Research On Staggered Grid Finite Difference Numerical Simulation Method With Variable Grid

As a common geophysical research method,seismic wave equation forward modeling has been widely studied in recent years.As the traditional simple structure of oil and gas exploration and development areas are gradually found,oil and gas exploration needs to advance to more sophisticated,more complex and deeper areas,so simulation methods with higher accuracy and resolution are required.The finite difference method is widely used in the numerical simulation of seismic wave equation because of its simple and intuitive mathematical principle and mature algorithm.In order to avoid the over-sampling of the high-speed region caused by fine grid,to ensure the computational accuracy of the low-speed region in the simulation region,and to improve the computational efficiency and save memory,the finite difference method with variable grid system is used in the numerical simulation in this paper.That is to say,the simulated area is divided into different grid sizes.In the low-speed area,a thinner spatial grid size is adopted,while in the high-speed area,a coarser spatial grid size is increased by a proportional factor.Different from the traditional interpolation method in which the changing grid directly interpolates the changing grid area,this paper adopts the viewpoint of energy conservation to characterize the energy of the entire simulation area,so as to ensure the energy conservation in the simulation process and find the conditions to be satisfied by the interpolation points.This method not only supports the theory of physics,but also guarantees the stability.Based on the previous algorithms,this paper studies this method and deduces the implementation process of energy conservation interpolation in detail.In this paper,the finite difference variable-grid forward modeling method of energy conservation interpolation is tested,and the model tests of one-dimensional medium,and threedimensional medium are carried out respectively.The energy and wave field snapshot in the simulation are characterized.The results show that compared with the traditional interpolation method,the finite difference forward simulation of energy conservation interpolation method can ensure the energy conservation in the process of propagation,satisfy the basic physical laws,and have good convergence.In the end,this paper concludes that compared with the traditional direct interpolation method,the energy conservation method is more in line with the laws of physics in theory,and the research on its accuracy is not limited to the results of numerical simulation,but rises to the theoretical height.Its convergence and accuracy are better than traditional methods.