Premium
CHEBYSHEV EXPANSIONS FOR THE SOLUTION OF THE FORWARD GRAVITY PROBLEM 1
Author(s) -
ZHAO S. K.,
YEDLIN M. J.
Publication year - 1991
Publication title -
geophysical prospecting
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.735
H-Index - 79
eISSN - 1365-2478
pISSN - 0016-8025
DOI - 10.1111/j.1365-2478.1991.tb00344.x
Subject(s) - discretization , chebyshev filter , mathematics , chebyshev polynomials , dimension (graph theory) , fast fourier transform , multipole expansion , fast multipole method , mathematical analysis , chebyshev iteration , chebyshev equation , factorization , boundary (topology) , physics , algorithm , combinatorics , classical orthogonal polynomials , quantum mechanics , orthogonal polynomials
A bstract Chebyshev expansions are used to solve the 3D forward gravity problem. Since the matrix factorization method is used to solve the coefficient equation system and the fast Fourier transform (FFT) technique is used to compute the forward and backward Chebyshev expansions, this method is very fast. Multipole expansions are used to calculate approximate boundary conditions (BCs) for realistic problems. When the length of any source‐body dimension is less than 70% of the minimum dimension of the computational domain, the relative error caused by the approximate BCs is about 1%. A cell‐average discretization method is suggested. The accuracy obtained by the cell‐average discretization is much better than that obtained by the traditional point‐injection discretization. The Chebyshev expansion technique was applied to four density models including a complex geological structure consisting of two normally faulted layers. Models which were finely sampled had a maximum relative error of about 1%.