2D FDM Simulation Of Seismic Oscillation In Local Terrain

Wave motion is an important physical form in nature.When the elastic wave is propagating in medium,its characteristics change with the variation of media's geometric and physical properties.In the exploration of geology,oil and gas,the elastic wave theory is commonly used for reconstructing the properties of underground medium.There are several approaches to solve elastic wave equation,such as FDM,FEM and the spectral element method.FDM is one of the most commonly used numerical schemes to solve the hyperbolic partial differential equation.The complete information of elastic wave field can be obtained by using the elastic wave equation's differential operators approximated with the finite difference grid.The program of finite difference method has high computational effect,and is simply to implement.Based on the finite difference formulation of the elastic wave equation obtained through finite difference method and the discrete form of the initial,boundary and absorbing boundaries,the numerical solution of the elastic wave equation can be simulated.The mainly contents are listed as follows:The finite difference formulation of 2D wave equation is derived by the finite difference method with regular grid.Under the stability condition,the initial,boundary and absorbing boundaries are written as discrete forms for constructing the finite difference equations of wave motion problem.A FDM program package for elastic wave motion problem is developed.Considering the complex shapes of free surface,the geometric parameters can be input automatically into the program based on the true geometry for solving the seismic wave problem in the real complex terrain.The partial terrain of Mount Lu is simulated by the FDM program to obtain the time history of its displacement,velocity and acceleration.Then,the influence of topography on seismic waves and dynamic response on free surface are analyzed.And,the effect of different hypocenter depths on propagation of seismic wave on the surface is observed.At last,the influence of different terrain on seismic wave propagation is discussed for making reference to real life.