Acoustic Wave Equations In Viscoelastic Media And Their Finite Difference Numerical Simulations

Forward modeling based on inversion and the result of forward modeling effects on the other work directly. Theoretically, there is no energy reduce when seismic wave propagation in elastic medium. But, actually, stratum is more close to the viscoelastic medium and the part of viscous factor will make the energy dissipation. In this thesis, we researched from the relative easily acoustic, introduced the acoustic wave equation in viscoelastic medium and did the numerical simulation of the finite difference method for the forward modeling.In this thesis, firstly, we started from the basic concept of viscoelastic medium, introduced some common viscoelastic medium model. We analyzed these models about the viscous part and deduced the wave equation in viscoelastic medium. Then, the thesis introduced common finite difference scheme and the core idea and difference scheme of nearly analytic discrete method. In the end, the nearly analytic discrete method was used into the acoustic wave equation in viscoelastic medium, the writer analyzed the stability of this method in different quality factor, and added the boundary of convolutional perfectly matched layer to this method in viscoelastic medium, which achieved a promising result. The amplitude attenuation of acoustic wave was researched in different quality factor. Through the trial of layered speed model and complex speed model, it demonstrated that this method id feasibility and we get a reliable conclusion and cognition.This method can effectively reduce the use of computer memory and possession of resources. It had little numerical dispersions when coarse grids are used, so that large operation time can be saved effectively and we can compute large-scale numerical simulation about forward modeling in viscoelastic media.