Astronomy and Astrophysics – Astronomy
Scientific paper
Oct 2009
adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=2009geoji.179..299v&link_type=abstract
Geophysical Journal International, Volume 179, Issue 036704, pp. 299-318.
Astronomy and Astrophysics
Astronomy
3
Transient Deformation, Geomechanics, Hydrology, Permeability And Porosity, Theoretical Seismology, Wave Propagation
Scientific paper
An asymptotic method, valid in the presence of smoothly varying heterogeneity, is used to derive a semi-analytic solution to the equations for fluid and solid displacements in a poroelastic medium. The solution is defined along trajectories through the porous medium model, in the manner of ray theory. The lowest order expression in the asymptotic expansion provides an eikonal equation for the phase. There are three modes of propagation, two modes of longitudinal displacement and a single mode of transverse displacement. The two longitudinal modes define the Biot fast and slow waves which have very different propagation characteristics. In the limit of low frequency, the Biot slow wave propagates as a diffusive disturbance, in essence a transient pressure pulse. Conversely, at low frequencies the Biot fast wave and the transverse mode are modified elastic waves. At intermediate frequencies the wave characteristics of the longitudinal modes are mixed. A comparison of the asymptotic solution with analytic and numerical solutions shows reasonably good agreement for both homogeneous and heterogeneous earth models.
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