Study Of Numerical Simulation Of Wave Equation With Finite Element Method And Well To Seismic Calibration

The forward modeling of wave equation plays a very important role in seismic data acquisition,processing and interpretation.In order to accurately simulate the propagation of seismic wave in underground medium,not only requiring geophysical model established is consistent with the actual formation,but also needing high precision numerical simulation method.Both finite difference method(FDM)and finite element method(FEM)are the very important methods in the numerical simulation of wave equation.Finite difference method is widely studied and applied because of its simple computer programming and high calculation efficiency,but can not accurately simulate the propagation of seismic wave in complex media,so it has too many problems to deal with in fine seismic exploration.Finite element method can divide arbitrary complex boundary effectively with flexible mesh,and it can accurately simulate the propagation of seismic wave in complex media,in addition,a variety of interpolation functions can provide the simulation results with different numerical precision.In this paper,a series of studies have been done for FEM.Firstly,explaining the basic theory of finite element method for solving wave equation,and studying the propagation characteristics of seismic wave in linear triangular element,linear rectangualar element,linear arbitrary quadrilateral element,bi-quadratic rectangular element,respectively,and then employing “compact storage format” to store structure stiffness matrix,so that the computational efficiency and memory occupation within an acceptable range,finally,the numerical dispersion and stability of seismic wave in rectangular and triangular grid are mainly studied,to provide the basic theory for the selection of mass matrix and element.In the process of well to seismic calibration,the conventional method for scale matching between acoustic log data and seismic data may result in losing the local information of acoustic log data,besides that,the consistency of synthetic seismograms based on convolution model and seismic trace nearby well is not vert high.In the previous issue,we employ the principle of minimum speed deviation and minimum thickness to stratify acoustic log data before depth-time conversion,stratified parameters are determined by the specific objective layer,seismic sampling interval and minimum two-way travel time,respectively.On the latter problem,we employ the wave equation to make synthetic seismogram,which considers the formation mechanism of wave field and the effect of seismic data procrssing on event.