The Application Of The High-order Difference Numerical Simulation To Elastic Wave Equation Of Seismic Wave Propagation

Elastic wave equation of seismic wave propagation is a equation which is widely used,particularly, it plays an important role in the exploration of geological and important naturalresources such as minerals, oil and gas. Thus the numerical simulation of seismic wavepropagation in the exploration of oil and natural gas research has attracted more and moreattention, it is very important for the research of seismic wave transmission mechanism andwave field imaging. The simulation is very conductive to the data collection and processing aswell as the examination of imaging method and the research of multi-wave exploration. Thefinite difference method is a very important method in seismic wave numerical simulation.Itis of such advantages with the speciality of accuracy, simple differential forms and strongadaptability.At present,exploration technology has begun to be used in the areas of complex structureand undulating surface, so better methods with more accuracy are needed by the complexityof geological structure to simulate the regulation of the real underground wave fieldpropagation. In order to explore the numerical simulation method with more adaptability andmore accuracy, the dissertation applies the method of the high-order finite difference tosimulate seismic wave on the basis of previous studies. The main tasks and achievements asfollows:Firstly, the high-order difference equations were derived from different equations whichincluded the second-order displacement equation and the first-order stress-velocity equations.Secondly, according to the different equation form, this dissertation used differentboundary conditions.The general form and high-order difference form of the transmissionboundary conditions(Liao Zhenpeng boundary conditions) and completely matched layerabsorbing boundary conditions(PML) have been deduced in this dissertation.Meanwhile, the dissertation analyzed and discussed the factors of the source, frequencydispersion and stability. The numerical frequency dispersion formula which is related to thesecond-order displacement wave equations have also been deduced and analysed.Finally, the dissertation achieved the numerical simulation and boundary conditions of the second-order displacement equation and the first-order stress-velocity equations, and theresults show that the infinite difference method of high-order can accurately simulate theseismic wave in the propagation of different kinds of media.