Viscoelastic Wave Numerical Simulation Technology Of Complex Medium

Geological information obtained by 2-D seismic exploration is incomplete, can’t completely describe the propagation rules of seismic wave in the formation. The dev-elopment of 3-D technology will improve the accuracy of seismic exploration. It is generally assumed that the medium is homogeneous and perfectly elastic in conven-tional seismic wave numerical simulation. However, the energy of seismic wave is gradually attenuated from shallow to deep when it propagated in actual layers. This is because the actual formation is complex which is inhomogeneous, non perfectly elastic, anisotropy and physical parameters continuously varying. Seismic wave numerical simulation truly reflect the propagation and energy changing law of seismic wave using inhomogeneous media instead of perfectly elastic media. It has great meaning for the oil and gas exploration when develop viscoelastic wave numerical simulation with inhomogeneous media.In this paper, mainly study numerical simulation algorithm in viscoelastic medium, then realize 3-D visco-elastic wave staggered-grid high-order finite difference numerical simulation by obtaining optimized coefficients, then get the seismic records and analyze the wave field characteristics. The main contents and achievements include the following aspects:Study the fundamental properties, establish the basic model of viscoelastic medium based on the basic theory of viscoelastic medium. Introduce the quality factor Q that characterize the attenuation characteristic of medium.According to the stress-strain relationship of Viogt viscoelastic medium, deduce the 3-D viscoelastic wave equation, and derive the first-order velocity-stress equation.Derive the staggering grid high-order finite difference algorithm, analyze and discuss several common questions about finite-difference algorithm, such as source excitation, the stability condition and absorb boundary condition. For the numerical dispersion, this paper calculate a new set of optimized difference coefficients with the extreme condition. Experimental results show that numerical simulation using by optimized staggered grid differential operators can more effectively suppress the numerical dispersion than the conventional Taylor series expansion differential coefficients.In homogeneous isotropic medium, using staggered grid high-order finite difference numerical simulation with viscoelastic wave equation, study propagation and absorption attenuation of seismic wave in viscoelastic medium. It found that there exists significant energy attenuation when seismic wave propagate in a viscoelastic medium, including distortion of reflected wave. Further research shows that the attenuation effect have a great influence on high frequency components with more the energy attenuation, and influence on shear wave stronger than longitudinal wave. Using the algorithm on complex 3-D viscoelastic media, can fully describe the propagation and wave field characteristics of seismic wave in viscoelastic medium. The stability and accuracy of the algorithm is well, and there is no numerical dispersion phenomena.According to statistical theory, establish inhomogeneous random medium model. Using forward simulation for different viscoelastic random medium model, then analyze the propagation law and wave field characteristics of seismic waves in viscoelastic random medium. Study the scattering phenomena and energy attenuation of seismic waves. It is found that:a. The perturbation stochastic of the random medium will produce scattered wave; b. With the increasing of correlation length, the energy of seismic wave is constantly changing, and the energy of seismic wave is weakened because of the mutual interference; c. The scattered wave can be recorded in the entire seismic record, however, the reflected wave is a special case of scattered wave; d. Since the viscous absorption attenuation of quality factor, the reflected wave form is distorted. Research on non-uniformity medium make the simulation results more close to the actual formation, and provide a reliable basis to the wave field imaging and actual seismic data processing.