Combining Magma Flow and Deformation Modeling to Explain Observed Changes in Tilt

Abstract

The understanding of magma ascent dynamics is essential in forecasting the scale, style and timing of volcanic eruptions. The monitoring of near-field deformation is widely used to gain insight into these dynamics, and has been linked to stress changes in the upper conduit. The ascent of magma through the conduit exerts shear stress on the conduit wall, pulling up the surrounding edifice, whilst overpressure in the upper conduit pushes the surrounding edifice outwards. How much shear stress and pressure is produced during magma ascent, and the relative contribution of each to the deformation, has until now only been explored conceptually. By combining flow and deformation modeling using COMSOL Multiphysics, we for the first time present a quantitative model that links magma ascent to deformation. We quantify how both shear stress and pressure vary spatially within a cylindrical conduit, and show that shear stress generally dominates observed changes in tilt close to the conduit. However, the relative contribution of pressure is not insignificant, and both pressure and shear stress must be considered when interpreting deformation data. We demonstrate that significant changes in tilt can be driven by changes in the driving pressure gradient or volatile content of the magma. The relative contribution of shear stress and pressure to the tilt varies considerably depending on these parameters. Our work provides insight into the range of elastic moduli that should be considered when modeling edifice-scale rock masses, and we show that even where the edifice is modeled as weak, shear stress generally dominates the near field deformation over pressurization of the conduit. While our model addresses cyclic tilt changes observed during activity at Tungurahua volcano, Ecuador, between 2013 and 2014, it is also applicable to silicic volcanoes in general.

Topography and Tilt at Volcanoes

“…To do this, we present results of 3D deformation modeling, using 10 m × 10 m digital elevation models (DEMs) of Tungurahua volcano, Ecuador and Soufrire Hills volcano, FIGURE 6 | (A-D) Amplification factor and difference due to the topographic effect on tilt produced by shear stress, where opposing slopes are included at either x = 2,500 or 9,000 m, as indicated by red dots. (E) Depth variant shear stress profile from flow modeling of Marsden et al (2019). (F) Amplitude and orientation of the displacement field produced by shear stress.…”

“…Broad centimeter to meter-scale uplift and subsidence over periods of months to years can be indicative of inflation and deflation of a magma reservoir at depth (Mogi, 1958). Close to the conduit, cyclic variations in tilt have been linked to shear stress exerted on the conduit wall as magma ascends (Beauducel et al, 2000;Neuberg et al, 2018;Marsden et al, 2019). Near-field deformation has also been linked to a pressure source in the upper edifice (Voight et al, 1999;Widiwijayanti et al, 2005;Hautmann et al, 2009).…”

“…• Reservoir pressure: A spherical reservoir centered directly below the summit at a depth of 8 km below the mean elevation, with a radius of 500 m and a pressure of 20 MPa. • Conduit shear stress: Reference depth-variant shear stress profile from Marsden et al (2019), derived through flow modeling, extending from the surface to a depth of 5 km. • Conduit pressure: Depth-variant over-pressure profile from the same model in Marsden et al (2019), similarly extending from the surface to a depth of 5 km.…”

“…(A-D) Amplification factor and difference due to the topographic effect on tilt produced by conduit pressure, where opposing slopes are included at either x = 500 or 1,500 m, as indicated by red dots. (E) Depth variant pressure profile from flow modeling ofMarsden et al (2019). (F) The amplitude and orientation of the displacement field produced by shear stress.…”

Drumbeat LP “Aftershocks” to a Failed Explosive Eruption at Tungurahua Volcano, Ecuador

“…Unrest at Tungurahua was typically associated with high rates of LP seismicity. Between the major explosive episodes of 2014 and 2016, heightened seismicity accompanied deformation and repeating tilt cycles (Bell et al, 2017; Marsden et al, 2019; Neuberg et al, 2018). This study focuses on an episode of drumbeats during one such cycle in November 2015.…”