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全波形反演不仅利用相位和振幅信息,还利用波形的细节变化,具有刻画模型精确细节的能力.在对稀疏矩阵直接LU分解求解的基础上,采用梯度预处理方法对声波介质速度模型进行了反射波全波形反演.采用误差反向传播算法计算目标函数梯度以及伪Hessian矩阵的对角线元素来做梯度预处理.数值模型的实验结果表明,利用有效的频率段便能反演出分辨率较高的速度结构,用低频反演出的结果作为高频反演的初始模型,减少了解的非唯一性.二维高斯光滑初始模型提供了有利的低频信息,得到较好的反演结果.伪Hessian矩阵的预处理吸收了高斯牛顿法的二次收敛优势,在不增加计算量的前提下,加快收敛速度.
Full waveform inversion not only utilizes the phase and amplitude information, but also utilizes the detail changes of waveforms and has the ability to depict the exact details of the model.On the basis of solving the direct LU decomposition of sparse matrix, the gradient media pretreatment method is applied to the acoustic media velocity model Reflected wave full waveform inversion.An error backpropagation algorithm is used to calculate the gradient of the objective function gradient and the pseudo-Hessian matrix diagonal elements to do the gradient preprocessing.Experimental results of the numerical model show that using the effective frequency segment can reverse the resolution The higher velocity structure, the result of low-frequency inversion is used as the initial model of high-frequency inversion to reduce the non-uniqueness of the solution.The two-dimensional Gaussian smooth initial model provides favorable low-frequency information and obtains better inversion results. The preprocessing of Hessian matrix absorbs the quadratic convergence advantage of Gauss Newton method, and accelerates the convergence speed without increasing the computational complexity.