角度域全波形反演研究

Research on angle domain full waveform inversion

本文基于二维声波方程在时间域研究了角度域全波形速度反演,由于不同地下反射角对应的梯度具有频率的多尺度性,在每个主频反演过程中,可以将全波形反演的梯度也进行角度域分解,分解为不同角度范围的角度域梯度.对比不同频率不同角度范围的梯度,表明梯度的垂向波数在不同频率不同角度具有一致性,即高频大角度梯度与低频小角度梯度可在垂向上波数范围一致.先后利用大角度到小角度梯度进行反演,在数据主频不变的情况下,实现角度域多尺度反演.同时,反演过程中去掉浅层超大角度(>80°)的梯度,有利于浅层速度细节准确刻画,而深层梯度局部反射角相对较小,因此不会对深层速度反演产生影响.

Angle domain full waveform inversion is investigated based on two dimensional acoustic wave equation in this paper. For the multi-scale characteristic of gradient from different range of local reflecting angle in the subsurface,for each dominant frequency,gradient is further decomposed into subsets according to local reflecting angle and then inversion is accomplished separately in sequence from large to small angle range. Comparing gradients of different local reflecting angles,vertical wavenumber of gradients shares consistency with each other,namely vertical wavenumber between gradient of large local reflecting angle by higher dominant frequency data and small local reflecting angle by lower dominant frequency data can be approximately the same. Further multi-scale inversion is realized by utilizing gradient with angle from large to small for data of certain dominant frequency. Furthermore,shallow details of the velocity can be better recovered by eliminating gradients of super large angle（〉 80°）. Because of the fact that local reflecting angle in deep stratum is relatively smaller,gradient elimination of super large angle will not affect velocity inversion.