# hankel_dlf#

empymod.transform.hankel_dlf(zsrc, zrec, lsrc, lrec, off, ang_fact, depth, ab, etaH, etaV, zetaH, zetaV, xdirect, htarg, msrc, mrec)[source]#

Hankel Transform using the Digital Linear Filter method.

The Digital Linear Filter method was introduced to geophysics by [Ghos70], and made popular and wide-spread by [Ande75], [Ande79], [Ande82]. The DLF is sometimes referred to as the Fast Hankel Transform FHT, from which this routine has its name.

This implementation of the DLF follows [Key12], equation 6. Without going into the mathematical details (which can be found in any of the above papers) and following [Key12], the DLF method rewrites the Hankel transform of the form

(1)#$F(r) = \int^\infty_0 f(\lambda)J_v(\lambda r)\ \mathrm{d}\lambda$

as

(2)#$F(r) = \sum^n_{i=1} f(b_i/r)h_i/r \ ,$

where $$h$$ is the digital filter.The Filter abscissae b is given by

(3)#$b_i = \lambda_ir = e^{ai}, \qquad i = -l, -l+1, \cdots, l \ ,$

with $$l=(n-1)/2$$, and $$a$$ is the spacing coefficient.

This function is loosely based on get_CSEM1D_FD_FHT.m from the source code distributed with [Key12].

The function is called from one of the modelling routines in empymod.model. Consult these modelling routines for a description of the input and output parameters.

Returns
fEMarray

Returns frequency-domain EM response.

kcountint

Kernel count. For DLF, this is 1.

convbool

Only relevant for QWE/QUAD.