Security analysis of this Biot/squirt models for revolution propagation in saturated media that are porous

Security analysis of this Biot/squirt models for revolution propagation in saturated media that are porous

Jiawei Liu, Wen-An Yong, Stability analysis associated with Biot/squirt models for revolution propagation in saturated porous news, Geophysical Journal Global.

Abstract

This work is focused on the Biot/squirt (BISQ) models for revolution propagation in saturated porous news. We reveal that the models allow exponentially exploding solutions, as time would go to infinity, once the characteristic squirt-flow coefficient is negative or features a non-zero imaginary component. We additionally reveal that the coefficient that is squirt-flow have non-zero imaginary components for a few experimental parameters or even for low angular frequencies. Since the models are linear, the presence of such exploding solutions suggests uncertainty associated with the BISQ models. This outcome, for the time that is first offers a theoretical description associated with well-known empirical observation that BISQ model just isn’t dependable ( perhaps maybe perhaps not in line with Gassmann’s formula) at low frequencies. It calls for a reconsideration regarding the trusted BISQ concept. Having said that, we show that the 3-D isotropic BISQ model is stable once the squirt-flow coefficient is good. In specific, the initial Biot model is unconditionally stable in which the squirt-flow coefficient is 1.

1 INTRODUCTION

The propagation of seismic waves in rocks with fluids happens to be being among the most research that is active in geoscience. Different theories (Biot 1956a; Dvorkin & Nur 1993; Mavko et al. 2009; MГјller et al. 2010) concentrate on relating attenuation and dispersion of seismic waves in planet materials to real properties of this stones and liquids. Attenuation means the exponential decay of revolution amplitude with distance and dispersion is just a variation of propagation velocity with frequency. The Biot and squirt-flow mechanisms are believed to be the most important ones (Dvorkin & Nur 1993; Yang & Zhang 2002) among the various mechanisms related to attenuation and dispersion. Continue reading “Security analysis of this Biot/squirt models for revolution propagation in saturated media that are porous”