3‐D Modeling of Irregular Volcanic Sources Using Sparsity‐Promoting Inversions of Geodetic Data and Boundary Element Method

Abstract

Geodetic observations of surface deformation associated with volcanic activities can be used to constrain volcanic source parameters and their kinematics. Simple analytical models, such as point and spherical sources, are widely used to model deformation data. The inherent nature of oversimplified model geometries makes them unable to explain fine details of surface deformation. Current nonparametric, geometry‐free inversion approaches resolve the distributed volume change, assuming it varies smoothly in space, which may detect artificial volume change outside magmatic source regions. To obtain a physically meaningful representation of an irregular volcanic source, we devise a new sparsity‐promoting modeling scheme assuming active magma bodies are well‐localized melt accumulations, namely, outliers in the background crust. First, surface deformation data are inverted using a hybrid L1‐ and L2‐norm regularization scheme to solve for sparse volume change distributions. Next, a boundary element method is implemented to solve for the displacement discontinuity distribution of the reservoir, which satisfies a uniform pressure boundary condition. The inversion approach is thoroughly validated using benchmark and synthetic tests, of which the results show that source dimension, depth, and shape can be recovered appropriately. We apply this modeling scheme to deformation observed at Kilauea summit for periods of uplift and subsidence leading to and following the 2007 Father's Day event. We find that the magmatic source geometries for these periods are statistically distinct, which may be an indicator that magma is released from isolated compartments due to large differential pressure leading to the rift intrusion.

Resolving Three-Dimensional Displacements Caused by Subsurface Fluid Activities From InSAR and Volumetric Strain Model: Adaptive Estimation of Model Parameters

“…However, + 2 is a large number, and non-linear inverse algorithms cannot be used to achieve multiple parameter inverses. According to elastic half-space theory, underground fluid reservoirs are divided into multiple blocks, with each block's volume change being equivalent to the product of its average volume change and each block's volume [33], therefore, we assumed a uniform sub-surface fluid volumetric change, , and Eq. ( 9) can be rewritten as:…”