采用混合共轭梯度迭代的频域地震数值模拟

Frequency-domain seismic numerical modeling by applying hybrid conjugate gradient iteration

当前频率域地震数值模拟中的时谐波动方程求解通常采用LU直接分解法或Krylov子空间迭代法。直接分解法占用内存大,耗费时间长,且难以模拟高维度、高密度地震采集;一般的Krylov子空间迭代法收敛速度较慢,在处理复杂模型时可能会出现不收敛的情况。为此,在现有共轭梯度类算法的基础上发展了一种优化的Krylov子空间法——混合共轭梯度算法,用于求解时谐波动方程。层状介质模型和标准模型的数值模拟结果表明:与LU直接法相比,新方法在保证模拟精度的前提下,可有效降低内存需要、减少计算用时;与双共轭梯度稳定迭代法相比,在处理复杂模型时具有更高的计算稳定性。

At present,LU decomposition method or the Krylov subspace iteration method is usually used to solve the time-harmonic wave equation in frequency-domain seismic modeling.The direct decomposition method takes up a lot of memory and is timeconsuming,and it can hardly simulate high-dimension,large-density seismic acquisition.The general Krylov subspace iteration method,however,converges slowly and may not converge while dealing with complex models.On the basis of the existing conjugate gradient algorithms,an optimized Krylov subspace method-the hybrid conjugate gradient algorithm,is developed to solve time-harmonic wave equations.The numerical simulations of the layered medium model and the standard model indicate that compared with LU decomposition method,the proposed method can effectively reduce the memory requirement and calculation time on the premise of ensuring accuracy.Compared with the stable bi-conjugate gradient iteration method,it has better computational stability in dealing with complex models.