用稀疏正则化反演基底起伏，提升地质建模精度。
2D Basement Relief Inversion using Sparse Regularization
- 采用平滑性、总变差等正则化方法约束反演解
- 遗传算法优化棱柱深度，使理论异常逼近观测值
- 平滑约束在模拟数据中表现最优，真实数据上各方法相当
基底起伏重力勘探在地球物理中至关重要，尤其用于油气和矿产勘探。该问题本质上是反演问题，需从观测重力异常推断地质模型参数。模型将基底起伏表示为均质密度的棱柱体，数据反映这些棱柱产生的重力异常。反演问题通常病态，微小数据扰动会导致解剧烈变化。为此，本文比较了多种正则化方法在重力反演中的应用，包括平滑性约束、总变差、离散余弦变换（DCT）和离散小波变换（DWT，使用Daubechies D4小波）。通过遗传算法（GA）优化棱柱深度，以最小化目标函数。GA模拟自然选择，筛选最优解。结果通过拟合度指标与误差分析评估，显示所有正则化方法与GA均有效；在合成模型中，平滑性约束表现最佳；在真实数据模型中，各方法性能相近。
原文摘要 · Abstract (English)
Basement relief gravimetry is crucial in geophysics, especially for oil exploration and mineral prospecting. It involves solving an inverse problem to infer geological model parameters from observed data. The model represents basement relief with constant-density prisms, and the data reflect gravitational anomalies from these prisms. Inverse problems are often ill-posed, meaning small data changes can lead to large solution variations. To mitigate this, regularization techniques like Tikhonov's are used to stabilize solutions. This study compares regularization methods applied to gravimetric inversion, including Smoothness Constraints, Total Variation, Discrete Cosine Transform (DCT), and Discrete Wavelet Transform (DWT) using Daubechies D4 wavelets. Optimization, particularly with Genetic Algorithms (GA), is used to find prism depths that best match observed anomalies. GA, inspired by natural selection, selects the best solutions to minimize the objective function. The results, evaluated through fit metrics and error analysis, show the effectiveness of all regularization methods and GA, with the Smoothness constraint performing best in synthetic models. For the real data model, all methods performed similarly.
Thank you to arXiv for use of its open access interoperability. PaperDance 不是 arXiv 官方产品；中文卡片由大模型生成，请以原文为准。