Finite difference modeling of the diffusive slow P-wave in poroelastic media

Shahin Moradi, Don C. Lawton and Edward S. Krebes


Biot's theory of poroelasticity predicts the presence of a slow P-wave in a fluid saturated medium due to the relative movement of the pore fluid with respect to the rock matrix. The slow P-wave, is highly diffusive in seismic frequencies and thus will not be observed in seismic data. However, in the case of zero fluid viscosity, this wave is a non-diffusive mode that travels through the medium. In this report both diffusive and non-diffusive modes are modeled using a previously developed finite-difference algorithm. It seems that in a uniform homogenous medium the amount of amplitude loss due to wave conversion in the diffusive case is very close to the one in the non-diffusive case. This shows that although the diffusive P-wave is not a traveling mode, it exists in the medium but dissipates quickly. The slow P-wave is particularly important where gas exists in the form of separate patches in the pore fluid. In those cases the wave conversions to the slow P-wave may dissipate a considerable amount of energy. Modeling wave propagation in such media is useful in monitoring studies for CO 2 sequestration.

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