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基于Cauchy先验分布的贝叶斯AVO反射率反演,可以产生类似于稀疏脉冲反演的结果,增强了对大反射系数的识别能力,反演过程中正则项和参数矩阵的计算都需要用到由上一步迭代所估计出的模型参数信息,因而反问题呈现非线性,此外该过程依赖于模型参数之间的线性统计关系,而且反演结果为反射率而非弹性参数,不利于储层预测和流体检测。贝叶斯AVO波形反演通过将反射率改写为弹性参数差分形式,直接从叠前地震数据中提取弹性参数,无需对弹性参数之间关系做线性假设。本文综合考虑上述两种方法的优点,在研究过程中仍然采用Cauchy先验分布,同时对贝叶斯AVO反射率的反演过程进行了修改,实现了基于Cauchy先验分布的AVO弹性参数弱非线性波形反演。本方法的提出有效避免了模型参数之间的线性假设,同时也能够从地震数据中直接反演得到纵、横波速度和密度。理论合成数据实验证明,此方法可以直接从叠前地震数据中提取弹性参数,而且在含有噪音的情况下也能得到比较准确的反演结果。
Bayesian AVO reflectance inversion based on Cauchy prior distribution can produce results similar to those of sparse pulse inversion and enhance the ability to recognize large reflection coefficients. The calculation of regularization term and parameter matrix in inversion process needs to be used To the model parameter information estimated by the previous iteration, the inverse problem is nonlinear. In addition, the process depends on the linear statistical relationship between the model parameters and the inversion result is the reflectivity instead of the elastic parameter, which is not good for the reservoir Prediction and fluid testing. Bayesian AVO Waveform Retrieval The elastic parameters are extracted directly from prestack seismic data by rewriting the reflectivity as a difference of elastic parameters without the need to make linear assumptions about the relationship between the elastic parameters. Considering the merits of these two methods, the Cauchy priori distribution is still used in the study, and the inversion of Bayesian AVO reflectivity is modified at the same time, and the weakness of AVO elastic parameters based on Cauchy’s prior distribution is achieved Linear waveform inversion. The proposed method effectively avoids the linear assumption between the model parameters, but also can be directly derived from the seismic data of longitudinal and shear wave velocity and density. Experiments on synthetic data show that this method can directly extract the elastic parameters from prestack seismic data and can obtain more accurate inversion results even with noises.