Open AccessSolution of the inverse problem for wave propagation using J ‐fraction expansion
Author(s) -
Hron M.,
Razavy M.
Publication year - 1977
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.1977.tb04205.x
Subject(s) - inverse problem , mathematical analysis , reflection coefficient , wavenumber , reflection (computer programming) , inverse , mathematics , fraction (chemistry) , wave equation , function (biology) , physics , geometry , optics , chemistry , organic chemistry , evolutionary biology , computer science , biology , programming language
Summary The system of difference equations with variable coefficients is solved using the J ‐fraction method. The solution is used to find the phase spectrum of the response (or of reflection coefficient) of a layered medium with known velocities. Also, the inverse problem is solved provided the reflection coefficient is a known function of the wavenumber. At low frequencies the numerical results are in very good agreement with the solution of the differential equation.