用图像修复思路重建地质结构，精度优于传统方法。
Geological Field Restoration through the Lens of Image Inpainting
- 将地质场建模为低秩张量，结合空间平滑性恢复缺失数据。
- 在SPE10模型上，不同采样密度下误差均低于普通克里金法。
- 适合地质建模、资源勘探领域，尤其适用于数据稀疏场景。
我们研究了在观测有限条件下地质场重构这一病态问题。工程师常需从稀疏的钻井数据等观测中重建地下地质场。受图像修复启发，我们将部分观测的空间场建模为多维张量，通过施加全局低秩结构和空间平滑性来恢复缺失值。采用交替方向乘子法求解优化问题。在SPE10 model 2基准测试中，该确定性方法在多种采样密度下相对平方误差均低于普通克里金法，并生成视觉连贯的重构结果。
原文摘要 · Abstract (English)
We study an ill-posed problem of geological field reconstruction under limited observations. Engineers often have to deal with the problem of reconstructing the subsurface geological field from sparse measurements such as exploration well data. Inspired by image inpainting, we model this partially observed spatial field as a multidimensional tensor and recover missing values by enforcing a global low rank structure together with spatial smoothness. We solve the resulting optimization via the Alternating Direction Method of Multipliers. On the SPE10 model 2 benchmark, this deterministic approach yields consistently lower relative squared error than ordinary kriging across various sampling densities and produces visually coherent reconstructions.
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