A Study on the Deviation of the Plumb Line in Japan

Abstract

The deviation of the plumb line are expressed by the well known formulae
where ψ, λ and A are latitude, longitude and azimuth, respectively, reckoned in the usual manner; the indices a and g stand for “astronomical” and “geodetic” respectively. These quantities are shown in Table I, Chapter I.
A glance at these results readily shows that the astronomical latitudes are generally greater than the geodetic latitude, while on the contrary, the astronomical longitudes are generally smaller than the geodetic longitude. Although the deviation of the plumb line at any given station is affected by local attraction of the surrounding mass, they are still too large and too systematic to be interpreted as arising solely from these local topographic effect. The larger part occured in all probability from errors with respect to the situation, shape and dimension of the reference ellipsoid we have taken in the geodetic work in Japan. There are several causes other than those here mentioned, which are generally different according to the type of adopted triangulation system, so that in Chapter I, these are fully examined for triangulation net. Then in Chapter II, the writer intended to obtain the most reliable reference ellipsoid which may represent the geoid in Japan. In Chapter III, some geophysical consideration was made on the residual. When redution is made in this way there is found some regularity in the distribution of the deviation of the plumb line which is geophysically of great interest. Notwithstanding the reference ellipsoid, which I have taken as most suitable for geoid in Japan, is more or less uncertain owing to the fact that the distribution of the astronomical stations are so limitted in the small area, it was perceived that this regularity is not disturbed.
The principal facts which were obtained are as follows:
i) The plumb line are always strongly attracted toward inland side from the sea side. There is no exception for Japan proper or Kyûsyû, Fig. 2.
ii) Examining the deviation of the plumb line and the gravity anomaly in Kwantô region, the close connection can be found for such small area. Compare Fig. 5 and Fig. 6.
iii) Drawing the undulation of geoid, it is apparent that, (Fig. 7),
(a) At north eastern Japan, the height of geoid above the reference ellipsoid is relatively higher than that of south-west Japan.
(b) The ridge of highest geoid runs parallel to the zone of maximum gravity, and it does not proceed to south-west Japan.
It seems that the crustal structure of these two regions are very different, and probably, the depth of the earth's crust at north-east Japan is relatively shallow compared with that of south-west Japan.
iv) Coirecting the effect due to topography for a distance of 1104km from the observed point, Fig. 11, it is concluded that the isostasy is apparently holding for Japan also.