Synthetic seismograms of nonlinear seismic waves in anisotropic (VTI) media

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 I 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.