The origin of earthquake ordinarily determined in seismology is probably the point where the earthquake motion first occurred. On the other hand from the viewpoint of earthquake engineering the center of the collapse of houses and other structures has even larger meaning than the above point seismometerically obtained. The destruction, however, is affected by a number of conditions such as the foundation and topography, though generally speaking, it will be a decreasing function of the distance from the center point.
The data studied in the present paper is the ratio of the collapsed houses in Tokyo and surrounding prefectures reported in “REPORTS OF THE IMPERIAL EARTHQUAKE INVESTIGATION COMMITTEE No. 100, A” (Tokyo 1925) by Dr. T. MATUZAWA. This percentage,
y, of the destructed houses, is transformed into
x by the MONONOBE formula,
y=100·1/√2π∫
x-∞exp(-
t2/2)
dt (1) and the following expression connecting
x and the distance
r is assumed, namely
x=
alog
10r+
b=
f(
r). (2) The coefficients
a and
b are determined by means of the least square method as
a=-2.786,
b=3.29 (unit of distance=km) (3) where the depth of focus is assumed to be 15km.
By the successive approximation, the most probable location of the center of destruction was determined in the sense of least squares, starting from the 1st approximation point given in Rika-Nenpyo; (139.3°E 35.2°N). (5) The result came out as (139.46°±0.02° 35.19°±0.01°). (6) If the depth of focus is assumed to be zero, the coefficient become
a=-2.432,
b=2.590 (8) and the center is (139.44°E±0.02°, 35.20°N±0.01°). (7) Anyway the resultant location is about 15km east of the first assumed point.
The method (program) can be applied for finding the center of any distribution given by a decreasing function
f(
r), in which
r is the distance between the center and the field point.
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