A mechanical model of the large-deformation 2005 Sierra Negra volcanic eruption derived from inSAR measurements

During the past decade, Space-borne Interferometric Synthetic Aperture Radar (InSAR) has been successfully used to measure millimeterto meter-level deformation on the surface due to physical process at depth including magma accumulation and migration, pressurization, and crystallization. The InSAR data of deformation have been explained using various source models of simple geometry. The InSAR data contain the effects of baseline, topography, deformation, and atmosphere. The topography effect is removed using a Digital Elevation Model (DEM). At Sierra Negra volcano in Isabela Island, Galápagos, both highand low-resolution DEMs are available, and their merits and demerits are complementary to each other. We develop an optimal algorithm to merge the two DEMs to produce a new DEM that is superior to both of the original DEMs. This DEM is used for InSAR processing throughout this work. The magma chamber at Sierra Negra is believed to be a sill at a shallow depth. In order to solve for the detailed geometry of the sill, we develop a new modeling technique. The method uses a uniformly pressurized crack as a forward function in a stochastic inversion scheme of simulated annealing. Binary parameters that represent the locations of the crack elements are optimized in the simulated annealing. This modeling approach provides physically more plausible and internally more consistent model than kinematic models. 2005 eruption at Sierra Negra poses a great challenge in forming interferograms inside the caldera of the volcano. An earthquake of Mw 5.4 occurred 3 hours prior to the onset of the eruption, and the maximum subsidence during the eruption is about 5.4 m at the center of the caldera. Due to this large and complex deformation, we were not able to form an intra-caldera interferogram using standard InSAR processing software. Thus, we develop a new interferogram formation algorithm that involves more robust SAR image v coregistration and range offset image subtraction. The resulting interferogram is used for modeling the 2005 eruption at Sierra Negra. The 2005 eruption at Sierra Negra was modeled using InSAR and GPS data. The model consists of three main parts: trapdoor faulting, dike intrusion, and opening-closing of a sill. The depth and the detailed geometry of the sill was estimated from an ascending and descending interferogram pair before the eruption. The estimated depth is 1.86 km ± 0.13 km. The GPS data were used to estimate preand post-eruptive inflation, and the deformation due to the inflation was removed from the InSAR data in order to effectively reduce the temporal baseline of the InSAR data. In the trapdoor faulting model, the estimated maximum slip ( 1.8 m) is at the bottom of the western end of the fault system, and about 1.5 m toward the surface, which matches the field observation very well. The equivalent moment magnitude of the total slip was estimated to be Mw 5.7 when the shear modulus is 30 GPa. For shear modulus of 10 GPa, it becomes Mw 5.4, which is the moment magnitude of the earthquake that occurred 3 hours prior to the onset of the eruption. The dike model showed average opening of 1.7 m and “reverse faulting” average dip slip of 1.6 m. The large dip slip is due to the interaction with the sill and the free surface. The the sill model is the sum of two components: interaction with the trapdoor faulting event and uniformly depressurized closing during the eruption. The interaction component showed a wedge-like opening distribution close to the fault system, and the uniformly depressurized sill accounted for the co-eruptive subsidence. The repeating cycle of trapdoor faulting and eruption can produce an accumulated wedge-like structure at depth as well as on the surface. We believe that the surface expression of this structure is shown as the characteristic C-shaped sinuous ridge inside the caldera of Sierra Negra. The estimated volume decrease at the sill was 0.124 km3, and the estimated extruded volume (dense rock equivalent) was about 0.120 km3. This similarity suggests that there may not have been substantial amount of volatiles in the magma before the eruption.