Estimating the Effect of Earth Elasticity and Variable Water

The speed of tsunami waves is typically calculated using the shallow-water 3 approximation over a rigid-body Earth. Recent comparisons of tsunami arrival 4 times from the March 11, 2011 tsunami suggest, however, that the standard for-5 mulation has errors around the one percent level, and it has been suggested that 6 the elasticity of the Earth can explain the discrepancy. While previous work has 7 indeed shown that such elastic deformation can modify tsunami speeds, the ef-8 fect has been neglected partly due to the difficulty in understanding how large 9 this elastic effect is. Here, we remedy this by providing a new derivation and 10 expression for how to incorporate the first-order effect that solid Earth elastic-11 ity and ocean water compressibility has on tsunami speeds. This result is shown 12 to agree approximately with previous theory, and helps to explain observed tim-13 ing discrepancies from the March 11, 2011 tsunami. The dispersive elastic cor-14 rection and the non-dispersive compressibility correction together may account 15 for the majority of the observed discrepancy.