e+02, 5.4457191012592898e+02, 6.3270229281225352e+02, 7.3509518924197266e+02, 8.5405876252615155e+02, 9.9227471560502534e+02, 1.1528587427833875e+03, 1.3394307643944169e+03, 1.5561965278371533e+03, 1.8080424144560632e+03]) dlf.factor = np.array([1.1618342427282831]) dlf.j0 = np.array([ 5.1818808036862153e-02, -2.9258492652779172e-01, 8.7289913080159265e-01, -1.8525183961240297e+00, 3.2096055660873608e+00, -4.9248158048315069e+00, 7.0219167445719828e+00, -9.4781099645811544e+00, 1.2098564895534539e+01, -1.4476661837664896e+01, 1.6146079632847474e+01, -1.6810370923047440e+01, 1.6506202923977266e+01, -1.5534747212675301e+01, 1.4267433361428399e+01, -1.2939053370802849e+01, 1.1628520257389562e+01, -1.0325503688577493e+01, 9.0574401975545840e+00, -7.8759096646654951e+00, 6.8446506699312666e+00, -5.9542991234257840e+00, 5.1830565431894602e+00, -4.4805481279340267e+00, 3.8608298760715378e+00, -3.3125736597743227e+00, 2.8648088091590589e+00, -2.4710577422247479e+00, 2.1450315408533416e+00, -1.8334353019592327e+00, 1.5850020809005190e+00, -1.3468969891769780e+00, 1.1802299801807625e+00, -9.9988174688478793e-01, 8.8503813256539254e-01, -7.3165077099639619e-01, 6.5909386165012596e-01, -5.3038429622108840e-01, 5.0119791866928076e-01, -3.8269840749371159e-01, 3.8622329595139565e-01, -2.6413330193320073e-01, 3.0353632730294311e-01, -1.7255655176111537e-01, 2.5119774955173280e-01, -9.8536724013140092e-02, 2.1755876398162183e-01, -3.4268716744688760e-02, 1.9925218957836366e-01, 1.8319735495994052e-02, 1.8963099219918259e-01, 5.7228135568732394e-02, 1.7266316834158107e-01, 6.8141322181604499e-02, 1.2468074033081850e-01, 2.1678852838804014e-02, 1.1114005126278175e-02, -1.0424806190544497e-01, -1.6473681128667569e-01, -2.3603153458714107e-01, -2.2093965064386309e-01, -7.5633542915308175e-02, 1.3358180223826097e-01, 3.3949946683489907e-01, 1.2815187347111337e-01, -2.2988301163130145e-01, -3.3425750283830036e-01, 4.4350537603751145e-01, -8.8943820418669634e-02, -1.8646079800862164e-01, 2.4494657419883456e-01, -2.0169045144304532e-01, 1.4661206655803793e-01, -1.0564640256629308e-01, 7.8487036158411266e-02, -6.0533748554794195e-02, 4.8243702864613026e-02, -3.9347085461672239e-02, 3.2489421068688185e-02, -2.6982535264609676e-02, 2.2530196869950080e-02, -1.8947601435977172e-02, 1.6017457455233256e-02, -1.3519422964231352e-02, 1.1318328695851308e-02, -9.3839154851987506e-03, 7.7256174599644543e-03, -6.3199190181430056e-03, 5.0986473606509210e-03, -3.9929354358609528e-03, 2.9783618569305080e-03, -2.0802747552777045e-03, 1.3429398653973710e-03, -7.9345560431147465e-04, 4.2530878973518046e-04, -2.0457624610548748e-04, 8.6750842046621606e-05, -3.1406113278782205e-05, 9.1385289919391839e-06, -1.8949818224609619e-06, 2.0794387557779629e-07]) dlf.j1 = np.array([ 4.1746363961646286e-06, -2.5993370843637242e-05, 9.2506838353721647e-05, -2.4318740269846489e-04, 5.2276050788732404e-04, -9.5803859755432658e-04, 1.5308357107396591e-03, -2.1584605764249656e-03, 2.7161344302423967e-03, -3.0845361397036195e-03, 3.2133980102756368e-03, -3.1305779240645847e-03, 2.9239120736637542e-03, -2.6680602560576316e-03, 2.4131379039476304e-03, -2.1549566068119440e-03, 1.9058200916563901e-03, -1.6533122444456158e-03, 1.4391633836110848e-03, -1.2363666069459527e-03, 1.0907227256323094e-03, -9.2712769282234358e-04, 8.2888526218099687e-04, -6.7675613963809832e-04, 6.3558641899842260e-04, -4.8591507683128695e-04, 5.1892328126100203e-04, -3.3190335155472070e-04, 4.6189809360776176e-04, -1.8326476919948130e-04, 4.7669939315323097e-04, -1.7380345519175726e-05, 5.9009214750893949e-04, 2.1645139320505843e-04, 8.5203135609860704e-04, 5.9560990889710838e-04, 1.3651107378683781e-03, 1.2606987195022564e-03, 2.3131990435032663e-03, 2.4572002938857678e-03, 4.0408430887840449e-03, 4.6278078809669602e-03, 7.1437051276295131e-03, 8.5723466849983495e-03, 1.2684763573137947e-02, 1.5643387012124067e-02, 2.2480928663078600e-02, 2.8124131719595692e-02, 3.9373999883133115e-02, 4.9445586323210833e-02, 6.7326587032714463e-02, 8.3541701874077570e-02, 1.0961776964853986e-01, 1.3118216481048459e-01, 1.6144181878027153e-01, 1.7704476632134886e-01, 1.9032654055463888e-01, 1.6333927603825021e-01, 1.1034442879456068e-01, -1.1282682226217962e-02, -1.4579378661401318e-01, -2.7560051939484942e-01, -2.3333751023296440e-01, -5.9615109981928909e-03, 3.2380356528743487e-01, 2.1970582679149839e-01, -2.8302631898505476e-01, -2.2706962776315812e-01, 4.7351258711649669e-01, -3.5417866045339608e-01, 1.6582378621661517e-01, -5.1221107687420810e-02, 3.5484710794282063e-03, 1.1614894738175324e-02, -1.4776256489774963e-02, 1.4194293010344678e-02, -1.2609914713728791e-02, 1.0854082569077052e-02, -9.2082270347668624e-03, 7.7880648968821110e-03, -6.6089268276601255e-03, 5.6159700146012417e-03, -4.7432063636330263e-03, 3.9609893136500528e-03, -3.2753768787828126e-03, 2.6945716306237466e-03, -2.2042319512562145e-03, 1.7733135127602079e-03, -1.3773733375919272e-03, 1.0137885881408651e-03, -6.9751488719640639e-04, 4.4545125438205673e-04, -2.6373575275283686e-04, 1.4519595835116970e-04, -7.4640168948626184e-05, 3.5826939350044606e-05, -1.5854604622793124e-05, 6.2412989356183992e-06, -2.0349222128793154e-06, 4.8072849734177625e-07, -6.0462736574031818e-08]) return dlf
[docs]def key_201_2012(): r"""Key 201 pt Hankel filter, as published in [Key12]_. Taken from file ``kk201Hankel.txt`` provided with SEG-2012-003_. License: http://software.seg.org/disclaimer.txt. """ dlf = DigitalFilter('Key 201 (2012)', 'key_201_2012') dlf.base = np.array([ 4.1185887075357082e-06, 4.6623077830484039e-06, 5.2778064058937756e-06, 5.9745606155328603e-06, 6.7632974390298035e-06, 7.6561600412698171e-06, 8.6668946776271221e-06, 9.8110623273521872e-06, 1.1106278265924788e-05, 1.2572483264760042e-05, 1.4232250593579901e-05, 1.6111133551969887e-05, 1.8238058880617237e-05, 2.0645772109076137e-05, 2.3371341696506312e-05, 2.6456729726989950e-05, 2.9949437945688260e-05, 3.3903239082024059e-05, 3.8379004719130766e-05, 4.3445642455208216e-05, 4.9181156785051293e-05, 5.5673850034776868e-05, 6.3023681838995322e-05, 7.1343808090545215e-05, 8.0762323056016586e-05, 9.1424231478173270e-05, 1.0349368102719458e-04, 1.1715648947091054e-04, 1.3262300547161834e-04, 1.5013134705348249e-04, 1.6995106759902750e-04, 1.9238730581535294e-04, 2.1778548356175115e-04, 2.4653662386513240e-04, 2.7908337099788406e-04, 3.1592680530155527e-04, 3.5763415767542709e-04, 4.0484754250000483e-04, 4.5829384344501882e-04, 5.1879590436097246e-04, 5.8728519754599128e-04, 6.6481616442494776e-04, 7.5258244942583781e-04, 8.5193527698548301e-04, 9.6440425461164468e-04, 1.0917209222795108e-03, 1.2358454107222641e-03, 1.3989966190390965e-03, 1.5836863762264436e-03, 1.7927581125735061e-03, 2.0294306362957340e-03, 2.2973476893787268e-03, 2.6006340455800008e-03, 2.9439590142573526e-03, 3.3326083277104117e-03, 3.7725655187922052e-03, 4.2706040416570154e-03, 4.8343915539089625e-03, 5.4726079656493079e-03, 6.1950790728715292e-03, 7.0129278325854246e-03, 7.9387456086585442e-03, 8.9867860248264830e-03, 1.0173184409377162e-02, 1.1516206210016314e-02, 1.3036528203437736e-02, 1.4757556829019875e-02, 1.6705788547622769e-02, 1.8911217773465227e-02, 2.1407798659484324e-02, 2.4233967845691123e-02, 2.7433236218606032e-02, 3.1054858792331431e-02, 3.5154593024557458e-02, 3.9795557242315927e-02, 4.5049202393557801e-02, 5.0996412085361466e-02, 5.7728747844643331e-02, 6.5349858773045680e-02, 7.3977077298642363e-02, 8.3743225592195963e-02, 9.4798660459030126e-02, 1.0731358818908403e-01, 1.2148068500391276e-01, 1.3751806344428075e-01, 1.5567263036799733e-01, 1.7622388825676111e-01, 1.9948823835583873e-01, 2.2582385189647586e-01, 2.5563618439697788e-01, 2.8938421793905067e-01, 3.2758752752368947e-01, 3.7083428029819565e-01, 4.1979029080811425e-01, 4.7520927168614446e-01, 5.3794443759467447e-01, 6.0896164107289685e-01, 6.8935424252422239e-01, 7.8035994327803426e-01, 8.8337984088275090e-01, 1.0000000000000000e+00, 1.1320158709991752e+00, 1.2814599321940212e+00, 1.4506329812931589e+00, 1.6421395578187052e+00, 1.8589280418463421e+00, 2.1043360464154781e+00, 2.3821418024579781e+00, 2.6966223273530128e+00, 3.0526192726543444e+00, 3.4556134647626755e+00, 3.9118092861497971e+00, 4.4282301962435247e+00, 5.0128268625854631e+00, 5.6745995670177445e+00, 6.4237367714291338e+00, 7.2717719763787807e+00, 8.2317612875478190e+00, 9.3184844237807365e+00, 1.0548672261378394e+01, 1.1941264417849103e+01, 1.3517700840802913e+01, 1.5302251891207787e+01, 1.7322392002874359e+01, 1.9609222670922968e+01, 2.2197951281441636e+01, 2.5128433154258410e+01, 2.8445785143962375e+01, 3.2201080245997971e+01, 3.6452133901787732e+01, 4.1264394108610787e+01, 4.6711949038112273e+01, 5.2878667676447755e+01, 5.9859491047029913e+01, 6.7761893895170928e+01, 7.6707539338295589e+01, 8.6834151956244213e+01, 9.8297638159222487e+01, 1.1127448647797397e+02, 1.2596448473034971e+02, 1.4259379589698909e+02, 1.6141844006140866e+02, 1.8272823602144376e+02, 2.0685126325595743e+02, 2.3415891294197226e+02, 2.6507160578622688e+02, 3.0006526470124555e+02, 3.3967864197737873e+02, 3.8452161375783919e+02, 4.3528456951608860e+02, 4.9274904109325632e+02, 5.5779973493719069e+02, 6.3143815278803334e+02, 7.1479801051045558e+02, 8.0916269245647072e+02, 9.1598501008114988e+02, 1.0369095690092008e+03, 1.1737980889093292e+03, 1.3287580659938624e+03, 1.5041752194232211e+03, 1.7027502211507524e+03, 1.9275402746900081e+03, 2.1820061829391980e+03, 2.4700656297055034e+03, 2.7961534952362003e+03, 3.1652901343571971e+03, 3.5831586684094545e+03, 4.0561924809477755e+03, 4.5916742642604040e+03, 5.1978481416012310e+03, 5.8840465913361650e+03, 6.6608341270911405e+03, 7.5401699459601114e+03, 8.5355920488578286e+03, 9.6624256676814348e+03, 1.0938019208165191e+04, 1.2382011340936813e+04, 1.4016633352832258e+04, 1.5867051413382505e+04, 1.7961754025908867e+04, 2.0332990628312182e+04, 2.3017268096126892e+04, 2.6055912791858576e+04, 2.9495706813754354e+04, 3.3389608239508460e+04, 3.7797566453568354e+04, 4.2787445110585410e+04, 4.8436066944688770e+04, 5.4830396510166145e+04, 6.2068879062685897e+04, 7.0262956194088882e+04, 7.9538781555028458e+04, 9.0039163080228551e+04, 1.0192576161830177e+05, 1.1538157981559623e+05, 1.3061377957221285e+05, 1.4785687144693290e+05, 1.6737632511421290e+05, 1.8947265645880660e+05, 2.1448605423174356e+05, 2.4280161749832361e+05]) dlf.factor = np.array([1.132015870999175]) dlf.j0 = np.array([ 1.5020099209519960e-03, -1.0381698214761684e-02, 3.6840860097595164e-02, -8.9903380392274704e-02, 1.7082286536833860e-01, -2.7115749656836280e-01, 3.7649328091859574e-01, -4.7220778569122657e-01, 5.4778211089647089e-01, -5.9823516853035097e-01, 6.2345791612185331e-01, -6.2650436648257724e-01, 6.1197225351173345e-01, -5.8470173866140451e-01, 5.4911055789616858e-01, -5.0878861684860843e-01, 4.6652106345430200e-01, -4.2426478870289325e-01, 3.8339538911933357e-01, -3.4472344791723936e-01, 3.0876891466890510e-01, -2.7570439368364807e-01, 2.4562331000974616e-01, -2.1839207265400126e-01, 1.9393194321380827e-01, -1.7198162962644575e-01, 1.5242270280410272e-01, -1.3494945901825492e-01, 1.1946763189654602e-01, -1.0565870880444576e-01, 9.3482355548033913e-02, -8.2612525279836244e-02, 7.3077763526174969e-02, -6.4536481281701225e-02, 5.7096310621587334e-02, -5.0384859605213800e-02, 4.4599557396733047e-02, -3.9316995063444334e-02, 3.4838544754296139e-02, -3.0664946477420088e-02, 2.7221072240291456e-02, -2.3901586108434601e-02, 2.1281566646364738e-02, -1.8612484595521447e-02, 1.6655386303461400e-02, -1.4472420076504743e-02, 1.3057747649606617e-02, -1.1226286001060300e-02, 1.0266818557930830e-02, -8.6738022421653585e-03, 8.1103368670848164e-03, -6.6573628142085938e-03, 6.4551189810889585e-03, -5.0524015117839084e-03, 5.1989014270506263e-03, -3.7597430078747883e-03, 4.2640545165292636e-03, -2.6994965688974474e-03, 3.5928000560587229e-03, -1.8061291289989019e-03, 3.1436470898586703e-03, -1.0244200001620755e-03, 2.8888297674091743e-03, -3.0605070741955765e-04, 2.8125907445050334e-03, 3.9337862066047565e-04, 2.9102041487017727e-03, 1.1170884769911178e-03, 3.1876763415953362e-03, 1.9097806429850762e-03, 3.6621020321465411e-03, 2.8203783587849949e-03, 4.3626885599390430e-03, 3.9050024915686802e-03, 5.3324923486866077e-03, 5.2303399394270488e-03, 6.6309348458396984e-03, 6.8775540687037451e-03, 8.3371689988226087e-03, 8.9468564745410102e-03, 1.0554326601376745e-02, 1.1562765604509096e-02, 1.3414536265660639e-02, 1.4879837399735491e-02, 1.7084241336519569e-02, 1.9088092654441269e-02, 2.1768513715084332e-02, 2.4416120601223806e-02, 2.7711234465350204e-02, 3.1127164234404547e-02, 3.5184140220277452e-02, 3.9497913113638941e-02, 4.4449762157204989e-02, 4.9758433269983887e-02, 5.5667457114992429e-02, 6.1949790434151823e-02, 6.8682064905571841e-02, 7.5616743950118387e-02, 8.2584983563572259e-02, 8.9193635262987042e-02, 9.4874686942005279e-02, 9.8891681869094042e-02, 1.0004294654495730e-01, 9.7016844329802857e-02, 8.7789596149914384e-02, 7.0509767592855419e-02, 4.2778853484849347e-02, 3.5584532926218175e-03, -4.7210453264879347e-02, -1.0489787743225988e-01, -1.6020950407348281e-01, -1.9459781573132096e-01, -1.8490774599542381e-01, -1.0754165020025190e-01, 3.6037727487476613e-02, 1.9759013047489976e-01, 2.6132313321851336e-01, 1.1713996822458939e-01, -1.8758779281301441e-01, -3.0238114997462151e-01, 4.8163135684567732e-02, 3.6399529664885466e-01, -1.4910233461562913e-01, -2.6373490348543854e-01, 4.0362661807718703e-01, -3.1409794650104578e-01, 1.8179369405131079e-01, -9.0738718042631769e-02, 4.2946487545160242e-02, -2.0586135807067835e-02, 1.0392667161913182e-02, -5.6117848068723023e-03, 3.2402025511569896e-03, -1.9858724388273777e-03, 1.2807317326135252e-03, -8.6253791756068252e-04, 6.0296590782143555e-04, -4.3548936996943465e-04, 3.2375891570874245e-04, -2.4698212240059978e-04, 1.9279062274925971e-04, -1.5357911509105972e-04, 1.2453787849367440e-04, -1.0255126402954421e-04, 8.5558482209476271e-05, -7.2170928476334345e-05, 6.1436863283080017e-05, -5.2693349406473615e-05, 4.5471255142623729e-05, -3.9433284158653591e-05, 3.4332971164795619e-05, -2.9987212220165472e-05, 2.6257657435614391e-05, -2.3037978256349448e-05, 2.0245071331016652e-05, -1.7812925644382519e-05, 1.5688305607849465e-05, -1.3827679492110470e-05, 1.2195005442258958e-05, -1.0760110818279243e-05, 9.4974857670959145e-06, -8.3853711343938338e-06, 7.4050612540713192e-06, -6.5403682860228500e-06, 5.7772102413267325e-06, -5.1032933218796731e-06, 4.5078641320869195e-06, -3.9815111951817114e-06, 3.5159993210292339e-06, -3.1041249680128287e-06, 2.7395854235553632e-06, -2.4168587823583312e-06, 2.1310948134441218e-06, -1.8780185742021288e-06, 1.6538488252707735e-06, -1.4552318768651144e-06, 1.2791890865306748e-06, -1.1230741959148155e-06, 9.8453630538596172e-07, -8.6148574493190796e-07, 7.5206242699701732e-07, -6.5460810334682633e-07, 5.6764451596029765e-07, -4.8985884555184997e-07, 4.2009674106879252e-07, -3.5736212641225517e-07, 3.0082215969939671e-07, -2.4981510481639669e-07, 2.0385823466866512e-07, -1.6265189071584773e-07, 1.2607416700611311e-07, -9.4158417913450858e-08, 6.7043911217063425e-08, -4.4891090827293947e-08, 2.7761325666544702e-08, -1.5480404355710375e-08, 7.5327300141098751e-09, -3.0524770418657847e-09, 9.5877856096830783e-10, -2.0575286298055636e-10, 2.2414416956474645e-11]) dlf.j1 = np.array([ 4.7827871332506182e-10, -2.9784175503440788e-09, 9.7723832770897220e-09, -2.2382340996085809e-08, 4.0446774329470848e-08, -6.1734815854553919e-08, 8.3293912185608189e-08, -1.0249453502284080e-07, 1.1780779749909977e-07, -1.2870061460834850e-07, 1.3559243438349901e-07, -1.3921010821521872e-07, 1.4065745722769670e-07, -1.4074881908375281e-07, 1.4051720878600928e-07, -1.4040746687777830e-07, 1.4127886061686993e-07, -1.4315595655055356e-07, 1.4689283208027915e-07, -1.5210916706348747e-07, 1.5989801550138741e-07, -1.6940918407911260e-07, 1.8227089415749844e-07, -1.9695856878603369e-07, 2.1603952427106760e-07, -2.3691320619292838e-07, 2.6369843208466607e-07, -2.9202021404039016e-07, 3.2852445086324662e-07, -3.6589094553627693e-07, 4.1487501036863030e-07, -4.6327136995173986e-07, 5.2852697369750518e-07, -5.9034983719954077e-07, 6.7710211611560898e-07, -7.5512942807901028e-07, 8.7062473466409799e-07, -9.6788530918130449e-07, 1.1222658353725904e-06, -1.2417228058919743e-06, 1.4493467036899140e-06, -1.5932456559208080e-06, 1.8747045814274419e-06, -2.0433320340041385e-06, 2.4285695351967146e-06, -2.6179926456520528e-06, 3.1511729661391781e-06, -3.3492412032881268e-06, 4.0964186613549959e-06, -4.2758275751239154e-06, 5.3371197552207799e-06, -5.4435423773626499e-06, 6.9725766921672099e-06, -6.9045562968161745e-06, 9.1397025436977438e-06, -8.7148373033635960e-06, 1.2029590806160379e-05, -1.0927976968519436e-05, 1.5912526719455299e-05, -1.3582559661331659e-05, 2.1176226828087565e-05, -1.6678205993448338e-05, 2.8384979250408712e-05, -2.0132088397797457e-05, 3.8372045311188108e-05, -2.3702184335455945e-05, 5.2385308850007940e-05, -2.6854373943701261e-05, 7.2318581557902158e-05, -2.8535361884516687e-05, 1.0108123118106823e-04, -2.6788477540644352e-05, 1.4319185407094621e-04, -1.8108424211338017e-05, 2.0573561552327273e-04, 3.6361648565843316e-06, 2.9991264692859609e-04, 4.8993332079278846e-05, 4.4354733854670903e-04, 1.3589101811995494e-04, 6.6515823521273764e-04, 2.9451991608624389e-04, 1.0105553806271136e-03, 5.7533964792254050e-04, 1.5535077418254303e-03, 1.0621193133794828e-03, 2.4128970258747457e-03, 1.8929698186109245e-03, 3.7800177772191607e-03, 3.2937343278959356e-03, 5.9612179800391544e-03, 5.6295935320552241e-03, 9.4422526803168080e-03, 9.4810228247137925e-03, 1.4979159139973408e-02, 1.5745093424331037e-02, 2.3708966370000140e-02, 2.5740590762136872e-02, 3.7232782843117498e-02, 4.1225008900614292e-02, 5.7507103212277359e-02, 6.4044642846235691e-02, 8.6091796551857253e-02, 9.4717139804457451e-02, 1.2172497389177185e-01, 1.2853597000398900e-01, 1.5450777327408322e-01, 1.4755964090969320e-01, 1.5621399202016978e-01, 1.1147620703185755e-01, 7.7489831356083380e-02, -2.7628266850147711e-02, -1.0198730178317840e-01, -2.2039889971111640e-01, -2.1185762869925318e-01, -1.6052415083152241e-01, 9.1649025798681089e-02, 2.3792823877700942e-01, 2.6075777853738125e-01, -1.5662188259001042e-01, -2.8932081756330175e-01, 1.3148519116247689e-02, 4.2691302759079564e-01, -4.0005050006489040e-01, 1.1513789407450359e-01, 9.3748244358717620e-02, -1.6037231301955096e-01, 1.5071857939129532e-01, -1.2120369075996129e-01, 9.4110656079982341e-02, -7.3742238434584328e-02, 5.9038567576124905e-02, -4.8288117528475852e-02, 4.0197054299576880e-02, -3.3919787720641081e-02, 2.8918247156763971e-02, -2.4845271759013743e-02, 2.1470449751150148e-02, -1.8635828020057092e-02, 1.6229579362363859e-02, -1.4170085406786529e-02, 1.2396084121011890e-02, -1.0860414401084047e-02, 9.5259444245356633e-03, -8.3628577447233381e-03, 7.3468029551253195e-03, -6.4576043210966359e-03, 5.6783439955994880e-03, -4.9946949167265437e-03, 4.3944258108608806e-03, -3.8670264019660858e-03, 3.4034180355556670e-03, -2.9957260668529964e-03, 2.6370977166248776e-03, -2.3215540117372982e-03, 2.0438677474690805e-03, -1.7994616759226389e-03, 1.5843226896713463e-03, -1.3949288614414647e-03, 1.2281869708886250e-03, -1.0813786997088304e-03, 9.5211407460757294e-04, -8.3829103020448140e-04, 7.3806018220987763e-04, -6.4979406671247244e-04, 5.7206022901230412e-04, -5.0359764543483573e-04, 4.4329604122300101e-04, -3.9017773206623073e-04, 3.4338166974098888e-04, -3.0214941633163506e-04, 2.6581280850704716e-04, -2.3378310479588391e-04, 2.0554143583887405e-04, -1.8063040107732216e-04, 1.5864667598176302e-04, -1.3923451235168759e-04, 1.2208003098625932e-04, -1.0690622166177854e-04, 9.3468580362568137e-05, -8.1551328581234316e-05, 7.0964174631531072e-05, -6.1539592468666665e-05, 5.3130609116145443e-05, -4.5609105983126460e-05, 3.8864648584181207e-05, -3.2803856352344075e-05, 2.7350296775876261e-05, -2.2444816150805301e-05, 1.8046076281584239e-05, -1.4130826937491561e-05, 1.0693106849359383e-05, -7.7412053314530284e-06, 5.2910576443698300e-06, -3.3552268362550323e-06, 1.9282956206367452e-06, -9.7253712572058755e-07, 4.1100807632959352e-07, -1.3553176263207053e-07, 3.0748587523233524e-08, -3.5668195345476294e-09]) return dlf
[docs]def wer_201_2018(): r"""Werthmüller 201 pt Hankel filter, 2018. Designed with the empymod add-on ``fdesign``, see https://github.com/empymod/article-fdesign. License: `Apache License, Version 2.0, <http://www.apache.org/licenses/LICENSE-2.0>`_. """ dlf = DigitalFilter('Werthmüller 201', 'wer_201_2018') dlf.base = np.array([ 8.653980893285999343e-04, 9.170399868578506730e-04, 9.717635708540675208e-04, 1.029752738345341345e-03, 1.091202360259058363e-03, 1.156318936280037154e-03, 1.225321288786770891e-03, 1.298441298197734088e-03, 1.375924682198844014e-03, 1.458031821470676028e-03, 1.545038634690233410e-03, 1.637237505747725754e-03, 1.734938266294200121e-03, 1.838469236921894991e-03, 1.948178330476121357e-03, 2.064434221206373505e-03, 2.187627583685520637e-03, 2.318172405660454734e-03, 2.456507379246002792e-03, 2.603097375137131825e-03, 2.758435004793547123e-03, 2.923042275846299189e-03, 3.097472346289414230e-03, 3.282311383351382318e-03, 3.478180533293271509e-03, 3.685738008752825322e-03, 3.905681300649099623e-03, 4.138749522080598965e-03, 4.385725892093550113e-03, 4.647440367666977670e-03, 4.924772432759196537e-03, 5.218654053788364042e-03, 5.530072811478751842e-03, 5.860075219597365645e-03, 6.209770241733286907e-03, 6.580333017937914017e-03, 6.973008813749223544e-03, 7.389117204870794542e-03, 7.830056511567909730e-03, 8.297308497682591086e-03, 8.792443350058264107e-03, 9.317124955107483966e-03, 9.873116490254248145e-03, 1.046228634904101083e-02, 1.108661441981135046e-02, 1.174819873906770597e-02, 1.244926254186268406e-02, 1.319216173291635694e-02, 1.397939280356631266e-02, 1.481360122115480543e-02, 1.569759031904567614e-02, 1.663433071714528685e-02, 1.762697030458526201e-02, 1.867884481811322647e-02, 1.979348905174003331e-02, 2.097464873531334692e-02, 2.222629312193481060e-02, 2.355262832652090660e-02, 2.495811146033087569e-02, 2.644746560896089893e-02, 2.802569570413705746e-02, 2.969810534264444649e-02, 3.147031460891126092e-02, 3.334827896114080786e-02, 3.533830924445728605e-02, 3.744709289831891358e-02, 3.968171642946591998e-02, 4.204968922592208086e-02, 4.455896879207719985e-02, 4.721798748965116282e-02, 5.003568087440296575e-02, 5.302151772380819111e-02, 5.618553185661335353e-02, 5.953835585119460899e-02, 6.309125677603129312e-02, 6.685617405236506106e-02, 7.084575957628110043e-02, 7.507342023504076645e-02, 7.955336296053971967e-02, 8.430064247129397115e-02, 8.933121186338736919e-02, 9.466197622039211612e-02, 1.003108494224146802e-01, 1.062968143451746283e-01, 1.126399866514113390e-01, 1.193616823889895873e-01, 1.264844896228644322e-01, 1.340323443416230609e-01, 1.420306108936851552e-01, 1.505061672234652703e-01, 1.594874951939309615e-01, 1.690047762990831426e-01, 1.790899930879975566e-01, 1.897770366412597776e-01, 2.011018204609656135e-01, 2.131024011570106513e-01, 2.258191063352318062e-01, 2.392946701171655144e-01, 2.535743767468323084e-01, 2.687062127671349665e-01, 2.847410282772538936e-01, 3.017327078129410922e-01, 3.197383514239506286e-01, 3.388184665571116749e-01, 3.590371713898611872e-01, 3.804624102975323052e-01, 4.031661821784713884e-01, 4.272247824042622599e-01, 4.527190592081252185e-01, 4.797346853730769523e-01, 5.083624461328500876e-01, 5.386985442530570767e-01, 5.708449233178135573e-01, 6.049096103082166609e-01, 6.410070786239048246e-01, 6.792586327676195523e-01, 7.197928159854947161e-01, 7.627458422329327359e-01, 8.082620539176789132e-01, 8.564944069583262376e-01, 9.076049847882753374e-01, 9.617655430324436594e-01, 1.019158086687097953e+00, 1.079975481742401877e+00, 1.144422103303022853e+00, 1.212714522384784388e+00, 1.285082233695329812e+00, 1.361768426844476521e+00, 1.443030803575896748e+00, 1.529142443766406734e+00, 1.620392723103028176e+00, 1.717088285521651159e+00, 1.819554073675149652e+00, 1.928134420893808709e+00, 2.043194208307565596e+00, 2.165120091018537973e+00, 2.294321797444361266e+00, 2.431233506198735572e+00, 2.576315305136151590e+00, 2.730054737463883274e+00, 2.892968440116886253e+00, 3.065603879901345419e+00, 3.248541193241110570e+00, 3.442395135709440002e+00, 3.647817147897402634e+00, 3.865497544561224075e+00, 4.096167834405143537e+00, 4.340603178295351583e+00, 4.599624994165753655e+00, 4.874103717369282940e+00, 5.164961725750846000e+00, 5.473176439271492555e+00, 5.799783604600056819e+00, 6.145880775710010013e+00, 6.512631002177978523e+00, 6.901266737578352739e+00, 7.313093981108034214e+00, 7.749496666359123154e+00, 8.211941311987910552e+00, 8.701981949908562441e+00, 9.221265347572652260e+00, 9.771536541883744320e+00, 1.035464470334362019e+01, 1.097254935013656407e+01, 1.162732693303372145e+01, 1.232117781324618733e+01, 1.305643365667540934e+01, 1.383556526940939513e+01, 1.466119090079532228e+01, 1.553608504199116247e+01, 1.646318774956322173e+01, 1.744561452546165370e+01, 1.848666678657500739e+01, 1.958984295904654616e+01, 2.075885023463468926e+01, 2.199761702862400270e+01, 2.331030618115176267e+01, 2.470132894631230158e+01, 2.617535981604930129e+01, 2.773735222865149197e+01, 2.939255521463919862e+01, 3.114653103598043415e+01, 3.300517387791185087e+01, 3.497472965617872376e+01, 3.706181700625468523e+01, 3.927344952507589682e+01, 4.161705934003131091e+01, 4.410052208441296528e+01, 4.673218336325475519e+01, 4.952088679849771324e+01, 5.247600374772711262e+01, 5.560746479634944706e+01, 5.892579312903905020e+01, 6.244213989259677078e+01, 6.616832166905808776e+01, 7.011686018497628936e+01, 7.430102439032442874e+01, 7.873487504841911289e+01, 8.343331198671111792e+01, 8.841212416722630962e+01, 9.368804274491759543e+01]) dlf.factor = np.array([1.0596741524693181]) dlf.j0 = np.array([ 2.940900904253498815e+00, -1.601154970027019786e+01, 3.574488144287594338e+01, -3.775710631592443178e+01, 9.347313619702582344e+00, 1.903333998229986435e+01, -1.266160545445113073e+01, -1.274822633210828471e+01, 1.499040669570122830e+01, 1.128114232815630835e+01, -3.141814347069891511e+01, 2.185520874118305557e+01, 4.204688908817206361e+00, -2.039396651211594147e+01, 1.703214350560853418e+01, -3.858035665251962953e+00, -5.664929771474184861e+00, 6.236013601339658763e+00, -8.349084962847823643e-01, -5.076648434675173682e+00, 8.069437229646323928e+00, -7.693517618528387558e+00, 5.264540454351635645e+00, -2.378232295562936471e+00, 9.488986688091295696e-02, 1.211665432819921451e+00, -1.641788465968915700e+00, 1.505783472315168181e+00, -1.120376089133631847e+00, 7.202627618735454318e-01, -4.293308092527763353e-01, 2.880519253847271255e-01, -2.765909110132210857e-01, 3.540771325316399709e-01, -4.702415607316920432e-01, 5.886079250132733032e-01, -6.804407177384068639e-01, 7.365579045711867501e-01, -7.516232294769148448e-01, 7.332518369461620278e-01, -6.840940481215002089e-01, 6.145375558739786248e-01, -5.263752170486778459e-01, 4.305607160730071659e-01, -3.307504282674695872e-01, 2.429511351824290011e-01, -1.749591466871897039e-01, 1.456366850874822316e-01, -1.595894233786172844e-01, 2.280395161025021433e-01, -3.413711397379035062e-01, 4.950015142033588056e-01, -6.617826176259098414e-01, 8.243458750063681340e-01, -9.468449720632085009e-01, 1.012979648696065826e+00, -9.946084380621768029e-01, 8.932243609342348512e-01, -7.019325270091921753e-01, 4.480078578272302381e-01, -1.456381084707468188e-01, -1.604285443826692914e-01, 4.506359421881006022e-01, -6.820827325803067165e-01, 8.491728004462286705e-01, -9.252486609867097700e-01, 9.260533367474167443e-01, -8.402031897556576645e-01, 6.982570225067336045e-01, -4.946654104012083719e-01, 2.669962789856030194e-01, -1.042528939201309117e-02, -2.319933928270803414e-01, 4.654858099944349514e-01, -6.436180173401860882e-01, 7.780252822887177011e-01, -8.272840865922600484e-01, 8.197748606729908794e-01, -7.271116816505861502e-01, 5.992292042110317629e-01, -4.191980233493379782e-01, 2.522483458861179417e-01, -8.121597742330896597e-02, -2.652177515646544220e-02, 1.028351781199190462e-01, -8.958878867947789315e-02, 4.230973855067972356e-02, 8.503909842995018009e-02, -2.142619566112575480e-01, 3.865561094837716705e-01, -5.104727910435372662e-01, 6.353554205789004872e-01, -6.678424785380696616e-01, 6.769052092946485910e-01, -5.740789051340543514e-01, 4.533865101372042683e-01, -2.311110970314779189e-01, 2.495118155831516429e-02, 2.508326503987150513e-01, -4.617568849058834579e-01, 7.064398492531979157e-01, -8.419497320020807862e-01, 9.894625411708843910e-01, -1.001995584015555441e+00, 1.027606495406535592e+00, -9.137586391106879979e-01, 8.347545540345707726e-01, -6.273557157264747497e-01, 4.895538883108097039e-01, -2.415916082478662963e-01, 1.027651673270286170e-01, 1.284590129111473078e-01, -2.133464520148750654e-01, 3.796869867196227544e-01, -3.706104772018420923e-01, 4.433984947033918766e-01, -3.235750823461782666e-01, 2.994380356487793549e-01, -7.888021235143724552e-02, -1.910472056257344828e-02, 3.043509756878240990e-01, -4.298489130677841108e-01, 7.233655581626995401e-01, -8.161936207950235556e-01, 1.054311731055406431e+00, -1.057859070622381603e+00, 1.189505276805579825e+00, -1.071819355511486993e+00, 1.077289848919564141e+00, -8.458743245226547636e-01, 7.443908003078970603e-01, -4.461507052923350813e-01, 2.868208498373531756e-01, 8.293917061440093941e-03, -1.688393814622326516e-01, 3.930003549460732160e-01, -5.148213607425790039e-01, 6.232961968619017412e-01, -6.962255871378753014e-01, 6.749680427277989780e-01, -7.157027353444623818e-01, 5.769543174180707945e-01, -6.151602424632486299e-01, 3.892025319337197864e-01, -4.506933666706669506e-01, 1.804687704243498336e-01, -2.727244303574414830e-01, 1.174346932607069939e-02, -1.137579568068424057e-01, -7.811421895993872488e-02, 1.779393134675293781e-02, -8.675295089134033022e-02, 1.335093001151206882e-01, -5.514694464669991220e-02, 2.441624548660136784e-01, -5.518933795483266236e-02, 3.328770195966135881e-01, -1.532145946078544430e-01, 3.579812932040986606e-01, -3.542418291888540516e-01, 3.138078445399646865e-01, -5.530414472417091165e-01, 2.996207005996078809e-01, -5.735406549188309944e-01, 4.429014477665748628e-01, -3.892397979507834505e-01, 6.319796721730875921e-01, -3.224362675105876264e-01, 5.280557016061210307e-01, -5.925152169592526885e-01, 3.097933933610434454e-01, -6.161398121500974989e-01, 5.824585099080735739e-01, -2.863603061506506120e-01, 5.579069742591284964e-01, -5.790177379949956737e-01, 1.778203303660013113e-01, -2.248159329174458654e-01, 4.570279405020428731e-01, -2.082694991220853942e-01, -1.639463813834285966e-01, 1.219471051626438846e-01, 1.315907246465166380e-01, -1.561922951483753763e-01, -9.000173966500184253e-02, 3.555651953426591794e-01, -4.594671107387718334e-01, 4.051183609553802301e-01, -2.826594312508529105e-01, 1.664628231342878961e-01, -8.573386548433219179e-02, 3.940897144775467459e-02, -1.632396319789397934e-02, 6.095399479649578345e-03, -2.034197210251703809e-03, 5.959585007671103435e-04, -1.489396688112877424e-04, 3.040429693056684047e-05, -4.735729642331119566e-06, 4.982902654694162416e-07, -2.645962918790746080e-08]) dlf.j1 = np.array([ -2.594301879688918743e-03, 2.339490069567079153e-02, -9.478827695764932559e-02, 2.269100107268227362e-01, -3.508900104631907935e-01, 3.515648778060092017e-01, -1.994483426338835574e-01, 9.293484158449249674e-03, 8.048790331434139966e-02, -5.691508909482047296e-02, 2.075411236619714023e-02, -5.275228907131672418e-02, 1.348060780914397960e-01, -1.939017682982676627e-01, 1.854125006516780250e-01, -1.238162114378456441e-01, 5.435433909585837137e-02, -1.270327896980103649e-02, 7.560629247467166685e-03, -2.713648547163816441e-02, 5.383176198347366936e-02, -7.463014212375274070e-02, 8.413254388281748986e-02, -8.280914671407160754e-02, 7.393816085156304507e-02, -6.119942568117115594e-02, 4.746907894866293082e-02, -3.450474036399159977e-02, 2.313104032185092293e-02, -1.354138672902785445e-02, 5.604638952874172256e-03, 9.486899997092870969e-04, -6.382314415042419746e-03, 1.091601370650388016e-02, -1.467479730415811347e-02, 1.771829574440562591e-02, -2.001990396213982823e-02, 2.152720536808908763e-02, -2.214634467574278301e-02, 2.181839780171816040e-02, -2.049006667874660528e-02, 1.819226618052163791e-02, -1.498058384418661862e-02, 1.101097898088004151e-02, -6.444381466006598655e-03, 1.527769500667217105e-03, 3.533045890696502513e-03, -8.470577184056853060e-03, 1.310891443998619434e-02, -1.722186749311952272e-02, 2.071070403809925978e-02, -2.340849145682623311e-02, 2.528895672008608583e-02, -2.620974028011485712e-02, 2.617463680378217042e-02, -2.501974545161460978e-02, 2.276381800709064221e-02, -1.923696679546721411e-02, 1.454384146700743972e-02, -8.605818651281786635e-03, 1.738844503682727928e-03, 5.947517515245405624e-03, -1.385885800081448037e-02, 2.171703574368676753e-02, -2.872814698074024550e-02, 3.461838232135941440e-02, -3.858941536214401807e-02, 4.060565074712448042e-02, -4.004001014668581715e-02, 3.725276070158690944e-02, -3.184536604257427045e-02, 2.462644816656397312e-02, -1.539955242663786951e-02, 5.437594699869644464e-03, 5.315602443775078317e-03, -1.514798704965643165e-02, 2.414409295479183482e-02, -3.032245442310742278e-02, 3.416403682006976389e-02, -3.375211066545635158e-02, 3.045425146826126819e-02, -2.272683240323554107e-02, 1.317397219169818418e-02, -6.119848802195663844e-04, -1.115685958739305421e-02, 2.344848055710842955e-02, -3.169397030448774938e-02, 3.817520279763731567e-02, -3.809651169502087376e-02, 3.552394037620545952e-02, -2.568176960339346032e-02, 1.487169880055576841e-02, 1.997965754252607837e-03, -1.644546122863936588e-02, 3.480415781283187349e-02, -4.677537576184215284e-02, 6.111820051573001178e-02, -6.590953690231306228e-02, 7.332112878498593667e-02, -6.941405787722150500e-02, 7.037058951810715168e-02, -5.921683716330301134e-02, 5.655416878814193554e-02, -4.097804417398832194e-02, 3.810136479256000241e-02, -2.058552251762190213e-02, 2.012009960638341116e-02, -1.904932224648239053e-03, 5.324133880430357950e-03, 1.357085636140308721e-02, -5.592398994521355186e-03, 2.589415408390925710e-02, -1.292224858788840886e-02, 3.561835458678683924e-02, -1.700336052804993919e-02, 4.302272543873187499e-02, -1.764501119714675936e-02, 4.776824187802861110e-02, -1.404967795338326469e-02, 4.909105531804618811e-02, -5.268363386320836297e-03, 4.641444115511134810e-02, 9.124170345995139680e-03, 3.991380510079723526e-02, 2.859680534219202416e-02, 3.073032173944831302e-02, 5.151734601415858261e-02, 2.097520864952298614e-02, 7.511832720419686638e-02, 1.354148686126329000e-02, 9.576070647813632319e-02, 1.140272504589405489e-02, 1.097360846564945647e-01, 1.641156037670641471e-02, 1.142607074214286172e-01, 2.822722328175052836e-02, 1.079741026261866604e-01, 4.397838549427537935e-02, 9.072532008032478668e-02, 5.865331390992817306e-02, 6.310580311949447185e-02, 6.592890500839264367e-02, 2.624768245556352575e-02, 5.954092122676180737e-02, -1.789442088462365327e-02, 3.555984804371448149e-02, -6.551973841104229146e-02, -4.489823587807304991e-03, -1.089659607197719371e-01, -5.052377390460756346e-02, -1.345089168583019634e-01, -8.286532978746213862e-02, -1.229744228392625760e-01, -7.728334735138943368e-02, -5.831402820224085293e-02, -2.088719549713474385e-02, 5.205792146829352207e-02, 6.258826423151815643e-02, 1.537593434905694390e-01, 9.979165672991972824e-02, 1.545936043232943868e-01, 1.442374184540378551e-02, 1.426608350698001064e-02, -1.462978689171700042e-01, -1.285617304470880462e-01, -1.519560295563492092e-01, -4.700754607069132507e-02, 1.106161196544740571e-01, 1.168039951766200457e-01, 2.366820009670577984e-01, -1.283956636561735531e-01, 1.406024618127853579e-02, -4.011626826391421763e-01, 2.656020926376266300e-01, -1.291178852844470371e-01, 5.190017993719785450e-01, -5.307617026829943851e-01, 2.388177316428383157e-01, -4.213777919843004205e-01, 7.425023205388556757e-01, -6.039491377476802203e-01, 2.966551251977549986e-01, -3.157763414193298090e-01, 5.842678377857475347e-01, -7.375386163194860289e-01, 6.321787190293964853e-01, -3.871768116388242809e-01, 1.635153404860406612e-01, -3.134030444480916111e-02, -2.007964312111037639e-02, 2.747060309825222202e-02, -1.969027573928272892e-02, 1.080160200622757964e-02, -4.917741573140644099e-03, 1.900872502605262596e-03, -6.228037791451519409e-04, 1.698280169898911708e-04, -3.718088395106743311e-05, 6.139140918052498045e-06, -6.796809441105533029e-07, 3.780807126974975489e-08]) return dlf
# 2. Fourier DLF (cosine/sine)
[docs]def key_81_CosSin_2009(): r"""Key 81 pt CosSin filter, as published in [Key09]_. Taken from file ``FilterModules.f90`` provided with 1DCSEM_. License: `Apache License, Version 2.0, <http://www.apache.org/licenses/LICENSE-2.0>`_. """ dlf = DigitalFilter('Key 81 CosSin (2009)', 'key_81_CosSin_2009') dlf.base = np.array([ 3.354626279025119e-04, 4.097349789797864e-04, 5.004514334406104e-04, 6.112527611295723e-04, 7.465858083766792e-04, 9.118819655545162e-04, 1.113775147844802e-03, 1.360368037547893e-03, 1.661557273173934e-03, 2.029430636295734e-03, 2.478752176666358e-03, 3.027554745375813e-03, 3.697863716482929e-03, 4.516580942612666e-03, 5.516564420760772e-03, 6.737946999085467e-03, 8.229747049020023e-03, 1.005183574463358e-02, 1.227733990306844e-02, 1.499557682047770e-02, 1.831563888873418e-02, 2.237077185616559e-02, 2.732372244729256e-02, 3.337326996032607e-02, 4.076220397836620e-02, 4.978706836786394e-02, 6.081006262521795e-02, 7.427357821433388e-02, 9.071795328941247e-02, 1.108031583623339e-01, 1.353352832366127e-01, 1.652988882215865e-01, 2.018965179946554e-01, 2.465969639416064e-01, 3.011942119122020e-01, 3.678794411714423e-01, 4.493289641172216e-01, 5.488116360940264e-01, 6.703200460356393e-01, 8.187307530779818e-01, 1e0, 1.221402758160170e+00, 1.491824697641270e+00, 1.822118800390509e+00, 2.225540928492468e+00, 2.718281828459046e+00, 3.320116922736548e+00, 4.055199966844675e+00, 4.953032424395115e+00, 6.049647464412947e+00, 7.389056098930650e+00, 9.025013499434122e+00, 1.102317638064160e+01, 1.346373803500169e+01, 1.644464677109706e+01, 2.008553692318767e+01, 2.453253019710935e+01, 2.996410004739703e+01, 3.659823444367799e+01, 4.470118449330084e+01, 5.459815003314424e+01, 6.668633104092515e+01, 8.145086866496814e+01, 9.948431564193386e+01, 1.215104175187350e+02, 1.484131591025766e+02, 1.812722418751512e+02, 2.214064162041872e+02, 2.704264074261528e+02, 3.302995599096489e+02, 4.034287934927351e+02, 4.927490410932563e+02, 6.018450378720822e+02, 7.350951892419732e+02, 8.978472916504184e+02, 1.096633158428459e+03, 1.339430764394418e+03, 1.635984429995927e+03, 1.998195895104119e+03, 2.440601977624501e+03, 2.980957987041728e+03]) dlf.factor = np.array([1.2214027581601701]) dlf.cos = np.array([ 1.746412733678043e-02, -7.658725022064888e-02, 1.761673907472465e-01, -2.840940679113589e-01, 3.680388960144733e-01, -4.115498161707958e-01, 4.181209762362728e-01, -3.967204599348831e-01, 3.608829691008270e-01, -3.171870084102961e-01, 2.744932842186247e-01, -2.324673650676961e-01, 1.971144816936984e-01, -1.634915360178986e-01, 1.381406405905393e-01, -1.125728533897677e-01, 9.619580319372194e-02, -7.640431432353632e-02, 6.748891657821673e-02, -5.097864570224415e-02, 4.853609305288441e-02, -3.293272689265632e-02, 3.677175984620380e-02, -1.969323595300588e-02, 3.053726798991684e-02, -9.301135480582538e-03, 2.895215492109734e-02, -1.875526095801418e-04, 3.181452657662026e-02, 9.025726238227111e-03, 3.955376604096631e-02, 1.966766645672513e-02, 5.318782805621459e-02, 3.300575875620110e-02, 7.409212944640006e-02, 4.972863917303501e-02, 1.029344264288086e-01, 6.776855697600163e-02, 1.357865756912759e-01, 7.511614666518443e-02, 1.522218287240260e-01, 3.034571997381229e-02, 8.802563675323094e-02, -1.689255322598353e-01, -1.756581788680092e-01, -6.123863775740898e-01, -5.098359641153184e-01, -6.736869803920745e-01, 4.599561125225532e-01, 8.907010262082216e-01, 1.039153770711999e+00, -2.178135931072732e+00, 8.040971159674268e-01, 5.659848584656202e-01, -9.349050336534268e-01, 8.006099486213468e-01, -5.944960111930493e-01, 4.369614304892440e-01, -3.292566347310282e-01, 2.547426420681868e-01, -2.010899026277397e-01, 1.609467208423519e-01, -1.299975550484158e-01, 1.056082501090365e-01, -8.608337452556068e-02, 7.027252107999236e-02, -5.735742622053085e-02, 4.673270108060494e-02, -3.793635725863799e-02, 3.060786160620013e-02, -2.446220554726340e-02, 1.927399223200865e-02, -1.486843016804444e-02, 1.111747692371507e-02, -7.939442960305236e-03, 5.298852472637883e-03, -3.200104589830043e-03, 1.665382777953919e-03, -6.913074254614758e-04, 1.999065225130592e-04, -2.955159288961187e-05]) dlf.sin = np.array([ 7.478326513505658e-07, -2.572850425065560e-06, 5.225955618519281e-06, -7.352539610140040e-06, 8.768819961093828e-06, -8.560004370841340e-06, 8.101932279460349e-06, -5.983552716117552e-06, 5.036792825138655e-06, -1.584355068233649e-06, 1.426050228179462e-06, 3.972863429067356e-06, -1.903788077376088e-06, 1.144652944379527e-05, -4.327773998196030e-06, 2.297298998355334e-05, -4.391227697686659e-06, 4.291202395830839e-05, 1.760279032167125e-06, 8.017887907026914e-05, 2.364651853689879e-05, 1.535031685829202e-04, 8.375427119939347e-05, 3.030115685600468e-04, 2.339455351760637e-04, 6.157392107422657e-04, 5.921808556382737e-04, 1.281873037121434e-03, 1.424276189020714e-03, 2.718506171172064e-03, 3.324504626808429e-03, 5.839859904586436e-03, 7.608663600764702e-03, 1.263571470998938e-02, 1.714199295539484e-02, 2.735013970005427e-02, 3.794840483226463e-02, 5.858519896601026e-02, 8.166914231915734e-02, 1.215508018998907e-01, 1.658946642767184e-01, 2.324389477118542e-01, 2.938956625118840e-01, 3.572525844816433e-01, 3.479235360502319e-01, 2.294314115090992e-01, -1.250412450354792e-01, -6.340986743027450e-01, -9.703404081656508e-01, -2.734109755210948e-01, 1.321852608494946e+00, 6.762199721133603e-01, -2.093257651144232e+00, 1.707842350925794e+00, -8.844618831465598e-01, 3.720792781726873e-01, -1.481509947473694e-01, 6.124339615448667e-02, -2.726194382687923e-02, 1.307668436907975e-02, -6.682101544475918e-03, 3.599101395415812e-03, -2.030735143712865e-03, 1.197624324158372e-03, -7.382202519234128e-04, 4.756906961407787e-04, -3.199977708080284e-04, 2.238628518300115e-04, -1.618377502708346e-04, 1.199233854156409e-04, -9.025345928219504e-05, 6.830860296946832e-05, -5.143409372298764e-05, 3.804574823200909e-05, -2.720604959632104e-05, 1.839913059679674e-05, -1.140157702141663e-05, 6.172802138985788e-06, -2.706562852604888e-06, 8.403636781016683e-07, -1.356300450956746e-07]) return dlf
[docs]def key_241_CosSin_2009(): r"""Key 241 pt CosSin filter, as published in [Key09]_. Taken from file ``FilterModules.f90`` provided with 1DCSEM_. License: `Apache License, Version 2.0, <http://www.apache.org/licenses/LICENSE-2.0>`_. """ dlf = DigitalFilter('Key 241 CosSin (2009)', 'key_241_CosSin_2009') dlf.base = np.array([ 1.015631471002490e-06, 1.139409969679808e-06, 1.278273779488425e-06, 1.434061399152754e-06, 1.608835391556724e-06, 1.804909691213134e-06, 2.024880239788185e-06, 2.271659355282662e-06, 2.548514289903414e-06, 2.859110487115151e-06, 3.207560110577854e-06, 3.598476487472605e-06, 4.037035187022686e-06, 4.529042542864016e-06, 5.081012526472398e-06, 5.700252989419669e-06, 6.394962416269964e-06, 7.174338469084136e-06, 8.048699760616019e-06, 9.029622468426732e-06, 1.013009359863071e-05, 1.136468292842132e-05, 1.274973590382314e-05, 1.430359004655643e-05, 1.604681773515003e-05, 1.800249857462311e-05, 2.019652496079635e-05, 2.265794488477607e-05, 2.541934651619925e-05, 2.851728965696073e-05, 3.199278977768923e-05, 3.589186104541253e-05, 4.026612553187130e-05, 4.517349666814366e-05, 5.067894599423484e-05, 5.685536335507487e-05, 6.378452193155948e-05, 7.155816088324133e-05, 8.027919993640778e-05, 9.006310199818260e-05, 1.010394018370932e-04, 1.133534210691922e-04, 1.271681921554341e-04, 1.426666168832257e-04, 1.600538879095432e-04, 1.795602054258330e-04, 2.014438249122027e-04, 2.259944763318926e-04, 2.535372000347300e-04, 2.844366501553267e-04, 3.191019224812033e-04, 3.579919707098018e-04, 4.016216828033581e-04, 4.505686978900301e-04, 5.054810539641999e-04, 5.670857676383036e-04, 6.361984595385052e-04, 7.137341527804347e-04, 8.007193874922814e-04, 8.983058117764621e-04, 1.007785429048510e-03, 1.130607703621563e-03, 1.268398751007239e-03, 1.422982867004443e-03, 1.596406680612247e-03, 1.790966250541270e-03, 2.009237464070060e-03, 2.254110140714601e-03, 2.528826292229256e-03, 2.837023045485535e-03, 3.182780796509667e-03, 3.570677233218250e-03, 4.005847942090417e-03, 4.494054401183452e-03, 5.041760259690979e-03, 5.656216913953108e-03, 6.345559512909110e-03, 7.118914664064660e-03, 7.986521265955502e-03, 8.959866066878890e-03, 1.005183574463358e-02, 1.127688752074056e-02, 1.265124056800531e-02, 1.419309074557768e-02, 1.592285150451168e-02, 1.786342415331403e-02, 2.004050106168401e-02, 2.248290581673552e-02, 2.522297483522721e-02, 2.829698548418685e-02, 3.174563637806794e-02, 3.561458621137186e-02, 3.995505826065390e-02, 4.482451855926687e-02, 5.028743672359186e-02, 5.641613950377735e-02, 6.329176835964070e-02, 7.100535373963698e-02, 7.965902028589801e-02, 8.936733892175319e-02, 1.002588437228037e-01, 1.124777336542896e-01, 1.261857817050387e-01, 1.415644766941340e-01, 1.588174261069207e-01, 1.781730517728984e-01, 1.998876140751445e-01, 2.242486047305353e-01, 2.515785530597565e-01, 2.822392961405233e-01, 3.166367693790532e-01, 3.552263809249515e-01, 3.985190410845142e-01, 4.470879265593564e-01, 5.015760690660555e-01, 5.627048688069557e-01, 6.312836455069260e-01, 7.082203534678000e-01, 7.945336025033340e-01, 8.913661439068313e-01, 1e0, 1.121873437571938e+00, 1.258600009929478e+00, 1.411989919667659e+00, 1.584073984994482e+00, 1.777130526914038e+00, 1.993715533243082e+00, 2.236696498819987e+00, 2.509290389936297e+00, 2.815106235624064e+00, 3.158192909689768e+00, 3.543092736108982e+00, 3.974901627494749e+00, 4.459336552847826e+00, 5.002811227833588e+00, 5.612521029693157e+00, 6.296538261026657e+00, 7.063919023701211e+00, 7.924823117849490e+00, 8.890648553371371e+00, 9.974182454814724e+00, 1.118977035755271e+01, 1.255350613666823e+01, 1.408344508312441e+01, 1.579984294826040e+01, 1.772542412146164e+01, 1.988568249156473e+01, 2.230921897527583e+01, 2.502812018133782e+01, 2.807838322380105e+01, 3.150039230874794e+01, 3.533945340427969e+01, 3.964639407257260e+01, 4.447823640552875e+01, 4.989895197340787e+01, 5.598030878164415e+01, 6.280282144920171e+01, 7.045681718843254e+01, 7.904363169956446e+01, 8.867695081296063e+01, 9.948431564193386e+01, 1.116088111737080e+02, 1.252109606547652e+02, 1.404708508514462e+02, 1.575905163233670e+02, 1.767966142764323e+02, 1.983434254093812e+02, 2.225162204838159e+02, 2.496350371896939e+02, 2.800589173104007e+02, 3.141906602856942e+02, 3.524821561077089e+02, 3.954403681553241e+02, 4.436340451771264e+02, 4.977012512868071e+02, 5.583578136649854e+02, 6.264067998114892e+02, 7.027491498229525e+02, 7.883956044626324e+02, 8.844800869450999e+02, 9.922747156050262e+02, 1.113206646211529e+03, 1.248876966913255e+03, 1.401081895975390e+03, 1.571836562957720e+03, 1.763401688186638e+03, 1.978313513746104e+03, 2.219417382261360e+03, 2.489905408044465e+03, 2.793358739351805e+03, 3.133794971288225e+03, 3.515721337084776e+03, 3.944194381980310e+03, 4.424886909764171e+03, 4.964163088324202e+03, 5.569162708566004e+03, 6.247895712256392e+03, 7.009348240300053e+03, 7.863601605484239e+03, 8.821965764840819e+03, 9.897129058743927e+03, 1.110332619922617e+04, 1.245652673160841e+04, 1.397464646459628e+04, 1.567778466808916e+04, 1.758849017910182e+04, 1.973205993892924e+04, 2.213687391406209e+04, 2.483477083506541e+04, 2.786146972804616e+04, 3.125704281960959e+04, 3.506644607636869e+04, 3.934011440312676e+04, 4.413462937990915e+04, 4.951346837840215e+04, 5.554784497578751e+04, 6.231765179269986e+04, 6.991251823808729e+04, 7.843299716507383e+04, 8.799189614865134e+04, 9.871577101076049e+04, 1.107466013664062e+05, 1.242436703743393e+05, 1.393856735794148e+05, 1.563730847668183e+05, 1.754308101510785e+05, 1.968111660402206e+05, 2.207972193980835e+05, 2.477065355324534e+05, 2.778953825268291e+05, 3.117634480807426e+05, 3.497591312076233e+05, 3.923854788500711e+05, 4.402068460108404e+05, 4.938563675768826e+05, 5.540443407602682e+05, 6.215676291359995e+05, 6.973202127822436e+05, 7.823050242024113e+05, 8.776472267317577e+05, 9.846091112290357e+05]) dlf.factor = np.array([1.1218734375719379]) dlf.cos = np.array([ 2.573985433748149e-03, -2.072044432524625e-02, 8.438091711547871e-02, -2.334480374945598e-01, 4.971637805522022e-01, -8.750461405249571e-01, 1.333415700757027e+00, -1.817857278999438e+00, 2.271742525614601e+00, -2.650839359834871e+00, 2.929816176240629e+00, -3.101605349462614e+00, 3.172849598553826e+00, -3.158333463387740e+00, 3.076219518145157e+00, -2.944689843059625e+00, 2.780024568942243e+00, -2.595719779969896e+00, 2.402350605158043e+00, -2.207779522612721e+00, 2.017594105093030e+00, -1.835527970829352e+00, 1.663920259620933e+00, -1.504039483923565e+00, 1.356423126734103e+00, -1.221057462742312e+00, 1.097607689766934e+00, -9.854831639668219e-01, 8.840006973665168e-01, -7.923704689421897e-01, 7.098300227775011e-01, -6.355744132962947e-01, 5.688875813158415e-01, -5.090282851725471e-01, 4.553774950936741e-01, -4.072828190689483e-01, 3.642362670434036e-01, -3.256737103445609e-01, 2.911959791480738e-01, -2.603152640455789e-01, 2.327331570309761e-01, -2.080218702094741e-01, 1.859749696667782e-01, -1.662071785063838e-01, 1.485969487672789e-01, -1.327839524784528e-01, 1.187272713875194e-01, -1.060740651133825e-01, 9.486317265574648e-02, -8.473151012328659e-02, 7.580053967300120e-02, -6.767828163371538e-02, 6.057579031791280e-02, -5.405178236455697e-02, 4.841846349893079e-02, -4.316208761750292e-02, 3.871284451741208e-02, -3.445743869419572e-02, 3.096708549327929e-02, -2.749651494490814e-02, 2.478846014781735e-02, -2.192620197391235e-02, 1.986356477133265e-02, -1.746376930197379e-02, 1.594249816296365e-02, -1.388258927979823e-02, 1.282624672523178e-02, -1.100069006189238e-02, 1.035664209512100e-02, -8.671560169935045e-03, 8.408376795833618e-03, -6.776738899031039e-03, 6.882686516736744e-03, -5.219834049623621e-03, 5.702385679308191e-03, -3.921653713596426e-03, 4.807988471764018e-03, -2.816192636608797e-03, 4.154713117406505e-03, -1.847264200719943e-03, 3.710210316571563e-03, -9.655983418104668e-04, 3.452896295365636e-03, -1.262640384889067e-04, 3.370827726760556e-03, 7.136760975744594e-04, 3.461099737561205e-03, 1.597372595722807e-03, 3.729726810304828e-03, 2.570391470398246e-03, 4.191950937402854e-03, 3.683048200124032e-03, 4.872941625227778e-03, 4.992964784095300e-03, 5.808908133499602e-03, 6.567853057094176e-03, 7.048649360560634e-03, 8.488493292803347e-03, 8.655425482515024e-03, 1.085182308666227e-02, 1.070880791806313e-02, 1.377379498928377e-02, 1.330579956040371e-02, 1.739106597624804e-02, 1.655975905406871e-02, 2.185942056374162e-02, 2.059407781725530e-02, 2.734455978483885e-02, 2.552438621384559e-02, 3.399650586625764e-02, 3.141687500736497e-02, 4.189054475997781e-02, 3.819877849864893e-02, 5.090221700189159e-02, 4.547666713650442e-02, 6.045737507914792e-02, 5.218516934955635e-02, 6.905902304597721e-02, 5.594605521455825e-02, 7.345454126722073e-02, 5.200083839448903e-02, 6.734587378298894e-02, 3.173662493273055e-02, 3.992917476294457e-02, -1.838550375569295e-02, -2.397773636392629e-02, -1.141550868458520e-01, -1.364180631421666e-01, -2.579978464039199e-01, -2.783350244258052e-01, -3.949234086091623e-01, -3.393321236784040e-01, -3.475708749988657e-01, -8.309968487457564e-02, 1.136203792647491e-01, 5.634934316303769e-01, 6.583850354915292e-01, 6.518868979555039e-01, -1.501485600802549e-01, -7.813033407168875e-01, -1.093007847302057e+00, 3.833853368779607e-01, 1.282013367267770e+00, 2.845449032623110e-01, -2.058783831648639e+00, 1.209750949676112e+00, 7.040614890578353e-01, -1.742049993519849e+00, 1.741132290073874e+00, -1.318424767807200e+00, 9.007174373555373e-01, -6.085273047132523e-01, 4.259667647291260e-01, -3.134807813694764e-01, 2.417216785355954e-01, -1.934461726074489e-01, 1.591659829008638e-01, -1.336457289506658e-01, 1.138988598115308e-01, -9.814397025931439e-02, 8.526827650704955e-02, -7.454576060490363e-02, 6.548369826637619e-02, -5.773569245976477e-02, 5.105043114013155e-02, -4.524038427505326e-02, 4.016204946284081e-02, -3.570311893510748e-02, 3.177392452843057e-02, -2.830160023880827e-02, 2.522601353974157e-02, -2.249687303433539e-02, 2.007163372774035e-02, -1.791395268505854e-02, 1.599253061462437e-02, -1.428022817956371e-02, 1.275338071888894e-02, -1.139125817575050e-02, 1.017563265146541e-02, -9.090426866557829e-03, 8.121424445062036e-03, -7.256028270711461e-03, 6.483056882115604e-03, -5.792571404381900e-03, 5.175727196581864e-03, -4.624645684779383e-03, 4.132303011690729e-03, -3.692432980935121e-03, 3.299442142508096e-03, -2.948335089474538e-03, 2.634648489517598e-03, -2.354392904061866e-03, 2.104001678817889e-03, -1.880286100963581e-03, 1.680395912528533e-03, -1.501784333722836e-03, 1.342176883640446e-03, -1.199543365542324e-03, 1.072072487299258e-03, -9.581487548508404e-04, 8.563313760453976e-04, -7.653349620480948e-04, 6.840119836821465e-04, -6.113371472348392e-04, 5.463938378836874e-04, -4.883625033668457e-04, 4.365105296790329e-04, -3.901830736548332e-04, 3.487945803629603e-04, -3.118210765665508e-04, 2.787934276328260e-04, -2.492915523784893e-04, 2.229394184733318e-04, -1.994006680996778e-04, 1.783747993871292e-04, -1.595938065118272e-04, 1.428191356382435e-04, -1.278388291932361e-04, 1.144647631077232e-04, -1.025299256786045e-04, 9.188578754406515e-05, -8.239993677764002e-05, 7.395418447973129e-05, -6.644317144520790e-05, 5.977325048819278e-05, -5.386141578322173e-05, 4.863431532204160e-05, -4.402750207962412e-05, 3.998490104646043e-05, -3.645833654257180e-05, 3.340701147193886e-05, -3.079679563171623e-05, 2.859897380035983e-05, -2.678774555509045e-05, 2.533483928373590e-05, -2.419702895729874e-05, 2.328604080003924e-05, -2.239597546920266e-05, 2.103439404619766e-05, -1.807670762071730e-05, 1.140396792815156e-05]) dlf.sin = np.array([ 1.967005545865218e-10, -1.433611192275181e-09, 5.386453134154996e-09, -1.393836398944422e-08, 2.810158973085062e-08, -4.733984167038972e-08, 6.976700567760687e-08, -9.291356831468874e-08, 1.145563482421100e-07, -1.331950589956367e-07, 1.481901450989667e-07, -1.595961894804095e-07, 1.679579344961122e-07, -1.740358177568700e-07, 1.786885513317428e-07, -1.826971268722640e-07, 1.868003120723728e-07, -1.915696157142666e-07, 1.975548111660444e-07, -2.051269356766739e-07, 2.147190183078524e-07, -2.265704864101776e-07, 2.410938637923347e-07, -2.584531304193038e-07, 2.791285853082430e-07, -3.032349303994803e-07, 3.314044275843927e-07, -3.636972724516131e-07, 4.009929886338131e-07, -4.432582392200706e-07, 4.917458331080907e-07, -5.462464678254600e-07, 6.085682267245114e-07, -6.781794860836133e-07, 7.577171014688372e-07, -8.460807541480724e-07, 9.471544157135390e-07, -1.058863057051342e-06, 1.186983447614987e-06, -1.327804017767932e-06, 1.489996440779015e-06, -1.667141139261620e-06, 1.872366272041974e-06, -2.094818002855587e-06, 2.354522121047758e-06, -2.633419506735300e-06, 2.962259516643178e-06, -3.311342165909682e-06, 3.728149200842658e-06, -4.164255374239495e-06, 4.693327995051689e-06, -5.236921095650869e-06, 5.909779848521176e-06, -6.585452434703418e-06, 7.443248817367435e-06, -8.280105308480091e-06, 9.376971248809820e-06, -1.040871066885904e-05, 1.181647694012281e-05, -1.308086489086373e-05, 1.489579590400169e-05, -1.643299839198172e-05, 1.878552965850708e-05, -2.063442929000397e-05, 2.370342044306427e-05, -2.589446630933835e-05, 2.992830392336809e-05, -3.247053052820925e-05, 3.781869997976733e-05, -4.067708157172121e-05, 4.783784240317701e-05, -5.089479936195305e-05, 6.058776523010633e-05, -6.357888851585346e-05, 7.685629664242167e-05, -7.926437938452345e-05, 9.768268830663251e-05, -9.856464123672343e-05, 1.244504845842736e-04, -1.221565888036176e-04, 1.590206705039449e-04, -1.507415982780862e-04, 2.039250063083074e-04, -1.849639094970543e-04, 2.626501374752980e-04, -2.252566203418921e-04, 3.400597277405926e-04, -2.715666525558665e-04, 4.430278995600817e-04, -3.228801423595561e-04, 5.813980073616601e-04, -3.764220699966869e-04, 7.694445136249034e-04, -4.263284243168565e-04, 1.028115335781203e-03, -4.614701220354354e-04, 1.388487108626009e-03, -4.619214991216924e-04, 1.897105649343108e-03, -3.932775423791962e-04, 2.624250467245377e-03, -1.975847083236173e-04, 3.676710851321636e-03, 2.209992359645100e-04, 5.217452274062335e-03, 1.018611500160813e-03, 7.495613223401942e-03, 2.446097853450125e-03, 1.089148041817982e-02, 4.900453419060485e-03, 1.598184015155261e-02, 8.998208308647400e-03, 2.362945832701593e-02, 1.567112707431810e-02, 3.509105555447196e-02, 2.626701074033223e-02, 5.210752870163974e-02, 4.258698097657578e-02, 7.685703204761107e-02, 6.665955544060372e-02, 1.114513473857200e-01, 9.975515861206709e-02, 1.562348056183209e-01, 1.395790799893133e-01, 2.054534357433025e-01, 1.738733232648114e-01, 2.384564666870356e-01, 1.692656404318401e-01, 2.076285145563062e-01, 6.214100432471348e-02, 4.085773864115237e-02, -2.120030217966462e-01, -2.788970968243500e-01, -5.635171222319378e-01, -4.755507221458447e-01, -4.867419491287002e-01, 1.066910067501506e-01, 4.614580501271743e-01, 1.034845302098941e+00, 3.764103855021101e-01, -4.329269419291238e-01, -1.455324167706572e+00, 2.071144418028701e-01, 1.349913786271064e+00, 1.542337659378029e-01, -2.228987932739951e+00, 2.446506150864118e+00, -1.378605681876207e+00, 3.206812625344759e-01, 2.465832348751217e-01, -4.315945927966289e-01, 4.376711630002494e-01, -3.868161577159704e-01, 3.284216175602037e-01, -2.770656717800635e-01, 2.349261553052497e-01, -2.007957619551110e-01, 1.729798893952139e-01, -1.500347821377614e-01, 1.308631829780874e-01, -1.146558086495966e-01, 1.008159744956652e-01, -8.889859962303459e-02, 7.856617356272111e-02, -6.955808615176720e-02, 6.166942945994992e-02, -5.473628487439387e-02, 4.862541225971129e-02, -4.322693473384397e-02, 3.844907736778588e-02, -3.421432802261911e-02, 3.045659361641401e-02, -2.711906111916627e-02, 2.415256336052804e-02, -2.151431084609744e-02, 1.916689229057781e-02, -1.707747503528641e-02, 1.521715619160838e-02, -1.356042905316614e-02, 1.208473893327246e-02, -1.077010938739636e-02, 9.598824634127222e-03, -8.555157475234823e-03, 7.625134538354346e-03, -6.796332507333996e-03, 6.057700364251606e-03, -5.399403681543913e-03, 4.812687767094041e-03, -4.289757047100644e-03, 3.823668521675937e-03, -3.408237481656769e-03, 3.037953955085763e-03, -2.707908575613410e-03, 2.413726747641181e-03, -2.151510135086631e-03, 1.917784628102023e-03, -1.709454048915126e-03, 1.523758948382411e-03, -1.358239922491303e-03, 1.210704945231195e-03, -1.079200272616089e-03, 9.619845235461060e-04, -8.575055877727934e-04, 7.643800504594847e-04, -6.813748575629618e-04, 6.073909770892527e-04, -5.414488385598928e-04, 4.826753570758706e-04, -4.302923695079621e-04, 3.836063290315453e-04, -3.419991209582663e-04, 3.049198778902062e-04, -2.718776857047081e-04, 2.424350838300435e-04, -2.162022738421805e-04, 1.928319597904253e-04, -1.720147520298727e-04, 1.534750738420537e-04, -1.369675168837808e-04, 1.222735976157924e-04, -1.091988723621016e-04, 9.757037355552881e-05, -8.723433410673846e-05, 7.805417075146385e-05, -6.990870062381882e-05, 6.269056792845232e-05, -5.630485890243343e-05, 5.066788212408145e-05, -4.570608516423470e-05, 4.135506222734868e-05, -3.755856918827694e-05, 3.426737683044253e-05, -3.143760307989191e-05, 2.902774010545716e-05, -2.699262909691761e-05, 2.527042803006811e-05, -2.375357212497184e-05, 2.222370982737331e-05, -2.021079897690936e-05, 1.673161082870818e-05, -1.011062914652405e-05]) return dlf
[docs]def key_601_CosSin_2009(): r"""Key 601 pt CosSin filter, as published in [Key09]_. Taken from file ``FilterModules.f90`` provided with 1DCSEM_. License: `Apache License, Version 2.0, <http://www.apache.org/licenses/LICENSE-2.0>`_. """ dlf = DigitalFilter('Key 601 CosSin (2009)', 'key_601_CosSin_2009') dlf.base = np.array([ 4.193795658379545e-13, 4.611744532326466e-13, 5.071345712552199e-13, 5.576750220213815e-13, 6.132522762484560e-13, 6.743682960028553e-13, 7.415750683158400e-13, 8.154795906142572e-13, 8.967493529935761e-13, 9.861183668479918e-13, 1.084393794306884e-12, 1.192463238353357e-12, 1.311302759467621e-12, 1.441985691199862e-12, 1.585692334293061e-12, 1.743720616910949e-12, 1.917497817252074e-12, 2.108593454426215e-12, 2.318733464020732e-12, 2.549815786387618e-12, 2.803927508441469e-12, 3.083363713789339e-12, 3.390648211442950e-12, 3.728556330330719e-12, 4.100139985484672e-12, 4.508755242294825e-12, 4.958092627785737e-12, 5.452210462680048e-12, 5.995571515297294e-12, 6.593083308338489e-12, 7.250142442598540e-12, 7.972683337929069e-12, 8.767231831670027e-12, 9.640964118639377e-12, 1.060177156501484e-11, 1.165833198149268e-11, 1.282018799944826e-11, 1.409783325797471e-11, 1.550280718022315e-11, 1.704779919504490e-11, 1.874676334524281e-11, 2.061504431754968e-11, 2.266951603261053e-11, 2.492873404668339e-11, 2.741310314151893e-11, 3.014506161605645e-11, 3.314928394441855e-11, 3.645290363056936e-11, 4.008575827241402e-11, 4.408065904870462e-11, 4.847368706270256e-11, 5.330451921911242e-11, 5.861678657753666e-11, 6.445846841902501e-11, 7.088232558484702e-11, 7.794637700130874e-11, 8.571442369448666e-11, 9.425662502767281e-11, 1.036501323659809e-10, 1.139797858912439e-10, 1.253388808606835e-10, 1.378300102300461e-10, 1.515659912515919e-10, 1.666708844157782e-10, 1.832811139395095e-10, 2.015466999209584e-10, 2.216326132895250e-10, 2.437202657885651e-10, 2.680091484480837e-10, 2.947186333457411e-10, 3.240899549293070e-10, 3.563883887954330e-10, 3.919056476030219e-10, 4.309625157605925e-10, 4.739117466835593e-10, 5.211412487888540e-10, 5.730775890021381e-10, 6.301898454205201e-10, 6.929938439272241e-10, 7.620568170224476e-10, 8.380025269479489e-10, 9.215168993763617e-10, 1.013354218547565e-09, 1.114343939805221e-09, 1.225398181062923e-09, 1.347519960861261e-09, 1.481812257420264e-09, 1.629487970506598e-09, 1.791880876089040e-09, 1.970457672722430e-09, 2.166831228460398e-09, 2.382775147940245e-09, 2.620239791206898e-09, 2.881369888954443e-09, 3.168523913282466e-09, 3.484295378919872e-09, 3.831536267304207e-09, 4.213382785077881e-09, 4.633283689646769e-09, 5.095031437631424e-09, 5.602796437537268e-09, 6.161164716006833e-09, 6.775179337847431e-09, 7.450385953931326e-09, 8.192882888347710e-09, 9.009376217182704e-09, 9.907240336387463e-09, 1.089458456577097e-08, 1.198032639067020e-08, 1.317427200280147e-08, 1.448720486772051e-08, 1.593098311881483e-08, 1.751864665746923e-08, 1.926453492671132e-08, 2.118441642204417e-08, 2.329563110917976e-08, 2.561724703496062e-08, 2.817023254594732e-08, 3.097764567011258e-08, 3.406484237209804e-08, 3.745970556295245e-08, 4.119289693271730e-08, 4.529813388035942e-08, 4.981249404222491e-08, 5.477675016944901e-08, 6.023573837886479e-08, 6.623876310337785e-08, 7.284004239922980e-08, 8.009919763207375e-08, 8.808179196460557e-08, 9.685992250925397e-08, 1.065128714941292e-07, 1.171278223234277e-07, 1.288006469995941e-07, 1.416367720190751e-07, 1.557521305622528e-07, 1.712742095775383e-07, 1.883432012166641e-07, 2.071132690207019e-07, 2.277539402927298e-07, 2.504516372327622e-07, 2.754113606638370e-07, 3.028585415563174e-07, 3.330410770729809e-07, 3.662315695240386e-07, 4.027297884538403e-07, 4.428653780963272e-07, 4.870008346523962e-07, 5.355347802793109e-07, 5.889055633621554e-07, 6.475952175842209e-07, 7.121338155538044e-07, 7.831042563084790e-07, 8.611475299365608e-07, 9.469685068647088e-07, 1.041342304099322e-06, 1.145121285920239e-06, 1.259242762255579e-06, 1.384737454267802e-06, 1.522738803610367e-06, 1.674493209434266e-06, 1.841371285602920e-06, 2.024880239788189e-06, 2.226677486252946e-06, 2.448585615267984e-06, 2.692608854363838e-06, 2.960951170092142e-06, 3.256036173787822e-06, 3.580529011116689e-06, 3.937360433110378e-06, 4.329753266092978e-06, 4.761251519570304e-06, 5.235752394978102e-06, 5.757541484385375e-06, 6.331331477060257e-06, 6.962304723487946e-06, 7.656160041269817e-06, 8.419164185644976e-06, 9.258208449505048e-06, 1.018087090410152e-05, 1.119548484259094e-05, 1.231121404458520e-05, 1.353813554148094e-05, 1.488733063008695e-05, 1.637098495656519e-05, 1.800249857462311e-05, 1.979660697197936e-05, 2.176951415818827e-05, 2.393903901584477e-05, 2.632477623698299e-05, 2.894827329821157e-05, 3.183322507298884e-05, 3.500568783873448e-05, 3.849431461164446e-05, 4.233061393470499e-05, 4.654923445622278e-05, 5.118827786912642e-05, 5.628964303744043e-05, 6.189940441800879e-05, 6.806822819529511e-05, 7.485182988770060e-05, 8.231147755840270e-05, 9.051454517561093e-05, 9.953512112007229e-05, 1.094546773357366e-04, 1.203628051672132e-04, 1.323580245299439e-04, 1.455486737213506e-04, 1.600538879095432e-04, 1.760046751370900e-04, 1.935450995580938e-04, 2.128335825953212e-04, 2.340443337691579e-04, 2.573689241213434e-04, 2.830180164443136e-04, 3.112232679432146e-04, 3.422394225150394e-04, 3.763466115419071e-04, 4.138528839787616e-04, 4.550969885867208e-04, 5.004514334406108e-04, 5.503258503435191e-04, 6.051706945350531e-04, 6.654813131082850e-04, 7.318024188804728e-04, 8.047330101246132e-04, 8.849317805958146e-04, 9.731230687146970e-04, 1.070103399639604e-03, 1.176748679314238e-03, 1.294022105465848e-03, 1.422982867004445e-03, 1.564795710394167e-03, 1.720741459398286e-03, 1.892228583209938e-03, 2.080805917449529e-03, 2.288176652922169e-03, 2.516213718478670e-03, 2.766976696914850e-03, 3.042730426689990e-03, 3.345965457471272e-03, 3.679420544254346e-03, 4.046107383222199e-03, 4.449337812751394e-03, 4.892753725239476e-03, 5.380359959910820e-03, 5.916560473681857e-03, 6.506198116773342e-03, 7.154598372314579e-03, 7.867617454986535e-03, 8.651695203120634e-03, 9.513913241963630e-03, 1.046205894342679e-02, 1.150469575999052e-02, 1.265124056800531e-02, 1.391204871893762e-02, 1.529850756672552e-02, 1.682313931596340e-02, 1.849971411981924e-02, 2.034337444916063e-02, 2.237077185616560e-02, 2.460021736763830e-02, 2.705184686635041e-02, 2.974780295409754e-02, 3.271243493901982e-02, 3.597251875342965e-02, 3.955749878839872e-02, 4.349975382930274e-02, 4.783488949419837e-02, 5.260205981627383e-02, 5.784432087483846e-02, 6.360901966877180e-02, 6.994822174465536e-02, 7.691918144183450e-02, 8.458485900156469e-02, 9.301448921066349e-02, 1.022842067155374e-01, 1.124777336542896e-01, 1.236871358174548e-01, 1.360136541668492e-01, 1.495686192226351e-01, 1.644744565771549e-01, 1.808657926171221e-01, 1.988906704408197e-01, 2.187118869522148e-01, 2.405084632083421e-01, 2.644772612998240e-01, 2.908347623678516e-01, 3.198190218163038e-01, 3.516918193780669e-01, 3.867410234545012e-01, 4.252831910822741e-01, 4.676664270099092e-01, 5.142735277066319e-01, 5.655254386995371e-01, 6.218850564650201e-01, 6.838614092123558e-01, 7.520142543193826e-01, 8.269591339433623e-01, 9.093729344682314e-01, 1.000000000000000e+00, 1.099658855126103e+00, 1.209249597657251e+00, 1.329762028121474e+00, 1.462284589434224e+00, 1.608014197485783e+00, 1.768267051433735e+00, 1.944490521336831e+00, 2.138276220496818e+00, 2.351374380574902e+00, 2.585709659315846e+00, 2.843398523651769e+00, 3.126768365186156e+00, 3.438378520705125e+00, 3.781043387568781e+00, 4.157857842756007e+00, 4.572225195142160e+00, 5.027887923468749e+00, 5.528961477624004e+00, 6.079971448520338e+00, 6.685894442279269e+00, 7.352203027890797e+00, 8.084915164305059e+00, 8.890648553371371e+00, 9.776680409528907e+00, 1.075101318607635e+01, 1.182244685164636e+01, 1.300065836967064e+01, 1.429628909867760e+01, 1.572104090280360e+01, 1.728778184056764e+01, 1.901066238646844e+01, 2.090524323509275e+01, 2.298863584203481e+01, 2.527965697096289e+01, 2.779899864266967e+01, 3.056941502105021e+01, 3.361592792392278e+01, 3.696605281482250e+01, 4.065004731687878e+01, 4.470118449330081e+01, 4.915605336268389e+01, 5.405488936332660e+01, 5.944193775124387e+01, 6.536585321400990e+01, 7.188013930965907e+01, 7.904363169956446e+01, 8.692102953975237e+01, 9.558347983006632e+01, 1.051092199988997e+02, 1.155842845271877e+02, 1.271032819937369e+02, 1.397702495600030e+02, 1.536995926118425e+02, 1.690171180448872e+02, 1.858611705259540e+02, 2.043838819929681e+02, 2.247525456786157e+02, 2.471511270676237e+02, 2.717819254343092e+02, 2.988674009670603e+02, 3.286521839819514e+02, 3.614052843722859e+02, 3.974225212493519e+02, 4.370291947183915e+02, 4.805830239207090e+02, 5.284773778776877e+02, 5.811448283170228e+02, 6.390610565695528e+02, 7.027491498229519e+02, 7.727843255351499e+02, 8.497991266773804e+02, 9.344891347292100e+02, 1.027619252024106e+03, 1.130030610186371e+03, 1.242648167054996e+03, 1.366489060708247e+03, 1.502671796040775e+03, 1.652426346864483e+03, 1.817105264773206e+03, 1.998195895104117e+03, 2.197333810327873e+03, 2.416317582195026e+03, 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-4.543183855105308e-05, 4.275474607475218e-05, -4.023540320295300e-05, 3.786451389972717e-05, -3.563332957269838e-05, 3.353361691763475e-05, -3.155762774924427e-05, 2.969807062617112e-05, -2.794808410995567e-05, 2.630121151787229e-05, -2.475137704630406e-05, 2.329286318387569e-05, -2.192028939321493e-05, 2.062859207259327e-05, -1.941300578777201e-05, 1.826904570832050e-05, -1.719249113666637e-05, 1.617937001166837e-05, -1.522594429630232e-05, 1.432869619293261e-05, -1.348431514822722e-05, 1.268968561560221e-05, -1.194187554794177e-05, 1.123812559543480e-05, -1.057583897135925e-05, 9.952571928920077e-06, -9.366024786065420e-06, 8.814033449847659e-06, -8.294561412310765e-06, 7.805692202122783e-06, -7.345622279264520e-06, 6.912654355788464e-06, -6.505191118069142e-06, 6.121729323201997e-06, -5.760854248417804e-06, 5.421234478300124e-06, -5.101617009901882e-06, 4.800822646167135e-06, -4.517741648025717e-06, 4.251329628341728e-06, -4.000603683148808e-06, 3.764638756304900e-06, -3.542564226345866e-06, 3.333560698953710e-06, -3.136856988686476e-06, 2.951727276827061e-06, -2.777488435826684e-06, 2.613497513360022e-06, -2.459149368278866e-06, 2.313874447883890e-06, -2.177136694710908e-06, 2.048431572667469e-06, -1.927284204758473e-06, 1.813247616245777e-06, -1.705901079034481e-06, 1.604848553527228e-06, -1.509717223666689e-06, 1.420156119370289e-06, -1.335834820016856e-06, 1.256442234951006e-06, -1.181685456128025e-06, 1.111288676892987e-06, -1.044992172405241e-06, 9.825513393481762e-07, -9.237357933971897e-07, 8.683285212104373e-07, -8.161250831545758e-07, 7.669328630553843e-07, -7.205703605348671e-07, 6.768665218548227e-07, -6.356601082847431e-07, 5.967991030550851e-07, -5.601401552062655e-07, 5.255480561062212e-07, -4.928952460659735e-07, 4.620613501444217e-07, -4.329327405101518e-07, 4.054021239180187e-07, -3.793681579064327e-07, 3.547350993344619e-07, -3.314124829852402e-07, 3.093148271853663e-07, -2.883613713159475e-07, 2.684758528630320e-07, -2.495863260342058e-07, 2.316250244413231e-07, -2.145282802422723e-07, 1.982365164330169e-07, -1.826943245023923e-07, 1.678506431892942e-07, -1.536590646985763e-07, 1.400782953273800e-07, -1.270727884794868e-07, 1.146135666342606e-07, -1.026792513877522e-07, 9.125729806412655e-08, -8.034537960134519e-08, 6.995280306790059e-08, -6.010176816322779e-08, 5.082816448601466e-08, -4.218145138533012e-08, 3.422301806844069e-08, -2.702234929053260e-08, 2.065039505532909e-08, -1.516986572337718e-08, 1.062287966342394e-08, -7.017537133414707e-09, 4.316406487987238e-09, -2.431042249536996e-09, 1.226580375862224e-09, -5.382153970216142e-10, 1.968534210247343e-10, -5.617276256001430e-11, 1.110014404476413e-11, -1.138077570686847e-12]) return dlf
[docs]def key_101_CosSin_2012(): r"""Key 101 pt CosSin filter, as published in [Key12]_. Taken from file ``kk101CosSin.txt`` provided with SEG-2012-003_. License: http://software.seg.org/disclaimer.txt. """ dlf = DigitalFilter('Key 101 CosSin (2012)', 'key_101_CosSin_2012') dlf.base = np.array([ 2.0861919529505731e-04, 2.4715373649416861e-04, 2.9280608324001184e-04, 3.4689098210084990e-04, 4.1096602956932233e-04, 4.8687652944195492e-04, 5.7680863591051896e-04, 6.8335231283852345e-04, 8.0957592239343885e-04, 9.5911459112023485e-04, 1.1362748983197658e-03, 1.3461589016632311e-03, 1.5948110718689737e-03, 1.8893923680282996e-03, 2.2383864667932735e-03, 2.6518440846418348e-03, 3.1416724294819243e-03, 3.7219781175407782e-03, 4.4094734312376538e-03, 5.2239576179017510e-03, 6.1888870903059369e-03, 7.3320509502793245e-03, 8.6863712898718453e-03, 1.0290851318025195e-02, 1.2191698617946518e-02, 1.4443655883987865e-02, 1.7111577462058016e-02, 2.0272297096513812e-02, 2.4016840672963606e-02, 2.8453047681987229e-02, 3.3708676899572396e-02, 3.9935085725073552e-02, 4.7311589138320786e-02, 5.6050623809926717e-02, 6.6403866086528832e-02, 7.8669480043444651e-02, 9.3200704342144572e-02, 1.1041602518632210e-01, 1.3081122834855582e-01, 1.5497367735510315e-01, 1.8359922902771786e-01, 2.1751227353489916e-01, 2.5768947608804055e-01, 3.0528790402199785e-01, 3.6167834929472320e-01, 4.2848480606401651e-01, 5.0763124026013273e-01, 6.0139699807591596e-01, 7.1248244908919167e-01, 8.4408675448036252e-01, 1.0000000000000000e+00, 1.1847123470331211e+00, 1.4035433452127262e+00, 1.6627951306696866e+00, 1.9699339218909298e+00, 2.3338050401035639e+00, 2.7648876465788206e+00, 3.2755965330612771e+00, 3.8806396566165793e+00, 4.5974417155800325e+00, 5.4466459652127988e+00, 6.4527087249057331e+00, 7.6446036982041701e+00, 9.0566563894375367e+00, 1.0729532647403058e+01, 1.2711409805273369e+01, 1.5059364144505244e+01, 1.7841014640463239e+01, 2.1136470328155472e+01, 2.5040637370464992e+01, 2.9665952270368855e+01, 3.5145619941201240e+01, 4.1637449888474563e+01, 4.9328400981848674e+01, 5.8439965702596865e+01, 6.9234548928058643e+01, 8.2023024956339754e+01, 9.7173690406781532e+01, 1.1512287083168806e+02, 1.3638748650020000e+02, 1.6157993923759994e+02, 1.9142574904764615e+02, 2.2678444843681012e+02, 2.6867433617818517e+02, 3.1830180340122359e+02, 3.7709607657233846e+02, 4.4675037793299668e+02, 5.2927068877893441e+02, 6.2703351991912803e+02, 7.4285435305182887e+02, 8.8006872410780306e+02, 1.0426282836881999e+03, 1.2352146010513620e+03, 1.4633739891011396e+03, 1.7336772332152309e+03, 2.0539088239603038e+03, 2.4332911434260495e+03, 2.8827500615431823e+03, 3.4152295913206981e+03, 4.0460646647905082e+03, 4.7934227652717464e+03 ]) dlf.factor = np.array([1.184712347033122]) dlf.cos = np.array([ 2.8672864360507005e-02, -1.5449802884956709e-01, 4.2925040863045694e-01, -8.2496971475989445e-01, 1.2478359182403629e+00, -1.5992674211324920e+00, 1.8243131715043821e+00, -1.9145396327623898e+00, 1.8934809645883464e+00, -1.7937055008120979e+00, 1.6483078327364769e+00, -1.4808155052910057e+00, 1.3101325252212712e+00, -1.1449152844956805e+00, 9.9343552640217170e-01, -8.5553234578004234e-01, 7.3519828220268879e-01, -6.2796652499267325e-01, 5.3738862198175896e-01, -4.5651464813036369e-01, 3.9045436622456964e-01, -3.2999349735142486e-01, 2.8305474305757988e-01, -2.3751637987170185e-01, 2.0529432395051081e-01, -1.7012553670055422e-01, 1.4940669628955736e-01, -1.2091379458447284e-01, 1.0958698756544492e-01, -8.4691552456171854e-02, 8.1619516737927278e-02, -5.7580267250933195e-02, 6.2518018553384166e-02, -3.6651105073235317e-02, 5.0237072673112150e-02, -1.9632218666205858e-02, 4.3459101512968681e-02, -4.6794536371076211e-03, 4.1441426761739050e-02, 9.7939747479241900e-03, 4.3892151379272520e-02, 2.5210891626024919e-02, 5.0808828645867020e-02, 4.2766233781071271e-02, 6.2117512490275244e-02, 6.2962730570568531e-02, 7.6696518689002652e-02, 8.4104539899597833e-02, 8.9777495214153097e-02, 9.8272696765763598e-02, 8.6678232290502866e-02, 8.2343990171152917e-02, 3.0869547033063837e-02, -1.4909949071839479e-02, -1.4329751745033240e-01, -2.5692197105974507e-01, -4.5564109546179643e-01, -5.2642966384443990e-01, -5.1460104261798389e-01, -5.5502691731699465e-02, 5.7834482024380740e-01, 1.1256064228777944e+00, 2.1383340001419898e-01, -1.3697558643383851e+00, -5.4094053515695928e-01, 2.1676624940285554e+00, -1.9426841601818654e+00, 1.0545870497149261e+00, -4.1963490722345465e-01, 1.2372791785903402e-01, -1.2484679132220721e-02, -2.3788674938364895e-02, 3.3114878230396952e-02, -3.3222597126475469e-02, 3.0358352472771119e-02, -2.6736813112701912e-02, 2.3150637102106384e-02, -1.9871405137636362e-02, 1.6972847239886572e-02, -1.4452497064151562e-02, 1.2279321682638183e-02, -1.0413813415050226e-02, 8.8158262043057916e-03, -7.4478769417757051e-03, 6.2764357354946447e-03, -5.2719066748527534e-03, 4.4086512878557960e-03, -3.6646129972605474e-03, 3.0209640546643227e-03, -2.4620010538490039e-03, 1.9748775511266975e-03, -1.5496766879546100e-03, 1.1795298139010500e-03, -8.6058717820595076e-04, 5.9202977915967969e-04, -3.7525986704164700e-04, 2.1195595608903056e-04, -1.0150060510905382e-04, 3.8158120462333111e-05, -9.8633310205821847e-06, 1.2936403297967877e-06 ]) dlf.sin = np.array([ 7.6040317586736167e-07, -3.5855391966011851e-06, 9.0786150697210513e-06, -1.5826177772027392e-05, 2.1667095104224339e-05, -2.4639596374368108e-05, 2.4408848809863509e-05, -2.0820021816183944e-05, 1.5067089085308662e-05, -7.0050769548280383e-06, -1.7958501740914329e-06, 1.2603332855969368e-05, -2.3184647095957185e-05, 3.6649243234792389e-05, -4.8925370942928653e-05, 6.6303764053919788e-05, -8.0743294791572212e-05, 1.0450895388320221e-04, -1.2159285962006951e-04, 1.5584791507883690e-04, -1.7545124243120011e-04, 2.2700988130497338e-04, -2.4734388406632239e-04, 3.2783247999524046e-04, -3.4332865428126714e-04, 4.7317261331939348e-04, -4.7006909503024977e-04, 6.8617937973613086e-04, -6.3341402749449334e-04, 1.0040019055114892e-03, -8.3487943140247750e-04, 1.4879378075097959e-03, -1.0636379989149227e-03, 2.2420753799874209e-03, -1.2790129815477512e-03, 3.4482247571698465e-03, -1.3737791982222189e-03, 5.4315927603032941e-03, -1.0998797914873670e-03, 8.7841427944231800e-03, 7.8319393204598608e-05, 1.4595208448653587e-02, 3.2659459359974446e-03, 2.4872512535509962e-02, 1.0650179022920168e-02, 4.3259641676705020e-02, 2.6322316164253033e-02, 7.6048270347343724e-02, 5.7170057234916666e-02, 1.3274290157636107e-01, 1.1202091605266952e-01, 2.2233535747440117e-01, 1.9149401437051311e-01, 3.3181854408276518e-01, 2.4683273185271720e-01, 3.5830743824321187e-01, 8.6048124656303501e-02, 2.9088009098110983e-02, -5.6704064209706251e-01, -6.2443346412861278e-01, -8.6749964898300636e-01, 4.0884911445599137e-01, 9.8650186504403581e-01, 9.1320791936604540e-01, -2.2349960681179670e+00, 9.8286263574585253e-01, 5.5290844435608977e-01, -1.0935816133485650e+00, 9.9396634297931441e-01, -7.5077030548862878e-01, 5.4988381646049755e-01, -4.1131875464082862e-01, 3.1720514147975598e-01, -2.5105433218659301e-01, 2.0252402542560796e-01, -1.6558013292126614e-01, 1.3663996383564952e-01, -1.1347727374114820e-01, 9.4653222413267277e-02, -7.9178837982785980e-02, 6.6352203986098701e-02, -5.5656395781301438e-02, 4.6692213065925491e-02, -3.9151702109559969e-02, 3.2786333094769089e-02, -2.7394200779191569e-02, 2.2811690851216111e-02, -1.8900773546804892e-02, 1.5548855145998195e-02, -1.2662527072754550e-02, 1.0164652782169520e-02, -7.9964742791471654e-03, 6.1136260652817258e-03, -4.4888557851635001e-03, 3.1132725338383527e-03, -1.9897463347909677e-03, 1.1299398381953670e-03, -5.4218278996456760e-04, 2.0450525067138600e-04, -5.3541173044258997e-05, 7.2320767464864696e-06 ]) return dlf
[docs]def key_201_CosSin_2012(): r"""Key 201 pt CosSin filter, as published in [Key12]_. Taken from file ``kk201CosSin.txt`` provided with SEG-2012-003_. License: http://software.seg.org/disclaimer.txt. """ dlf = DigitalFilter('Key 201 CosSin (2012)', 'key_201_CosSin_2012') dlf.base = np.array([ 9.1898135789795544e-07, 1.0560236258145801e-06, 1.2135021985967225e-06, 1.3944646218148563e-06, 1.6024129035298632e-06, 1.8413712856029165e-06, 2.1159641213409353e-06, 2.4315053665758195e-06, 2.7941014160203776e-06, 3.2107692750032131e-06, 3.6895723534572921e-06, 4.2397765100647990e-06, 4.8720293663446341e-06, 5.5985663607919089e-06, 6.4334475306554683e-06, 7.3928296035848751e-06, 8.4952786646994725e-06, 9.7621294498526205e-06, 1.1217898218180574e-05, 1.2890757193898812e-05, 1.4813079758803961e-05, 1.7022066946117209e-05, 1.9560467359658073e-05, 2.2477404450316962e-05, 2.5829327159387539e-05, 2.9681102325729859e-05, 3.4107269997169212e-05, 3.9193485939077079e-05, 4.5038179255745865e-05, 5.1754457203059970e-05, 5.9472294054641452e-05, 6.8341046380689574e-05, 7.8532343415514477e-05, 9.0243408448527221e-05, 1.0370087551467150e-04, 1.1916517524538292e-04, 1.3693557475562244e-04, 1.5735596909953090e-04, 1.8082153637169376e-04, 2.0778638524439160e-04, 2.3877234293696414e-04, 2.7437905368319086e-04, 3.1529558312353735e-04, 3.6231375319194681e-04, 4.1634346555562428e-04, 4.7843031014898881e-04, 5.4977579956440249e-04, 6.3176062087820603e-04, 7.2597135488438745e-04, 8.3423117980991972e-04, 9.5863515369401899e-04, 1.1015907582204575e-03, 1.2658644886123726e-03, 1.4546353912032167e-03, 1.6715565847497888e-03, 1.9208259560556996e-03, 2.2072673980160704e-03, 2.5364241622125167e-03, 2.9146661326298548e-03, 3.3493130964692705e-03, 3.8487763976105395e-03, 4.4227217140193290e-03, 5.0822561091888648e-03, 5.8401429774594740e-03, 6.7110490428654943e-03, 7.7118281914628686e-03, 8.8618476298971925e-03, 1.0183362682074693e-02, 1.1701947477049383e-02, 1.3446989862853833e-02, 1.5452260123909515e-02, 1.7756564507909106e-02, 2.0404496209307014e-02, 2.3447298342546899e-02, 2.6943855605395223e-02, 3.0961833823176868e-02, 3.5578989426519304e-02, 4.0884674203786789e-02, 4.6981564448367090e-02, 5.3987647963491189e-02, 6.2038507377358290e-02, 7.1289943955573878e-02, 8.1920992687256264e-02, 9.4137386993145250e-02, 1.0817554010518914e-01, 1.2430712016577938e-01, 1.4284430758454120e-01, 1.6414583639372404e-01, 1.8862393651527715e-01, 2.1675231128725500e-01, 2.4907530463166816e-01, 2.8621843526798946e-01, 3.2890050183176844e-01, 3.7794749315816500e-01, 4.3430857292399505e-01, 4.9907444798513595e-01, 5.7349847587571534e-01, 6.5902091994412060e-01, 7.5729682151433553e-01, 8.7022802845825153e-01, 1.0000000000000000e+00, 1.1491241000036050e+00, 1.3204861972090955e+00, 1.5174025129350848e+00, 1.7436837970197381e+00, 2.0037090739411751e+00, 2.3025103862617100e+00, 2.6458701753619409e+00, 3.0404331839891712e+00, 3.4938350461726517e+00, 4.0148500529942019e+00, 4.6135609537963891e+00, 5.3015540788430497e+00, 6.0921435594709612e+00, 7.0006289848698273e+00, 8.0445914816976902e+00, 9.2442339463025291e+00, 1.0622772013767669e+01, 1.2206883329864255e+01, 1.4027223820279268e+01, 1.6119020948027551e+01, 1.8522755439841418e+01, 2.1284944674394648e+01, 2.4459042892590269e+01, 2.8106475650897377e+01, 3.2297828536610695e+01, 3.7114213149203508e+01, 4.2648836782420439e+01, 4.9008806183799550e+01, 5.6317200298209784e+01, 6.4715452107403038e+01, 7.4366085659245940e+01, 8.5455861253972017e+01, 9.8199389653503559e+01, 1.1284328525648564e+02, 1.2967093861180905e+02, 1.4900800062891784e+02, 1.7122868461604187e+02, 1.9676300810421012e+02, 2.2610511460175258e+02, 2.5982283632295099e+02, 2.9856868294999509e+02, 3.4309246908417492e+02, 3.9425582475436693e+02, 4.5304886979204105e+02, 5.2060937475742980e+02, 5.9824477922157064e+02, 6.8745749350484289e+02, 7.8997397351448706e+02, 9.0777813134110693e+02, 1.0431497281803040e+03, 1.1987084925641964e+03, 1.3774648176845108e+03, 1.5828780189083436e+03, 1.8189232788935387e+03, 2.0901685758341446e+03, 2.4018630835612289e+03, 2.7600387542291814e+03, 3.1716270494286800e+03, 3.6445930787218194e+03, 4.1880897414655765e+03, 4.8126348548959668e+03, 5.5303146962783048e+03, 6.3550178980975252e+03, 7.3027042226581152e+03, 8.3917134174545281e+03, 9.6431201283206228e+03, 1.1081141738683076e+04, 1.2733607027476588e+04, 1.4632494715248606e+04, 1.6814552320467552e+04, 1.9322007302220827e+04, 2.2203384251427578e+04, 2.5514443944955918e+04, 2.9319262435339933e+04, 3.3691471058779483e+04, 3.8715681358217458e+04, 4.4489122496788041e+04, 5.1123522849071662e+04, 5.8747272182953282e+04, 6.7507906274902969e+04, 7.7574962041275547e+04, 8.9143258438494697e+04, 1.0243666662452392e+05, 1.1771244234227551e+05, 1.3526620436579350e+05, 1.5543765535274608e+05, 1.7861715581389511e+05, 2.0525327841984577e+05, 2.3586148883699448e+05, 2.7103412108532194e+05, 3.1145184046243853e+05, 3.5789681586586579e+05, 4.1126785642601945e+05, 4.7259780537596118e+05, 5.4307352776633098e+05, 6.2405887883026747e+05, 7.1712109748508944e+05, 8.2406113574115187e+05, 9.4694851095649926e+05, 1.0881613554026424e+06 ]) dlf.factor = np.array([1.149124100003605]) dlf.cos = np.array([ 4.8963534801291350e-04, -3.2447354678906376e-03, 1.0952238450063470e-02, -2.5330877509368774e-02, 4.5603964620893764e-02, -6.8751965018998398e-02, 9.1055170868309943e-02, -1.0955571014254684e-01, 1.2271886285618731e-01, -1.3032033375840532e-01, 1.3300188933965829e-01, -1.3178555117707785e-01, 1.2775414321103981e-01, -1.2185305954486332e-01, 1.1484395399555812e-01, -1.0727994394369871e-01, 9.9560982839136489e-02, -9.1939517526987313e-02, 8.4590736600088562e-02, -7.7600019560680286e-02, 7.1031733586497212e-02, -6.4890821187381778e-02, 5.9196016139512468e-02, -5.3915848643058928e-02, 4.9055780940812956e-02, -4.4567058676679240e-02, 4.0457261282427506e-02, -3.6666941211080724e-02, 3.3213645139589902e-02, -3.0027761601860024e-02, 2.7141909473138912e-02, -2.4473692903024750e-02, 2.2075499247215292e-02, -1.9847468573710642e-02, 1.7867265714909791e-02, -1.6011026177709484e-02, 1.4388810260485966e-02, -1.2844078700958564e-02, 1.1528724140086060e-02, -1.0242160186713188e-02, 9.1906684982280187e-03, -8.1147007847875829e-03, 7.2916108124280446e-03, -6.3832919299231621e-03, 5.7602923199031935e-03, -4.9801561547513692e-03, 4.5359177425499482e-03, -3.8467889983387665e-03, 3.5670373081260649e-03, -2.9327308045782176e-03, 2.8105929470807834e-03, -2.1944294961424278e-03, 2.2311101317977000e-03, -1.5941611249750095e-03, 1.8000275448786861e-03, -1.0989791755701920e-03, 1.4951672246892860e-03, -6.7966542661269437e-04, 1.3003578629701799e-03, -3.0965377717395037e-04, 1.2052335925762474e-03, 3.6106423804137471e-05, 1.2052407466848229e-03, 3.8238957499821198e-04, 1.3018966393838437e-03, 7.5508986898323120e-04, 1.5033588524742210e-03, 1.1828448709658736e-03, 1.8253815899842722e-03, 1.6989785802421903e-03, 2.2927582125052783e-03, 2.3438821839617966e-03, 2.9413764369870584e-03, 3.1679810467363173e-03, 3.8210431939779545e-03, 4.2354668717297693e-03, 4.9992627735887547e-03, 5.6289926876045100e-03, 6.5661551724297195e-03, 7.4555038861999377e-03, 8.6406325432364806e-03, 9.8532339747283270e-03, 1.1377691235455435e-02, 1.2999446350215346e-02, 1.4975945575967134e-02, 1.7117326788278663e-02, 1.9682681677977296e-02, 2.2477549053870567e-02, 2.5789277329789900e-02, 2.9383250822409085e-02, 3.3599553377482397e-02, 3.8111654527735343e-02, 4.3330483453611145e-02, 4.8751291534594260e-02, 5.4854616146235546e-02, 6.0801696080654326e-02, 6.7092281900802533e-02, 7.2264672303858538e-02, 7.6684426491380325e-02, 7.7748740946138262e-02, 7.5380953371380677e-02, 6.5034557293637621e-02, 4.5881721095444840e-02, 1.0745068396029680e-02, -4.1063368584660725e-02, -1.1762555750610600e-01, -2.1286042283609111e-01, -3.2473691853928877e-01, -4.1889667952194926e-01, -4.5782693031141991e-01, -3.5587281978710816e-01, -6.6666111275991896e-02, 4.1398275206290663e-01, 8.2532976945066749e-01, 7.4155935075441382e-01, -2.2362177591765958e-01, -1.2468909757950963e+00, -5.6409324151001772e-01, 1.6313369576910255e+00, 1.3693670120559179e-01, -1.9009211808491244e+00, 2.1011582166679363e+00, -1.4539662980149537e+00, 8.1038085852727904e-01, -4.1770604353721019e-01, 2.1941406706811120e-01, -1.2468136830432722e-01, 7.8269403871874657e-02, -5.3876922626623532e-02, 3.9875972155938078e-02, -3.1099121841349150e-02, 2.5148873022191463e-02, -2.0846754019080382e-02, 1.7576952842787749e-02, -1.4997498936892097e-02, 1.2906795835689719e-02, -1.1178868977228673e-02, 9.7305065956261819e-03, -8.5038781802097181e-03, 7.4569676118292445e-03, -6.5580949021930646e-03, 5.7826495893214484e-03, -5.1110604027691945e-03, 4.5274795600497757e-03, -4.0188948307658011e-03, 3.5745070845087227e-03, -3.1852787667663190e-03, 2.8435964846781139e-03, -2.5430124541388067e-03, 2.2780422183555945e-03, -2.0440036868883257e-03, 1.8368872847487388e-03, -1.6532500255010323e-03, 1.4901283117434534e-03, -1.3449656159356862e-03, 1.2155521334433954e-03, -1.0999741706045096e-03, 9.9657152340340712e-04, -9.0390146341796690e-04, 8.2070821214142624e-04, -7.4589699233026084e-04, 6.7851191397762147e-04, -6.1771708408859378e-04, 5.6278043567672292e-04, -5.1305986066984307e-04, 4.6799130039041709e-04, -4.2707850066888483e-04, 3.8988418417160815e-04, -3.5602243103677837e-04, 3.2515209207027528e-04, -2.9697108796156711e-04, 2.7121146954596444e-04, -2.4763512919344816e-04, 2.2603006942123759e-04, -2.0620715318264257e-04, 1.8799727229799711e-04, -1.7124887513989931e-04, 1.5582580442025662e-04, -1.4160541245686331e-04, 1.2847693068685222e-04, -1.1634006683069419e-04, 1.0510380008256007e-04, -9.4685353393630364e-05, 8.5009334765365045e-05, -7.6007041962903359e-05, 6.7615916583788370e-05, -5.9779122420642347e-05, 5.2445208782622779e-05, -4.5567833380983288e-05, 3.9105728752033442e-05, -3.3023834075077836e-05, 2.7297600234901939e-05, -2.1922306831363493e-05, 1.6926318238944308e-05, -1.2382788632218085e-05, 8.4107903563777150e-06, -5.1548458966523642e-06, 2.7349863491621416e-06, -1.1775367755450835e-06, 3.6617415171458042e-07, -6.1920666642164617e-08]) dlf.sin = np.array([ -5.8602704468975832e-10, 4.8048608865691248e-09, -1.9771446411637653e-08, 5.5269671219669613e-08, -1.1943308954933238e-07, 2.1463221286467290e-07, -3.3618689168303137e-07, 4.7460375561491547e-07, -6.2010393774690030e-07, 7.6676687291580134e-07, -9.1382097135454670e-07, 1.0643058622431453e-06, -1.2227765259769829e-06, 1.3937672563527502e-06, -1.5810499935024131e-06, 1.7877429029287643e-06, -2.0163554732931835e-06, 2.2692361668040396e-06, -2.5484456753753459e-06, 2.8562454180065290e-06, -3.1946379472885138e-06, 3.5660627245815181e-06, -3.9725086879521357e-06, 4.4166880900049553e-06, -4.9004832484318760e-06, 5.4270061911978838e-06, -5.9978954164211254e-06, 6.6168927621162747e-06, -7.2851116079354270e-06, 8.0072717151050409e-06, -8.7834623074537534e-06, 9.6200272666869681e-06, -1.0515203893806995e-05, 1.1478097778214146e-05, -1.2503644637963446e-05, 1.3605711023452051e-05, -1.4773445946482213e-05, 1.6028992588028293e-05, -1.7351362255724533e-05, 1.8777046268328975e-05, -2.0267260460262344e-05, 2.1883367382220654e-05, -2.3555377916627267e-05, 2.5387811572432832e-05, -2.7256008695400006e-05, 2.9339419633021675e-05, -3.1417660496931868e-05, 3.3800354252141579e-05, -3.6099620853251731e-05, 3.8851364451479363e-05, -4.1374814496544362e-05, 4.4599458677506889e-05, -4.7332670414243943e-05, 5.1188885345556143e-05, -5.4081411276216648e-05, 5.8817223325521029e-05, -6.1748595688031771e-05, 6.7759540724914998e-05, -7.0477668174613142e-05, 7.8405578637928987e-05, -8.0416390943704734e-05, 9.1318327863896956e-05, -9.1689586953474345e-05, 1.0732811343723065e-04, -1.0434243728703050e-04, 1.2768616500544454e-04, -1.1822963938719640e-04, 1.5431866320930474e-04, -1.3280640984775213e-04, 1.9025153589598097e-04, -1.4674319163166278e-04, 2.4032678429752795e-04, -1.5722591368834836e-04, 3.1241839074880459e-04, -1.5869843609971545e-04, 4.1950672592888611e-04, -1.4061987157747521e-04, 5.8323092045218519e-04, -8.3489051752646859e-05, 8.3998754956665807e-04, 4.8166642275560894e-05, 1.2514134018618409e-03, 3.1809381315641577e-04, 1.9223958368384385e-03, 8.3977376473052937e-04, 3.0319286374562394e-03, 1.8135564849093052e-03, 4.8856220017935168e-03, 3.5901028334771145e-03, 8.0038676866840078e-03, 6.7764383041831900e-03, 1.3266048500372144e-02, 1.2406252926137538e-02, 2.2134422870406390e-02, 2.2191911862939541e-02, 3.6963935749189471e-02, 3.8829525301567067e-02, 6.1308824849773652e-02, 6.6140947825550744e-02, 9.9797901699075597e-02, 1.0824048046010233e-01, 1.5616018092254505e-01, 1.6533327222825650e-01, 2.2564430322919368e-01, 2.2062815143611000e-01, 2.7477185256445674e-01, 2.1146243753121693e-01, 2.0743923168031805e-01, 2.9273136481935752e-03, -1.1875521395824359e-01, -4.8782254186329055e-01, -5.6383218637505039e-01, -7.0493717238569553e-01, -4.5783079000773212e-02, 4.9572887642641605e-01, 1.2793243232592335e+00, 7.6984445533323119e-04, -1.0809022247360809e+00, -9.7826142685914264e-01, 2.4412168561816161e+00, -1.5742192933752286e+00, 1.0474779812704657e-01, 6.8117592802985916e-01, -8.1735467756558944e-01, 6.8894183180797697e-01, -5.2159909808793825e-01, 3.8460793473043292e-01, -2.8421923628404017e-01, 2.1211949229810861e-01, -1.5993330303166020e-01, 1.2163508069999608e-01, -9.3164674694277416e-02, 7.1777818840364910e-02, -5.5578938642792224e-02, 4.3227895023256115e-02, -3.3758552896064629e-02, 2.6463811011765734e-02, -2.0820205680643536e-02, 1.6436812641415149e-02, -1.3019659797407497e-02, 1.0346416487448091e-02, -8.2481070073694342e-03, 6.5957434607522691e-03, -5.2904671538314026e-03, 4.2562264095930237e-03, -3.4343067314751316e-03, 2.7792243881857633e-03, -2.2556298932160214e-03, 1.8359634980842480e-03, -1.4986732799921144e-03, 1.2268558973329326e-03, -1.0072161412856525e-03, 8.2926783836384434e-04, -6.8471812797056032e-04, 5.6699154764304634e-04, -4.7086106657177131e-04, 3.9216119658083232e-04, -3.2756429146830335e-04, 2.7440564055551230e-04, -2.3054635199842104e-04, 1.9426558644629048e-04, -1.6417564894421281e-04, 1.3915493002405042e-04, -1.1829482010512426e-04, 1.0085758994667589e-04, -8.6242897629566575e-05, 7.3961097310559017e-05, -6.3611923024107272e-05, 5.4867429384991716e-05, -4.7458310810428852e-05, 4.1162907677974120e-05, -3.5798353789658158e-05, 3.1213433790926005e-05, -2.7282808824825689e-05, 2.3902339183058118e-05, -2.0985288286859604e-05, 1.8459236223596745e-05, -1.6263565819420051e-05, 1.4347411857118876e-05, -1.2667986114133353e-05, 1.1189208624850740e-05, -9.8805899457079486e-06, 8.7163210286869178e-06, -7.6745372470670224e-06, 6.7367316776180222e-06, -5.8873002689814021e-06, 5.1132081051238435e-06, -4.4037712527232031e-06, 3.7505516230790782e-06, -3.1473609977624753e-06, 2.5903624227147574e-06, -2.0782393943789611e-06, 1.6123579385552092e-06, -1.1967503151651560e-06, 8.3762259929749212e-07, -5.4201864582008082e-07, 3.1540800169690699e-07, -1.5849870094735947e-07, 6.4517602920670347e-08, -1.8937067758737377e-08, 3.0164202265996216e-09 ]) return dlf