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Tsunami height and earthquake magnitude: Theoretical basis of an empirical relation
Author(s) -
Comer Robert P.
Publication year - 1980
Publication title -
geophysical research letters
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 2.007
H-Index - 273
eISSN - 1944-8007
pISSN - 0094-8276
DOI - 10.1029/gl007i006p00445
Subject(s) - seismology , amplitude , seismic moment , scaling , geology , magnitude (astronomy) , earthquake magnitude , slip (aerodynamics) , tsunami earthquake , fault (geology) , geodesy , physics , geometry , mathematics , optics , astronomy , thermodynamics
The relation between maximum far‐field tsunami amplitude H and earthquake magnitude M w has recently been investigated empirically by Abe (1979) who noted that for large circum‐Pacific earthquakes M w ≃ log H + B, where B depends on the source location and on the region of tsunami observations. We have predicted theoretically the scaling of far‐field tsunami amplitudes with seismic moment and fault area, by combining relations between seismic parameters (assuming constant stress drop) by estimating scaling relations between fault area, average slip, and tsunami source dimensions, and by using some results from basic hydrodynamics. The theoretical predictions imply relations of the form M w = (4/3) log H + B′ if dispersion during the propagation of the tsunami waves is neglected, and M w = (2/3) log H + B″ in the highly dispersive limit, which closely match and bracket the empirical relation.