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由于地震数据频带范围的有限性以及噪声、正演近似等因素的影响,地震反演是一个高度不适定的反问题。为了得到稳定唯一的解,通常在反演目标函数中加入光滑化约束,常用的是Tikhonov正则化约束。这种正则化对解是全局光滑的,在构造边缘位置会产生模糊。为了解决边缘模糊的问题,同时保证抗噪的作用,本文采用Huber-Markov随机场约束边缘保护的方法求解叠前纵横波速度和密度三参数反演问题。对于待反演的参数,通过Markov邻域系统建立起纵向和横向上的约束。通过Huber边缘惩罚函数阈值的合理设置,达到在层内区域采用二次型函数抑制噪声得到平滑的结果;在边缘位置则采用线性函数,避免边缘的模糊化。通过无噪和有噪合成地震记录的反演,验证了方法的正确性,分析了正则项与反演效果的关系。
Because of the limited frequency range of seismic data and the influence of noise, forward approximation and other factors, seismic inversion is a highly ill-posed inverse problem. In order to obtain a stable and unique solution, the smoothing constraint is usually added to the inversion objective function, commonly used is the Tikhonov regularization constraint. This regularization solution is globally smooth and vague in constructing the edge position. In order to solve the problem of edge blur and ensure the anti-noise effect, Hubble-Markov random field constrained edge protection method is used to solve the three-parameter inversion of prestack P-wave velocity and density. For the parameters to be inverted, the vertical and horizontal constraints are established by the Markov neighborhood system. Through the reasonable setting of the Huber edge penalty function threshold, the quadratic function is used to suppress the noise in the intra-layer region to get the smoothed result. At the edge position, the linear function is adopted to avoid the blurring of the edge. The correctness of the method is verified by inversion of the noisy and noisy synthetic seismograms, and the relationship between the regularized term and the inversion effect is analyzed.