汶川地震断层应力强度因子分析超奇异积分法

 地震作为复杂瞬态断裂破坏物理过程，其机制研究是一个多学科交叉问题；同震断层处应力/能量积累释放规律，为从断裂角度研究地震机制提供了一个切入点；应力强度因子（应力角度）和应变能强度因子（能量角度）是断裂力学/物理学的两个最基本的参数。本文应用非线性边界元和主部分析法，将汶川地震断层破坏过程转化为解以断层位移间断为未知函数超奇异积分方程组问题，定义了断层处应力强度因子；利用有限部积分概念及体积力法，为方程组建立了数值解法，编制了Fortran程序，得到断层处应力强度因子数值结果；通过研究应力强度因子随断层位置变化规律，分析了汶川地震断层破坏过程；结合应变能强度因子理论，通过对宏微观电磁破坏过程进一步深入模拟研究可得到电磁辐射破坏变化规律，为地震短临预测提供理论支持和帮助。

Application of Hypersingular Integral Equation Method to Study Earthquake Fault in Wenchuan

Based on the nonlinear boundary element and the main-part analysis method, the problem of earthquake fault in Wenchuan is reduced to a set of hypersingular integral equations coupled with nonlinear boundary integral equations, in which the unknown functions are the general displacement discontinuities. The behavior of the general singular stress indexes around the crack front terminating at the fault surface is analyzed and the stress intensity factors are defined. A numerical method for the problem is put forward with the extended displacement discontinuities being approximated by the product of basic density functions and polynomials. Finally, the radiation distributions simulated by stress intensity factors against fault length, width and height at the crack surface are obtained, which can reveal the mechanism on co-seismal slip. The future work will focus on using the extended volume energy density function and Richter magnitude scale geophysics theory to analyze the extended macro/micro electromagnetic earthquake fault mechanism.