基于压缩感知技术的全波形反演

发布时间：2018-09-14 11:36

【摘要】：全波形反演技术虽然已经得到了成功应用,但其求解一个最小二乘非凸优化问题的计算量仍是一个很大的难题。通过随机降采样技术可以减少反演过程中炮数和频率数,从而可以极大程度地降低全波形反演的计算量;然而这种方法受到奈奎斯特采样定律例证的"维数灾难"的限制以及背离‘摩尔定律’现象。为此,研究了基于改进压缩感知的随机化降维技术,应用压缩感知理论减少随机采样;联合随机采样和稀疏促进技术,成功减少了地震数据的维数,同时保持了有效信息。通过该项技术的应用,牛顿类方法的计算量相当于全波场采样梯度类算法的计算量;将稀疏约束应用在反演过程中的模型更新上,不改变波形反演的目标函数,并且能够压制由欠采样产生的虚像噪声。北海模型数据测试结果证明了该方法的可行性和有效性。
[Abstract]:Although the full waveform inversion technique has been successfully applied, it is still a big problem to solve a least square non-convex optimization problem. The random demultiplexing technique can reduce the number of shots and frequencies in the inversion process, thus greatly reducing the computation of the full waveform inversion. However, this method is limited by the dimension disaster exemplified by Nyquist's sampling law and deviates from Moore's law. For this reason, a randomized dimensionality reduction technique based on improved compression perception is studied, which uses compression sensing theory to reduce random sampling, and combines random sampling and sparsity promotion technology to reduce the dimension of seismic data and maintain effective information at the same time. Through the application of this technique, the computational cost of Newtonian method is equivalent to that of the full-wave sampling gradient algorithm, the sparse constraint is applied to the updating of the model in the inversion process, and the objective function of waveform inversion is not changed. And can suppress the virtual image noise generated by the under-sampling. The test results of Beihai model data show that the method is feasible and effective.
【作者单位】：加拿大英属哥伦比亚大学;
【分类号】：P631.4

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