最大熵方法在偏移速度分析中的推广及应用

Application of maximum entropy method in pre_stack depth migration velocity analysis

(瑞普索公司,美国得克萨斯州休斯敦 TX 77450)

Repsol, Houston, TX 77450, USA

三维叠前深度偏移需要通过一个相对准确的速度来获得地层深处的结构。作为一种反问题方法，偏移速度分析利用共成像点道集上的剩余曲率成像点来反演速度模型。但由于非线性问题的线性化、噪声及不具物理意义的模型参数化假设，偏移速度分析是不适定和病态的。为了得到合理的和稳定的解我们必须使用正则化方法。首先对统计学中的贝叶斯定理和经典的基于信息论的最大熵方法进行了回顾；然后将模型参数的导数项引进到经典最大熵方法，将其推广到正则化速度模型中，使得既能得到合理的解，同时又能保持速度模型的间断面；最后，通过讨论一个数值算例说明了算法的适用性。

3D pre-stack depth migration needs an accurate velocity model to image subsurface structures. As an inverse problem, migration velocity analysis tries to infer the velocity model from the picked residual curvatures on common image-point gathers (CIGs). Because of noisy data, the linearization of nonlinear problems, and inadequate parameterization of the model, migration velocity analysis is thought to be ill-posed and ill-conditioned. Reasonable solutions can be obtained only by adequately defined regularization. Firstly, the basic aspects of the Bayes’ theorem and the classical “information-based” maximum-entropy method were reviewed. Then, the classical maximum-entropy method was extended by an incorporating model derivative into a maximum-entropy computation. This has the effect of intra-region smoothing including the preservation of sharp boundaries. Finally, a numerical example proves the effectiveness of the proposed algorithm.