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

Abstract

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 ∼ 1:5M 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 ∼ 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.

A Consistent High‐Resolution Catalog of Induced Seismicity in Basel Based on Matched Filter Detection and Tailored Post‐Processing

“…For the conversion between Ω 0 and M o , we replicated the physical parameters used by GEL (density ρ =2,650 kg/m 3 , S velocity β =3,450 km/s, and average radiation pattern of S waves FS =0.63; T. Spillmann, personal communication, 2015). Our M w estimates were averaged over all three borehole stations and compare well to GEL's M w estimates (3,552 events, Figure S4a) and to the M w estimates calculated by Bethmann et al () for a subset of the SED catalog (195 events, Figure S4c). For the sake of completeness, we document here that the M w estimates of GEL and Bethmann et al () are also in good agreement with each other (Figure S4d).…”

“…Our M w estimates were averaged over all three borehole stations and compare well to GEL's M w estimates (3,552 events, Figure S4a) and to the M w estimates calculated by Bethmann et al () for a subset of the SED catalog (195 events, Figure S4c). For the sake of completeness, we document here that the M w estimates of GEL and Bethmann et al () are also in good agreement with each other (Figure S4d).…”

“…Locations are based on master‐event relocation provided by N. Deichmann (personal communication, 2018). Moment magnitudes were obtained by F. Bethmann (personal communication, 2011) as presented in Bethmann et al () for 195 events (until end of 2007); for the remaining 31 events, we converted local magnitudes, M L —as obtained by N. Deichmann (personal communication, 2018) using the median value of four station magnitudes (Deichmann & Ernst, ; Deichmann et al, )—into M w using the scaling relation of Bethmann et al, ( M w = 0.633· M L + 0.766).…”

Pore pressure behavior at the shut‐in phase and causality of large induced seismicity at Basel, Switzerland

“…The magnitude of induced seismicity at Basel was estimated by several different research groups, on behalf of GEL [ Dyer et al ., ; Dyer et al ., ; Mukuhira et al ., ] and on behalf of SED [ Deichmann and Giardini , ; Edwards et al ., ; Bethmann et al ., ]. GEL estimated the moment magnitude with a spectral fitting method on P / S waveforms from several borehole stations, and they also estimated the moment magnitude in time domain using amplitude of first arrival of P wave at the deepest station [ Dyer et al ., ].…”

A Method for Calibration of the Local Magnitude Scale Based on Relative Spectral Amplitudes, and Application to the San Juan Bautista, California, Area

“…On a larger scale, Shearer et al (2006) estimated that β ≈ 1:0 for M ≲3 earthquakes in southern California. The small scaling factor β < 1:5 often observed for local magnitudes of small earthquakes may arise because the seismic waves at the recording frequencies depend on the earthquake source duration (Hanks and Boore, 1984;Deichmann, 2006;Edwards et al, 2010;Bethmann et al, 2011), because earthquake characteristics change with magnitude (Ben-Zion and Zhu, 2002), or because attenuation is larger at the higher dominant frequencies of smaller earthquakes (Deichmann, 2006;Edwards et al, 2010;Bethmann et al, 2011).…”