Transformation of Gravity Anomalies in Large Territories (the Case of the Kuril Island Arc)

Abstract

An algorithm and a program for transformation of gravity anomalies for large territories are presented. They use a spherical shape of the Earth and the geodetic coordinates of measuring points. The calculations employ the “quasi-ellipsoidal” model of V.V. Kavraisky, which allows the transition from the geodetic to the spherical coordinate system with increased accuracy. The algorithm is based on a sourcewise approximation of the field values located at the nodes of a regular grid with the latitude-dependent depths of the equivalent sources. To determine the source masses, the system of linear algebraic equations is solved by the steepest descent gradient method with an accelerated calculation of the step. The results of transformation of the gravitational field in the Bouguer reduction for the Kuril Island arc, the adjacent water and land areas located within 40°–54° N, 142°–162° E and having a total area of about 2.4 mln km², are presented. A slight difference between the results of recalculating the gravity anomalies into the upper half-space using the “spherical” and “quasi-ellipsoidal” models of the Earth is experimentally established.