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

Abstract

[1] 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 À54 +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.Citation: Masterlark, T., K. L. Feigl, M. Haney, J. Stone, C. Thurber, and E. Ronchin (2012), Nonlinear estimation of geometric parameters in FEMs of volcano deformation: Integrating tomography models and geodetic data for Okmok volcano, Alaska,

Post-Eruptive Inflation of Okmok Volcano, Alaska, from InSAR, 2008–2014

“…Our analysis indicates that the source location responsible for surface deformation at Okmok during 2008-2014 is very close to-effectively the same as-that active before, during, and after the 1997 and 2008 eruptions [1,10,11,16,[18][19][20]42]. Additionally, similar to deformation trends during 1992-2008, the source strength varied over time during [2008][2009][2010][2011][2012][2013][2014], reflecting changes in the rate of supply to the shallow magma storage zone beneath the volcano.…”

“…Although we have results spanning 2011-2014 from TerraSAR-X track 93, we did not include these in modeling of source geometry because of the presence of numerous unwrapping errors. Deformation at Okmok has been modeled using a point source within a homogenous isotropic elastic half-space [17] in previous studies e.g., [1,9,10,16,18,28,30,42]. Lu et al [18] concluded that the synthetic interferograms for the best fit Mogi source are indistinguishable from those for the best fit prolate spherical sources; therefore, the Mogi [17] source is employed in the current analysis for computational simplicity.…”

Volcano deformation source parameters estimated from InSAR: Sensitivities to uncertainties in seismic tomography

“…Previous studies of Okmok demonstrated that models simulating a variable (heterogeneous) distribution of material properties, such as the existence of a caldera filled with weak materials, as determined from seismic tomography models, will lead to estimates of source depths that are significantly deeper than estimates from models having a uniform (homogeneous) distribution of material properties. This result is due to a focusing of the strain within the weak caldera materials [ Masterlark , ; Masterlark et al , , , ]. The purpose of this study is to quantify how deformation source parameters estimated from inverse analyses of geodetic data are influenced by uncertainties in the seismic tomography model.…”

“…Note that shear wave velocities vary in both horizontal and vertical directions. Modified from Masterlark et al [].…”

Repeated magmatic intrusions at El Hierro Island following the 2011–2012 submarine eruption

“…Furthermore, the analytical source models used to invert the ground deformation data are characterized by being flat Earth models that assume a simple pressure source in a homogeneous, isotropic, elastic half-space. Heterogeneities of the crust, in both lithology and temperature for example, affect the deformation signal observed in the surface (Masterlark et al, 2012); however this information is not available for use in this study. Despite their limitations, the elastic half-space models are widely used primarily because of the simplicity of the equations, the good approximation of the sources obtained, and the rapid processing times, making these A C C E P T E D M A N U S C R I P T 32 models useful for near-real time volcano monitoring (Lisowski, 2007).…”