Importance of horizontal seafloor motion on tsunami height for the 2011 M=9.0 Tohoku-Oki earthquake

It is now clear that the 2011 Tohoku-Oki earthquake ruptured the subduction interface all the way to the Japan Trench. However, there is significant disagreement about just how much slip occurred at the trench, with most geodetic studies locating only a small fraction of the maximum slip there, whereas broadband seismic studies put the majority of the slip near the trench. Measurements of seafloor displacement near the trench also imply more slip there than is estimated by the geodetic studies. Here, by means of a joint inversion of displacement measurements and seafloor pressure data, we show that it is possible to reconcile geodetic and seismic studies and that a considerable amount of slip indeed occurred at the trench, with slip magnitudes reaching 57-74% of the maximum slip. The seafloor displacement predicted by our model agrees very well with independent measurements made close to the trench. We also find good agreement between our tsunami model and independent measurements of tsunami height in the ocean and on land. Re-running of the inversion without the near-field pressure gauge data, however, leads to underprediction of the flooding on land, even when the seafloor geodetic data are still included. Thus, even if the seafloor geodetic measurements had been available in real time, they would still not have allowed reliable prediction of near-field tsunami inundation. Close to the trench, the dip of the plate interface is shallow, which serves to decrease the vertical motion of the sea floor for any given slip. However, the horizontal motion is conversely larger. Because the ocean floor slopes steeply near the trench, it acted like a giant wedge, converting the horizontal motion of the ground into an uplift of the water column and causing the peak initial tsunami wave height to be twice as high as it would have been from vertical displacement alone.