Detection of Low‐Frequency Earthquakes in Broadband Random Time Sequences: Are They Independent Events?

Abstract

Low‐frequency earthquakes (LFEs) are detected primarily from continuous seismograms using a matched‐filter technique with an impulsive template waveform in a relatively narrow frequency band. However, this method can also detect events from some kinds of random time sequences without clearly isolated events. Here this fact is demonstrated via simple numerical simulations using the synthetic moment accelerations from a model of broadband slow earthquake, the Brownian slow earthquake (BSE) model, and a totally random noise sequence. The matched‐filter technique identifies time sections including relatively isolated pulse‐like fluctuations, as signals in both time sequences, depending on the threshold. These waveforms, stacked relative to the signal timing, show a clear impulse similar to the assumed template in both time sequences, which highlights that we might potentially misinterpret an original time sequence as containing many isolated pulse‐like events. An important difference exists between the BSE model and random noise at frequencies much lower than the analyzed frequency band, with the stacked BSE sequence containing coherent signals at very low frequencies, which are not visible in the noise. Real observations in the Cascadia subduction zone also contain similar coherent signals at low frequencies, suggesting that these LFE signals are coincident with some slow slip. Therefore, so‐called LFEs might potentially be a misinterpretation due to signal processing, or at least they are the tip of the iceberg, with these signals forming a component of a very broadband slow‐earthquake‐like slip process that possibly occurs over sub‐second to multi‐year timescales.

Bridging the gap between low-frequency and very-low-frequency earthquakes

“…The present study clearly shows that the stacked LFE waveforms include continuous signals that range from the LFE and tremor frequency bands (> 1 Hz) to the VLFE frequency band (0.01-0.10 Hz). This is consistent with results for LFE families in the Cascadia subduction zone for periods of < 16 s (Ide 2019). The broader frequency range in the present study is due to the large number of stacked signals, the high sensitivity of the tiltmeters at lower frequencies, and quiet observational conditions at the bottom of the Hi-net boreholes.…”

“…Its slope, ω, is almost constant, and the deviation from this constant slope can be explained by the error. The results from LFEs in Cascadia (Ide 2019) are also plotted in Fig. 4 to highlight the high degree of consistency between these two studies.…”

“…The large amplitudes of the BSE model at lower frequencies are largely consistent with the observations of the present study and those from Cascadia, with the exception of a deviation slightly below 1 Hz. This deviation reflects the spectral shape of the template wave that was used to make the stacked wave for the BSE model, as explained in detail by Ide (2019). However, the omega-square model is proportional to ω 2 at frequencies below its corner frequency as described in detail in Additional file 2: Text S1, such that the deviation from the observations is significant at very low frequencies.…”

“…The average was taken for each of the analyzed frequency bands, except for the case that noise was dominant. Blue inverted triangles, red diamonds, and yellow squares represent the results of this study, the BSE model (Ide 2019), and the omega-square model (Aki 1967), respectively. Green pentagons and hexagons represent data from Cascadia (Bostock et al 2015), as presented by Ide (2019)…”

Low-Frequency Tremors Immediately After the 2011 Tohoku-Oki Earthquake Detected by Near-Trench OBS Observations

“…For example, spatiotemporal coincidence of LFTs and very low frequency earthquakes (VLFEs; e.g., Yamashita et al, 2015) and another type of slow earthquake has been observed in the Hyuga-nada region (Yamashita et al, 2015) and the Nankai subduction zone (Kaneko et al, 2018;Toh et al, 2018). Such a relationship between different types of slow earthquake phenomena suggests that this series of different dominant frequencies is a united broadband phenomenon (Ide, 2008;Ide, 2019), and it is important to use as many types of slow earthquakes to detect the broadband phenomenon and their spatiotemporal associations.…”