Ocean contribution to co-seismic crustal deformation and geoid anomalies: Application to the 2004 December 26 Sumatra-Andaman earthquake

Large earthquakes do not only heavily deform the crust in the vicinity of the fault, they also change the gravity field of the area affected by the earthquake due to mass redistribution in the upper layers of the Earth. Besides that, for sub-oceanic earthquakes deformation of the ocean floor causes relative sea level changes and mass redistribution of water that have again a significant effect on the gravity field. To model these deformations, sea level changes and gravity field perturbations self-consistently we use an adapted version of the sea level equation (SLE) that has been used for glacial isostatic adjustment studies. The sea level equation, next to our normal mode model for seismic solid earth modeling, allows us to compute a gravitationally self-consistent solution for the co-seismic relative sea level, surface deformation and geoid height changes. We apply our geographically detailed models to the case of the 2004 December 26 Sumatra-Andaman earthquake. Recent studies that have modeled the ocean mass effect on co-seismic gravity change for this specific earthquake show model results that indicate a broad negative change in geoid height around the fault due to ocean water redistribution (de Linage et al., 2009; Melini et al., 2010). Our model results for the ocean contribution to geoid height differ from these studies in the sense that we find a pattern similar to the elongated dipole pattern of the solid earth model outputs for gravity and vertical deformation, together with a relatively small broad negative geoid height change. We explain the relation between outcomes for geoid height, relative sea level and vertical deformation of the ocean floor and we confront our model results with a least squares estimation of the co-seismic discontinuity in GRACE-derived gravity field time series. We show that taking into account the contribution of ocean water redistribution to the co-seismic geoid height change next to a compressible solid earth model is essential to explain the predominant negative co-seismic geoid anomalies from the GRACE gravity field solutions. Besides, we introduce a detailed approach to modeling an earthquake in a normal mode model that better approximates realistic continuous slip on the fault plane than models that do not distribute slip with depth. To demonstrate the importance of the slip distribution we show the differences in outcomes for modeled geoid height and vertical deformation.