Patent ID: 7219115

Claim:
A method for prospecting for natural resources in a time invariant geophysical system by obtaining a stable and accurate solution for an ill-conditioned system of normal equations associated with a prediction filter whose observed output is defined as a time advanced version of the input using Gram_Schmidt process of orthonormalisation comprising the steps of: (a) obtaining a set of digitized data relating to a time-invariant geophysical system, which have natural resources and stored in an array; and eliminating arithmetic mean from the data to make it a zero mean process; (b) determining the optimum filter length/optimum order of an autoregressive model; (c) creating segments X(P,I) of the said digitized data from step (a) above, for I=1, N−M, P=1, . . . M.; (d) changing the range of X(P,I) to (−1,1); (e) formulating the vectors g i (x t )′s, where g i (x t )=[d i (x k+1 ) d i (x k+2 ) . . . d i (x N )], and deriving the system of normal equations in terms of g i (x t )′s; (f) computing the orthonormal vectors of f i (x t )′s using Gram_Schmidt process of orthonormalisation; (g) rewriting the system of normal equations in terms of the orthonormal vectors f i (x t )′s, (h) solving the new system of normal equations for determining the digital Weiner filter or an autoregressive operator, (i) obtaining a spectrum output, and (j) applying the spectrum output to identifying the natural resources.