重力鉛直勾配の異常を考慮した重力異常を求める一方法
1964 年 10 巻 1 号 p. 18-23
詳細
1964 年 10 巻 1 号 p. 18-23
Usually, gravity anomalies are computed assuming the normal value of the vertical gradient of gravity. It is much desirable, however, that the anomaly of the vertical gradient of gravity is taken into consideration for computing the values of gravity anomaly. The writer derived a formula for calculating the gravity anomaly of the latter sense from the horizontal distribution of the gravity anomaly of the former sense accord ing to Dr. Tsuboi's successive approximation method.
If the horizontal distribution of the gravity anomaly on the sea level is expressed by
Δg0 ''=∑Amn sin cos mx sin con ny
the aimed gravity anomaly considering the anomaries of vertical gradient of gravity designated by Δg0 ''will be given by
Δg0 ''=∑(1+√m2+n2H)Amn sin cos mx sin con ny
Dr. Kumagai introduced a new idea of “ Station Bouguer Anomaly” and derived a formula for the same purpose as the writer's. But it can be proved that his formula is one of the approximations to the exact formula. In order to determine the gravity anomaly of dgo' with the accuracy better 0.1 mgal, using the writer's formula, the following condition must be fulfilled;
(√m2+n2H)2>1/10Amn
This condition is also needed for the Dr. Kumagai's method. If the condition is not fulfilled, the series which appears in the writer's formula will diverge and the gravity anomaly, Δg0 '', will not be able to be computed.
