Some equivalent bodies and ambiguity in magnetic and gravity interpretation

Abstract

The problem of ambiguity in potential field interpretation has long been recognised and arises from the fact that any observed field can be caused by an infinite variety of source distributions. This has not deterred modellers from proposing simple source distributions whose anomalies match the observed data but do not necessarily indicate the true geological picture. The underlying assumption in modelling is that a given geological unit is representable by a homogeneous body of restricted geometry. Knowledge of the geology enables us to justify such an assumption. This justification may take the form of a large number of rock property measurements and the consequent recognition that different lithologies may be distinguished by their responses. In addition, the expected structure is normally far from random and thus the model may be used with some degree of confidence. Where the rock properties are highly variable to the point where individual lithologies are hot distinguishable and/or where the structure is complex then the inherent ambiguity may well lead to a grossly misleading model. If the observed data do not indicate this complexity then the structure cannot be reliably determined. We propose the term "observational ambiguity" for the case where the data does not distinguish between one geological structure and another. In general, we should seek the simplest source distribution consistent with our knowledge of the geology and whose anomalies match the observed data. A more complex model is not justified and should not be proposed. We also propose the term "model ambiguity" for a set of models of similar geometry, that are equally possible. The remainder of this paper is devoted to experiments to derive such equivalent models. There are a number of classic demonstrations of ambiguity in the literature (e.g. Skeels 1947) but these are confined to discussions of the gravity field. The clearest examples are the concentric spheres and the set of lens-shaped discs both of which are equivalent sets to the point mass (e.g. Johnson, Jupp and van Klinken, 1977).