Estimating the stress drop (Δσ) occurring during an earthquake allows us to characterize the mechanical state of the area surrounding its source. The magnitude (Mw) and the source radius (r) of an earthquake are usually assumed to scale such that Δσ is constant. We typically refer to this assumption as self-similarity of earthquakes.
However, estimates of Δσ can vary by at least four orders of magnitude (e.g., Cocco et al., 2016, DOI: 10.1007/s10950-016-9594-4). It is an open question to what extent this variability is caused by methodological and data uncertainties, or it is a manifestation of different physical processes (Abercrombie et al., 2025, DOI: 10.1785/0120240158). This is especially true for smaller events, due to a strong correlation between source and propagation terms in the waveform modeling.
In this study, we obtain precise relative source parameters (seismic moment, corner frequency and stress drop) estimates analyzing the spectral ratios of co-located events with similar source mechanisms. This allows us to get rid of the propagation term in the waveform modeling, and to focus on the effects of the assumed source model on the stress drop.
We analyze pairs of events recorded during 2017 in North Ibaraki region (Japan) by a high-resolution temporary seismic network operated by AIST and by Hi-net stations, and during Pawnee and Prague earthquakes in Oklahoma (2011 and 2016, respectively). Overall, we explore a range of magnitudes from M = 0.7 to M = 5.8.
We find that source model and self-similarity are not always compatible and that in general a strong correlation exists between stress drop estimates and the source parameter γ that describes the decay of source spectrum at high frequencies (γ = 2 in the model). This emphasizes the importance of considering γ as a free parameter when modeling earthquake source spectra.
Moreover, our approach allows us to investigate potential differences among catalog and moment magnitudes through the inferred relative seismic moment estimates. For the small events in Ibaraki, we find differences larger than 0.5 units between local magnitude (Ml) and moment magnitude, supporting previous evidence of non-linear relationships between Ml and Mw (e.g., Uchide and Imanishi, 2018, DOI:10.1002/2017JB014697). This highlights the importance of expanding Mw catalogs to smaller magnitudes, as statistical analysis of Ml catalogs may be affected by systematic biases.
This study was supported by TRANSFORM², funded by the European Commission under project number 101188365 within the HORIZON-INFRA-2024-DEV-01-01 call.