From the Cover: Spatiotemporal variations of seismicity before major earthquakes in the Japanese area and their relation with the epicentral locations

Using the Japan Meteorological Agency earthquake catalog, we investigate the seismicity variations before major earthquakes in the Japanese region. We apply natural time, the new time frame, for calculating the fluctuations, termed β, of a certain parameter of seismicity, termed κ₁. In an earlier study, we found that β calculated for the entire Japanese region showed a minimum a few months before the shallow major earthquakes (magnitude larger than 7.6) that occurred in the region during the period from 1 January 1984 to 11 March 2011. In this study, by dividing the Japanese region into small areas, we carry out the β calculation on them. It was found that some small areas show β minimum almost simultaneously with the large area and such small areas clustered within a few hundred kilometers from the actual epicenter of the related main shocks. These results suggest that the present approach may help estimation of the epicentral location of forthcoming major earthquakes.In this study, we investigate the evolution of seismicity shortly before main shocks in the Japanese region, N2546E125148, using Japan Meteorological Agency (JMA) earthquake catalog as in ref 1. For this, we adopted the new time frame called natural time since our previous works using this time frame made the lead time of prediction as short as a few days (see below). For a time series comprising N earthquakes (EQs), the natural time χ_k is defined as χ_k = k/N, where k means the k^th EQ with energy Q_k (Fig. 1). Thus, the raw data for our investigation, to be read from the earthquake catalog, are χ_k = k/N and pk=Qk/∑n=1NQn, where p_k is the normalized energy. In natural time, we are interested in the order and energy of events but not in the time intervals between events.Open in a separate windowFig. 1.EQ sequence in (A) conventional time and (B) natural time. In B, Q_k is given in units of the energy ε corresponding to a 3.5M_JMA EQ.We first calculate a parameter called κ₁, which is defined as follows (2, 3), from the catalog.κ1=∑k=1Npkχk2−(∑k=1Npkχk)2=〈χ2〉−〈χ〉2.[1]We start the calculation of κ₁ at the time of initiation of Seismic Electric Signals (SES), the transient changes of the electric field of Earth that have long been successfully used for short-term EQ prediction (4, 5). The area to suffer a main shock is estimated on the basis of the selectivity map (4, 5) of the station that recorded the corresponding SES. Thus, we now have an area in which we count the small EQs of magnitude greater than or equal to a certain magnitude threshold that occur after the initiation of the SES. We then form time series of seismic events in natural time for this area each time a small EQ occurs, in other words, when the number of the events increases by one. The κ₁ value for each time series is computed for the pairs (χ_k,p_k) by considering that χ_k is “rescaled” to χ_k = k/(N +1) together with rescaling pk=Qk/∑n=1N+1Qn upon the occurrence of any additional event in the area. The resulting number of thus computed κ₁ values is usually of the order 10² to 10³ depending, of course, on the magnitude threshold adopted for the events that occurred after the SES initiation until the main shock occurrence. When we followed this procedure, it was found empirically that the values of κ₁ converge to 0.07 a few days before main shocks. Thus, by using the date of convergence to 0.07 for prediction, the lead times, which were a few months to a few weeks or so by SES data alone, were made, although empirically, as short as a few days (6, 7). In fact, the prominent seismic swarm activity in 2000 in the Izu Island region, Japan, was preceded by a pronounced SES activity 2 mo before it, and the approach of κ₁ to 0.07 was found a few days before the swarm onset (8). However, when SES data are not available, which is usually the case, it is not possible to follow the above procedure. To cope with this difficulty, in the previous work (1), we investigated the time change of the fluctuation of the κ₁ values during a few preseismic months for each EQ (which we call target EQ) over the large area N2546E125148 (Fig. 2A) for the period from 1 January 1984 to 11 March 2011, the day of M9.0 Tohoku EQ. Setting a threshold M_JMA = 3.5 to assure data completeness of JMA catalog, we were left with 47,204 EQs in the concerned period of about 326 mo: ∼150 EQs per month. For calculating the β values, we chose 200 EQs before target EQs to cover the seismicity in almost one and a half months.Open in a separate windowFig. 2.(A) The 47,204 EQs with M_JMA ≥ 3.5 that occurred during the period of our study. (B) Contours of the number of EQs per month within R = 250 km. Solid diamonds show the epicenters of six shallow EQs investigated in this study. (C) Contours of the natural time window W used in each of the 12,476 areas of radius R = 250 km with offset 0.1° from one another that have at least eight EQs per month.To obtain the fluctuation β of κ₁, we need many values of κ₁ for each target EQ. For this purpose, we first took an excerpt comprised of W successive EQs just before a target EQ from the seismic catalog. The number W was chosen to cover a period of a few months. For this excerpt, we form its subexcerpts Sj={Qj+k−1}k=1,2,…,N of consecutive N = 6 EQs (since at least six EQs are needed (2) for obtaining reliable κ₁) of energy Q_j+k?1 and natural time χ_k = k/N each. Further, pk=Qj+k−1/∑k=1NQj+k−1, and by sliding S_j over the excerpt of W EQs, j=1,2,…,W−N+1 (= W − 5), we calculate κ₁ using Eq. 1 for each j. We repeat this calculation for N=7,8,…,W, thus obtaining an ensemble of [(W − 4)(W − 5)]/2 (= 1 + 2 +…+ W − 5) κ₁ values. Then, we compute the average μ(κ₁) and the SD σ(κ₁) of thus obtained ensemble of [(W − 4)(W − 5)]/2 κ₁ values. The variability β of κ₁ for this excerpt W is defined to be β ≡ σ(κ₁)/μ(κ₁) and is assigned to the (W + 1)^th EQ, i.e., the target EQ.The time evolution of the β value can be pursued by sliding the excerpt through the EQ catalog. Namely, through the same process as above, β values assigned to (W + 2)^th, (W + 3)^th, … EQs in the catalog can be obtained.We found in ref. 1 that the fluctuation β of κ₁ values exhibited minimum a few months before all of the six shallow EQs of magnitude larger than 7.6 that occurred in the study period. A minimum of β ≡ σ(κ₁)/μ(κ₁) means large average and/or small deviation of κ₁ values (e.g., see ref. 9).In the present work, we calculate the β values for small areas before the six large EQs, which showed β minima of the large area.