【摘要】 数值计算方法是考察非线性弹性波在介质中(如岩石)传播特征的重要手段.非线性弹性波的数值模拟存在陡峭间断面(点)、数值振荡以及误差的指数级增长等现象而破坏数值解的稳定性、收敛性,能否消减上述现象的不利影响成为制约数值方法有效与否的重要因素.文中同时引入了FCT算子和幅值限制器,采用中心差分格式对具有垂直对称轴的横向各向同性(VTI)介质中的二维非线性弹性波进行数值模拟,从而克服了上述困难;介绍了适用于非线性弹性波的吸收边界条件,给出了差分方程的稳定性条件.在验证了方法的有效性后成功地获取了二维VTI介质中非线性弹性波的三分量地震正演记录,表明非线性波在传播过程中会发生波形畸变等现象.更多还原

【Abstract】 Numerical methods are the most important ways to study nonlinear wave propagation in solid. However, numerical modeling for nonlinear seismic waves is faced with problems such as steep gradients, shocks and unphysical oscillations. Accordingly, some special treatments have been presented to solve these problems. However, in our knowledge, there is no effective method to overcome these problems by far. In this paper, we report a second order central finite difference (FD) scheme based on a modified flux-corrected transport (FCT) technique, for short, we called it MFCTFD. We present the stability criterion of this algorithm, and the modified absorbing boundary conditions which are suitable to the nonlinear seismic waves. With numerical experiments we testify the validity of this numerical method, and achieve the synthetic seismograms of nonlinear seismic waves with three components in two-dimensional transverse isotropic (with vertical symmetry axis) solid media. The result shows that waveform distortion will occur during the process of nonlinear wave propagation.更多还原