Many unknowns exist regarding the energy radiation processes of the inland low-frequency earthquakes (LFEs) often observed beneath volcanoes. To evaluate their energy radiation characteristics, we estimated the scaled energy for LFEs and regular earthquakes in and around the focal area of the 2008 Mw 6.9 Iwate-Miyagi earthquake. We computed the source spectra for regular earthquakes, deep LFEs, and shallow LFEs by correcting for the site and path effects from direct S-waves. We computed the radiated energy and seismic moments, and obtained the scaled energy (eR) for 1464 regular earthquakes, 169 deep LFEs, and 52 shallow LFEs. The eR for regular earthquakes is in the order of 10-5 to 10-4, typical for crustal earthquakes, and tends to become smaller near volcanoes and shallow LFEs. In contrast, eR is in the order of 10-7 and 10-6 for deep and shallow LFEs, respectively, one to three orders of magnitude smaller than that for regular earthquakes. This result suggests that LFEs are associated with a much lower stress drop and/or slower rupture and deformation rates than regular earthquakes. Although the energy magnitudes derived from radiated energy generally show good agreement with the local magnitudes for the three types of earthquakes, the moment and local magnitudes show a large discrepancy for the LFEs. This suggests that the local magnitude based only on the maximum amplitude of the observed seismic records may not provide good information on the static sizes of LFEs whose eR values are substantially different from those of regular earthquakes.

We investigated the effects of the propagation path and site amplification of shallow tremors along the Nankai Trough. Using far-field S-wave propagation from intraslab earthquake data, the amplification factors at the DONET stations were 5–40 times against an inland outcrop rock site. Thick (~5 km) sedimentary layers with VS of 0.6–2 km/s beneath DONET stations have been confirmed by seismological studies. To investigate the effects of thick sedimentary layers, we synthesized seismograms of shallow tremors and intraslab earthquakes at seafloor stations. The ratios of the maximum amplitudes from the synthetic intraslab seismograms between models with and without thick sedimentary layers were 1–2. This means that the estimated large amplifications are primarily controlled by thin lower-velocity (< 0.6 km/s) sediments just below the stations. Conversely, at near-source (≤ 20 km) distances, 1-order amplifications of seismic energies for a shallow tremor source can occur due to thick sedimentary layers. Multiple S-wave reflections between the seafloor and plate interface are contaminated in tremor envelopes; consequently, seismic energy and duration are overestimated. If a shallow tremor occurs within underthrust sediments, the overestimation becomes stronger because of the invalid rigidity assumptions around the source region. After 1-order corrections of seismic energies of shallow tremors along the Nankai Trough, the scaled energies of seismic slow earthquakes were 10-10–10-9 irrespective of the region and source depth. Hence, the physical mechanisms governing seismic slow earthquakes can be the same, irrespective of the region and source depth.

We investigated the effects of the propagation path and site amplification of shallow tremors along the Nankai Trough. Using far-field S-wave propagation from intraslab earthquake data, the amplification factors at the DONET stations were 5–40 times against an inland outcrop rock site. Thick (~5 km) sedimentary layers with VS of 0.6–2 km/s beneath DONET stations have been confirmed by seismological studies. To investigate the effects of thick sedimentary layers, we synthesized seismograms of shallow tremors and intraslab earthquakes at seafloor stations. The ratios of the maximum amplitudes from the synthetic intraslab seismograms between models with and without thick sedimentary layers were 1–2. This means that the estimated large amplifications are primarily controlled by thin lower-velocity (< 0.6 km/s) sediments just below the stations. Conversely, at near-source (≤ 20 km) distances, 1-order amplifications of seismic energies for a shallow tremor source can occur due to thick sedimentary layers. Multiple S-wave reflections between the seafloor and plate interface are contaminated in tremor envelopes; consequently, seismic energy and duration are overestimated. If a shallow tremor occurs within underthrust sediments, the overestimation becomes stronger because of the invalid rigidity assumptions around the source region. After 1-order corrections of seismic energies of shallow tremors along the Nankai Trough, the scaled energies of seismic slow earthquakes were 10-10–10-9 irrespective of the region and source depth. Hence, the physical mechanisms governing seismic slow earthquakes can be the same, irrespective of the region and source depth.

Estimating the radiated energy of small-to-moderate (Mw < 5) events remains challenging because their waveforms are strongly distorted during wave propagation. Even when near-source records are available, seismic waves pass through the shallow crust with strong attenuation; consequently, high-frequency energy may be significantly dissipated. Here, we evaluated the degree of energy dissipation in the shallow crust by estimating the depth-dependent attenuation (Q-1) by modeling near-source (< 12 km) waveform data in northern Ibaraki Prefecture, Japan. High-quality waveforms recorded by a downhole sensor confined by granite with high seismic velocity helped to investigate this issue. We first estimated the moment tensors for M1–4 events and computed their synthetic waveforms, assuming a tentative one-dimensional -model. We then modified the -model in the 5–20 Hz range such that the frequency components of the synthetic and observed waveforms of small events (Mw < 1.7) matched. The results show that the Q-value is 55 at depths of < 4 km and shows no obvious frequency dependence. Using the derived -model, we estimated the moment-scaled energy (eR) of 3,884 events with Mw 2.0–4.5. The median eR is 3.6×10-5 , similar to the values reported for Mw >6 events, with no obvious Mw dependence. If we use an empirically derived Q-model (~350), the median eR becomes a one-order underestimation (3.1×10-6). These results indicate the importance of accurately assuming the Q-value in the shallow crust for energy estimation of small events, even when near-source high-quality waveforms are available.