Simulation of fine-scale electrical conductivity fields using resolution-limited tomograms and area-to-point kriging
Simulation of fine-scale electrical conductivity fields using resolution-limited tomograms and area-to-point kriging
复制标题
使用分辨率有限的断层扫描和面到点克里金法模拟精细尺度电导率场
DOI：
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发表时间：
2019
影响因子：
2.8
通讯作者：
K. Holliger
中科院分区：
文献类型：
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作者：
Raphäel Nussbaumer;N. Linde;G. Mariéthoz;K. Holliger
确定性地球物理反演方法产生断层图像与强大的印记，需要解决其他不适定的反问题的正则化条款。虽然这样的层析成像能够充分评估探测的地下的较大尺度特征，但较细尺度的细节往往无法解决。然而，表示这些精细尺度的结构细节通常是期望的，并且对于某些应用甚至是强制性的。为了解决这个问题，我们已经开发了一个两步的方法，基于区域到点克里金生成细尺度多高斯实现平滑断层图像。具体来说，我们使用一个协同克里格系统，在该系统中，平滑，低分辨率的断层图像相关的精细尺度的异质性，通过线性映射操作。该映射基于模型分辨率和使用围绕最终层析成像模型的线性化计算的后验协方差矩阵。这反过来又允许我们进行协方差和互协方差模型的分析计算。该方法进行测试的异质性合成的2-D分布的电导率，探测与基于表面的电阻率层析成像（ERT）调查。结果表明，这种技术的能力，再现一个已知的地质统计模型表征的精细尺度结构，同时保留大规模的结构确定的平滑约束层析反演。实现的地球物理正演响应与参考合成数据之间的小差异归因于潜在的线性化。总的来说，该方法提供了一种有效和快速的替代更全面，但计算更昂贵的方法，例如，马尔可夫链蒙特卡洛技术。此外，所提出的方法可以用来生成精细尺度的多元高斯实现从几乎任何平滑约束的反演结果给出相应的分辨率和后验协方差矩阵。
Deterministic geophysical inversion approaches yield tomographic images with strong imprints of the regularization terms required to solve otherwise ill-posed inverse problems. While such tomograms enable an adequate assessment of the larger-scale features of the probed subsurface, the finer-scale details tend to be unresolved. Yet, representing these fine-scale structural details is generally desirable and for some applications even mandatory. To address this problem, we have developed a two-step methodology based on area-to-point kriging to generate fine-scale multi-Gaussian realizations from smooth tomographic images. Specifically, we use a co-kriging system in which the smooth, low-resolution tomogram is related to the fine-scale heterogeneity through a linear mapping operation. This mapping is based on the model resolution and the posterior covariance matrices computed using a linearization around the final tomographic model. This, in turn, allows us for analytical computations of covariance and cross-covariance models. The methodology is tested on a heterogeneous synthetic 2-D distribution of electrical conductivity that is probed with a surface-based electrical resistivity tomography (ERT) survey. The results demonstrate the ability of this technique to reproduce a known geostatistical model characterizing the fine-scale structure, while simultaneously preserving the large-scale structures identified by the smoothness-constrained tomographic inversion. Small discrepancies between the geophysical forward responses of the realizations and the reference synthetic data are attributed to the underlying linearization. Overall, the method provides an effective and fast alternative to more comprehensive, but computationally more expensive approaches, such as, for example, Markov chain Monte Carlo techniques. Moreover, the proposed method can be used to generate fine-scale multivariate Gaussian realizations from virtually any smoothness-constrained inversion results given the corresponding resolution and posterior covariance matrices.