P07

Statistical Models for Activity of Low-frequency Earthquakes〇Tomoaki NISHIKAWA

1. Introduction2015 (Kato & Nakagawa, 2020). I used the goodness-Slow earthquakes are slow fault slip events (e.g., Ideof-fit test (GFT) method (Wiemer & Wyss, 2000;& Beroza, 2023). Quantifying and monitoring slow

Woessner & Wiemer, 2005) and determined theearthquake activity characteristics are important

minimum magnitude of the LFEs to be analyzed (Mbecause they may change before large earthquakes

0.6).

occur (Matsuzawa et al., 2010; Luo & Liu, 2019).
Statisticalseismicity

forregions downdip of the megathrust seismogenic zones.

quantifying seismicity characteristics. However, noThese band-like regions were divided into subregions

standard statistical model exists for slow earthquake

in a manner similar to that of Ide and Nomura (2022).

activity.

low-frequency

In and around the band-like regions, rectangles of 0.2 °earthquakes (LFEs), a type of slow earthquake, hasin latitude and longitude were placed at 0.1° intervals

only recently begun. LFEs are characterized by low

to create subregions. Each subregion was required todominant frequencies (1–10 Hz) compared to fast

contain at least 100 M ≥ 0.6 LFEs, and LFE activity inmicroearthquakes of comparable seismic momenteach subregion was analyzed. Consequently, 43 sub-(Shelly et al., 2007; Nishikawa et al., 2023).

regions were included in the analysis.

Statisticalmodels

modeling

areofusefulIn the Nankai Trough, LFEs occur in band-like

Constructing a statistical model that successfully

I used two existing LFE activity models. One is

describes the LFE activity is important for betterproposed by the Lengliné et al. (2017). In their models,characterization and forecasting. However, existing

the LFE occurrence rate was assumed to be the sum ofstatistical LFE activity models (Lengliné et al., 2017;

the stationary background rate and aftershock rates of

Tan & Marsan, 2020; Ide & Nomura, 2022) have neverpast LFEs. Furthermore, in this model, the shape of thebeen compared, and it is unclear which model best

aftershock rate kernel is not assumed a priori but isdescribes LFE activity.

determined based on the observed data using piecewiseThis study applies the existing statistical LFE

constant discretization. In this study, I used 15

activity models (Lengliné et al., 2017; Ide & Nomura,piecewise constants to discretize the aftershock rate2022) to LFE activity along the Nankai Trough andkernel. I call the above model the L-type model.

comparetheirperformances

using

Akaike’s

Ide and Nomura (2022) proposed a statistical model

information criterion (AIC; Akaike 1974). Based on thefor tectonic tremors (i.e., LFE swarms) (Shelly et al.,model comparison, I propose a new model that2007). Their model is based on an approach different

incorporates existing model features.

from that of Lengliné et al. (2017). Ide and Nomura(2022) described the probability distribution of tremor

2. Data and Models

interevent times using a mixture of lognormal andThis study used a high-quality LFE catalog in theBrownian passage-time (BPT) distributions andNankai subduction zone from April 2004 to August

forecasted tremor interevent times. Furthermore, theirmodel depends only on the time elapsed since the lastcannot be described by a simple power-law decay andevent and does not depend on detailed tremor activity

that there is decay stagnation (1.0×10-2 to 2.0×10-1

history.

days). This is a general feature of the LFE activity inUpon applying the Ide and Nomura (2022) model tothe Nankai Trough.

LFE activity along the Nankai Trough, an additional

The complex shape of the LFE aftershock rate

log-normal distribution was added to the model. This isprobably explains why the ETAS model, which

because short-term LFE clustering often displays two

assumes a simple power-law decay a priori, ischaracteristic timescales (tens of seconds and a few

significantly inferior to the L- and IN-type models.

hours) as pointed out by Kato and Nakgawa (2020). I
call the above model the L-type model.

4. Discussion and Conclusions

I also used the epidemic-type aftershock-sequence

Although the IN-type model is superior in more(ETAS) model (Ogata, 1988), which is the standard

subregions, the IN- and L-type model performances are

statistical seismicity model for fast regular earthquakes.

competitive. Based on these results, I examine whether

This model is similar to the L-type model. In this model,

the incorporation of both IN- and L-type model features

however, the shape of the aftershock rate kernel isresults in a superior model. The IN-type model has theassumed to be a simple power-law decay a priori.

characteristic of using a small number of parameters toThe L-type, IN-type, and ETAS models wererepresent the LFE occurrence rate. The L-type modelcompared based on AIC (Akaike, 1974). The L-type,considers the LFE activity history. I propose a newIN-type, and ETAS models had 16, 8, and 5 model

model incorporating both features. Specifically, aparameters, respectively. A model with a smaller AIC

hybrid model was developed in which the L-type

was considered to be significantly better than a model

aftershock rate kernel was represented by a small

with a larger AIC when the AIC difference (∆AIC)

number of parameters, similar to the IN-type model.

between the models was 2 or greater.

The AIC was used to compare the modelperformance. In most subregions (41 of the 433. Results
The IN-type, L-type, and ETAS models weresubregions), the hybrid model was significantly
superior to the L-type model.

superior in 25, 13, and 1 of the 43 subregions,

The hybrid model was superior to the IN-type model

respectively. The IN- and L-type models were superiorin 26 of the 43 subregions. The IN-type model wasin three of the remaining four subregions, with nosuperior in 15 of the remaining subregions. There weresignificant differences between them. In the remaining

no significant differences in performance between thesubregion, the ETAS and L-type models were superior,remaining two subregions. Compared with the previous

with no significant difference between them. Theseresults, the number of subregions in which the IN-type

results indicate that although there were moremodel performed the best decreased substantially (fromsubregions in which the IN-type model performed

25 to 15).

better, the IN- and L-type model performances wereThe above analysis demonstrates that the hybrid

competitive. In particular, the L-type model wasmodel is superior to the L-type model. Furthermore, thesuperior to the IN-type model in several subregions ofhybrid model outperformed the IN-type model in many

Shikoku and east of Ise Bay.

subregions and could be considered the best model inIn addition, I found that the LFE aftershock rates

this study.