利用时间分裂的错格伪谱法模拟地震波在基于改进BISQ模型的双相介质中的传播

Modelling of seismic wave propagation in two-phase medium based on reformulated BISQ model using time-splitting staggered pseudospectral method

改进的BISQ(Biot-Squirt)模型中各参数具有明确的物理意义和可实现性,在不引入特征喷流长度的情况下可将Biot流动和喷射流动两种力学机制有机地结合起来;而高精度的地震波场数值模拟技术是研究双相介质地震波传播规律的重要手段。本文从本构方程、动力学方程和动力学达西定律出发,推导了基于改进BISQ模型的双相各向同性介质的一阶速度--应力方程组;采用时间分裂错格伪谱法求该方程组的数值解,模拟半空间及层状双相介质中的地震波场。数值模拟结果表明:①与传统方法相比,时间分裂错格伪谱法波场数值模拟的精度更高,压制网格频散效果更好;②在非黏滞相界情况下,慢纵波呈传播性,而在黏滞相界情况下,慢纵波呈扩散性,以静态模式出现在震源位置;③双相介质分界面处,各类波型复杂的反射透射规律可由数值模拟结果清晰展现。

The reformulated BISQ model involves the parameters which have clear physical meanings and can be feasibly estimated by independent measurements.This model combines the Biot flow and squirt-flow mechanism to avoid introducing a complicated parameter of characteristic squirt flow length.High precision seismic wavefield simulation is an important technique for the investigation of waves propagating in two-phase media.We deducted one-order velocity-stress equations of the two-phase isotropic media based on the constitutive equations,dynamical equations and dynamic Darcy＇s law.And,we implemented the time-splitting staggered pseudospectral method for the calculation of the seismic waves propagating in the halfspace and layered model of the two-phase isotropic media.Numerical modeling results indicate that the time-splitting staggered pseudospectral algorithm has a higher precision and can suppress grid numerical dispersion more effectively; the slow P wave propagated in two-phase media when the fluid is inviscid,but becomes diffusive when the fluid is viscid,and there is the presence of the static slow mode at the source location; and all the waves reflected and transmitted at the interface of two-phase media can be revealed clearly by the numerical modeling results.