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

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.