Inversion of Potential Field Data Using the Structural Index as Weighting Function Rate Decay

Nonparametric inverse methods provide a general framework for solving potential-field problems. The use of weighted norms leads to a general regularization problem of Tikhonov form. We present an inversion method to estimate the source density distribution from potential field measurements using a flexible depth weighting function in the Tikhonov formulation. Our approach is close to the formulation proposed by Li and Oldenburg (1996), but differs significantly in the definition of the weighting function, which in our formalism is not given with a fixed exponent but with the structural index of the Euler Deconvolution theory as exponent. Hence the allowed values for the weighting function exponent depend on the range of structural index for magnetic sources, being 0≤N≤3. Simple tests on 2D sources such as dipoles, dipole lines, dykes or contacts, validate our hypothesis. The main aspect of the proposed inversion scheme is that it brings a new link between two widely used types of inverse methods, namely the Euler deconvolution and the block model solution of a Tikhonov-form regularization problem with additional a priori information.