VTI介质中非线性对地震波频率和频宽变化的约束

Constraints of the nonlinearity in VTI media on seismic wave frequency and bandwidth changes

采用改进型FCT有限差分法分别模拟各向同性、具有垂直对称轴的横向各向同性（VTI）以及非线性VTI介质中地震波场,随后采用小波分析探讨VTI介质中非线性对地震波频率和频宽变化的约束.数值模拟及分析结果表明：介质各向异性会引发地震记录中各波型的能量随炮检距的变化,而介质各向异性与非线性的耦合作用则会进一步加剧这种变化.在遵守能量守恒原理的前提下,介质的非线性会引发地震波场中各波型间能量的再分配.同时还会引发地震波速度的波动,且随着入射角的增大,波动幅度变小.这些现象在频率域内的响应表现为主频和频宽的降低或增大、地震记录中与各波型相对应的瞬时主频和频宽峰值出现时刻的偏移以及它们随炮检距变化而表现出的幅值波动.在本文给定的弱非线性介质中（非线性炽较薄且远离震源）,在震源能量较低的情况下,介质的非线性效应会造成地震波瞬时主频和频宽相对于线性介质情况分别为1/10～1/4和1/10～1/3左右的变化量.此外,随着入射波能量的下降,介质非线性所造成的地震波瞬时特征（振幅、主频、频宽）的变化量减小,但随着地震波在穿越非线性介质时路径的加长,非线性作用的累积效应使得波形畸变和频率分布特征的变化（尤其是频宽）等现象得以维持.

Using the finite difference method （FDM） with a transformed FCT technique, we get the numerical seismic records corresponding to isotropic, VTI and nonlinear VTI media, respectively. Then, wavelet transform is adopted to calculate and analyze seismic wave frequency and bandwidth changes induced by the nonlinearity in VTI media. In seismic records, we found that the energy of different modes of seismic waves vary with the increase of source-receiver distance because of medium anisotropy, especially, these variations will be enlarged by the combination effect of medium anisotropy and nonlinearity. Namely, because of medium nonlinearity, the energy of different modes of seismic waves is reassigned and displayed in records but fits the energy conservation law. Companying with that, the wave velocities have lateral variations which close to constants when the incident angles are large enough. The corresponding responses to these facts appear in the frequency domain as instantaneous dominant frequency and bandwidth increase or decrease, different dominant frequency and bandwidth locations and their amplitude variations with the increase of souree-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 medium nonlinearity produces about 1/10 - 1/4 and 1/10 - 1/3 differences of instantaneous dominant frequency and 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 phenomena as the waveform distortion and instantaneous dominant frequency and bandwidth variations in records.