Inversion for slip distribution for the 2012 Costa Rica earthquake

On 5 September 2012, a major megathrust earthquake (Mw=7.6) ruptured the plate interface beneath the Nicoya Peninsula, Costa Rica. This event was centered 12 km offshore of the central Nicoya coast, at a depth of 18 km. The maximum slip exceeded 2 meters, and the rupture spread outward along the plate interface to encompass 3000 km² of the Nicoya seismogenic zone. More than 1700 aftershocks were recorded within the first 5 days. These aftershocks outlined two distinct rupture patches; one centered on the central coast and the other beneath the southern tip of the peninsula.

We formulate a Bayesian inverse problem to infer the coseismic slip on the fault plane based on instantaneous surface displacements and changes in well heads in order to image the remaining “locked” patch that has been inferred previously. We compute the maximum a posteriori (MAP) estimate of the posterior slip distribution on the fault, and use a local Gaussian approximation around the MAP point to characterize the uncertainty. The elastic deformation is computed using a finite element method that allows for the spatial variation of elastic properties that has been observed in the crust overlying the seismogenic zone. We solve the optimization problem using gradients obtained from adjoints. The linearity of the inverse problem allows for the efficient solution of the optimal experimental design problem for the placement of the GPS stations to monitor the remaining locked patch. In the future, the results obtained here will provide the initial condition for a time-dependent poroelastic model for fault slip and fluid migration due to overpressure caused by a megathrust earthquake. This will provide constraints on the crustal permeability structure in a tectonically active region.