Open AccessInversion of travel‐time data for laterally heterogeneous velocity structure ‐ linearization approach
Author(s) -
Firbas Petr
Publication year - 1981
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.1981.tb02742.x
Subject(s) - slowness , linearization , kinematics , inversion (geology) , mathematical analysis , inverse problem , perturbation (astronomy) , quadratic equation , inverse , mathematics , geometry , geodesy , geology , nonlinear system , physics , classical mechanics , seismology , quantum mechanics , tectonics
Summary A method for solving the inverse kinematic problem for two‐dimensional laterally heterogeneous velocity structure is proposed. The method is based on the linearization approach and ray theory. The mathematical procedure proposed is an iterative one and at each step a quadratic form is minimized, so that a relatively large system of linear equations must be solved. The perturbation part of the two‐dimensional slowness function is expressed at each step in the form of a two‐fold series of polynomials, orthogonal over a rectangular area. This rectangular area has been obtained through the transformation of an irregular area covered by rays of refracted waves (i. e. surface to surface diving waves). Model examples illustrating the proposed method as well as the velocity model obtained for a part of a refraction profile across Czechoslovakia are presented.