M_m: A variable-period mantle magnitude for intermediate and deep earthquakes

We extend to the case of intermediate and deep earthquakes the mantle magnitude developed for shallow shocks by okal and Talandier (1989). Specifically, from the measurement of the spectral amplitude of Rayleigh waves at a single station, we obtain a mantle magnitude, M_m, theoretically related to the seismic moment of the event through {Mathematical expression} The computation of M_minvolves two corrections. The distance correction is the same as for shallow shocks. For the purpose of computing the frequency-dependent source correction, we define three depth windows: Intermediate (A) (75 to 200 km); Intermediate (B) (200-400 km) and Deep (over 400 km). In each window, the source correction C_S is modeled by a cubic spline of log₁₀T. Analysis of a dataset of 200 measurements (mostly from GEOSCOPE stations) shows that the seismic moment of the earthquakes is recovered with a standard deviation of 0.23 units of magnitude, and a mean bias of only 0.14 unit. These figures are basically similar to those for shallow events. Our method successfully recognizes truly large deep events, such as the 1970 Colombia shock, and errors due to the potential misclassification of events into the wrong depth window are minimal.