基于数据自适应加权的叠前深度偏移成像方法

Pre-stack depth migration based on data-adaptive weighting

随着高性能计算机技术的快速发展和“两宽一高”采集技术的广泛应用,高分辨率、高保真的反演成像成为研究热点。首先从Bayes估计理论框架下的地震波反演成像出发,指出Bayes估计理论是地震波反演成像的基础,基于所选择波场预测器(一般为常密度标量声波方程)的波场预测残差的先验概率分布和要反演的模型参数的先验概率分布决定了模型参数的后验概率密度,后验概率密度的最大化是地震波反演成像最佳解的判定准则。在波场预测器为线性、预测误差为高斯白噪情况下,Bayes估计可在最小二乘意义下实现,并可以得到无偏和方差最小的参数估计结果。实际数据的不完备、线性化的正问题不能很好地模拟数据中的地震波场,使得数据协方差阵和模型协方差阵的引入成为必然。鉴于模型参数的正则化在反演成像中已有充分的讨论,重点讨论了加权最小二乘反演成像框架下数据协方差(逆)算子的作用,说明了数据加权处理在叠前深度偏移中的必要性。在将加权系数矩阵视为对角矩阵的基础上,提出了采用倾角扫描和动态时间规整算法确定数据加权系数,并将其应用于叠前深度偏移成像中。理论和实际数据的数值实验结果表明数据协方差(逆)算子能够有效提高偏移成像质量。

With the rapid development of high-performance computer technology,and the technology for the acquisition of broadband,wide-azimuth and high-density (BWH) data,the seismic inversion imaging with high-resolution and high-fidelity has become a hot research topic.This paper firstly identifies the foundation of seismic inversion imaging in the Bayesian estimation theory.The posterior probability density relative to the model parameters is controlled by two terms,namely the prior probability distribution of the wavefield residual based on the predictor of wave equation (generally,the constant-density acoustic wave equation),and the prior probability distribution of the model parameters to be inverted.The criterion for determining the optimal solution for the seismic inversion imaging is the maximization of the posterior probability density.If the wavefield predictor is linear and the prediction residual can be assimilated to Gaussian white noise,the Bayesian estimation can be realized in the sense of the least squares,and an estimated result with unbiased and minimum variance can be obtained.Due to imperfections in the actual data,and because the linearized forward problem cannot simulate the whole wavefield,it is necessary to consider the application of the covariance matrix between data and model.Under the framework of the weighted least squares migration,the function of the data covariance (inverse) operator is analyzed,and the need for data weighting in pre-stack depth migration is explained.Then,under the hypothesis that the matrix of the weighted coefficients is diagonal,the use of the dip scanning and dynamic time warping algorithm is proposed to determine the weighted coefficient in the pre-stack depth migration.Finally,it is reported that tests on theoretical and field data showed that the data covariance (inverse) operator can improve the quality of the migration imaging.