Solving Inverse Problems for Potential Fields for Nonuniform Data with Error

Abstract

The interpretation of data from potential fields meets substantial difficulties when these data are not uniform- In such a case the nonlinear, and even the linear regressional models do not have good statistical properties if directly applying the data fitting using least squares. To avoid this we propose an “uniformized” data fitting. Then one must use some cubature formula. The choice of this cubature formula is not unique and must be flexible with respect to the addition of information on the properties of the sources of the field. Here we present an idea how to overcome this obstacle which we demonstrate in detail in the case of geomagnetism and paleomagnetism. In a subsequent paper we shall demonstrate the realization of the same idea in the case of gravimetry and magnetics.