On precisely modelling surface deformation due to interacting magma chambers and dykes

Abstract

Combined data sets of InSAR and GPS allow us to observe surface deformation in volcanic settings. However, at the vast majority of volcanoes, a detailed 3-D structure that could guide the modelling of deformation sources is not available, due to the lack of tomography studies, for example. Therefore, volcano ground deformation due to magma movement in the subsurface is commonly modelled using simple point (Mogi) or dislocation (Okada) sources, embedded in a homogeneous, isotropic and elastic half-space. When data sets are too complex to be explained by a single deformation source, the magmatic system is often represented by a combination of these sources and their displacements fields are simply summed. By doing so, the assumption of homogeneity in the half-space is violated and the resulting interaction between sources is neglected. We have quantified the errors of such a simplification and investigated the limits in which the combination of analytical sources is justified. We have calculated the vertical and horizontal displacements for analytical models with adjacent deformation sources and have tested them against the solutions of corresponding 3-D finite element models, which account for the interaction between sources. We have tested various double-source configurations with either two spherical sources representing magma chambers, or a magma chamber and an adjacent dyke, modelled by a rectangular tensile dislocation or pressurized crack. For a tensile Okada source (representing an opening dyke) aligned or superposed to a Mogi source (magma chamber), we find the discrepancies with the numerical models to be insignificant (<5 per cent) independently of the source separation. However, if a Mogi source is placed side by side to an Okada source (in the strike-perpendicular direction), we find the discrepancies to become significant for a source separation less than four times the radius of the magma chamber. For horizontally or vertically aligned pressurized sources, the discrepancies are up to 20 per cent, which translates into surprisingly large errors when inverting deformation data for source parameters such as depth and volume change. Beyond 8 radii however, we demonstrate that the summation of analytical sources represents adjacent magma chambers correctly.

Time-dependent deformation of Uturuncu volcano, Bolivia, constrained by GPS and InSAR measurements and implications for source models

“…If we consider an overpressure bound of 10 MPa, added volume of 0.1 km 3 , and shear modulus of 40 GPa, we estimate the radius for larger (lower) reservoir to be ~5 km, and thus source interaction is non-negligible for some ranges in our homogeneous inversions. We therefore suggest that the depths and volumes in the homogenous inversions previously presented can be underestimated by up to 30% (Pascal et al, 2014). The volume and overpressure can also be modulated by assuming viscoelastic conditions (e.g., Hickey et al, 2013), and therefore we do not place a strong emphasis on a single "best-fit" model and instead emphasize the range of solutions to guide further exploration with a finite-element model.…”

“…Inversions for multiple sources in a half-space must be interpreted with caution since the presence of a second source violates the boundary condition assumptions. Pascal et al (2014) quantified the conditions under which multiple source inversions are valid by numerically modeling a suite of dualreservoir configurations. According to this study, as long as vertically aligned sources are greater than 8 times the largest source radius, inversion results are not significantly biased.…”

“…These two points are important, since they may factor into the lack of deformation observed to date in some arcs (Ebmeier et al, 2013) or the general scarcity of subsidence signals accompanying episodes of volcanic uplift. However, the assumption of vertical alignment is not always valid, and analytical predictions for surface displacements do not consider source interaction (e.g., Pascal et al, 2014).…”

Deposit loading and its effect on co-eruptive volcano deformation

“…Following Gottsmann and Odbert (2014), we apply the Brocher equation (Brocher, 2005) to the same seismic tomography data (Paulatto et al, 2010;Sevilla et al, 2010) and retrieve estimates of crustal elastic parameters beneath Montserrat. We fit a polynomial function to these estimates for z ≤ 0 and assume a constant Young's modulus in the volcanic edifice above the ellipsoid (z > 0).…”

“…Alternative pressure source geometries have also been explored in order to explain observations, including spheroidal (Yang et al, 1988) and planar (dyke) sources (Okada, 1985). It is generally recognised that simple elastic models are imperfect (Pascal et al, 2013) but can provide a fast and useful diagnosis of volcanogenic ground deformation. Complicating details, including realistic crustal rheology, magma source geometry, overpressure profiles and surface loading effects, are often neglected in order to make modelling tractable.…”