FOREquivalent sources are useful in processing upward-and downward-continued fields, field total magnetic field profiles. A lines-of-dipoles reduced to the pole, amplitude spectrum of the distribution, obtained by solving the linear infield, and band-passed field. A theoretical example verse problem, provides an analytic base for comdemonstrates the validity of the approach, and a puting the following quantities from an observed field example shows that reasonable results are field: first and second vertical derivative fields, readily obtained. INTRODUCTION Solutions to the inverse problem of potential theory have been presented and extensively discussed by many authors (e.g., Hall, 1958; Corbato, 1965; Hahn, 1965; Zidarov, 1965;Bott, 1967; Johnson, 1969; Emilia and Bodvarsson, 1969;Bodvarsson, 1971). The object of these papers is to provide geologically and geophysically feasible interpretations of observed potential field anomalies. Recently Dampney (1969) and Needham (1970) have shown that equivalent sources, obtained as solutions to the inverse gravity problem, can be used to further process the observed gravity field. In both papers the theoretical field of a distribution of point masses, computed on the basis of the original field observations, is used to analytically determine those observations on a different surface.Potential fields can be extensively processed using equivalent source solutions of the inverse problem. In particular, the pertinent analytic equation as obtained from a final equivalent source distribution is used to calculate each of the following quantities directly from the observed total magnetic field: first and second vertical derivative fields, upward-and downward-continued fields, field reduced to the pole, amplitude spectrum of the field, and band-passed field. Other quantities such as horizontal and vertical field components, higher-order vertical derivatives, horizontal derivatives, and power and phase spectra may be calculated using the equivalentsource technique, but they are not considered further.
THE METHODThe inverse problem of potential theory, in its general form, involves direct use of field observations to estimate parameters that describe an acceptable source configuration; the theoretical field of a model source configuration is a linear function of the magnitude parameter (e.g., mass or magnetization amplitude) and a nonlinear function of the source location and geometry. One of many algorithms available is used to iterativeI\. adjust an initially assumed set of source-botl!. parameters, and formal acceptance of a set of parameters depends on whether it gives the particular "fit" required between the theoretical and observed fields.The ambiguity in modeling potential fields is quite evident when solving the inverse problem. The final set of parameters describing a source configuration depends on the initially assumed set of variable parameters. In turn, the initial model depends on the purpose of the individual studyand whether known geological and geophysical d...