线性黏弹性介质中波动方程的反散射解

Inverse scattering solution of wave equation in linear viscoelastic medium

针对线性动弹性介质中的均匀波情况，我们通过小波变换，探讨了零炮检距、常背景速度情况下三维波动方程反散射问题的求解。在能量吸收比较小的假设下，利用此法可得到两套及演速度扰动函数和反射函数的公式。这些公式适合于讨论常规地震资料的反演问题。在资料的上限频率不高时，介质的黏滞性将导致地震波发生一个常数的相位延迟。

By making wavelet transform,we research into the inverse scattering solution of 3D wave equation of homogeneous wave in linear viscoelastic medium in the case of zero offset and constant background velocity. Two sets of inverse formula of velocity perturbation and reflection functions are deduced under the hypothesis of small energy absorption. The formulae can be used to discuss the inversion of conventional seismic data. The viscoelasticity of a medium makes seismic wave have a constant phase delay when upper-limit frequency of the data is not high.