Numerical Computation Method Of Downward Continuation Of Potential Fields

The downward continuation of potential fields plays an important role not only in gravity and magnetic data interpretation, but also in geomagnetic navigation. The downward continuation problem is essentially the solution of the Fredholem integral equation of the first kind. And the equation is ill-posed. The point of this research is how to get stability, high precision, strong anti-noise ability and efficient calculation for downward continuation of potential fields.The field downward continuation problem is typical of the first class of convolution type linear inversion problem, whether direct solution or the iterate solution is actually to solve the problem through the generalized inverse, but every method has its advantages and disadvanta-ges.Like we commonly used Tikhonov normalization and Landweber iteration method. Tikhonov method is suitable for getting the generalized inverse problem easier, but damping factor is sensitive, Landweber method is suitable for getting the generalized inverse problem harder, in other words Landweber methods get the needed generalized inverse which is used for solving inverse problem through iteration, this method need the efficiency of iterative calculation is relatively low. In order to research potential field of downward continuation method systemat-icially, this article firstly introduces solving the direct normalization method for generalized inv-erse-the Singular Value Decompostion method, when the amount of data calculation is small, this algorithm can be used to calculate in spatial domain, while the large number data exists, we must adopt frequency domain method, the iteration algorithm for spatial domain or frequency domain and frequency domain combined with the iterative algorithm, so the iterative method research in this paper is priority among priorities. For iterative algorithm usemi-convergent "phenomenon, we interpret this phenomenon at the end of this chapter through the singular value decomposition principle, this is reason why this paper includes singular value decomposition method.The iterative method talk about in this article included integral iteration method proposed by Shizhe Xu academician and existing Tikhonov normalization iterative method, also included field downward continuation of the correlation coefficient method proposed by this article. We realize the potential field downward continuation of krylov subspace method through using the Barzilai-Borwein method to solve the downward equations of rapid downward continuation method, accelerated Landweber iterative method-potential field downward continuation v semis-iteration method, and contains the this article firstly applied krylov subspace method (CGNR, LSQR, GMRES, MINRES, Lanczos)to field downward continuation. In addition, in application of the potential field downward continuation of krylov subspace method, introducing fast Fourier transform algorithm is a very important step,or it will be limited by the large number of data.