Abstract: In this paper the author discusses the possibility of the improvement of the accuracy of the fictitious single layer density by collocation method using various kinds of gravity data. The uniquness of the solution is proved and the eovariance between the single layer density and the linear functionals of the disturbing potential are derived.In the second part of the paper, the computation of the single density and terrain correction by Fast Fourier Transform method is proposed. Simulating test shows that the FFT method is very fast and accurate.