The Traveling Pilot Point method. A novel approach to parameterize the inverse problem for categorical fields
Prashanth Khambhammettu, Philippe Renard & John Doherty
| Résumé |
Categorical parameter distributions are common-place in
hydrogeological systems consisting of geologic fa cies/categories
with distinct properties, e.g., high-permeability channels embedded
in a low-permeability ma trix. Parameter estimation is difficult in
such systems because the discontinuities in the parameter space
hinder the inverse problem. Previous research in this area has been
focused on the use of stochastic methods. In this paper, we present
a novel approach based on Traveling Pilot points (TRIPS) combined
with subspace parameter estimation methods to generate realistic
categorical parameter distributions that honor calibration
constraints (e.g., - measured water levels). In traditional
implementations, aquifer properties (e.g., hydraulic conductivity)
are estimated at fixed pilot point locations. In the TRIPS
implementation, both the properties associated with the pilot
points and their locations are estimated. Tikhonov regularization
constraints are incorporated in the param eter estimation process
to produce realistic parameter depictions. For a synthetic aquifer
system, we solved the categorical inverse problem by combining the
TRIPS methodology with two subspace methods: Null Space Monte Carlo
(NSMC) and Posterior Covariance (PC). A posterior ensemble developed
with the rejection sampling (RS) method is compared against the
TRIPS ensembles. The comparisons indicated similarities between the
various ensembles and to the reference parameter distribution.
Between the two subspace methods, the NSMC method produced an
ensemble with more variability than the PC method. These
preliminary results suggest that the TRIPS methodology has promise
and could be tested on more complicated problems. |
| Mots-clés |
Inverse problem; Categorical inversion; Traveling pilot points; Multiple-point statistics; Null Space Monte Carlo; Linear sub-space methods |
| Citation | Khambhammettu, P., Renard, P., & Doherty, J. (2020). The Traveling Pilot Point method. A novel approach to parameterize the inverse problem for categorical fields. Advances in Water Resources, 138, 103556-103570. |
| Type | Article de périodique (Anglais) |
| Date de publication | 2-2020 |
| Nom du périodique | Advances in Water Resources |
| Volume | 138 |
| Pages | 103556-103570 |
| URL | https://doi.org/10.1016/j.advwatres.2020.103556 |