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在用稀疏矩阵的LU分解技术对频率域粘弹性声波方程进行直接求解的基础上,根据失配函数二范数最小准则,用预条件梯度类方法对粘弹性声波介质的速度结构进行了逐频反演.局部非均匀介质模型和层状介质模型速度结构反演的实验结果表明,不同频率能够反映地下介质的多尺度物性结构(低频数据对应与介质物性的大尺度结构),用低频反演结果作为高频反演的初值逼近这一顺序模式,能大大改善反演过程中解的非唯一性.而且,在反演过程中用Hess矩阵的对角线元素来做梯度类方法的预条件算子,能够吸收了高斯牛顿法的二次收敛优势,使得本文算法具有较快的收敛速度.
Based on the LU decomposition technique of sparse matrix, the velocity structure of viscoelastic acoustic wave was solved by the preconditioned gradient method based on the minimum norm of mismatch function and the minimum norm of mismatch function The frequency inversion results show that different frequencies can reflect the multi-scale physical structure of underground media (low-frequency data corresponds to the large-scale structure of medium properties), and the low-frequency inversion As the initial value of high-frequency inversion approximates this order model, the result of the inversion can greatly improve the non-uniqueness of the solution in the inversion process. Moreover, using the diagonal elements of the Hess matrix as the gradient method in the inversion process The precondition operator can absorb the quadratic convergence advantage of Gauss Newton method and make the algorithm of this paper have faster convergence speed.