Weighted RML using ensemble-methods for data assimilation

TL;DR

This paper explores a weighted RML approach using ensemble methods for data assimilation, focusing on hybrid models with potentially multimodal posteriors and the necessity of analytic transformations.

Contribution

It introduces a method to apply weighting in hybrid data assimilation models with analytic transformations, addressing multimodal posterior challenges.

Findings

Weighted RML can handle multimodal posteriors effectively.

Analytic transformations are crucial for applying the proposed weighting method.

The approach extends ensemble smoothers to hybrid models with black-box components.

Abstract

The weighting of critical-point samples in the weighted randomized maximum likelihood method depend on the magnitude of the data mismatch at the critical points and on the Jacobian of the transformation from the prior density to the proposal density. When standard iterative ensemble smoothers are applied for data assimilation, the Jacobian is identical for all samples. If a hybrid data assimilation method is applied, however, there is the possibility that each ensemble member can have a distinct Jacobian and that the posterior density can be multimodal. In order to apply a hybrid method iterative ensemble smoother, it is necessary that a part of the transformation from the prior Gaussian random variable to the data be analytic. Examples might include analytic transformation from a latent Gaussian random variable to permeability followed by a black-box transformation from permeability to state variables in porous media flow, or a Gaussian hierarchical model for variables followed by a similar black-box transformation from permeability to state variables. In this paper, we investigate the application of weighting to both types of examples.