Angular Dispersion Due to Random Magnetization

Abstract

Summary The angular probability distribution generated by adding a set of randomly oriented vectors to a set of constant parallel vectors has been studied. If one random vector of constant length is added to each constant vector, the resultant angular probability distribution departs widely from the distribution used by Fisher as the basis for palaeomagnetic analysis. However, if n random vectors of equal length are added to each constant vector and if n > 6, the resulting angular probability distribution is nearly identical to that proposed by Fisher over most of the range of angular dispersions encountered in palaeomagnetic investigations. Equations are developed from which the mean intensity of random magnetization can be calculated, given the mean total intensity and the angular dispersion. These parameters, in turn, are related to the ratio of random to non-random magnetization for each ferromagnetic mineral grain in a rock specimen. I. Introduction Analysis of the natural remanent magnetization of a rock commonly reveals the presence of several components of magnetization, each due to a different magnetizing process occurring at a different time during the rock’s history. Even under ideal conditions two components are present, a stable magnetization constant in magnitude and direction from specimen to specimen, and a second component which varies randomly in direction. This second component may be introduced during the collection, the measurement, or the partial demagnetization of the specimen. It may also be present as a fundamental property of natural remanent magnetization, as most processes by which rocks become magnetized do not impart perfectly uniform magnetization to an entire rock formation. Whatever its origin, a randomly oriented component of magnetization is invariably present and produces an angular dispersion in measurements of the remanent magnetization of rocks. I 345