Correlation between Heights of Younger and Older Shorelines for Estimating Rates and Regional Differences of Crustal Movements
1968 Volume 7 Issue 4 Pages 171-181
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1968 Volume 7 Issue 4 Pages 171-181
The study of crustal movements depending upon former shorelines has been one of the intersting fields of the Japanese Quaternary. Herein an attempt was made for estimating the rates and regional differences of Quaternary crustal movements in Japan by using correlation between the heights of older and younger shorelines. The method of approach is as follows:
In a coastal region, the heights of former shorelines of two different ages (t1 and t2 years B. P.) are measured. Pairs of older and younger shoreline-heights in close distance are designated as h1 and h2 respectively (fig. 4). When many pairs of h1 and h2 are obtained in a coastal region, the values are compared on a correlation diagram. Six regions studied are shown in fig. 1 and 11 cases of correlation obtained from the six regions are shown in fig. 3. In four regions, Kanto, Muroto Peninsula, Nishitsugaru and Osado, shoreline-heights of three different ages were measured and two correlation diagrams were drawn for each region.
From fig. 3, it can be said that the relationship between h1 (in ordinate) and h2 (in abscissa) is linear in most cases. Therefore, the regression line,
h1=ah2+b (1)
was applicable to many cases, and calculated values of ‘a’ and ‘b’ are shown in each case. Under what conditions is it possible to be applicable to the above equation (1) for variables of h1 and h2?
When we use the signs shown in fig. 4, h1 and h2 are expressed as follows:
h1=z1+v1(t1-t2)+v2t2 (2)
h2=z2+v2t2 (3)
where z1 and z2 are sea-level heights of eutstatic change, v1 and v2, mean rates of crustal movements. From (1), (2) and (3), the following equation is led (a≠1):
v2=t1-t2/t2(a-1)v1+z1-az2-b/t2(a-1) (4)
That is, v2 is expressed by a linear formula of v1, where the gradient and intercept are constants peculiar to the concerning region. Therefore, (4) is also expressed by the following formula, using ‘m’ and ‘n’ which are constants peculiar to the concerning region:
v2=mv1+n (5)
where ‘m’ means how v1 is succeeded by v2, and is named, therefore, a ‘successional coefficient of the rate of crustal movement’. On the other hand ‘n’ means the rate of crustal movement which is added after t2 years B. P. and is uniform through the whole concerning region. Therefore, ‘n’ is named a ‘regional addend of the rate of crustal movement’. A model of areal distribution of v1 and v2 is shown in fig. 5 (in case of m=3).
If (5) is right in one region, (1) is also led, then ‘a’ and ‘b’ are expressed as follows:
a=1/m(t1/t2-1)+1 (6)
b=(z1-z2)-1/m(t1/t2-1)(nt2+z2) (7)
That is, ‘a’ is a function of ‘m’, and ‘b’ is a function of ‘m’ and ‘n’. For the correlated two shorelines of plural regions, if ‘a’ of each region is equal to one another, then ‘m’ is the same. Moreover, if ‘a’ values of many regions, having different geologic structures and different physical properties of rock, are equal, then every ‘m’ value can be estimated as 1, because it is improbable that ‘m’ values of various regions take the same value except 1. (m=1_??_a=t1/t2)
