Seismic Wave Frequency and Bandwidth Changes Induced by the Nonlinearity in VTI Media

Abstract

Using the finite difference (FD) method with a transformed FCT technique reported by our previous paper, we get the numerical synthetic seismograms corresponding to the isotropic, transversely isotropic with a vertical symmetry axis (VTI) and nonlinear VTI media, respectively. After that, wavelet transform is adopted to calculate and analysis the seismic wave frequency and spectral bandwidth variations induced by the nonlinearity in VTI media. In the seismic records, we found that the energy of different mode of seismic waves varies with the increase of source-receiver distance because of media anisotropy, especially, these variations will be enlarged by the combination effect of media anisotropy and nonlinearity. Namely, because of media nonlinearity, the energies of different mode of seismic waves are reassigned and displayed in records but fit the energy conservation law. Companying with that, the wave velocities become lateral variations which close to constants when the incident angles are large enough. The corresponding responses to these facts are shown in frequency domain as instantaneous dominant frequency and spectral bandwidth increase or decrease, different dominant frequency and spectral bandwidth locations and their amplitudes variations with the increase of source-receiver distance. When the nonlinear layer which has weak nonlinearity is thin and far away from the seismic source which has low energy, compared with the corresponding results in linear media, the media nonlinearity produces about 1/10~1/4 and 1/10~1/3 differences of instantaneous dominant frequency and spectral bandwidth. These instantaneous feature differences of seismic waves induced by the nonlinearity of media become weaker and weaker with the decrease of source energy. However with the increase of the seismic wave travel path within the nonlinear layer, the nonlinear accumulation effect could still keep such facts as the waveform distortion and instantaneous dominant frequency and spectral bandwidth variations obvious in records.