Analytical solutions for gravity changes caused by triaxial volumetric sources

Abstract

Intrusion of magma through the host rock or into an existing magma chamber deforms the Earth's crust and also changes the surface gravity field. The intrusion mass is a key parameter for characterizing the nature of the activity and its future evolution. Joint analyses of the measured surface displacements and gravity changes can constrain the intrusion mass, beside the other parameters of the deformation source, that is, its location, shape,

Microgravity Change During the 2008–2018 Kı̄lauea Summit Eruption: Nearly a Decade of Subsurface Mass Accumulation

“…The local free-air gradient depends significantly on the source of deformation and may be different for, for example, post-glacial rebound (Olsson et al, 2015) compared to volcano deformation involving subsurface fluid redistribution, where the free-air gradient or Bouguer corrected free-air gradient (Vajda et al, 2020(Vajda et al, , 2021) may be more suitable. Free-body geometry inversions or coupled inversions of surface deformation and gravity (Nikkhoo & Rivalta, 2021) may provide an alternative to recover source parameters; however, mass accumulation without commensurate surface deformation that involves non-elastic behavior, for example, density changes through degassing or the compressibility of gas-rich magma (Rivalta & Segall, 2008), makes joint inversions of gravity and deformation nontrivial. Furthermore, because multiple processes and sources may have been active over the 2009-2015 period, we adopted a classical approach, applying a (theoretical) correction for the observed vertical surface deformation before completing point source gravity inversions.…”

“…Summit eruptive activity between 2008 and 2018 was captured by a diverse set of geodetic observations, including campaign and continuous Global Navigation Satellite System (GNSS), borehole tilt, InSAR, and campaign and continuous microgravity (Poland, Miklius, et al, 2021). Deformation data are an effective tool for investigating changes in subsurface volume and pressure beneath Kılauea (Bemelmans et al, 2021;Jo et al, 2015); however, only gravity measurements can provide constraints on whether surface deformation is accompanied by subsurface changes in mass-information that is critical for understanding the source of geodetic change (Carbone et al, 2017;Nikkhoo & Rivalta, 2021). Mass accumulation may be a precursor to volcanic activity (Rymer, 1994), making the technique valuable and widely adopted in volcano monitoring to produce quantitative estimates of source characteristics at volcanoes worldwide (Carbone & Greco, 2007;Miller et al, 2017).…”

A New Analysis of Caldera Unrest through the Integration of Geophysical Data and FEM Modeling: The Long Valley Caldera Case Study

“…We validate the FEM model by performing a benchmark calculation for a vertical prolate ellipsoid in a flat homogeneous domain and comparing the numerical results to the analytical solutions by [47] (see Appendix A).…”

“…We first compare the horizontal and vertical components of displacement on the stress-free surface on ±40 km EW profile (Figure A1a). Successively, we calculate the gravity changes due to the source deformation and to an intruding fluid with a density of 2700 kg/m 3 using the method described in the main text (Section 2.4) and compare them with the analytical solutions from [47] (Figure A1b,c). For the gravity contribution from the mass change (δ g2V ), we also checked with the solutions from [60].…”