Abstract
In this present context, mathematical modeling of the propagation of surface waves in a fluid saturated poro-elastic medium under the influence of initial stress has been considered using time dependent higher order finite difference method (FDM). We have proved that the accuracy of this finite-difference scheme is 2M when we use 2nd order time domain finite-difference and 2M-th order space domain finite-difference. It also has been shown that the dispersion curves of Love waves are less dispersed for higher order FDM than of lower order FDM. The effect of initial stress, porosity and anisotropy of the layer in the propagation of Love waves has been studied here. The numerical results have been shown graphically. As a particular case, the phase velocity in a non porous elastic solid layer derived in this paper is in perfect agreement with that of Liu et al. (2009).
Highlights
The simulation of surface waves propagating in a fluid saturated poro-elastic media is of great importance to seismologists due to its possible applications in geophysical prospecting, reservoir engineering and survey techniques for understanding the cause and estimation of damage due to natural and manmade hazards
We have proved that the accuracy of this finite-difference scheme is 2M when we use 2nd order time domain finite-difference and 2M-th order space domain finite-difference
Virieux [7,8] have used velocity-stress finite difference method for the propagation of P-SV wave and SH wave in heterogeneous media
Summary
The simulation of surface waves propagating in a fluid saturated poro-elastic media is of great importance to seismologists due to its possible applications in geophysical prospecting, reservoir engineering and survey techniques for understanding the cause and estimation of damage due to natural and manmade hazards. Liu et al [20] employed a plane wave theory and the Taylor series expansion of dispersion relation to derive the FD coefficients in the joint time-space domain for the scalar wave equation with second-order spatial derivatives. They demonstrated that the method has greater accuracy and better stability than the conventional method. Lie et al [25] developed a time-space domain dispersion-relationbased staggered-grid finite-difference schemes for modeling the scalar wave equation. In this paper, following [22,25] we have modeled the Love waves in a fluid saturated poro-elastic media under the influence of initial stress using time-space domain higher order finite difference method. It is observed that the anisotropic parameter in the porous layer and the porosity of the layer both have the increasing effect but the initial stress field has an decreasing effect on the phase velocity of Love wave
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