Forward Modeling Of Acoustic And Viscoacoustic Wave Based On The Lattice Boltzmann Method

At present,geophysicists usually use the finite difference method and the finite element method to study the propagation of underground seismic waves.These methods are based on macroscopic hypothesis using the wave equation or its simplified form.The wave equation or its simplified form has many approximate conditions,and may lead to relatively large computational errors.In order to reduce the error,geophysicist had proposed a completely different seismic wave forward modeling method: the lattice Boltzmann method(LBM).The lattice Boltzmann method has already had a great mature application and achievement in hydrodynamics.Lattice Boltzmann method is a microscopic continuous and macroscopically discrete method.The method simulates the motion and interaction of particles on a discrete grid(migration,collision,transmission,reflection,etc.)from a microscopic point of view,then shows the state of macroscopic media based on the distribution of a large number of microscopic particles.This paper attempts to apply this method to the forward modeling of seismic waves.In this paper,the development of the lattice Boltzmann method is briefly described,then some numerical simulations are carried out,and the absorption boundary of the method is also studied.In order to verify the correctness of the lattice Boltzmann method,this paper also uses the lattice Boltzmann method and finite difference method for numerical experiment simulation,and compares the similarities and differences between their results.In this paper,we build the connection between the lattice Boltzmann method and the finite difference method based on the wave equation.Compared with the traditional method,the lattice Boltzmann method has the following advantages: the clear physical meaning,easily handled boundary conditions,easy parallel and so on.