地震波形多尺度反演的一点讨论

基于在反演过程中对初始模型依赖性强、易陷入局部极值等问题，本文引入小波分析，提出多尺度地震波形反演方法，从而将参数反演问题转化到小波域中重要系数优化问题。利用多尺度之间的内在联系及小波域中重要系数的稀疏性，有将改进了局部极值、计算量等问题。并对几种多尺度反演策略进行了比较讨论。基于波动方程正演及褶积模型的两种反演方法的数值实便结果显示了本方法良好的效果。

A DISCUSSION ABOUT MUTLISCALE SEISMIC WAVEFORM INVERSION

Due to the problem that the presence of numerous local minimum and the dependence on initial model mentioned in paper 1] , the method of multiscale seismic waveform by wavelet transform is proposed in this paper. Different from the traditional inversion methods which process optimization parameters in physical space or frequency domain, multiscale inversion aims to decompose the problem into scale sequence and performing the calculations based on the significant coefficients. The calculation amount and local minimum are reduced taking advantage of sparseness of significant coefficients by wavelet transform. Due to the multiscale method combined with a spatial relativity, a numerical algorithm based on wavelet decomposition can be thought to offer an interesting compromise between precision, efficiency. Several multiscale inversion strategies are comparatively discussed. Numerical results show that the two methods respective basis on wave equation and convolution model is good efficient.