ИСТИНА

The problem of determination of the contribution to the gravitational field of the Earth from dipole-distributed anomalous masses, distributed relative to the reference ellipsoid as on height, and laterally, and presented in the form of expansion in terms of spherical functions, is solved in the quadratic approximation. The analytical formulas, expressing the expansion coefficients of the square of some function on sphere, initially specified also in the form a spherical function expansion, through the coefficients of this initial expansion, are derived. We developed the recurrent algorithms, allowing to accelerate process of deriving of formulas and to avoid operative memory overflow. To illustrate the results we calculated the contribution of the quadratic terms to the Earth’s gravitational field up to the degree N=18 from the relief and from the density jump at Mohorovicic discontinuity (M) up to N=9. We have shown, that the contribution of the quadratic terms from the jump at M is an order of magnitude larger than the contribution from the relief, while the total contribution is approximately of the same order of smallness as the linear contribution. Moreover, the total quadratic contribution from the dipole for some harmonics exceeds the linear contribution , and it is for half of coefficients more than 0.01 % from the linear. Maps of distribution of the total quadratic and linear contribution to the anomalies of the external gravity on the Earth’s ellipsoid show, that the linear contribution mainly correlates with the relief heights or with the M depths , i.e., it is positive for the continents and negative for the oceans, while the contribution of the quadratic terms correlates with squares of these heights and depths, i.e., it is positive everywhere. In the order of magnitude the quadratic contribution is comparable to the linear, therefore, using only the linear approximation in interpreting of gravitational anomalies, we can obtain incorrect estimates for the contribution of the crust’s boundaries to the Earth’s gravity and incorrect estimates for correlation between these boundaries and the gravitational anomalies. The contribution of the quadratic terms is particularly pronounced in the satellite zone, where it can even exceed the linear contribution for some regions in absolute value, so the total contribution may be opposite in sign to the linear contribution ( e.g. for Pacific basins). That can distort significantly the interpretation of satellite data. The work was supportted by RFBR ( project 08-05 00256}.