A pattern‐search‐based inverse method

Abstract

[1] Uncertainty in model predictions is caused to a large extent by the uncertainty in model parameters, while the identification of model parameters is demanding because of the inherent heterogeneity of the aquifer. A variety of inverse methods has been proposed for parameter identification. In this paper we present a novel inverse method to constrain the model parameters (hydraulic conductivities) to the observed state data (hydraulic heads). In the method proposed we build a conditioning pattern consisting of simulated model parameters and observed flow data. The unknown parameter values are simulated by pattern searching through an ensemble of realizations rather than optimizing an objective function. The model parameters do not necessarily follow a multi-Gaussian distribution, and the nonlinear relationship between the parameter and the response is captured by the multipoint pattern matching. The algorithm is evaluated in two synthetic bimodal aquifers. The proposed method is able to reproduce the main structure of the reference fields, and the performance of the updated model in predicting flow and transport is improved compared with that of the prior model.

Groundwater Level Mapping Using Multiple-Point Geostatistics

“…However, when the groundwater level is considered as a random variable, the salient question is how to find its training image. Thus, the concept of "ensemble training images" proposed by Zhou et al [6] is utilized here. Specifically, the simulated groundwater level maps after modeling the full physics are used as the training images for the estimation.…”

“…In this work, we propose to use MPS for groundwater level mapping for the first time. To do this, we borrowed the concept of "ensemble training images", which has been applied in the context of inverse modeling for groundwater flow and transport modeling [6], for the purpose of groundwater level estimation. In addition, we compare the results of MPS with those from two-point statistics-based methods such as Kriging in a hypothetical example, and highlight the significance using MPS for groundwater level estimation.…”

Ensemble Kalman filtering for hydraulic conductivity characterization: Parallelization and non-Gaussianity

“…Return to the step 3 and repeat the processes until all the observed data are assimilated. Zhou et al (2011Zhou et al ( , 2012 have shown that the NS-EnKF is a good alternative in the characterization of non-Gaussian distributed conductivity fields. However, since the NS-EnKF is based in the EnKF, it has the same drawbacks, that is, the appearance of spurious correlations between distant points and the underestimation of the final uncertainty.…”

“…Inverse modeling in hydrogeology and petroleum engineering has a long tradition (see Zhou et al (2014) for a review) but, again, most inverse models rely on the assumption that hydraulic conductivity follows a multiGaussian model. Recent attempts to couple inverse approaches and non multiGaussian random functions have been attempted by Sun et al (2009);Sarma and Chen (2009);Jafarpour and Khodabakhshi (2011);Hu et al (2012b); Zhou et al (2011Zhou et al ( , 2012; Attia and Sandu (2014), among others, with different degrees of success. The common denominator of all these proposals is that they are variants of algorithms that work for multiGaussian fields.…”

“…They rely on the existence of a training image exhibiting the types of patterns to be present in the final models, from which to infer the higher-order statistics. Some available algo-rithms and codes are SNESIM (Strebelle, 2002), FILTERSIM , SIMPAT (Arpat and Caers, 2007) , DS (Mariethoz et al, 2010), En-PAT , and others (e.g., Zhou et al, 2012;Chugunova and Hu, 2008;Mirowski et al, 2009;Boucher, 2009;Honarkhah and Caers, 2010).…”