基于宽度学习的直流电阻率法数据去噪与反演研究

直流电阻率法是常用的浅地表电性结构成像方法，在工程勘察、环境以及地质灾害监测等领域具有广泛应用。直流电阻率法作为主动源探测方法，本身具有较强的抗干扰能力，但随着经济的发展，人文电磁干扰（特高压输电网及大型设备接地放电等）越来越强、分布越来越广，直流电阻率法观测数据正面临着日益严重的噪声干扰。此外，在实际应用中，直流电阻率法三维反演和四维（电性结构随时间变化）监测逐渐成为主流，如何在提升反演精度的同时保证计算效率、增强监测的时效性是直流电阻率法面临的另一个问题。近年来，机器学习在地球物理数据去噪及反演方面取得了显著的应用效果，而宽度学习作为一种较新的机器学习方法，具有结构简单、效率高、非线性映射能力强的优点。因此，本论文尝试利用宽度学习来解决直流电阻率法面临的上述两方面问题，开展直流电阻率法数据去噪和反演研究。

首先，本文构建宽度学习去噪框架对直流电阻率法的时间域数据进行去噪。理论合成数据表明训练得到的宽度学习网络能有效压制时间域数据中的噪音，提高数据信噪比，提升反演结果准确性。为了进一步验证宽度学习去噪方法的有效性和实用性，我们开发了可采集电位差时间域数据的直流电阻率法装置并进行了室内模拟实验。实验结果表明宽度学习网络能有效去除测量电极电位差时间域数据中的噪音，去噪后的反演结果可以更准确地指示异常体。

然后，本文构建了宽度学习设计初始模型的反演框架，将宽度学习预测结果作为初始模型，利用有限内存拟牛顿法进行反演计算。合成数据测试表明所构建的宽度学习网络可以很好地刻画异常体特征，利用宽度学习设计的初始模型可以提高有限内存拟牛顿法反演收敛速度和精度。此外，当测线较为稀疏时，传统的梯度类算法很难准确刻画测线旁侧的异常体，但宽度学习方法可以通过大量样本训练，建立测线观测数据对旁侧异常体的映射，实现对旁侧异常体的更准确描述。野外控制实验表明，宽度学习能够设计可靠的初始模型，有利于提高反演的收敛速度，提升反演结果的精度。实际考古应用表明，宽度学习方法在实际异常体探测中具有潜在优势。

最后，本文开展了基于宽度学习的直流电阻率法四维监测研究。在实际应用中，不同采集时刻的背景噪音差异会导致反演结果中出现虚假的电性结构变化，降低了电性结构监测的准确度。为此，本文在正则化反演目标函数中添加时移约束项，对相邻时刻电阻率模型变化进行约束，采用宽度学习设计不同时刻的初始反演模型，并对多次监测数据进行时移反演。合成数据和野外实验测试均表明，本文提出的时移反演方法能有效抑制噪音引起的虚假异常。相对于均匀初始模型时移反演结果，宽度学习设计初始模型时移反演可以提高反演的收敛速度和精度。

The direct-current (DC) resistivity method is a frequently employed technique for exploration and monitoring, extensively applied in engineering surveys, environmental assessments, and geological hazard monitoring. As an active source detection method, the DC resistivity method possesses robust anti-noise capabilities. However, with the development of the economy, human-generated electromagnetic interference (such as Ultra High Voltage transmission networks and discharge from large equipment grounding) is becoming more prevalent and intense. Consequently, the observational data obtained through the DC resistivity method are increasingly subject to serious noise interference. In addition, in practical applications, three-dimensional inversion and four-dimensional monitoring (which involves monitoring electrical structure changes over time) using the DC resistivity method have gradually become mainstream. Improving inversion accuracy while ensuring computational efficiency and enhancing monitoring timeliness is another challenge encountered by the DC resistivity method. In recent years, machine learning has yielded significant advancements in the application of denoising and inversion of geophysical data. As a relatively new machine learning method, broad learning possesses the advantages of a simple structure, high efficiency, and robust nonlinear mapping capability. Therefore, to address the aforementioned problems faced by the DC resistivity method, this paper conducts research on data denoising and inversion for the DC resistivity method.

Firstly, this paper proposes a broad learning denoising framework to denoise the time-domain data acquired through the DC resistivity method. Theoretical synthetic data indicates that the trained broad learning network can effectively eliminate noise from time-domain data. To further verify the effectiveness and practicability of the broad learning denoising, we developed a DC resistivity device that can collect potential difference time domain data and conducted indoor simulation experiments. Experimental results demonstrate that broad learning can effectively eliminate noise from the time-domain data, leading to inversion results that more accurately delineate anomaly bodies.

Secondly, this paper constructs an inversion framework for the initial model designed by broad learning. The prediction results obtained from broad learning serve as the initial model for the L-BFGS to perform inversion calculations. The synthetic data demonstrated that the constructed broad learning network effectively characterizes anomalies. Further tests indicated that utilizing the initial model designed with broad learning enhances the convergence speed and accuracy of the L-BFGS inversion. Furthermore, when survey lines are relatively sparse, traditional gradient-based algorithms often struggle to accurately depict anomalies adjacent to the survey lines. However, broad learning can establish a mapping of the observation data to the anomalies adjacent to the survey lines through extensive sample training, thereby achieving a more precise description of the anomalies beside the survey lines. Field control experiments demonstrate that broad learning can design a dependable initial model, leading to enhanced convergence speed and improved accuracy of inversion results. Moreover, practical archaeological applications indicate that the broad learning holds potential advantages for real-world anomaly detection.

Finally, this paper conducts a study on four-dimensional monitoring of DC resistivity based on broad learning. In practical applications, variations in background noise at different acquisition times may lead to false changes in electrical structure in the inversion results, thereby compromising the accuracy of electrical structure monitoring. The paper proposes incorporating a time-lapse constraint term into the regularized inversion objective function, utilizing broad learning to design initial inversion models at different time points, and performing time-lapse inversion on multiple monitoring datasets. Both synthetic data and field experimental tests demonstrate that the proposed method in this article effectively suppresses false anomalies caused by noise. Compared with time-lapse inversion results based on homogeneous initial models, using designed initial models enhances convergence speed and accuracy.

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