The Application Of Pseudo-spectral Forward Modeling Of Seismic Wave Field In Visco-elastic Medium

The word 'viscoelasticity' comes from model theory. In another word, we can represent that by some models, which are serially or in parallel made of the basic elements - spring and dashpot, such as, Maxwell model, Kelvin-Voigt model, standard linear solid model. In different occasion and in different books or magazines, we often find some words, such as, creep, relaxation, viscosity, damping, intrinsic friction, which all belong to the characters of viscoelasticity or fluid.When we study the long-range movement (such as, convection of mantle, movement of plate, movement of formation, gestation of earth quake and so on) and accurately research instantaneous processes, we have to consider the viscoelasticity of the earth. On the other hand, the disappearance of surge of earth is the best evidence that proves that the medium in earth is viscoelastic medium. In the seism exploration, because of many factors, there is attenuation of wave. Although there is not one theory that can describe all factors, it is obvious that the viscoelasticity of medium is one of the important factors.The constitutive relation of viscoelastic medium has two forms-differential operator form of stress strain constitutive relation and integral operator form of stress strain constitutive relation, and they are corresponding, and the later can be educed from the former. They have their own merit: differential form is directly educed from ideal model, so it can directly model and qualitatively explain viscoelasticity of medium and the parameters of the model have clear conception. However, it is essential for better describing viscoelasticity to use complicated model, which leads to perplexingconstitutive equation, and because of the difficulty researchers can only use some simple models, such as, Maxwell model, Kelvin-Voigt model, standard linear solid model to model wave propagation in viscoelastic medium. The integral form roots in principle of superposition and has a more simple uniform. Then we can get the constitutive equation if we have relaxation modulus E(t) and flexible modulus J(t).In this research, on the base of the theory of model, we get the equation by integral form constitutive relation, and in this process we use corresponding principle. Then the process becomes compact and universal. So we have the hope that models wave propagation using more complicated models.In this research, we model wave propagation in several kinds of model. According to 1-D modeling, the wave in viscoelastic medium has distinct attenuation by comparing with the wave in elastic medium. P-wave and S-wave all have these characteristic. Though the parameters of Burgers model near quantitatively these of S.L.S. Compared with modeling in S.L.S medium, the wave in burgers medium has more attenuation and the velocity of S-wave is very smaller. These phenomena all are consistent with what we theoretically analyze.