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频率域全波形反演虽然克服了时间方向上的局部极小值问题,但是地下介质的复杂性使其在空间域仍然存在局部极小值缺陷。在优化梯度法基础上,本文采用预条件双共轭梯度稳定算法和多重网格方法计算反演中的波场传播和目标函数的梯度,在保证计算速度的同时,减小计算机内存的消耗。频率域波形反演和多重网格的多尺度性质有效改善问题极小值缺陷,加快反演的收敛速度。以局部非均匀的三孔模型和Marmousi模型的数值模拟结果验证了该算法的有效性。
Although full-waveform inversion in frequency domain overcomes the problem of local minima in time domain, the complexity of underground media makes it still exist local minima in space domain. Based on the optimized gradient method, the preconditioned bi-conjugate gradient stabilization algorithm and multi-grid method are used to calculate the wave field propagation and the gradient of the objective function in the inversion, which can reduce the computer memory consumption while ensuring the computing speed. Frequency domain waveform inversion and multiscale nature of multiple grids effectively reduce the minimum defects of the problem and speed up the convergence of the inversion. The effectiveness of this algorithm is verified by the numerical simulation of the locally non-uniform three-hole model and the Marmousi model.