Research On Forward Simulation Methods Of Seismic Wave Fields In Complex Mediums

As a key part of Full Waveform Inversion,geophysical scholars attach more and more importance to the forward modeling of seismic wave fields in recent years.The status of forward modeling of seismic wave fields become more and more important,the maturing forward modeling technology also makes Full Waveform Inversion in the application of seismic exploration becomes more and more possible.There are many methods of forward modeling of seismic wave fields,usually it could be divided into three caregories--wave equation method,integral method and geometric ray method.In this thesis,we start from the wave equation method,based on the seismic wave field of complex media,we compare and analyse the advantages and disadvantages of several wave field forward modeling methods,and research a series of questions of finite-difference method thoroughly,we give the process of analysis and the summary of of the results.At last,we propose some effective improvement programs that can be implemented for potential problems.Research and results achieved in the final of this thesis are:1.From the perspective of solid mechanics, we analysis the seismic medium model that used in this thesis-- acoustic medium model, the focal point of our research is the characters of acoustic medium model, besides,an exhaustive derivation of acoustic wave equation is given.2.The principles of the finite-difference method and give the corresponding flow chart are mainly researched in this thesis.In addition,the formulas of the finite-difference method that based on Taylor formula and some other mathematical methods is derivated. We research the rules and processes of grid meshing of regular grid and staggered grid, and then select three kinds of complex medium models to simulate, by comparing and analyzing the results, some major problems are found when using the finite-difference method to implement the wave equation forward modeling.3.Another two different kinds of the forward modeling numerical methods that based on wave equation--finite element method and pseudospectral method are researched in this thesis.From the development process and basic principles of these two methods, we compare them with the finite-difference method to identify their own advantages and disadvantages.4.Two key issues of the wave equation finite-difference forward modeling are researched thoroughly in this thesis--the boundary condition and numerical dispersion.Calculated by the models, we compare and analyze of the two different kinds of boundary conditions--Clayton boundary and Perfectly Matched Layer,and finally find a very appropriate boundary condition.It is not only economize the costs of calculating,but also has a nice graphic effects.Apart from this,we analyze numerical dispersion and the cause of it in detail in theory.Further,we eliminate numerical dispersion well by improving the differential accuracy and using the Flux Corrected Transport technology.Then we propose an optimized technology of Flux Corrected Transport,we test and verify the correctness and effectiveness of this method by model calculating.At last,we use Perfectly Matched Layer and the optimized technology of Flux Corrected Transport to complete the forward simulation of three different kinds of complex mediums,and get good results.