Coseismic deformation obtained from surface ocean currents in a flat bottom ocean

Seismic tsunami sources are often inferred by inverting a combination of data from onshore and offshore instruments. However, these measurements are often geographically sparse and far from the source, leading to declining resolutions in some areas, especially near the shallower parts of the rupture. We present a method for inverting dense sea surface current fields induced by tsunamigenic earthquakes to determine the distribution of deformation at the sea bottom, assuming a flat ocean floor and instantaneous deformation. We relate synthetic and real vertical deformation from earthquakes with current fields using a linear fluid model. The resulting fields are inverted using uncertain weighted constrained least squares to estimate the initial deformation. Measurement noise and the use of a simplified fluid model are taken into account by the addition of covariance matrices that act as weights over the kernel. We use linear constraints and a priori information of the subduction zone to suppress inversion artifacts. The linear formulation of the inverse problem allows for a simple analysis and quantification of the uncertainties and limitations of our method. We show that this method allows us to recover the extent, magnitude, and distribution of the underwater portion of the coseismic deformation for both synthetic and real cases. The inverted vertical deformation field maintains a constant resolution in the domain. Our results suggest that geographically dense surface current data measured directly above the source can be used to study subduction tsunamigenic earthquakes.