Denoising CSEM Data Using Least-Squares Method Based on Mixed Basis of Fourier Series and Legendre Polynomials
Denoising CSEM Data Using Least-Squares Method Based on Mixed Basis of Fourier Series and Legendre Polynomials
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DOI：
10.1109/tgrs.2023.3326345
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发表时间：
2023
影响因子：
8.2
通讯作者：
Yang Yang-Yang;Changyu Zhou;Heng Zhang;Yonghui Peng;Huaifeng Sun
中科院分区：
文献类型：
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作者：
Yang Yang-Yang;Changyu Zhou;Heng Zhang;Yonghui Peng;Huaifeng Sun
可控源电磁法（CSEM）测量应用广泛，但由于仪器或环境因素的影响，CSEM测量所获得的数据常常受到噪声的干扰。针对这一问题，提出了一种基于最小二乘反演的去噪方法，有效地处理了CSEM数据中的非周期噪声。该方法在时域中选择特定的重建区域，建立超定方程，得到噪声。然而，重建区域的选择条件苛刻，只能选择仅由信号和白色高斯噪声组成的区域作为理想重建区域，限制了该方法的应用。通过在超定方程中引入勒让德多项式，提出了一种改进的方法。利用这种改进的方法，包含其他类型的噪声的区域也可以被选择作为重建区域，扩大了适用范围。为了避免病态矩阵可能带来的计算误差，在超定方程中引入正则化因子。同时，为了定量评价该方法的去噪效果，引入了包络评价方法，提出了一种通过残余噪声评价去噪效果的“塌陷算法”。通过仿真和真实的案例研究，证明了所提出的去噪和评价过程的正确性和有效性。
Controlled-source electromagnetic (CSEM) surveys are widely used, but due to the influence of instrumental or environmental factors, the data obtained from CSEM surveys are often disturbed by noise. To address this problem, a denoising method based on least-squares inversion has been proposed to effectively deal with the nonperiodic noise in CSEM data. This method selects special reconstruction areas in the time domain and establishes an overdetermined equation to obtain the noise. However, the condition in selecting reconstruction areas is rigorous, according to which only an area merely consisting of signal and white Gaussian noise can be chosen as an ideal reconstruction area, limiting the application of this method. In this article, an improved method was proposed by introducing the Legendre polynomials into the overdetermined equation. Using this improved method, areas containing other kinds of noise can also be chosen as reconstruction areas, extending the scope of application. To avoid the possible calculation error that comes from an ill-conditioned matrix, a regularization factor is introduced into the overdetermined equation as an option. Meanwhile, to quantitatively evaluate the effect of this proposed method, the envelope evaluation method is involved and a “collapse algorithm” is proposed to evaluate the denoising effect through residual noise. Through simulation and real case study, the validity and effectiveness of the proposed denoising and evaluating process are proved.