Tsunami height and earthquake magnitude: Theoretical basis of an empirical relation

Abstract

The relation between maximum far‐field tsunami amplitude H and earthquake magnitude Mw has recently been investigated empirically by Abe (1979) who noted that for large circum‐Pacific earthquakes Mw ≃ 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 Mw = (4/3) log H + B′ if dispersion during the propagation of the tsunami waves is neglected, and Mw = (2/3) log H + B″ in the highly dispersive limit, which closely match and bracket the empirical relation.