Calculation of the piezomagnetic field arising from uniform regional stress in inhomogeneously magnetized crust (II): Limitation in general cases

Abstract

One of the difficulties encountered in modeling the piezomagnetic field is determining the distribution of the initial magnetizations. A previous study showed that, in the case that data are available regarding the magnetic total force anomaly and that the directions of the initial magnetizations are assumed to be uniform, the piezomagnetic field arising from the regional stress is uniquely determined, although the intensities of the initial magnetizations are not uniquely determined. The present study considers a more general situation in which the directions of the initial magnetizations are unknown. The problem addressed here is whether the piezomagnetic field is determined uniquely. To this end, a set of expressions is derived to describe the relation among the initial magnetizations, the magnetic anomalies corresponding to the initial magnetization, and the resultant piezomagnetic field. The expressions show that the correspondence between magnetic anomalies and the piezomagnetic field is not one-to-one. This result suggests that observations of the piezomagnetic field provide quantitative estimations of changes in stress only if we can assume that the directions of the initial magnetizations are uniform.