A new solution for displacements and gravity changes caused by pressurized (triaxial) ellipsoidal cavities in a half-space: source configuration and implications for joint inversions

Deformation source inversions have played a substantial role in our present understanding of magma plumbing systems at active volcanoes. Such inversions mostly rely on analytical models for uniformly-pressurized cavities as idealized representations of expanding magma bodies. The most common analytical cavity models used for rapid inversions are the isotropic point-source, the finite spheroidal cavity model and tensile dislocations or cracks. All these models have very specific shapes which cannot represent potentially significant deviations of magma chambers from axisymmetric geometries; thus, this aspect of volcano deformation sources has largely remained unexplored. Potential deviations from spherical and spheroidal shapes may explain the long-wavelength systematic residuals often encountered in inversions of deformation data. Even if the biases in the inferred deformation source parameters are small, they may translate into large biases in the mass change constrained through joint inversion of deformation and gravity data.
The next step to promote our understanding about volcano deformations is to explore these complexities in the source geometries and their implications. We develop a finite ellipsoidal cavity model (finite ECM) that is a solution for surface displacements and deformation-induced gravity changes caused by finite pressurized ellipsoidal cavities. The model can be used to constrain deformation source parameters and subsurface mass changes caused by magmatic intrusions and other processes pressurizing relatively shallow magma chambers. The model is in the form of a distribution of triaxial point sources with depth-dependent spacing and strengths. We systematically validate and benchmark the model by using analytical and numerical solutions. Also through these comparisons, we explore the limitations of the finite ECM. In particular, we analyze the biases in the inferred source depth, volume change and mass change due to the approximations inherent in the model. The finite ECM is computationally efficient and can be used for coupled inversions of deformation and gravity data.