Staggered Grid Finite-difference Numerical Simulation Of Seismic Wave In Viscoelastic Media

With the rapid development of oil and gas industry in China, The precision anddifficulty of oil and gas exploration are increasing. This requires that we mustunderstand the propagation rules of seismic wave in the underground medium clearly.Seismic numerical simulation technology is an important means which is used tostudy seismic wave propagation rules in the field of seismic exploration. In traditionalseismic wave numerical simulation technology, we usually suppose that the earthmedia is homogeneous and completely elastic. Under the condition of this assumption,the theoretical research results are very different with real results. The reason is thatwhen the seismic wave propagates in real formation, the viscosity of formation causethe loss of seismic wave energy. And in the deeper formation the loss is more serious.This anelastic behavior of real earth media can be described well by a viscoelasticmodel．In this paper，the numerical simulation method of viscoelastic model and the lawof attenuation about seismic wave were mainly researched and studied．The researchcontents and results mainly includes the following aspects:1. On the basic properties of viscoelastic medium, three common viscoelastic mediummodels are constructed and their constitutive equation is presented. In this paper,several absorption and attenuation parameters of seismic wave and their mutualrelationship are analyzed in detail.2. Based on the theory of seismic wave, the regular grid and high order staggered gridfinite difference methods are deduced and several problems in the seismic wavenumerical simulation are discussed, such as seismic source, the stability conditionanalysis and the selection of absorption boundary conditions, etc.3. In this paper，absorption and attenuation of seismic wave in viscoelastic media havebeen analyzed from the theory through viscoelastic wave equation which were derived from the basic concept of viscoelastic media．The elastic wave equation inviscoelastic media was solved by high order staggered grid finite differencemethods，which achieved the numerical simulation of seismic wave in viscoelasticmedia．4. The paper took advantage of the properties of P-wave and S-wave to deducevelocity-stress equations which is used to separate a hybrid wavefield of P-waveand S-wave in viscoelastic media. And the high order staggered grid finitedifference method is used in numerical simulation. The analysis of modelingwavefield proved the correctness of this method.5. On the basic the absorption and attenuation properties of seismic wave, the papergave two methods which are used to distinguish oil and gas. The result of modelsimulation proved the effectiveness of the two methods.