rðY i ; Y j Þ ¼
1
2
E½ðY i À Y j ފ
2
ð1Þ
where, Y i and Y j are the lengths of slip at the i-th and j-th element respectively.
And, semivariogram ‘r(Yi, Yj)’ is defined as follows:
rðY i ; Y j Þ ¼ r
2
Y Â ð1 À q YiYj Þ
ð 2Þ
where, r Y is standard deviation of fault plane and q YiYj is the correlation coefficient
between Yi and Yj.
In this study, this correlation is assumed to depend on h that is distance between
two elements, and the correlation coefficient is defined as follows:
r h
ð Þ ¼
1
2N h
ð Þ
X N h
ð Þ
i¼1
Y X 1i
ð ÞÀY X 2i
ð Þ
ð
Þ
2
ð3Þ
Provided that N(h) is the number of pairs that fulfill (4) include X 1i ; X 2i
ð
Þ .
h À
Mh
2
5 X 1i À X 2i
j
j5 h þ
Mh
2
ð4Þ
where, Dh is assumed 1.34 km. Figure 2a is r(h) obtained from Eq. (3). Figure 2b
shows N(h) for each bin. In Fig. 2a, fitted parabola that is determined from
least-squares method is denoted.
Table 1 Average and standard deviation of logarithmic slip of West Off Fukuoka Earthquake
Average
Standard deviation
3.90
0.87
Fig. 2 Semivariogram
showing spatial correlation of
slip obtained from slip
distribution during West Off
Fukuoka Earthquake
Ground Motion Prediction for Regional Seismic Risk Analysis …
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