基于全变分原理的多震源混合数据直接偏移方法

多震源混合地震采集技术,即将多个震源以一定编码方式连续地激发,得到多炮混合的地震数据.该技术能减少地震采集时间,节约采集成本,但是混合数据的直接偏移会在成像剖面中引入严重的串扰噪声,影响成像效果.从数学上看,地震成像属于典型的数学物理反问题,可以采用线性反演方法求解一个正则化约束的最小二乘(LS)优化问题,获得更高质量的成像结果.全变分(TV)正则化方法是图像去噪和复原领域中广泛应用的热点技术,其能在去除噪声的过程中保留图像的边缘信息和不连续性.在对TV图像去噪复原方法原理分析的基础上,本文将多震源混合数据直接偏移成像问题转换成图像复原的极小化能量泛函问题,用TV正则化代替传统最小二乘偏移(LSM)中的L2范数正则化,提出基于全变分原理的混合数据直接偏移方法.该方法使用基于梯度的快速迭代收缩阈值与快速梯度投影组合算法——FISTA/FGP求解最优化问题,能有效压制串扰噪声,增强同相轴连续性,提高成像分辨率.理论模型测试结果表明:将本方法应用于混合数据,无论是去噪效果还是成像精度都得到显著改善.

Direct migration method of multi-source blended data based on total variation

In acquisition of multi-source blended data, multiple sources are continuously shot and geophones continuously receive seismic signals to acquire blended shot records overlapping in both the spatial and temporal domains. Relative to the traditional seismic acquisition, blended acquisition can decrease the effective survey duration and reduce the cost of surveys. However, this continuously shooting and recording strategy can lead to complex blended wave fields and create great difficulties to the following migration imaging. There are two migration imaging methods about the blended data at this stage: to perform the migration processing directly on the blended data without any pre-separation, or recovery the blended data to individual shot data, which is called "deblending", then conduct standard migration processing to these deblended data. The first method has a high processing efficiency, but the multi-source direct migration is usually not satisfactory because of the crosstalk contamination. The second method has low efficiency and the source separation has serious influence on imaging quality. All things considered, the direct migration method has a better prospect of application, so this article studies a direct migration method of blended data which can effectively remove the crosstalk. Mathematically, the seismic imaging can be regarded as a typical mathematical and physical inverse problem and a better imaging result can be obtained by solving a regularized least-squares (LS) problem with a linear inversion method. The total variation (TV) regularization method is widely used in image denoising and restoration fields. It can produce a denoised image where edges and discontinuities are preserved. On the basis of analyzing the principles of TV image denoising and restoration method, in this paper, we formulate the direct migration of multi-source seismic data as a problem of minimizing the energy functional of image restoration, use the TV regularization to replace the L2 norm regularization in the traditional least-squares migration (LSM) and propose a TV norm constrained migration method. The proposed method employs a gradient-based algorithm—a combination of fast iterative shrinkage-thresholding algorithm and fast gradient projection method (FISTA/FGP) to solve the optimization problem. It combines the advantages of FISTA and FGP, which is simple in algorithm, convenient to realize and stable. To test the validity and adaptability of our migration method, numerical experimentations are carried out on a horizontally-layered medium model, SEG/EAGE fault model and 2D Marmousi model, respectively. First, we compute the prestack Kirchhoff migration, the L2 norm constrained LSM and TV norm constrained migration for the horizontally-layered medium model. The results show that the TV norm constrained migration can effectively suppress the migration artifacts and crosstalk and the image quality is better than the other two. For the case of data containing noise, this article adds 15% Gauss white noise into the synthetic blended data of the SEG/EAGE fault model and applies the TV norm constrained migration with different values of the optimization parameters. The results indicate that our algorithm has good anti-noise performance and point out that there is influence of the selection of regularization parameters on the imaging results. So considering the denoise effect and fidelity of migration imaging, an assigned range of these optimization parameters is proposed. For the complex medium case, we compute the standard migration and TV norm constrained migration for the blended data of the 2D Marmousi model and use the conventional data TV norm constrained migration as a reference. The imaging results and waveform comparison both indicate that our method can yield desired migration imaging of complex geological structures. For the crosstalk noise caused by direct imaging of blended data, we propose a direct migration method based on TV regularization. The results of theoretical model experiments show that our method can effectively suppress the random noise, migration artifacts and crosstalk noise, enhance the continuity of seismic events and improve the imaging resolution. TV norm constrained migration belongs to an iterative migration algorithm based on least-square optimization and has a prominent imaging effect. However, it is also a computing-expensive algorithm. With the development of the computer performance and the parallel programming technology, the computational cost can be reduced, which can enable our method to practical applications.