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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.
In this paper, the angular velocity full-waveform velocity inversion is studied in the time domain based on the two-dimensional acoustic wave equation. Since the gradient corresponding to different subsurface reflection angles has the multi-scale frequency, during each frequency inversion, the full waveform inversion The gradient of angle domain decomposition is also decomposed into angle domain gradient of different angle range.Comparing the gradient of different angle range with different frequency shows that the vertical wavenumber of gradient is consistent at different frequencies with different angles, Small-angle gradient can be consistent in the vertical wavenumber range.Having been using the large-angle to small-angle gradient inversion, the multi-scale inversion of the angle domain is realized under the condition of unchanged data frequency.At the same time, the shallow layer Super-high-angle (> 80 °) gradients facilitate the accurate characterization of shallow velocity detail, while deep-gradient partial reflectances are relatively small and therefore do not affect deep velocity inversion.