Parameter estimation by ensemble Kalman filters with transformed data: Approach and application to hydraulic tomography
Parameter estimation by ensemble Kalman filters with transformed data: Approach and application to hydraulic tomography
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DOI：
10.1029/2011wr010462
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发表时间：
2012-04
影响因子：
5.4
通讯作者：
A. Schöniger;Wolfgang Nowak;H. Franssen
中科院分区：
文献类型：
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作者：
A. Schöniger;Wolfgang Nowak;H. Franssen
在大气和海洋科学中，环绕卡尔曼滤波器（EnkFs）是一种成功的状态变量估计工具。最近的研究已经准备了EnKF参数估计在地下水的应用。只有当所有涉及的变量都是多元高斯时，EnKF才是贝叶斯更新意义上的最优。地下水流和输运状态变量，但是，一般不显示高斯依赖于水力测井电导率和彼此之间，即使测井电导率是多高斯。为了在这种情况下改进EnKF，我们对观察到的状态应用非线性单调变换，使它们成为高斯（高斯变形，GA）。Béal等人（2010）最近在状态估计的背景下提出了类似的想法。我们的工作转移和适应这种方法的参数估计。此外，我们解决了测量误差的转换中的治疗，并提供了几个多变量分析工具，以评估预期的有用性GA事先。为了说明，我们首次将EnKF应用于多高斯对数电导率场中的三维水力层析成像参数估计。结果表明：（1）遗传算法实现了降深数据作为测井电导率函数的隐式伪线性化，（2）这使得参数识别和流量和输运预测更准确。将EnKFs与GA相结合，产生了一种计算效率高的工具，用于提高精度的非线性反演数据。这是一个有吸引力的好处，因为粒子滤波器等非线性化方法在计算上要求极高。
Ensemble Kalman filters (EnKFs) are a successful tool for estimating state variables in atmospheric and oceanic sciences. Recent research has prepared the EnKF for parameter estimation in groundwater applications. EnKFs are optimal in the sense of Bayesian updating only if all involved variables are multivariate Gaussian. Subsurface flow and transport state variables, however, generally do not show Gaussian dependence on hydraulic log conductivity and among each other, even if log conductivity is multi‐Gaussian. To improve EnKFs in this context, we apply nonlinear, monotonic transformations to the observed states, rendering them Gaussian (Gaussian anamorphosis, GA). Similar ideas have recently been presented by Béal et al. (2010) in the context of state estimation. Our work transfers and adapts this methodology to parameter estimation. Additionally, we address the treatment of measurement errors in the transformation and provide several multivariate analysis tools to evaluate the expected usefulness of GA beforehand. For illustration, we present a first‐time application of an EnKF to parameter estimation from 3‐D hydraulic tomography in multi‐Gaussian log conductivity fields. Results show that (1) GA achieves an implicit pseudolinearization of drawdown data as a function of log conductivity and (2) this makes both parameter identification and prediction of flow and transport more accurate. Combining EnKFs with GA yields a computationally efficient tool for nonlinear inversion of data with improved accuracy. This is an attractive benefit, given that linearization‐free methods such as particle filters are computationally extremely demanding.