M_TSU: Recovering seismic moments from tsunameter records

We define a new magnitude scale, M_TSU, allowing the quantification of the seismic moment M₀ of an earthquake based on recordings of its tsunami in the far field by ocean-bottom pressure sensors ("tsunameters") deployed in ocean basins, far from continental or island shores which are known to affect profoundly and in a nonlinear fashion the amplitude of the tsunami wave. The formula for M_TSU, M_TSU = log₁₀ M₀ - 20 = log₁₀ X (ω) + C_D ^TSU + C_S ^TSU + C₀, where X (ω) is the spectral amplitude of the tsunami, C_D ^TSU a distance correction and C_S ^TSU a source correction, is directly adapted from the mantle magnitude M_m introduced for seismic surface waves by Okal and Talandier. Like M_m, its corrections are fully justified theoretically based on the representation of a tsunami wave as a branch of the Earth's normal modes. Even the locking constant C₀, which may depend on the nature of the recording (surface amplitude of the tsunami or overpressure at the ocean floor) and its units, is predicted theoretically. M_TSU combines the power of a theoretically developed algorithm, with the robustness of a magnitude measurement that does not take into account such parameters as focal geometry and exact depth, which may not be available under operational conditions in the framework of tsunami warning. We verify the performance of the concept on simulations of the great 1946 Aleutian tsunami at two virtual gauges, and then apply the algorithm to 24 records of 7 tsunamis at DART tsunameters during the years 1994-2003. We find that M_TSU generally recovers the seismic moment M₀ within 0.2 logarithmic units, even under unfavorable conditions such as excessive focal depth and refraction of the tsunami wave around continental masses. Finally, we apply the algorithm to the JASON satellite trace obtained over the Bay of Bengal during the 2004 Sumatra tsunami, after transforming the trace into a time series through a simple ad hoc procedure. Results are surprisingly good, with most estimates of the moment being over 10²⁹ dyn-cm, and thus identifying the source as an exceptionally large earthquake.