Research On Finite Difference Numerical Simulation Method Based On GPU Acceleration

Numerical simulation of seismic wave field is not only an important foundation of seismology,but also an important research direction in seismic exploration.It can also provide theoretical basis for seismic data acquisition,data processing and interpretation in complex areas.With the increasing difficulty of seismic exploration,the propagation and characteristics of seismic waves in different media can be studied through numerical simulation of seismic wave fields.The finite difference method is an approximate data solution that directly converts the differential problem into an algebraic problem with high accuracy.It is the most widely used method in the field of numerical simulation and plays an important role in the field of numerical simulation of seismic wave fields.Different geological structures will produce different seismic wavefields.Therefore,it is of great significance to study the propagation of seismic waves of different structural models by using the theory of finite difference numerical simulation method.In this paper,the finite difference method is used to simulate the propagation of elastic waves in two dimensional isotropic media.First,the second order motion equation and the first order velocity-stress equation of elastic waves are derived.Based on these equations,the difference schemes of higher order conventional leshes and high order staggered grids are derived,and the corresponding difference coefficients are given.The factors influencing the stability and dispersion of finite difference are analyzed,and the corresponding solutions are put forward.I The boundary conditions of seismic numerical simulation are studied,the Higdon absorbing boundary and PML absorbing boundary are studied emphatically,the expressions of first and second order Higdon boundary and PML boundary are derived,and their absorption effccts are compared by model calculation.It is concluded that the absorption effect of PML is relatively good.In order to analyze the propagation law of elastic waves in isotropic media,the fracture model,the pore model and the Corner-edge model are established,and the PML absorbing boundary is added to the iinite difference numerical simulation of high order staggered meshes.By analyzing the wave field snapshots and the simulated records of each model at different times,the following conclusions are drawn:The transverse wave and the longitudinal wave produce refleeted wave field and transmitted wave field at the interfacc,the diffraction wave field generated by the crack is similar to the scattered wave field generated by the holes,and the diffraction waves generated by the plurality of cracks are mutually excited sources,so that the diffraction waves are continuously formed,and the wave fields are mutually superposed and interfered,so that more complex wave fields are generated,and the multi-hole model generation wave field is also very complex;the greater the density between cracks or holes,the stronger the energy of wave fields they produce,which can be used to determine the density of underground cracks or holes.In the Corner-edge model,the reflected waves,transmission waves,cross-section reflection waves,converted waves of the interface and Diffraction wave at the corner of the interface can be seen.In the seismic wave numerical simulation of large-scale models,in order to save storage space and computing time,GPU and corresponding CUDA programming make multi-thread parallelism be applied to the numerical simulation of seismic wave field.This paper mainly introduces the structure of GPU,gives the basic mode of CUDA programming,and analyzes the acceleration effect and calculation precision of GPU through the trial calculation of the model from simple to complex.By comparing the results of CPU and GPU,it is concluded that the results accelerated by GPU are consistent with those of CPU.And as the model space becomes thinner and the order of the finite difference increases,the required computing time increases,and the acceleration effect of the GPU becomes more pronounced.Therefore,parallel acceleration with GPU can not only guarantee the calculation accuracy,but also save computing time greatly.