The Application Of The Dynamic Lattice Method In Seismic Wave Simulation In Anisotropic Media

Exploring the properties of the geological materials and the structures underneath is one of the main research areas of geophysics.The seismic waves that propagate in the geological materials provide us with important information regarding to the status of the underground media.Investigating the seismic waves in various kinds of geological materials allows us to fully make use of the seismic signal.As the investigation goes on,we come to know that the anisotropy widely exists in the actual media.It is necessary to take the anisotropy into account when processing the seismic data otherwise it will lead to inaccuracy or even fatal error.As a result,we need plenty of tools to simulate the seismic wave propagation in the anisotropic media.Basing on the continuum mechanics,the wave equation mathematically describes seismic waves.However,analytical solution only applies to a few simple cases,thus the seismic wave simulations are mainly carried out by numerical methods which give approximate solutions to the wave equation.Different from the wave-equation-based methods,another type of numerical methods are also built to simulate the dynamics of the geological materials.These methods discretize the media into the so called discrete particle models in which particles interact with each other;and use the discrete particle model to simulate the dynamic behaviors of the geological materials.Apart from seismic wave simulation,these particle based methods are implemented in simulating other material behaviors such as deformation and fracturing.For this reason,this type of numerical methods have a boarder application.In terms of seismic wave simulation,former particle based methods all focus on isotropic media.In this article,a new particle based method called the dynamic lattice method is brought up to simulate seismic wave propagation in anisotropic media.In order to achieve anisotropic wave simulation,this article builds several anisotropic particle lattice models in both 2-dimensional and 3-dimensional cases;and the relation between the parameters that describe the elastic properties of these lattice models and those of the continuum models are fully analyzed.The dynamic lattice method calculates the dynamics of the particles in the lattice models and uses the displacements of the particles to simulate the seismic waves that propagates in the anisotropic media.The phase velocity dispersion in the particle lattice model is also analyzed in this article.According to the dispersion analysis,the high-order lattice model which includes non-adjacent particle interactions is built to suppress the dispersion in the lattice model.Basing on the high-order lattice model,this article establishes the high-order dynamic lattice method.Numerical tests show that this method can be used to simulate seismic wave propagation in anisotropic media.This article lays the theoretical foundation of the dynamic lattice method and shows the numerical examples of this method on seismic wave simulation in anisotropic media.