Relation between Tsunami Magnitude and Wave Energy

Based on the attenuation of the maximum wave height with the distance along the continental shelf from the earthquake epicenter, the tsunami magnitude of Imamura-Iida scale, m, are determined. According to the present method of making use of far-field tsunami waves observed by many tide gauges, the tsunami magnitude can be estimated within the accuracy of about ±0.5. For example, the tsunami magnitude of the 1960 Chile tsunami is the largest where m=4.5. The 1952 Kamchatka and the 1964 Alaska tsunamis are m=4. Using the data of the seismic fault model analyzed from the observed tsunami waves and the crustal deformation of the ocean floor, the relation between tsunami energy Et and tsunami magnitude m is expressed as log Et=0.7m+19.1. The tsunami energy is reduced by one-fifth with the decrease of magnitude in unity. The potential energy is the order of 1021 ergs for large tsunami (m=3) and of 1013 ergs for small tsunami (m=-1). The average vertical displacement in a tsunami source, estimated by using the tsunami energy and the source area, is 1 to 1.5 meters for large tsunami and 10 to 20 cm for small tsunami. The tsunami magnitude m is good closely related to the earthquake magnitude of Kanamori scale Mw which is estimated from the strain energy released in earthquakes or the seismic wave energy. Combining Mw and the seismic moment M0, which is empirically expressed as log M0 = 0.77m + 26.89