SUMMARYElectrical resistivity tomography (ERT) is widely used to image the Earth’s subsurface and has proven to be an extremely useful tool in application to hydrological problems. Conventional smoothness-constrained inversion of ERT data is efficient and robust, and consequently very popular. However, it does not resolve well sharp interfaces of a resistivity field and tends to reduce and smooth resistivity variations. These issues can be problematic in a range of hydrological or near-surface studies, for example mapping regolith-bedrock interfaces. While fully Bayesian approaches, such as those using Markov chain Monte Carlo sampling, can address the above issues, their very high computation cost makes them impractical for many applications. Ensemble Kalman inversion (EKI) offers a computationally efficient alternative by approximating the Bayesian posterior distribution in a derivative-free manner, which means only a relatively small number of ‘black-box’ model runs are required. Although common limitations for ensemble Kalman filter-type methods apply to EKI, it is both efficient and generally captures uncertainty patterns correctly. We propose the use of a new EKI-based framework for ERT which estimates a resistivity model and its uncertainty at a modest computational cost. Our EKI framework uses a level-set parametrization of the unknown resistivity to allow efficient estimation of discontinuous resistivity fields. Instead of estimating level-set parameters directly, we introduce a second step to characterize the spatial variability of the resistivity field and infer length scale hyperparameters directly. We demonstrate these features by applying the method to a series of synthetic and field examples. We also benchmark our results by comparing them to those obtained from standard smoothness-constrained inversion. Resultant resistivity images from EKI successfully capture arbitrarily shaped interfaces between resistivity zones and the inverted resistivities are close to the true values in synthetic cases. We highlight its readiness and applicability to similar problems in geophysics.

中文翻译：

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使用集合卡尔曼反演进行具有不确定性量化的地下电阻率的高效多尺度成像

总结电阻率断层扫描 (ERT) 广泛用于对地球地下进行成像，并已被证明是解决水文问题的非常有用的工具。传统的 ERT 数据的平滑约束反演高效且稳健，因此非常受欢迎。然而，它不能很好地分辨电阻率场的尖锐界面，并且倾向于减少和平滑电阻率变化。这些问题在一系列水文或近地表研究中可能存在问题，例如绘制风化层-基岩界面。虽然完全贝叶斯方法，例如使用马尔可夫链蒙特卡洛采样的方法，可以解决上述问题，但它们非常高的计算成本使得它们对于许多应用程序不切实际。集成卡尔曼反演 (EKI) 通过以无导数的方式近似贝叶斯后验分布提供了一种计算效率高的替代方案，这意味着只需要相对少量的“黑盒”模型运行。尽管集成卡尔曼滤波器类型方法的常见限制适用于 EKI，但它既有效又通常能正确捕获不确定性模式。我们建议使用新的基于 EKI 的 ERT 框架，以适度的计算成本估计电阻率模型及其不确定性。我们的 EKI 框架使用未知电阻率的水平集参数化，以允许有效估计不连续电阻率场。而不是直接估计水平集参数，我们引入第二步来表征电阻率场的空间变异性并直接推断长度尺度超参数。我们通过将该方法应用于一系列合成和现场示​​例来演示这些功能。我们还通过将它们与从标准平滑约束反演中获得的结果进行比较来对我们的结果进行基准测试。来自 EKI 的结果电阻率图像成功地捕获了电阻率区域之间的任意形状的界面，并且反演的电阻率接近合成情况下的真实值。我们强调它对地球物理学中类似问题的准备和适用性。我们还通过将它们与从标准平滑约束反演中获得的结果进行比较来对我们的结果进行基准测试。来自 EKI 的结果电阻率图像成功地捕获了电阻率区域之间的任意形状的界面，并且反演的电阻率接近合成情况下的真实值。我们强调它对地球物理学中类似问题的准备和适用性。我们还通过将它们与从标准平滑约束反演中获得的结果进行比较来对我们的结果进行基准测试。来自 EKI 的结果电阻率图像成功地捕获了电阻率区域之间的任意形状的界面，并且反演的电阻率接近合成情况下的真实值。我们强调它对地球物理学中类似问题的准备和适用性。