Anisotropic Parameters Inversion Based On The Second Generation Wavelet Transforms

Most kinds of rocks are anisotropic to the seismic exploration, which has been discovered during long term of actual exploration and test. When seismic wave propagating in the mediums of earth, physical properties of it such as velocity,polarization direction,amplitude and attenuation all have directional properties, which is called seismic anisotropy and relevant mediums are called anisotropic mediums. The method to assume the medium of earth to be isotropic has benefited a lot to the field exploration all the times. However , as the exploration of subtle reservoir becoming more difficult ,to invert anisotropic parameters and describe reservoir delicatly has been the problem of subtle reservoir exploration activities that need to be solved now.There are many methods to invert anisotropic parameters, among which waveform inversion based on wave equation uses more seismic wave information of kinematics and kinetics so it can get better effect. Waveform inversion includes lineal seismic waveform inversion and nonlinear seismic waveform inversion.In the lineal seismic waveform inversion the relationship between observed seismic data and velocity is linearized approximlately. And nonlinear seismic waveform inversion transforms inversion problem to nonlinear problem which is more close to reality. Because there are many local minimum points in objective function waveform inversion's effectiveness is weak when processing anamorphic data and actual data. At the same time the calculated amount of waveform inversion using wave equation is big comparatively because it constantly repeats forward modeling algorithm in the inversion course .The result is better when theory of wavelet analysis is used in the problem of wave equation inversion. Wavelet analysis is one kind of multiscale analysis method which analyses matters in a series of nesting air space. Objective function presents comparatively strong convexity and lesser local extreme values on wide scale which is favour of converging to optimized values . So firstly to get a better estimation of parameter using iterate inversion on wide scale , then using this estimation as initial value on mini scale till to get global optimum of original problem. Furthermore, wavelet analysis has fast algorithm of decomposition and reconstitution and this is can improve efficiency apparently when calculated amount is very big .This paper realizes 2-D wavefield simulation of VTI medium by the finite element numerical simulation analysis. According to the results of forward modeling, combining the theory of second generation wavelet transforms with the method of the time domain pre-stack full-wave field parameters inversion, anisotropic parameters inversion of VTI medium are performed perfectly.Numerical examples demonstrate that combining the theory of second generation wavelet transforms with the inversion method of anisotropic parameters is valuable for the improvement of efficiency and precision of inversion. The next step of the study in this field which is pointed out is to use the theory of second generation wavelet transforms with the idea of optimization.