Open AccessSome effects of the memory kernel singularity on wave propagation and inversion in poroelastic media—I. Forward problems
Author(s) -
Hanyga Andrzej,
Seredyńska M
Publication year - 1999
Publication title -
geophysical journal international
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.302
H-Index - 168
eISSN - 1365-246X
pISSN - 0956-540X
DOI - 10.1046/j.1365-246x.1999.00775.x
Subject(s) - poromechanics , mathematical analysis , wavefront , mathematics , laplace transform , wave propagation , smoothing , scalar (mathematics) , singularity , porous medium , physics , geometry , optics , geology , porosity , statistics , geotechnical engineering
Summary A class of scalar partial differential equations with delay is studied. The results are particularly relevant for various models of porous media. An exact fundamental solution is derived for a subclass defined by a relation between the coefficients of the differential operator. For the general case, asymptotic expansions in the time domain for pulse propagation and the Born approximation for low‐frequency effects are applied. Wavefront smoothing and pulse shift are demonstrated by analysis of exact and approximate solutions. It is shown that the assumption of constant dynamic permeability, commonly used in poroelastic wave propagation problems, is qualitatively inconsistent with the equations studied in this paper.