T-wave duration, magnitudes and seismic moment of an earthquake—application to tsunami warning

We present a study of the duration, 6, of T wave trains propagating over teleseismic distances in the ocean, and recorded at island stations, in relation to the various magnitudes (m_b, M_s, M_w) of the parent earthquake. Theoretical models based on scaling laws predict relations of the form log₁₀ Θ=a+bM, with the slope b equal to 1/3 at low magnitudes, but increasing to 1/2 (and eventually to 1) because of the effect of saturation of the magnitude scales. The investigation of an extensive dataset using records of more than 400 Pacific earthquakes shows a remarkable agreement with these theoretical slopes. In the case of truly large earthquakes (M_w> 7), such relations allow an estimation of the earthquake's seismic moment at ultra-long periods within 1 to 2 hr of the origin time, with important applications to efficient tsunami warning.