A cellular automata‐based deterministic inversion algorithm for the characterization of linear structural heterogeneities

Abstract

Inverse problem permits to map the subsurface properties from a few observed data. The inverse problem can be physically constrained by a priori information on the property distribution in order to limit the nonuniqueness of the solution. The geostatistical information is often chosen as a priori information; however, when the field properties present a spatial locally distributed high variability, the geostatistical approach becomes inefficient. Therefore, we propose a new method adapted for fields presenting linear structures (such as a fractured field). The Cellular Automata‐based Deterministic Inversion (CADI) method is, as far as we know when this paper is produced, the first inversion method which permits a deterministic inversion based on a Bayesian approach and using a dynamic optimization to generate different linear structures iteratively. The model is partitioned in cellular automaton subspaces, each one controlling a different zone of the model. A cellular automata subspace structures the properties of the model in two units (“structure” and “background”) and control their dispensing direction and their values. The partitioning of the model in subspaces permits to monitor a large‐scale structural model with only a few pilot‐parameters and to generate linear structures with local direction changes. Thereby, the algorithm can easily handle with large‐scale structures, and a sensitivity analysis is possible on these structural pilot‐parameters, which permits to considerably accelerate the optimization process in order to find the best structural geometry. The algorithm has been successfully tested on simple, to more complex, theoretical models with different inversion techniques by using seismic and hydraulic data.

Identifying Flow Networks in a Karstified Aquifer by Application of the Cellular Automata‐Based Deterministic Inversion Method (Lez Aquifer, France)

“…We dedicate this section to describe briefly the main concepts of the CADI method. For more details about the theory of this method, we invite the readers to refer to Fischer et al (2017b).…”

“…In this paper, we apply a novel structural inversion method, the Cellular Automata-based Deterministic Inversion (CADI), to invert the steady state hydraulic head data recorded during a hydraulic tomography to image the spatial distribution of the hydraulic transmissivities in the fractured and karstified Lez aquifer (Southern France). The theoretical aspects of the CADI method have been developed in a previous article (Fischer et al, 2017b). This method is based on the Cellular Automata (CA) concept to parameterize the model.…”

Hydraulic tomography of discrete networks of conduits and fractures in a karstic aquifer by using a deterministic inversion algorithm

“…(1) Inversions in an equivalent porous media were led by using geostatistical approaches in which the statistical characteristics of hydraulic properties are used as a priori information to constraint the inversion. Among these tools we cite: sequential successive linear estimator (Yeh and Liu 2000 ;Ni and Yeh 2008 ;Hao et al 2008 ;Illman et al 2009 ;Sharmeen et al 2012), pilot-point (Lavenue and de Marsily 2001), transitional-probability (Wang et al 2017), anisotropy directions (Meier et al 2001), multi-scale resolution (Ackerer and Delay 2010), or structural approaches: probability perturbation method (Caers and Hoffman 2006), imageguided (Soueid Ahmed et al 2015), and cellular automata-based (Fischer et al 2017).…”

Harmonic pumping tomography applied to image the hydraulic properties and interpret the connectivity of a karstic and fractured aquifer (Lez aquifer, France)

“…the sequential successive linear estimator, Ni and Yeh 2008 ;Hao et al 2008 ;Illman et al 2009 ;Sharmeen et al 2012). Other methods for inversion of complex discrete structures involve introducing constraints of a priori knowledge to the inverse model using a guided image (Hale 2009;Soueid Ahmed et al 2015), a training image (Lochbühler et al 2015), a probability perturbation (Caers and Hoffman 2006), a transition probability distribution (Wang et al 2017), a multi-scale resolution (Ackerer and Delay 2010), a level-set method (Lu and Robinson 2006;Cardiff and Kitanidis 2009b), or based on cellular automata (Fischer et al 2017b).…”

“…Then, in section 3 we briefly introduce the numerical model setup and the Cellular Automatabased Deterministic Inversion (CADI) algorithm. Further details of our inverse algorithm can be found in Fischer et al (2017b). In section 4 we present the inversion results obtained with the CADI method at the Terrieu field site and the efficiency of the method in reproducing the observed hydraulic responses.…”