Implications for Non-Self Similar Energy and Moment Scaling of Small-to-Moderate Earthquakes Along the NAFZ: Source Displacement Spectra Derived from Coda Waves

For decades, the seismological community has debated the scaling relationships of earthquake sources. The debate centers around whether the scaled energy (E_R/M₀) remains uniform across all magnitudes, indicating self-similarity, or if there is an increase in scaled energy with seismic moment, M₀. To contribute to this discussion, we analyzed coda derived source displacement spectra of 303 local earthquakes that occurred in and around the segments of the North Anatolian Fault Zone (NAFZ) within the Sea of Marmara. Our database includes digital waveform recordings of the events that were occurred between 2018 and 2020 (2.5≤ M_L ≤5.7 within a radius of 200 km) and were recorded at 49 seismic stations operated by the Kandilli Observatory and Earthquake Research Institute (KOERI) in the study area. We employed a joint inversion technique to optimize source-, path-, and site-specific factors simultaneously. This was achieved by comparing the observed coda envelope with its physically derived representative synthetic coda envelope based on Radiative Transfer Theory. Our inversion process, conducted across various frequency bands, enabled us to make reliable coda-based seismic moment (M₀) and moment magnitude estimates (M_w-coda) consistent with local catalogue magnitudes. The variation of the scaled energy (E_R/M₀) calculated from the total seismic radiated energy (E_R) using coda-derived source displacement spectra for each event tends to increase with seismic moment across most magnitude ranges. This indicates that the crustal earthquakes with M_w-coda 2.5 and M_w-coda 5.7 in this laterally heterogeneous region are likely to follow non-self-similarity. Our findings imply different rupture dynamics working for large earthquakes than small ones and relatively more efficient seismic energy radiation for larger earthquakes along the northwestern part of the NAFZ.