Analytical and numerical model estimates of ground surface displacements in dual magma chamber setting

Magmatic overpressure in shallow- and mid-crustal magma chambers (MC) can deform the crustal host rocks. Stress field produced by such deformation often control the nucleation and subsequent crack formation for magma emplacement. A direction of physical volcanology is concerned with determination of the volcanotectonic ground surface displacements that can aid in monitoring and sometimes forecasting magmatic eruptions. The existing Mogi Model can analytically calculate surface displacements due to overpressure in a single MC by considering elastic deformation of a finite crustal section. Many geological and geophysical studies report that magma plumbing systems represent an array of randomly placed interconnected MCs, and there is a need of theoretical estimation of their ground surface displacement. In this study we present a new analytical formulation to estimate surface displacement in terms of both vertical as well as horizontal directions above a dual MC setting. Our analytical solution finds support from finite element (FE) models performed with the same set of geometrical and physical parameters. The off-axis chambers considered in our model are separated along both vertical and horizontal directions. The present study suggests that with increasing horizontal chamber separation (S_h) the vertical ground displacement above the two chambers gradually changes from a single peak into an indistinct double-peak, and finally two prominent independent, high-amplitude peaks. On the other hand, on increasing the vertical separation (S_v) between two off-axis chambers we observed that the initial double peaks merged to produce a single peak situated roughly above the middle of the two chambers. Stress map obtained from the FE models shows that the deformation of two MCs can only interact when located within a critical distance, else their deformation remains independent. Interestingly, our study suggests that the magnitude of stress field strongly depends on the strength of the mechanical interaction between two neighboring chambers.