アイソクロン・バックプロジェクション法による２００７能登半島地震の震源過程
Rupture process of the Notohanto Earthquake (2007/3/25), by using an Isochrones Back-projection
Method and Strong motion data(Nelson Pulido, 29/3/2007)
1- Fault Model
We estimated the source process of the 2007/3/25 Notohanto earthquake (latitude 37.236, longitude 136.652 anddepth 11km) by using an Isochron Backprojection Method (IBM) and K-NET waveforms.
We use a fault model corresponding the F-net solution (strike 58 degrees and dip 66 degrees), and assume the starting
point of the rupture corresponding to the Hi-net hypocenter solution (37.236N, 136.652E, depth 11km). The fault
length is set to 36 km and the fault width to 24 km (Figure 1). This fault geometry is set to correspond to the model
used for the source inversion by Aoi and Sekiguchi (2007).

2- Method
The IBM method differs from conventional earthquake source inversion approaches, in that the calculation ofGreen’s functions is not required. The idea of the procedure is to directly back-project amplitudes of seismograms
envelopes around the source into a space image of the earthquake rupture.
The method requires the calculation of theoretical travel times between a set of grids points distributed across thefault plane, and every station. For this purpose and for simplicity we assume a multi-layered 1D model. All travel
times are adjusted by a station correction factor, calculated by taking the difference between observed and theoreticaltravel times at each station. Next we calculate the rupture time of every grid within the fault plane by assuming somearbitrary constant rupture velocity value, and obtain the isochrones distribution across the fault plane by adding
subfaults rupture times and the corresponding travel times for every station. We select waveforms that have clear P
and S wavelets, which means stations located approximately between 40 km and 150km from the epicenter. We
extract P-wave windows between the origin time of the earthquake and the theoretical arrival of the S-wave, and taper
1s of the waveforms at the end. We band-pass filter the data between 1Hz and 30Hz, and calculate the waveforms
envelopes using the root-mean-square of the original waveforms and their Hilbert transform. We calculate a grid“brigthness” by adding all the envelope amplitudes corresponding to every grid isochron time for all stations. In thisway we scan for all possible isochrons contributions to the grid total brigthness from the shortest to the longest
possible isochrons time values. The final result is a distribution of the brightness across the fault plane, which gives us
an idea of the location of asperities within the fault plane. The present method is an extension of the source imaging
method by Festa et. al. (2006) by incorporating high frequency seismograms (Pulido et. al., 2007).
3- Data
To estimate the fault brigthness we choose 35 K-NET stations of NIED, with distances ranging from 40km to 150km
from the epicentre (Figure 2). For the calculation of travel times we used a velocity model developed for the Kanto
region (Ukawa et. al., 1984).
4- Results
We obtained an image of the brigthness distribution across the fault plane of the Notohanto earthquake (Figure 3).
Our results show that the grids with the largest brightness within the fault plane, corresponds to a region 10 km above
the hypocenter. Another patch of large brightness is observed at the bottom of the northern end of the fault plane.
These large brightness regions are located close to the large slip areas obtained in the source model by Aoi andSekiguchi (2007). We obtained that a rupture velocity of 2.1 km/s maximizes the total fault plane brigthness for theNotohanto earthquake.
5- Disclaimer
The results of the source process obtained by the present methodology are preliminary and therefore future updatesof the model might be expected. On the other hand the present methodology is currently at a development stage, andtherefore we may incorporate future changes.
6- References
Aoi, S, and H. Sekiguchi, 2007. Rupture process of the 2005/3/25 Noto-Hanto Earthquake by using Near-fault data(preliminary version), http://www.kyoshin.bosai.go.jp/k-net/topics/noto070325/
Festa, G., and A. Zollo. 2006. Fault slip and rupture velocity inversion by isochrone backprojection, Geophys. J.
Int.,166, 745-756.
Pulido, N., S. Aoi, and H. Fujiwara, 2007. Rupture process of the 2005 Fukuoka-ken Seiho Oki Earthquake by using
Isochrones Back-projection Method, Japan Geoscience Union Meeting 2007 Proceedings, S151-P007.
Ukawa, M., M. Ishida, S. Matsumura, and K. Kasahara, 1984. Hypocenter Determination Method of the Kanto-Tokai
Observational Network for Microearthquakes, Research Notes of the National Research Center for Disaster
Prevention No. 53.

Figure 1. Fault model of the 2007/3/25 Notohanto earthquake. The assumed fault length is 36 km and the fault
width is 24 km. The star represents the Hi-net hypocenter. The crosses represent the first 2 days of aftershocks,with magnitude larger than 2.

Figure 2. K-NET stations used for the source imaging of the 2007/3/25 Notohanto earthquake. The assumed
fault plane is shown by a red rectangle. The star represents the Hi-net hypocenter. The crosses represent the first
2 days of aftershocks, with magnitude larger than 2.

Figure 3. Total fault plane brightness during the 2007/3/25 Notohanto earthquake, obtained by the Isochrons
Backprojection Method and using K-NET data. A star depicts the hypocenter. The brightness scale has beennormalized.