The Method of Fundamental Solutions for Solving the Inverse Problem of Magma Source Characterization

Abstract

Volcano is one of the geodynamic phenomena causing irreparable damages. As lava accumulates in reservoir and then comes to the surface, geometry of the source can be used to predict volcanic eruptions. In this study, using the inverse method of fundamental solutions (MFS) and taking into account the effect of topography, the geometry of the source including shape, depth and centre position of the magma tank is estimated. The MFS is a numerical method for solving boundary value problems with known partial differential equations. The displacement field calculated in the previous studies using InSAR for deflation mode of Cerro Blanco volcano was utilized in this study. It was estimated that the magma source of the volcano is a sphere with a radius of 1 km located at a horizontal position of ($1.001\pm 4e-6,-1.001\pm 1e-6$) km and the depth of about 10 km from the summit with respect to the defined coordinate system. This finding is consistent with that of recent studies in which inversion of InSAR data was used to analyse the geometry of the magma source. The RMSE between the deformation fields of the magma source calculated in the previous studies and that of the study herein via MFS was approximately 3 mm.

Keywords:

• Magma source
• inverse MFS
• boundary value problem
• meshless method
• volcano

Acknowledgements

Sar data have been provided by the European Space Agency. We would also like to thank Professor Carlo Alberto Brunori for providing the InSAR displacement data of the study area.

Disclosure statement

No potential conflict of interest was reported by the authors.