Study On One-way Wave Equation Forward Modeling And Inverse Q Migration In Viscoelastic TI Media

Pactice have proven that the real subsurface medium is not ideally elastic, but widely anisotropic. Both of these two factors have an impact on the propagation of seismic wave in subsurface media. Thus viscoelastic and anisotropic problems are no longer a purely academic issue but a crucial factor of seismic exploration theory and method study, especially with the higher requirement to resolution for seismic exploration method and technology. It will severely restrict the effective use of seismic data if we don’t consider the viscoelastic and anisotropic properties of subsurface media. Therefore, viscoelastic and anisotropic theory and its related technology are now becoming one of the popular issues in the field of seismic exploration. In this paper we first introduced the wave propagation theory of viscoelastic and anisotropic media, and then studied the one-way wave equation forward modeling, illumination analysis and inverse Q migration method in viscoelastic and anisotropic media.In this paper, we firstly derived elastic wave equation of general viscoelastic anisotropic media according to elastic dynamic theory and constitutive equation of viscoelastic anisotropic media, based on Kelvin-Voigt model. Substituting the general solution of plane wave into wave equation, we established Christoffel equation of viscoelastic anisotropic media. We simplified the form of the above equations by applying Thomsen anisotropic parameters and quality factor Q into wave equation and Christoffel equation. According to the symmetry of anisotropic media, we deduced the wave equation and Christoffel equation of viscoelastic TI media by degenerating the equations. We decoupled the dispersion equation of viscoelastic anisotropic media by applying acoustic approximation theory of Alkhalifah. We can easily obtain the corresponding explicit q P wave dispersion equation of viscoelastic TI model based on Kelvin-Voigt model, and it is easy to achieve numerical simulation using one-way wave equation method. Compared with two-way wave equation method, one-way wave equation method does not have as much wavefield information, but it has advantages in computing efficiency, resource consumption, accuracy and SNR in wavefield modeling. However, the traditional one-way wave equation method cannot handle the variation of viscoelastic and anisotropic media simutaneously. In this paper, we solved this problem by improving two popular one-way wave equation methods.Split-step Fourier method is one of the most popular one-way wave equation method, which extrapolates the wavefield in frequency-wavenumber domain and frequency-space domain. This method can handle the lateral velocity variation of media and has higher calculating efficiency. In order to adapt to lateral variation of elastic parameters and extend this method to viscoelastic TI media forward modeling, we added interpolation step in the calculation process of split-step Fourier method based on the idea of phase shift and interpolation. We simulated the q P wavefield of viscoelastic VTI media, viscoelastic HTI media and viscoelastic elliptical TTI media with the new method, and validated the correctness and accuracy of the new method by theoretical analysis and comparison with two-way wave equation method and traditional split-step Fourier method.In this paper we improve the generalized-screen method to further enhance the accuracy of forward modeling in viscoelastic TI media. Compared with split-step Fourier method, the calculation efficiency of generalized-screen method is relatively low, but it has higher computational accuracy and is more suitable for complex media. And the generalized-screen operators can control the accuracy of the extended operators by taking different orders of approximation of the dispersion relation. Thus we can obtain forward modeling results with different precision to adapt to the requirements of seismic exploration for the balance of accuracy and efficiency. We defined the perturbation parameters of viscoelastic TI media, and re-deduced the propagation operators of generalized-screen method so that this method can handle the variation of viscoelasticity and anisotropy simutaneously. We extended the generalized-screen propagation operators to viscoelastic TI media, and calculated the corresponding q P wavefield of viscoelastic VTI media, viscoelastic HTI media and viscoelastic elliptical TTI media. Then we verified the correctness and accuracy of the new method by theoretical analysis and comparison with two-way wave equation method and traditional split-step Fourier method.Illumination analysis can discribe the energy distribution of seismic waves in subsurface media quantificationally. It can help to optimize the design of acquisition system, then improve the quality and efficiency of field seismic data acquisition by taking full account of the illumination analysis method of the actual subsurface media. In this paper we calculated the seismic illumination intensity of viscoelastic TI media based on improved generalized-screen forward modeling method. Illumination analysis based on one-way wave equation forward modeling has low computation cost and higher calculating efficiency. Tough it does not involve all the types of wave, it has accurate results of reflection and transmission wave. In this paper, we calculated the source illumination intensity and plane wave illumination intensity of viscoelastic TI media, and analyzed the impact of viscoelasticity and anisotropy on seismic wave energy distribution to provide practical reference to the design of seismic data acquisition system.The properties of actual subsurface media is more complex considering viscoelasticity and anisotropy, and the seismic wave will be affected by these properties in the process of propagation. The anisotropic property of the media makes the propagation of seismic wave different with that in isotropic media and that will be recorded in the seismic data. Isotropic migration method can not take anisotropy into account, leading to false imaging results. And the viscoelastic property of media may lead to energy attenuation and phase distortion of seismic wave, thus reduce the resolution and signal-to-noise ratio of seismic data. Then the resolution of the seismic imaging will be reduced. In this paper we proposed post-stack and pre-stack inverse Q migration method in viscoelastic TI media based on improved one-way wave propagation operators. Compared with traditional migration methods, our new method can not only obtain the correct seismic imaging results by considering the influence of anisotropy, but also compensate the attenuated seismic energy during the process of migration. Therefore the precision of seismic exploration is improved.