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自从发现震电现象以来,众多学者进行了相关研究.其中,Pride提出了一套描述流体饱和孔隙介质中震电波场的耦合与传播的宏观控制方程组,该方程组后来被广泛地应用到相关的震电研究中.Chen发展了一套广义反透射系数方法并将其应用到层状介质合成地震图的研究当中,该方法数值计算效率高并且可以处理带弯曲界面层状介质这种复杂模型.基于Pride的震电波场控制方程组,我们将Chen的广义反透射系数方法推广应用到层状孔隙介质中震电波场的数值模拟研究中,但是在数值计算过程中发现,当含源层的厚度相对于地震波波长较大时(即高频情况),会出现数值计算的不稳定,此即为高频不稳定性问题.针对高频不稳定性问题,一种自然的处理方法就是在原来的含源层中插入两个虚拟界面,构造出一个新的含源薄层,但是这会带来一些额外的计算量,此外,由于虚拟含源薄层的厚度是有限的,必须针对具体模型参数设定一个合适的厚度值.高频不稳定性问题同样存在于层状介质合成地震图的数值计算过程中,Chen提出了一种解析的处理方法,即在原含源层内引入一无限薄的虚拟含源薄层,通过解析的方法解决高频不稳定性问题,该方法不会降低计算效率且适用于任意参数模型.本文首先对层状孔隙介质中的震电波场数值计算公式进行分析,指出源项积分中的指数增长因子是导致高频不稳定性问题的根本原因;其次将Chen在合成地震图数值模拟研究中采用的解析处理方法推广到震电波场研究中,得到了适用于数值计算的公式;然后给出数值算例,并针对一个含源层过厚的模型,比较了自然处理方法和解析处理方法,两种方法得到的结果具有相当好的一致性,而解析处理方法计算效率更高,证实了本文给出的解析处理方法在解决层状孔隙介质震电波场数值模拟的高频不稳定性问题方面的有效性.
Since the discovery of the phenomenon of electroshock, many scholars have carried out relevant research, among them, Pride proposed a set of macroscopic control equations describing the coupling and propagation of the seismic field in fluid-saturated porous media, which has been widely applied to the correlation Chen developed a set of generalized anti-transmission coefficient method and applied it to the study of synthetic seismograms of layered media. The numerical method is computationally efficient and can handle complex models of layered media with curved interfaces Based on Pride ’s system of seismic wavefield control equations, we generalize Chen’ s generalized inverse transmissivity method to the numerical simulation of the seismic wave field in layered porous media. However, When the thickness is larger than the wavelength of the seismic wave (that is, the high frequency), numerical instability occurs, which is the problem of high frequency instability. A natural solution to the high frequency instability problem is to use the original Contains two virtual interfaces in the source-containing layer to construct a new source-containing layer, but this will bring some additional computational load. In addition, since the virtual source-containing thin The thickness is finite, and a suitable thickness value must be set for the specific model parameters.High frequency instability problem also exists in the numerical calculation of layered media composite seismograms, Chen proposed an analytical approach, That is to say, an infinite thin layer of virtual source is introduced into the original source layer, and the high-frequency instability problem is resolved by analytical method, which does not reduce the computational efficiency and is suitable for any parameter model.In this paper, The numerical calculation formulas of the seismic wave field in the paper are analyzed. It is pointed out that the exponential growth factor in the integral of source term is the root cause of the high-frequency instability problem. Secondly, the analytical processing method adopted by Chen in the numerical simulation of synthetic seismograms is generalized to In the research of the seismic wave field, a formula suitable for numerical calculation is obtained. Then a numerical example is given. For a model with too thick a source layer, natural processing methods and analytical processing methods are compared. The results obtained by the two methods have Quite good consistency, and the analytic processing method is more efficient in computing. It proves that the analytical processing method given in this paper is effective in solving the problem that the seismic response of layered porous media Validity of wavefield numerical simulation of high frequency instability problems.