Open AccessSlowness—time mapping of near offset seismic reflection data
Author(s) -
Harding A. J.
Publication year - 1985
Publication title -
geophysical journal of the royal astronomical society
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.302
H-Index - 168
eISSN - 1365-246X
pISSN - 0016-8009
DOI - 10.1111/j.1365-246x.1985.tb05104.x
Subject(s) - slowness , seismogram , bessel function , hankel transform , amplitude , aliasing , synthetic seismogram , mathematical analysis , fourier transform , transformation (genetics) , cylindrical harmonics , mathematics , geology , optics , filter (signal processing) , geophysics , physics , computer science , seismology , classical orthogonal polynomials , gegenbauer polynomials , orthogonal polynomials , computer vision , gene , biochemistry , chemistry
Summary. The transformation of a set of seismograms to the delay time‐slowness, τ—p, domain is presented as a sequence of Fourier and Bessel transforms, For a horizontally layered medium, this sequence gives an exact cylindrical wave decomposition of the response to a point source; correctly compensating for the phase shifting and geometrical spreading associated with transmission through the Earth. The resultant τ—p map or ‘slant stack’ contains true amplitude and phase information. The spatial aliasing properties of the transformation, when applied to a dataset, are greatly improved by the use of only outgoing waves in the Bessel transform. This is equivalent to using Hankel functions rather than Bessel functions, and is justified by the absence of incoming waves from most datasets. The WKBJ approximation to the medium response enables predictions to be made about the shape and amplitude variation with slowness of truncation effects. Theoretically the τ—p transformation is reversible, thus the τ—p domain is a suitable one in which to perform filtering operations before seismogram reconstruction.