频率域有限差分数值模拟地震波衰减和震电效应特征

地震波在地下含流体孔隙介质中传播时，会引起中观尺度的"局域流"，进而产生地震波震电效应.基于Biot（1941）固结理论的准静态方程，在频率域中采用空间有限差分方法，正演模拟虚岩石物理岩样的地震波衰减和震电效应.与时间域虚岩石物理方法相比，该方法既可以直接求取任一频率下的地震波衰减和电势，便于应用于实际岩样的预测分析，也避免了讨论岩样外表面施加的力源函数表达式及时间剖分稳定性条件等问题.首先利用周期性层状介质模型验证了本文所描述方法的有效性，并进一步求取分析了周期性层状介质两种不同特征单元的渗流电流密度及电势，数值模拟结果表明由中观尺度"局域流"引起的震电效应电势振幅数量级在实验室测量范围之内，随后，分析研究了四种不同高渗介质占比值的地震衰减及震电效应特征.最后，将本文提出的震电效应数值计算方法推广至二维，并求取了二维斑块饱和模型的地震波衰减、速度频散、电势的振幅和相位角数值结果.

Research of seismic attenuation and seismoelectric effect by the finite-difference method in frequency domain

The seismoelectric effect will occur because of the mesoscopic wave-induced fluid flow with the propagation of seismic wave in the saturated rocks. Utilizing the Biot's equations in the porous medium, we calculate the attenuation and seismoelectric effect of the patchy saturated model by the finite-difference method in frequency domain. Comparing with the method in time domain, the result of any frequency can be easily and directly obtained and there is no need to discuss the stress source function and time stability of numerical scheme for the method we propose in this paper. We test and verify the accuracy of the method presented in the context by the model of porous layers alternately saturated with different porosity. And then the amplitude and phase angles of electrical potential for the White's model are obtained. The results show that the magnitude of seismoelectric signals induced by mesoscopic wave-induced fluid flow can be measurable for the laboratory setups. And then the numerical results of seismic attenuation and seismoelectric effect are calculated for four kinds of cases of the models containing different proportions of high permeability media. Finally, the seismic attenuation and dispersion and the amplitude and phase angles of electrical potential for 2D patchy saturated model are calculated using the method we propose in this paper.