Scaling Relations of Local Magnitude versus Moment Magnitude for Sequences of Similar Earthquakes in Switzerland

Theoretical considerations and empirical regressions show that, in the magnitude range between 3 and 5, local magnitude, M-L, and moment magnitude, M-w, scale 1:1. Previous studies suggest that for smaller magnitudes this 1: 1 scaling breaks down. However, the scatter between M-L and M-w at small magnitudes is usually large and the resulting scaling relations are therefore uncertain. In an attempt to reduce these uncertainties, we first analyze the M-L versus M-w relation based on 195 events, induced by the stimulation of a geothermal reservoir below the city of Basel, Switzerland. Values of M-L range from 0.7 to 3.4. From these data we derive a scaling of M-L similar to 1.5 M-w over the given magnitude range. We then compare peak Wood-Anderson amplitudes to the low-frequency plateau of the displacement spectra for six sequences of similar earthquakes in Switzerland in the range of 0.5 <= M-L <= 4.1. Because effects due to the radiation pattern and to the propagation path between source and receiver are nearly identical at a particular station for all events in a given sequence, the scatter in the data is substantially reduced. Again we obtain a scaling equivalent to M-L similar to 1.5M(w). Based on simulations using synthetic source time functions for different magnitudes and Q values estimated from spectral ratios between downhole and surface recordings, we conclude that the observed scaling can be explained by attenuation and scattering along the path. Other effects that could explain the observed magnitude scaling, such as a possible systematic increase of stress drop or rupture velocity with moment magnitude, are masked by attenuation along the path.