基于层状双孔介质的地震波反射和透射系数频散特性研究

摘要

We studied the dispersive characteristics of P-wave reflection and transmission coefficients at the interface of two kinds of media under the vertical incidence of P-waves.The upper and lower sides of the interface were layered double-porosity shale media and layered double-porosity sandstone media,respectively.Three types of reflected and transmitted P-waves existed at the interface of the upper and lower double-porosity media when the P-waves propagated perpendicularly to the interface.Based on the properties of the layered double-porosity media,we introduced six boundary conditions at the interface.According to the wave equations of layered double-porosity media,the P-wave reflection and transmission coefficients were calculated based on the plane wave analysis.The results demonstrate that when fluid exists in the porous media,the P-wave reflection and transmission coefficients are related to the frequency and the dispersion phenomenon occurs.Wave-induced fluid flow is the main mechanic for the dispersion of the P-wave reflection and transmission coefficients.In addition,the results also indicate that the local fluid flow and macroscopic Biot flow can cause the dispersion of the reflection and transmission coefficients in the seismic band and ultrasonic band,respectively.We have further analyzed the effects of rock parameters on dispersive curves of reflection and transmission coefficients.%本文研究了纵波垂直入射情况下两种介质分界面处的纵波反射和透射系数的频散特性,分界面上下两侧分别为层状双孔页岩介质和层状双孔砂岩介质.当纵波沿垂直于分界面的方向传播至分界面处时,会在上层双孔介质中产生三类反射纵波,在下层双孔介质中产生三类透射纵波.基于层状双孔介质的特性,给出了分界面处的六个边界条件.根据层状双孔介质的波动方程,利用平面波分析得到了纵波的反射和透射系数.结果表明:当多孔介质中存在流体时,纵波的反射和透射系数与频率相关,即存在频散现象.波致流体流动是造成纵波反射和透射系数频散的主要原因.此外,结果还表明局部流体流动引起地震频带内反射和透射系数的频散,宏观Biot流引起超声频带内反射和透射系数的频散.本文同时对岩石参数对反射和透射系数频散曲线的影响进行了研究.