A variational approach to estimating the state of a magma reservoir from observed displacement

TL;DR

This paper introduces a variational numerical method to estimate magma reservoir states from surface displacement data, addressing the inverse problem with a high-condition-number linear system.

Contribution

It presents a novel variational approach that formulates the inverse problem as a minimization of a combined data and derivative norm, enabling reservoir state estimation.

Findings

The method effectively estimates reservoir stress distribution from displacement data.

High precision arithmetic is necessary to solve the high-condition-number linear system.

The approach provides a feasible solution to a challenging inverse problem.

Abstract

We propose a numerical procedure to solve an inverse problem that estimates the state of a magma reservoir from observed surface displacement of a volcano. Our variational approach aims to find the minimizer of a cost function consisting of a norm concerning both data and derivative, which evaluates the misfit between the estimated and observed displacement. The extremal of the cost function leads to a linear system, to find the stress distribution on the reservoir surface, has very high condition number, but it is feasible to get appropriate solution by using high precision arithmetic.