Snell’s Law Applied to Tsunamis: Simulations and Observations

Abstract

At the edge of a continental shelf, where the depth of the ocean column can vary rapidly by a factor of $$\sim $$ 20, tsunamis are expected to be severely refracted in application of Snell’s Law. We use beaming techniques applied to numerical simulations under the shallow-water approximation, in the geometry of two real-life provinces of the Pacific Basin featuring sharp bathymetric discontinuities and extended shelves (Southeastern Alaska and Nicaragua). We conclude that tsunamis do indeed undergo refraction under Snell’s Law with equivalent refraction indices as high as 5. We apply the same technique to actual records of the 2011 Tohoku tsunami by an array of seafloor pressure sensors off the coast of Southern California, and similarly observe Snell refraction despite a smaller velocity contrast and the presence of a shelf with extremely irregular bathymetry. Finally, we show numerically that for a source and a linear array of receivers both deployed on a well developed continental shelf bordering a deep basin, the tsunami will develop a head wave in all ways similar to the familiar case of refraction seismology.