Analytical Solutions for Gravity Changes Caused by Triaxial Volumetric Sources

Abstract

Volcanic crises are often associated with magmatic intrusions or the pressurization of magma chambers of various shapes. These volumetric sources deform the country rocks, changing their density, and cause surface uplift. Both the net mass of intruding magmatic fluids and these deformation effects contribute to surface gravity changes. Thus, to estimate the intrusion mass from gravity changes, the deformation effects must be accounted for. We develop analytical solutions and computer codes for the gravity changes caused by triaxial sources of expansion. This establishes coupled solutions for joint inversions of deformation and gravity changes. Such inversions can constrain both the intrusion mass and the deformation source parameters more accurately.

Plain Language Summary: Volcanic crises are usually associated with magmatic fluids that intrude and deform the host rocks before potentially breaching the Earth's surface. It is important to estimate how much fluid (mass and volume) is on the move. Volume can be determined from the measured surface uplift. Mass can be determined from surface gravity changes. The fluid intrusion increases the mass below the volcano, thereby increasing the gravity and pressurizing the rocks. This dilates parts of the host rock and compresses other parts, changing the rock density and redistributing the rock mass. This causes secondary gravity changes, called deformation‐induced gravity changes. The measured gravity change is always the sum of the mass and deformation‐induced contributions. Here, we develop mathematical equations for the rapid estimation of these deformation‐induced gravity changes caused by arbitrary intrusion shapes. This way we can take the mass contribution apart from the deformation contribution. We show that by using this solution not only the intrusion mass, but also other intrusion parameters, including the volume, depth, and shape can be calculated more accurately.

Key Points;

We develop analytical solutions for gravity changes due to the point Compound Dislocation Model simulating triaxial expansions.

Rapid coupled inversions of deformation and gravity changes, accounting for deformation‐induced gravity changes are now possible.

For shallow sources, estimation errors in the chamber volume change may lead to large biases in the simulated gravity changes.