偶应力理论框架下的弹性波数值模拟与分析

在经典地震学理论框架下,先人发展了数不胜数的地震技术,为社会发展做出了巨大贡献;可是,当前的技术仍有难以逾越的障碍,亟需破局.高铁地震学联合研究组,在河北定兴采集到大量数据;其中可见含有大量的旋转运动分量.由于基于经典连续介质力学推导弹性波动方程时,从理论出发点上就去除了旋转项,且在其理论框架内,介质被视为一个连续的质量体.而事实上,不论是人造还是天然的介质都存在着复杂的内部结构,广义连续介质力学更适合描述具有更加复杂内部结构的情况.于是,我们尝试启用广义连续介质力学理论,推导偶应力理论框架下的弹性波动方程;将其数学表达形式以及数值模拟结果与传统弹性波动方程进行对比.研究探索推导的具非对称性的波动方程所具有的理论意义和应用价值.

Numerical modelling and analysis for elastic wave equations in the frame of the couple stress theory

In the frame of conventional seismology,geophysicists have made a great contribution to the development of our society by developing numerous seismic exploration technologies.However,the current technologies still exist some hurdles to be overcome.The field data acquired in Dingxing,Hebei provided by the joint research group of High-Speed Rail Seismology show that there existing a large amount of rotational ground-motions.In the conventional continuum mechanics theory,the media are modeled to be a continuum mass without internal structures,and the elastic wave equation based on the conventional continuum mechanics theory do not contain the free term describing the rotational ground-motions essentially.As a matter of fact,no media are ideal continuum,whether natural or man-made media,there are complex internal structural characteristics.Generalized continuum mechanics is more suitable for describing situations with more complex internal structures.Therefore,we try to apply the generalized continuum mechanics theory to derive the elastic wave equation based on the couple stress theory and compare its mathematical expression and synthetic seismograms with that of the conventional elastic wave equation.Study and explore the theoretical significance and application value of the asymmetric elastic wave equation that we derived.