Relationship of Tsunami Intensity to Source Earthquake Magnitude as Retrieved from Historical Data

Operational prediction of near-field tsunamis in all existing Tsunami Warning Systems (TWSs) is based on fast determination of the position and size of submarine earthquakes. Exceedance of earthquake magnitude above some established threshold value, which can vary over different tsunamigenic zones, results in issuing a warning signal. Usually, a warning message has several (from 2 to 5) grades reflecting the degree of tsunami danger and sometimes contains expected wave heights at the coast. Current operational methodology is based on two main assumptions: (1) submarine earthquakes above some threshold magnitude can generate dangerous tsunamis and (2) the height of a resultant tsunami is, in general, proportional to the earthquake magnitude. While both assumptions are physically reasonable and generally correct, statistics of issued warnings are far from being satisfactory. For the last 55 years, up to 75% of warnings for regional tsunamis have turned out to be false, while each TWS has had at least a few cases of missing dangerous tsunamis. This paper presents the results of investigating the actual dependence of tsunami intensity on earthquake magnitude as it can be retrieved from historical observations and discusses the degree of correspondence of the above assumptions to real observations. Tsunami intensity, based on the Soloviev-Imamura scale is used as a measure of tsunami “size”. Its correlation with the Ms and Mw magnitudes is investigated based on historical data available for the instrumental period of observations (from 1900 to present).