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An algorithm and a program for transformation of gravity anomalies for large territories are presented. The spherical shape of Earth is taken into account and the geodetic coordinates of measuring points are used. The calculations use the «quasi-ellipsoidal» model of V.V. Kavraisky, which allows the transition from geodesic to spherical coordinate system with increased accuracy. The algorithm is based on a source-like approximation of the field values, located in the nodes of a regular network, with the depths of the equivalent sources, depending on the latitude. To determine the source masses, the system of linear algebraic equations is solved by the fastest gradient descent method with an accelerated step calculation. The results of transformation of the gravity field in the Bouguer reduction for the Kuril island arc, the adjacent water areas and parts of land, located within 40°–54° N, 142°–162° E are presented with a total area of about 2.4 million km2. A slight difference between the recalculation results of gravity anomalies into the upper half-space using the «spherical» and «quasi-ellipsoidal» models of the Earth was experimentally established.
Dolgal et al. (Sat,) studied this question.