Aquifer structure identification using stochastic inversion

Harp, Dylan R.; Dai, Zhenxue; Wolfsberg, Andrew; Vrugt, Jasper A.; Robinson, Bruce A.; Vesselinov, Velimir V.

doi:10.1029/2008gl033585

Cited by 57 publications

(59 citation statements)

References 14 publications

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“…While much effort has been focused on developing inversion strategies for covariance-based spatial-correlation models, little has been applied to the Markov-chain approach (e.g. Harp et al 2008). This paper presents a strategy that implements a Markov-chain spatial-correlation framework into a stochastic inversion.…”

Section: Theoretical Discussion Of Stochastic Representations Of Stramentioning

confidence: 98%

“…The calibration of a conditional Markov-chain model to hydraulic data was proposed by Zhenxue Dai in a personal communication in 2007. This proposal provided the impetus for the research presented in Harp et al (2008), where a synthetic 2-D 2-unit (2 stratigraphic unit) aquifer was analyzed utilizing the concept of a representative realization of a spatial correlation model. Harp et al (2008) inverted structural parameters from 2-unit Markov-chain models in vertical and lateral directions (e.g.…”

Section: Introductionmentioning

confidence: 99%

“…This proposal provided the impetus for the research presented in Harp et al (2008), where a synthetic 2-D 2-unit (2 stratigraphic unit) aquifer was analyzed utilizing the concept of a representative realization of a spatial correlation model. Harp et al (2008) inverted structural parameters from 2-unit Markov-chain models in vertical and lateral directions (e.g. facies mean lengths and volumetric facies proportions) obtaining head predictions from a single stochastic realization for each geostatistical model.…”

Section: Introductionmentioning

confidence: 99%

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Stochastic inverse method for estimation of geostatistical representation of hydrogeologic stratigraphy using borehole logs and pressure observations

Harp

Vesselinov

2010

Stoch Environ Res Risk Assess

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An approach is presented for identifying statistical characteristics of stratigraphies from borehole and hydraulic data. The approach employs a Markov-chain based geostatistical framework in a stochastic inversion. Borehole data provide information on the stratigraphy while pressure and flux data provide information on the hydraulic performance of the medium. The use of Markov-chain geostatistics as opposed to covariance-based geostatistics can provide a more easily interpreted model geologically and geometrically. The approach hinges on the use of mean facies lengths (negative inverse autotransition rates) and mean transition lengths (inverse crosstransition rates) as adjustable parameters in the stochastic inversion. Along with an unconstrained Markov-chain model, simplifying constraints to the Markov-chain model, including (1) proportionally-random and (2) symmetric spatial correlations, are evaluated in the stochastic inversion. Sensitivity analyses indicate that the simplifying constraints can facilitate the inversion at the cost of spatial correlation model generality. Inverse analyses demonstrate the feasibility of this approach, indicating that despite some low parameter sensitivities, all adjustable parameters do converge for a sufficient number of ensemble realizations towards their ''true'' values. This paper extends the approach presented in Harp et al. (to (1) statistically characterize the hydraulic response of a geostatistical model, thereby incorporating an uncertainty analysis directly in the inverse method, (2) demonstrate that a gradient-based optimization strategy is sufficient, thereby providing relative computational efficiency compared to global optimization strategies, (3) demonstrate that the approach can be extended to a 3-D analysis, and (4) introduce the use of mean facies lengths and mean transition lengths as adjustable parameters in a geostatistical inversion, thereby allowing the approach to be extended to greater than two category Markov-chain models.

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Section: Theoretical Discussion Of Stochastic Representations Of Stramentioning

confidence: 98%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Stochastic inverse method for estimation of geostatistical representation of hydrogeologic stratigraphy using borehole logs and pressure observations

Harp

Vesselinov

2010

Stoch Environ Res Risk Assess

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“…Hydraulic conductivity distributions in alluvial fans can be assigned according to the various hydrofacies simulated by conditional indicator geostatistical methods (Eggleston and Rojstaczer, 1998;Fogg et al, 1998;Weissmann et al, 2002a, b;Ritzi et al, 2004Ritzi et al, , 2006Proce et al, 2004;Dai et al, 2005;Harp et al, 2008;Hinnell et al, 2010;Maghrebi et al, 2015;Soltanian et al, 2015;Zhu et al, 2016a). However, the geostatistical methods require the stationary assumption; i.e., the distribution of the volumetric proportions and correlation lengths of hydrofacies converge to their mean values in the simulation do-main.…”

Section: Introductionmentioning

confidence: 99%

Modeling 3-D permeability distribution in alluvial fans using facies architecture and geophysical acquisitions

Zhu

Gong

Dai

et al. 2017

Hydrol. Earth Syst. Sci.

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Abstract. Alluvial fans are highly heterogeneous in hydraulic properties due to complex depositional processes, which make it difficult to characterize the spatial distribution of the hydraulic conductivity (K). An original methodology is developed to identify the spatial statistical parameters (mean, variance, correlation range) of the hydraulic conductivity in a three-dimensional (3-D) setting by using geological and geophysical data. More specifically, a large number of inexpensive vertical electric soundings are integrated with a facies model developed from borehole lithologic data to simulate the log 10 (K) continuous distributions in multiplezone heterogeneous alluvial megafans. The Chaobai River alluvial fan in the Beijing Plain, China, is used as an example to test the proposed approach. Due to the non-stationary property of the K distribution in the alluvial fan, a multiplezone parameterization approach is applied to analyze the conductivity statistical properties of different hydrofacies in the various zones. The composite variance in each zone is computed to describe the evolution of the conductivity along the flow direction. Consistently with the scales of the sedimentary transport energy, the results show that conductivity variances of fine sand, medium-coarse sand, and gravel decrease from the upper (zone 1) to the lower (zone 3) portion along the flow direction. In zone 1, sediments were moved by higher-energy flooding, which induces poor sorting and larger conductivity variances. The composite variance confirms this feature with statistically different facies from zone 1 to zone 3. The results of this study provide insights to improve our understanding on conductivity heterogeneity and a method for characterizing the spatial distribution of K in alluvial fans.

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“…However, prior model comes with its associated uncertainty. A general approach to incorporate the uncertainties in all prior knowledge (as well as data and model errors) is the probabilistic approach [Kaipio and Somersalo, 2007;Tarantola, 2005a;Kitanidis, 2012;Harp et al, 2008;Ye and Khaleel, 2008;Dai et al, 2010].…”

Section: Introductionmentioning

confidence: 99%

Learning sparse geologic dictionaries from low-rank representations of facies connectivity for flow model calibration

Liu

Jafarpour

2013

Water Resour. Res.

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[1] Sparse geologic dictionaries provide a novel approach for subsurface flow model representation and calibration. Learning sparse dictionaries from prior training data sets is an effective approach to describe complex geologic connectivity patterns in subsurface imaging applications. However, the computational cost of sparse learning algorithms becomes prohibitive for large models. Performing the sparse dictionary learning process on smaller image patches (segments) provides a simple approach to address this problem in image processing applications. However, in underdetermined subsurface flow model calibration inverse problems, reconstruction of a segmented image can introduce significant structural distortion and discontinuity at the boundaries of the segments. This paper proposes an alternative sparse learning approach where the sparse dictionaries are learned from low-rank representations of the large-scale training data set in spectral domains (e.g., frequency domain). The objective is to develop a computationally efficient dictionary learning approach that emphasizes large-scale spatial connectivity patterns. This is achieved by removing the strong spatial correlations in the training data, thereby eliminating a large number of insignificant components from the sparse learning computation. In addition to improving the computational complexity, sparse learning from low-rank training data sets suppresses the small-scale details from entering the reconstruction of large-scale connectivity patterns, thereby providing a regularization effect in solving the resulting illposed inverse problems. We apply the proposed approach to travel-time tomography inversion and nonlinear subsurface flow model calibration inverse problems to demonstrate its effectiveness and practicality.Citation: Liu, E., and B. Jafarpour (2013), Learning sparse geologic dictionaries from low-rank representations of facies connectivity for flow model calibration, Water Resour. Res., 49,[7088][7089][7090][7091][7092][7093][7094][7095][7096][7097][7098][7099][7100][7101]

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Aquifer structure identification using stochastic inversion

Cited by 57 publications

References 14 publications

Stochastic inverse method for estimation of geostatistical representation of hydrogeologic stratigraphy using borehole logs and pressure observations

Stochastic inverse method for estimation of geostatistical representation of hydrogeologic stratigraphy using borehole logs and pressure observations

Modeling 3-D permeability distribution in alluvial fans using facies architecture and geophysical acquisitions

Learning sparse geologic dictionaries from low-rank representations of facies connectivity for flow model calibration

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