Efficient solution of large-scale matrix of acoustic wave equations in 3D frequency domain

In 3D frequency domain seismic forward and inversion calculation,the huge amount of calculation and storage is one of the main factors that restrict the processing speed and calculation efficiency.The frequency domain finite-difference forward simulation algorithm based on the acoustic wave equation establishes a large bandwidth complex matrix according to the discretized acoustic wave equation,and then the frequency domain wave field value is obtained by solving the matrix equation.In this study,the predecessor's optimized five-point method is extended to a 3D seven-point finite-difference scheme,and then a perfectly matched layer absorbing boundary condition(PML)is added to establish the corresponding matrix equation.In order to solve the complex matrix,we transform it to the equivalent real number domain to expand the solvable range of the matrix,and establish two objective functions to transform the matrix solving problem into an optimization problem that can be solved using gradient methods,and then use conjugate gradient algorithm to solve the problem.Previous studies have shown that in the conjugate gradient algorithm,the product of the matrix and the vector is the main factor that affects the calculation efficiency.Therefore,this study proposes a method that transform bandwidth matrix and vector product problem into some equivalent vector and vector product algorithm,thereby reducing the amount of calculation and storage.

Seismic hazard analysis of Tianjin area based on strong ground motion prediction

Taking Tianjin as an example,this paper proposed a methodology and process for evaluating near-fault strong ground motions from future earthquakes to mitigate earthquake damage for the metropolitan area and important engineering structures.The result of strong ground motion was predicted for Tianjin main faults by the hybrid method which mainly consists of 3D finite difference method and stochastic Green's function.Simulation is performed for 3D structures of Tianjin region and characterized asperity models.The characterized asperity model describing source heterogeneity is introduced following the fault information from the project of Tianjin Active Faults and Seismic Hazard Assessment.We simulated the worst case that two earthquakes separately occur.The results indicate that the fault position,rupture process and the sedimentary deposits of the basin significantly affect amplification of the simulated ground motion.Our results also demonstrate the possibility of practical simulating wave propagation including basin induced surface waves in broad frequency-band,for seismic hazard analysis near the fault from future earthquakes in urbanized areas.