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

ZHENG Hai-Shan,ZHANG Zhong-Jie,TIAN Xiao-BoInstitute of Geology and Geophysics,Chinese Academy of Sciences,Beijing 100029,China  
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 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 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.
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