Toward a Universal Frequency of Occurrence Distribution for Tsunamis: Statistical Analysis of a 32-Year Bottom Pressure Record at Axial Seamount

Detailed examination of a 32-year record of high-resolution bottom pressure measurements at Axial Seamount (and vicinity) in the northeast Pacific identified a total of 41 tsunamis between 1986 and 2018. All of the events were associated with tsunamigenic earthquakes with magnitudes of 7.0 and greater. Statistical analysis of the data reveals that the time series of maximum tsunami amplitude and root-mean-square (RMS) tsunami amplitude follow strict power-law distributions, with considerably less deviation than for coastal tide gauge records. The high statistical reliability of the seamount record is attributable to the long duration of the observations and to the low signal-to-noise ratio of digital open-ocean bottom pressure records. The power law for the RMS tsunami amplitude is especially stable and follows a pure Pareto distribution (with exponent, beta = 1.24) even when the minimum threshold is increased to the point that only a few events remain in the time series. Plain Language Summary We use a unique 32-year time series of nearly continuous bottom pressure measurements near the summit of an active submarine volcano (Axial Seamount) to determine the amplitudes of all tsunamis (big and small) that occurred in the Pacific Ocean between 1986 and 2018. The data were then used to derive an empirical power-law relationship between the "size" (amplitude) of the tsunami waves and their frequency of occurrence. Derivation of the power-law provides a major step toward the establishment of a tsunami size-frequency law equivalent to the Gutenberg-Richter law for earthquake magnitude.