The relation between differential stress, driving pressure ratio, tensile strength and reservoir failure in a magmatic system – Towards eruption forecasting

Abstract

In this study a relation is established between differential stress (σd), driving magma pressure ratio (R′) and tensile strength (T) of a rock mass in a volcanic system. It is shown that in σd vs. R′ space, the T curve follows equation of rectangular hyperbola and for dyking or volcanic eruption to occur, this T curve must be exceeded. It is proposed that this theoretical relation can be exploited to understand magma reservoir failure and for volcanic eruption forecasting. Applicability of this concept is demonstrated on Santorini volcanic system (Greece) for which considerable background information is available from previous studies. Published dyke orientation and aspect ratio data from Santorini yield σd and R′ values of 8.04 MPa and 0.22 respectively. Considering a weak quality host rock mass in Santorini, tensile strength curve for T = 1.5 MPa is plotted in σd vs R′ space. Considering magma reservoir volume and rock physical property estimates to be valid, and assuming σd and absolute stress to be constant, it is argued that change in reservoir dynamics would be controlled by variations in volume of magma released from the deeper magma reservoir to shallow reservoir (Vr) in Santorini. Values of R′ and Vr for the events of non-dyking in Santorini are also calculated. Minimum R′ and Vr required to induce dyking and eruption are estimated and it is concluded that the proposed theory can be generally applied for eruption forecasting.