Backus-Gilbert inversion of potential field data in the frequency domain and its application to real and synthetic data

Abstract

An algorithm for the inversion of potential field data in the frequency domain using the Backus-Gilbert method is represented. This leads to an underdetermined system of linear algebraic equations. It can be easily solved because the matrix has nonzero elements only on its main diagonal. Since the solution represents a harmonic function, its extremes are located at the boundary of the model. This leads to unacceptable distribution functions of physical parameters. Therefore the concept of weighted minimum length was introduced. Advantages and drawbacks of weighting in the frequency domain are discussed. Theoretical as well as practical examples suggest that the algorithm may be applied in practice. A comparison of the Backus-Gilbert inversion in space domain and frequency domain from a numerical point of view shows the advantages of the proposed algorithm.