Subduction zone earthquakes show varying energy release patterns and frequency content, based on their tectonic settings and hypocentral depths. Resolving these features from the nonlinear and non-stationary seismograms is a challenge. Our work in the Japan Trench follows studies by Huang et al. (1998, 2001) and Zhang et al. (2003), who demonstrated the use of empirical mode decomposition to separate records into multiple timescales, or intrinsic mode functions (IMFs). Zhang et al. observed that IMFs 2-5 represented the source rupture process for the 1994 Northridge earthquake. Chauhan (master’s thesis, 2019) used time-frequency distributions, short-time Fourier and continuous wavelet transforms, of IMFs of strong-motion data for a pair of interplate-intraslab earthquakes to identify the dominant, short duration, low-frequency energy release for the intraslab event. He found a high correlation between the original signal and a linear combination of IMFs 3 and 4, possibly representing the source. Chatterjee et al. (AGU, 2018) observed an association between time-frequency-energy distributions of certain IMFs and moment rate functions (MRFs) from teleseismic waveform models, for five earthquakes. Chatterjee et al. (AGU, 2019) and Mache et al. (AGU, 2019) used Hilbert spectral analysis (Huang et al., 1998) of IMFs selected based on their frequency and energy and observed better match between the two. This new function, which they regard as the Energy Rate Function (ERF), can reproduce the MRF’s essential elements, i.e., its duration and shape, but Mache (master’s thesis, 2020) observed that results depended on the selection of stations. As the next step, Mache and Rajendran (JpGU-AGU, 2020) based the selection criteria on the slip distribution, strike, and JMA intensity distribution maps (JMA 1996) and applied the method to 7 earthquakes from various tectonic settings of the Japan Trench. Here we present an overview of the various methods for analyzing KiK-net strong-motion data for selected earthquakes to extract information on their time-frequency-energy distributions. The ERF generated through this analysis is a physically compatible expression of the MRF and, therefore, more useful in predicting the shaking effects of earthquakes.

The occurrence of a large number of earthquakes in the inter and intraplate settings of the Japan Trench leads to ruptures with varying frequencies. To capture the temporal distribution of energy and their ranges of frequencies, we have used the Intrinsic Mode Functions (IMFs) derived from the vertical components of the strong-motion records. Here we present an “energy release function”, which is yet another way of representing frequency-dependent energy release. Without the assumptions of the area of slip and elastic moduli, this provides a new representation of the energy released at the source. Choice of the appropriate IMF and thus the range of frequencies representing the source was based on the best fitting teleseismic model for the same earthquake. We analysed the strong-motion records for three earthquakes (all in the magnitude range of 7.1 to 7.3), representing interplate, intraplate, and intraslab settings and used borehole data from the KiK-net. These were the Miyagi 2005 (Interplate), Tohoku 2011 (Intraslab), and Honshu 2012 (intraplate). We used the Hilbert-Huang Transform, a combination of Empirical Mode Decomposition (EMD) and Hilbert Transform (HT) to develop the spectra for vertical components of each of these earthquakes. A combination of the IMFs within the frequency band (0.1 to 3 Hz) that mostly represent the frequency range used for teleseismic source inversion (0.01 to 2 Hz) was used to develop the spectra in each case. The shape of the spectra generally mimics that of the moment rate function. Where the moment-rate function follows a single pulse, the spectrum is able to generate its shape, and the sub-events are represented through independent pulses of energy. We believe that the representation of an earthquake source based on its frequency content and temporal pattern has important applications in predicting the shaking effects of an earthquake.