Wave Field Numerical Simulation Of High-order Finite Difference With Variable Grid

Seismic wave field numerical simulation is one of the important research contents of exploration seismology.High precision and efficiency numerical simulation is an important means to study the fluctuation phenomenon and plays an important role in the exploration and development of oil and gas reservoirs.With the gradual development of oil and gas exploration,the focus of seismic exploration has shifted from the shallow middle-level and the simple rough structure to the deep complex heterogeneous structure.In this case,it is very important to accurately calculate these fine(low-velocity)rock formations and ensure the efficiency of the entire simulation.For conventional finite difference method,the whole simulation region is divided into the same size grid.In order to calculate this fine rock formation,it is necessary to divide the entire simulation area with smaller meshes to reduce numerical dispersion and improve simulation accuracy.In this way,the number of sampling points at each wave increases when the wave field is calculated,which will inevitably increase the amount of calculation and reduce the simulation efficiency.Therefore,it is necessary to develop a more flexible method of seismic wave numerical simulation for complex geological structure.In this paper,the high-order finite-difference algorithm based on the conventional(staggered)mesh of the acoustic wave equation is studied.The stability and numerical dispersion of finite difference forward modeling are analyzed.There is a contradiction between the numerical dispersion and the simulation efficiency in the numerical simulation of the finite difference based on the conventional grid.A variable-step staggered grid finite difference algorithm is proposed.According to the change of the velocity of the medium,the area is divided by grids of different sizes,and then the staggered grid algorithm is used to calculate the wave field value.For the grid transition region during calculation,the wavefield difference formula is deduced through the change of the step size of the specified boundary grid.Wave field calculation for all transition zone grid points in a cycle,the stable transition of the simulation area from the large(small)grid to the small(large)grid is realized.Artificial boundary problem introduced for computer numerical simulation,Contrastive analysis through the multiple transmitting boundary condition,Clayton and the perfectly matched layer(PML)absorption boundary condition,it has been found that using the PML boundary conditions for numerical simulation of wavefields has high calculation efficiency and good effect on boundary reflection absorption.Finally,the numerical simulation of wave field is carried out by establishing different medium model,compared with the conventional(staggered)grid algorithm from three aspects of simulation precision,calculation efficiency and memory demand.The resultsshow that variable step staggered grid algorithm is superior to conventional(staggered)grid algorithms in computational efficiency,simulation accuracy,etc.The research content of thispaper lays a solid theoretical and technical foundation for the follow-up seismic exploration work and seismic inversion research.