Physics – Geophysics
Scientific paper
May 1999
adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=1999geoji.137..319h&link_type=abstract
Geophysical Journal International, Volume 137, Issue 2, pp. 319-335.
Physics
Geophysics
14
Poroelasticity, Reservoir Geophysics, Viscoelasticity, Wave Propagation
Scientific paper
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.
Hanyga Andrzej
Seredynska Malgorzata
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