Study And Application Of High-Precision Finite Difference Numerical Simulation Method Based On Gradient Operator

The numerical simulation of seismic wave propagation is a method of seismic wave prediction through numerical calculation.It is a tool and a means that can play an important role in all aspects of seismological research and seismic exploration,and is integrated in seismic acquisition,processing and interpretation Under the trend,the quality of seismic data processing and the correctness of geological interpretation often depend on the knowledge of seismic wave propagation characteristics.Therefore,it is extremely important to study stable and efficient numerical simulation methods.In this paper,based on the analysis of the transformation process from the elastic wave equation to the acoustic wave equation,the derivation of the gradient operator into the solution of the wave field equation is derived,and the approximate analytical discretization(NAD)algorithm of the acoustic wave equation is obtained.The NAD algorithm is based on the traditional difference method and uses the displacement value of the node to approximate the spatial high-order partial derivative of the node.When reconstructing the wave field,the effect of the gradient reflecting the change trend of the function is fully considered,and the gradient is used in the construction of the difference format.And displacement together to reconstruct the wave field of the next time layer,with fewer grid points,to obtain higher numerical accuracy and stability.The NAD algorithm can effectively suppress numerical dispersion,and accurate amplitude and phase information can also be obtained in large space steps.Also with the same numerical simulation accuracy,the NAD algorithm can use a coarse grid to obtain accurate simulation results,so the introduction of gradient operators makes the storage required for the calculation smaller and more efficient.Based on the NAD algorithm,programming simulation of the collapse column model of the complex structure of the coal field,analysis of single shot records,trace records and wave field snapshots of the model.Model testing shows that the NAD algorithm can effectively suppress numerical dispersion,improve numerical simulation accuracy,and improve computational efficiency.It is a forward method with great research value and significance.