Study Of Three-term AVO Inversion Method

Multi-fold technology is the method that lithology properties of stratum are repeatedly observed, and AVO analysis reveal the relation between amplitude variation with offset and elastic parameters of stratum. AVO inversion identifies fluid content in reservoir pores and predicts oil and gas by using the amplitude variation with offset.The three-term linearized AVO equation is typically too ill-conditioned to be reliably solved for. The traditional AVO inversion usually makes problem stable by solving for two parameters rather than three, thus introducing bias into the estimate. The method based on Bayes theorem can incorporate probabilistic constraints with the likelihood function, the three-term inversion can be constrained so as to give stable estimates, but with minimal bias. This paper establishes parameter covariance matrix in the Bayes optimization algorithm of three-term inversion problem, and studiesγratio variation with depth, making the parameter covariance matrix change as a function of depth. Tests on synthetic and real data show that the reliable parameters etamates in AVO inversion are obtained by implementing a series of theoretical improvements to the formulation of the inverse problem.How to obtain the parameter of density is one important problem that should be considered, because the information from density of stratum provides the potential to quantify fluid saturation within the reservoir. In order to estimate reliable density term, long offsets are required. NMO stretch and offset-dependent tuning introduce problematic distortions at these offsets, influencing the validity of the estimated parameter. Under the framework of Bayes throy, NMO operator and convolutional model are incorporated into the forward model, NMO stretch and offset-dependent tuning is considered in AVO waveform inversion. The probability function is used to describe the likelihood function for the l p norm, which can give better estimates in the presence of spurious noise; and Cauchy prioir distribution leads to sparse reflectivity, which only responds to anomalous fluid or large changes in lithology and improves the resolution of the estimated parameter.Elastic impedance inversion method which uses the technique of angle gather stack and requires an appropriate angle instead of the range of angles, reduce the accuracy and validity of inversion. In recent years, the development of AVO simultaneous inversion can improve the reliability of inversion. In the paper, we present a new approach to the simultaneous pre-stack inversion. According to post-stack impedance inversion method, we present one order derivative model and converlutional model for AVO inversion based on Beyes's optimization algorithm, which is suitable for elastic impedance and density inversion method which utilizes the whole angle information of the pre-stack data. The likelihood function distribution is assumed Gaussian, and the prioir probability function is assumed an adjusted Huber distribution, which meet the distribution pattern of model parameters. Both synthetic and real seismic data examples demonstrate that the estimated P-impedance, S-impedance and density are reliable by using the method, which has a greater potential in application.In order to quantitatively analyze the uncertainty in AVO parameter estimates, based on Bayesian framework, the analytic relationships for estimates of uncertainty in two-term and three-term inversion were tested and verified by a modeling study. Moreover the interrelatedness of different parameter vectors has been established. For the optimization problem, The AVO inversion is solved using Newton-Raphson, while the AVO waveform inversion and AVO simultaneous inversion are solved using conjugate gradient or programming and simplex for l1 norm problem.