Based on the Aki-Richards approximate equations for reflection coefficients and Bayes theorem, we developed an inversion method to estimate P- and S-wave velocity contrasts and density contrast from combined PP and PS data. This method assumes that the parameters satisfy a normal distribution and introduces the covariance matrix to describe the degree of correlation between the parameters and thus to improve the inversion stability. Then, we suppose that the parameter sequence is subject to the Cauchy distribution and employs another matrix Q to describe the parameter sequence sparseness to improve the inversion result resolution. Tests on both synthetic and real multi-component data prove that this method is valid, efficient, more stable, and more accurate compared to methods using PP data only.
Considering Zoeppritz equations, reflections of PP and PS are only the function of ratios of density and velocity. So the inversion results will be the same if the ratios are the same but values of density, velocities of P- wave and S-wave are different without strict constraint. This paper makes efforts to explore nonlinear simultaneous PP and PS inversion with expectation to reduce the ambiguity of AVO analysis by utilizing the redundancy of multi-component AVO measurements. Accurate estimation of ratio parameters depends on independence of input data. There are only two independent AVO attributes for PP reflectivity （i.e. intercept and gradient） and two for PS reflectivity （i.e. pseudo-intercept and pseudo-gradient or extreme amplitude）, respectively. For individual PP and PS inversion, the values of least-squares objective function do not converge around a large neighborhood of chosen true model parameters. Fortunately for joint PP and PS inversion the values of the least-squares objective function show closed contours with single minima. Finally the power function fitting is used to provide a higher precision AVO attributes than traditional polynomial fitting. By using the four independent fitting attributes （two independent attributes for PP and PS respectively）, the inversion of four ratio parameters （velocities and densities） would be estimated with less errors than that in traditional method.
The main problems in seismic attribute technology are the redundancy of data and the uncertainty of attributes, and these problems become much more serious in multi-wave seismic exploration. Data redundancy will increase the burden on interpreters, occupy large computer memory, take much more computing time, conceal the effective information, and especially cause the ＂curse of dimension＂. Uncertainty of attributes will reduce the accuracy of rebuilding the relationship between attributes and geological significance. In order to solve these problems, we study methods of principal component analysis （PCA）, independent component analysis （ICA） for attribute optimization and support vector machine （SVM） for reservoir prediction. We propose a flow chart of multi-wave seismic attribute process and further apply it to multi-wave seismic reservoir prediction. The processing results of real seismic data demonstrate that reservoir prediction based on combination of PP- and PS-wave attributes, compared with that based on traditional PP-wave attributes, can improve the prediction accuracy.
Ye YuanYang LiuJingyu ZhangXiucheng WeiTiansheng Chen
