Near‐Source Waveform Modeling to Estimate Shallow Crustal Attenuation and Radiated Energy of <i>M</i>_w 2.0–4.5 Earthquakes

Abstract Estimating the radiated energy of small‐to‐moderate ( M w &lt; 5) earthquakes remains challenging because their energy decay significantly during wave propagation. Even when near‐source records are available, seismic waves pass through the shallow crust with strong attenuation, which can bias energy estimates. This study evaluated the degree of energy dissipation in the crust through modeling near‐source (&lt;12 km) waveform data in northern Ibaraki Prefecture, Japan. High‐quality waveforms recorded at a downhole sensor confined by granite with high seismic velocity helped to investigate this issue. We first estimated the moment tensors for M 1–4 events and computed their synthetic waveforms, assuming a tentative one‐dimensional attenuation ( Q −1 ) model. We then modified the Q −1 ‐model in the 5–20 Hz range such that the frequency components of the synthetic and observed waveforms of microearthquakes ( M w &lt; 1.7) matched. The results show that the Q s ‐value is as low as 55 at depths of &lt;4 km with no obvious frequency dependence. Using the derived Q −1 ‐model, we estimated the moment‐scaled radiated energy ( e R ) of 3,884 events with M w 2.0–4.5. The median e R is 3.5 × 10 −5 , similar to the values reported for M w &gt; 6 events, with no obvious M w dependence. If we use an empirically derived Q s ‐model, the median e R becomes a one‐order underestimation (2.0 × 10 −6 ). More than 70% of the energy is dissipated in the shallow crust for events with M w &lt; 4. These results demonstrate the need for an accurate understanding of shallow crustal attenuation for energy estimation of small events, even with near‐source high‐quality data.