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With the present study we introduce a fast and robust method to calculate thesource displacement spectra of small earthquakes on a local to regional scale.The work is based on the publicly available Qopen method of full envelopeinversion which is further tuned for the given purpose. Important sourceparameters -- seismic moment, moment magnitude, corner frequency andhigh-frequency fall-off -- are determined from the source spectra by fitting asimple earthquake source model. The method is demonstrated by means of a dataset comprising the 2018 West Bohemia earthquake swarm. We report momentmagnitudes, corner frequencies, and centroid moment tensors inverted from shortperiod body waves with the Grond package for all earthquakes with a localmagnitude larger than 1.8. Moment magnitudes calculated by envelope inversionshow a very good agreement to moment magnitudes resulting from theprobabilisitc moment tensor inversion. Furthermore, source displacement spectrafrom envelope inversion show a good agreement with spectra obtained by multipletaper analysis of the direct onsets of body waves, but are not affected by thelarge scatter of the second. The seismic moments obtained with the envelopeinversion scale with corner frequencies according to $M_0 \proptof_{\mathrm{c}}^{-4.7}$. Earthquakes of the present data set result in a smallerstress drop for smaller magnitudes. Self-similarity of earthquake rupture isnot observed. Additionally, we report frequency-dependent site amplification atthe used stations.

Fast and robust earthquake source spectra and moment magnitudes from envelope inversion