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 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. Other 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 geoid anomaly due to ocean water redistribution or do not specify the effects on gravity. Our model results differ from these studies in the sense that they do not show a broad drop in relative sea level or broad negative geoid anomaly due to ocean effects. The ocean contribution to relative sea level and geoid height that we modeled shows patterns similar to the di-pole of both the inputs for the SLE: the vertical deformation of the ocean floor and geoid anomaly from the solid Earth model. We argue how our results make sense from a geophysical perspective and how the similarity between inputs and outputs of the SLE can be expected. While inclusion of the seismic sea-level equation, next to solid Earth models, does not have a large impact on relative sea-level and surface deformation we conclude that the sea-level equation is essential for modeling gravity changes due to sub-oceanic earthquakes as in the modeled case of a mainly dip-slip earthquake positive and negative geoid anomalies can decrease up to 30%. Besides the implementation of the SLE, a detailed approach to modeling an earthquake in a normal mode model is shown that better approaches a realistic continuous slip on the fault plane than normal mode models that only use a few point sources or distribute seismic point sources on a line at a specific depth. Next, we show the differences in resulting vertical deformation and geoid anomaly with respect to simpler normal mode models.