Nonlinear estimation of geometric parameters in FEMs of volcano deformation: Integrating tomography models and geodetic data for Okmok volcano, Alaska

Abstract

The internal structure, loading processes, and effective boundary conditions of a volcano control the deformation observed at the Earth's surface. Using finite element models (FEMs), we simulate the response due to a pressurized magma chamber embedded in a domain having a distribution of elastic material properties. We present the Pinned Mesh Perturbation method (PMP) to automate the mesh generation process in response to perturbations of the position of a simulated magma chamber within an FEM domain. Using InSAR‐observed deformation for the 1997 eruption of Okmok volcano, Alaska, as an example, we combine PMP with nested Monte Carlo methods to estimate a set of linear and nonlinear parameters that characterize the depressurization and location of the magma chamber beneath Okmok's caldera. The three‐dimensional FEMs used in the PMP method simulate the distribution of material properties of tomography models and account for the irregular geometry of the topography and bathymetry. The estimated depth of an assumed spherical magma chamber is 3527−54+55 m below sea level and is sensitive to the distribution of material properties. This depth is consistent with lithostatic pressure constraints and very long period tremor observations. The fit of this FEM to the InSAR data is a significant improvement, at the 95% confidence level, compared to the fit of a corresponding FEM having homogeneous material properties. The methods presented here allow us to construct deformation models that integrate tomography models with geodetic observations, in an effort to achieve a deeper understanding of active volcanoes.