弹性波传播中由微结构相互作用导致的尺度效应分析

Scale effect of microstructure interaction in elastic wave propagation

相比于传统弹性波动方程,非对称弹性波动方程增加的独立自由项,包含有介质特征尺度参数.基于非对称弹性波动方程,可以分析弹性波传播中,由介质内微孔缝隙结构相互作用所导致的地震波传播尺度效应.本文从介质应变能密度函数出发,并结合几何方程和平衡方程,给出修正偶应力理论下的非对称弹性波动方程以及对应的非对称SH型横波波动方程的数学表达式,并在三层煤层模型上进行数值模拟,将检波器分别设置在地表和煤层中线,通过改变介质特征尺度参数值,合成地震记录,研究分析弹性波传播中,由介质内微孔缝隙结构相互作用所导致的尺度效应,对地震记录的影响及规律,并得出以下结论和认识:(1)非对称弹性波动方程模拟的弹性波传播表现出明显的尺度效应;(2)地震记录需要考虑介质内部多尺度的微孔缝隙相互作用的影响.

Compared with conventional elastic wave equations,the independent free term in the asymmetric elastic wave equations contains the parameter of characteristic scale of media.The scale effect of seismic wave propagation caused by microporous interaction in media can be observed in synthetic seismograms when performing numerical modelling using asymmetric elastic wave equations.In this paper,starting from the strain energy density function,and combining the geometric equations and the equilibrium equations,we derive the asymmetric elastic wave equations and the corresponding asymmetric SH-wave equations based on the modified couple stress theory.Then,we perform numerical modelling on a coal-seam three-layer model.By setting receivers along the surface and midline of the coal-seam three-layer model,meanwhile,changing the parameter values of the characteristic scale of the media,we obtain synthetic seismograms,and analyze the influence of the scale effect caused by microporous interaction in the media on the seismograms.In the end,drawing the following conclusions and understandings:(1)Seismograms generated by the asymmetric elastic wave equations show obvious scale effects.(2)The influence of the multi-scale of the microporous interaction in the media on seismograms need to be considered.