Automatic computation of moment magnitudes for small earthquakes and the scaling of local to moment magnitude

P>Moment magnitudes (M-W) are computed for small and moderate earthquakes using a spectral fitting method. 40 of the resulting values are compared with those from broadband moment tensor solutions and found to match with negligible offset and scatter for available M-W values of between 2.8 and 5.0. Using the presented method, M-W are computed for 679 earthquakes in Switzerland with a minimum M-L = 1.3. A combined bootstrap and orthogonal L1 minimization is then used to produce a scaling relation between M-L and M-W. The scaling relation has a polynomial form and is shown to reduce the dependence of the predicted M-W residual on magnitude relative to an existing linear scaling relation. The computation of M-W using the presented spectral technique is fully automated at the Swiss Seismological Service, providing real-time solutions within 10 minutes of an event through a web-based XML database. The scaling between M-L and M-W is explored using synthetic data computed with a stochastic simulation method. It is shown that the scaling relation can be explained by the interaction of attenuation, the stress-drop and the Wood-Anderson filter. For instance, it is shown that the stress-drop controls the saturation of the M-L scale, with low-stress drops (e.g. 0.1-1.0 MPa) leading to saturation at magnitudes as low as M-L = 4.