Hilbert–Huang Transform and Energy Rate Functions for Earthquake Source Characterization—A Study from the Japan Trench

The Hilbert–Huang Transform (HHT) has been sparsely applied to problems in seismology, although previous studies have pointed to its broad scope. In this maiden attempt, we use the HHT to represent earthquake energy release duration and frequency content and compare the results with two conventional inversion methods. By selecting examples from interplate, intraplate, and intraslab settings, we demonstrate that the HHT has the power to discriminate energy release of earthquakes with different tectonic affiliations. We observe that the dominant frequencies for energy release are higher for intraslab earthquakes than for interplate and intraplate events. We use the empirical mode decomposition-based HHT and introduce a new parameter, which we name the energy rate function (ERF), to quantify the energy release. By employing empirical Green’s functions to remove the path and site effects and using a linear combination of a select set of intrinsic mode functions, we generate the station-specific relative measure of energy that we refer to as relative ERFs (RERFs). Averaged over RERFs from multiple stations, the ERF represents a measure of the total relative energy release, comparable to the moment rate functions (MRFs) and SCARDEC source time functions (STFs). Results for six of the seven earthquakes we analyzed show high cross correlation with the STFs (0.84 ± 0.03) and MRFs (0.79 ± 0.06), but there are mismatches between ERFs and MRFs or STFs when the energy release is complex and involves multisegment or bilateral ruptures. The proposed method is computationally efficient, requiring only 3.46 ± 2.62 s on average, compared to ~20 min (~1200 s) for the teleseismic inversion method we employ. With its ability to represent the seismic source in terms of energy release, the ERF method has the potential to evolve not as an alternative to waveform inversion but as a rapid time–frequency analysis tool, useful for earthquake hazard assessment.