Smart pilot points using reversible‐jump Markov‐chain Monte Carlo

Abstract

Pilot points are typical means for calibration of highly parameterized numerical models. We propose a novel procedure based on estimating not only the pilot point values, but also their number and suitable locations. This is accomplished by a trans-dimensional Bayesian inversion procedure that also allows for uncertainty quantification. The utilized algorithm, reversible-jump Markov-Chain Monte Carlo (RJ-MCMC), is computationally demanding and this challenges the application for model calibration. We present a solution for fast, approximate simulation through the application of a Bayesian inversion. A fast pathfinding algorithm is used to estimate tracer travel times instead of doing a full transport simulation. This approach extracts the information from measured breakthrough curves, which is crucial for the reconstruction of aquifer heterogeneity. As a result, the ''smart pilot points'' can be tuned during thousands of rapid model evaluations. This is demonstrated for both a synthetic and a field application. For the selected synthetic layered aquifer, two different hydrofacies are reconstructed. For the field investigation, multiple fluorescent tracers were injected in different well screens in a shallow alluvial aquifer and monitored in a tomographic source-receiver configuration. With the new inversion procedure, a sand layer was identified and reconstructed with a high spatial resolution in 3-D. The sand layer was successfully validated through additional slug tests at the site. The promising results encourage further applications in hydrogeological model calibration, especially for cases with simulation of transport. Key Points:An inversion with flexible pilot points settings is presented The inversion is validated with a tracer tomography field study Pathfinding algorithm approximates transport behavior of tracers

Synthetic fracture network characterization with transdimensional inversion

“…Bodin and Sambridge [] have proposed an rjMCMC application for seismic tomography and Jiménez et al . [] utilized the concept to invert tracer tomography experiments in porous media with pilot points. Mondal et al .…”

“…Every injection is simulated as an independent experiment, starting from a tracer‐free state. In practice, however, this could be performed as a multitracer experiment with simultaneous injections of different types of tracers [e.g., Jiménez et al ., ].…”

“…Equivalent to the hypothetical case, three sources and three receiver points are used, located at the right and left edge of the domain at known fracture ends. The same initial and boundary conditions are used as in the previous case, but the experiment is only performed in one direction without swapping the injection and observation well, which is considered to be a more realistic scenario [ Doro et al ., ; Djibrilla Saley et al ., ; Jiménez et al ., ]. The experimental time was set to 2000 s and the concentrations were measured every 20 s. Given the longer time of the experiment, much more data points are collected than in the hypothetical case.…”

Soil moisture estimation using tomographic ground penetrating radar in a MCMC–Bayesian framework

“…Our proposed approach does not require direct permittivity measurements at the pilot points, and is integrated with multi-chain MCMC design, which is more feasible for efficient inversion and monitoring of changes of permittivity field. Jimenez et al (2016) applied the pilot point concept as well, but the reference field was a deterministic field. Romary's model (Romary 2009) used truncated Karhunen-Loeve expansion (Loeve 1955), which is effective for dimension reduction, but the approach usually leads to inverted fields smoother than the true case.…”

“…The sampling is often done using MCMC. Pioneering work has been done using MCMC for inversion of high dimensional problems (Hunziker et al 2017;Jimenez et al 2016;Laloy et al 2015;Romary 2009;Rubin et al 2010). These approaches have been successfully applied to solve various synthetic and real case inversion problems (Mara et al 2016;Zanini and Kitanidis 2008).…”