On Identifying Magnetized Anomalies Using Geomagnetic Monitoring Within a Magnetohydrodynamic model

Abstract

This paper is a continuation and an extension of our recent work [13] on the identification of magnetized anomalies using geomagnetic monitoring, which aims to establish a rigorous mathematical theory for the geomagnetic detection technology. Suppose a collection of magnetized anomalies is presented in the shell of the Earth. By monitoring the variation of the magnetic field of the Earth due to the presence of the anomalies, we establish sufficient conditions for the unique recovery of those unknown anomalies. In [13], the geomagnetic model was described by a linear Maxwell system. In this paper, we consider a much more sophisticated and complicated magnetohydrodynamic model, which stems from the widely accepted dynamo theory of geomagnetics.

On Identifying Magnetized Anomalies Using Geomagnetic Monitoring

“…As remarked earlier, we shall basically follow the general strategy developed in [8], but there are also several new technical developments in the current setup of out study. We would also like to mention in passing some related literature on the low-frequency asymptotic analysis of the Maxwell system [3,4,[7][8][9][10][11][12].…”

“…The magnetic anomaly detection was mathematically investigated [8,9] by two of the authors of the present article. In [8], a Maxwell system is used for the the geomagnetic model, whereas in [9], a magnetohydrodynamic system is used for the geomagnetic model.…”

“…In [8], a Maxwell system is used for the the geomagnetic model, whereas in [9], a magnetohydrodynamic system is used for the geomagnetic model. Both [8] and [9] deal with the case that the geomagnetic variation is caused by the presence of certain magnetized anomalies, which e.g. corresponds to a specific practical scenario of submarine detection.…”

“…That is, the magnetic anomaly already exists, and its growth or shrinkage causes the geomagnetic variation. In order to establish the unique recovery results in such a new situation, we basically follow the general strategy developed in [8,9] by combining low-frequency asymptotics and various linearization techniques. However, there are several new challenges that require some new technical developments.…”

“…It is emphasized that in (1.11), we do not assume that the Earth's geomagnetic field in the case with no anomaly is known a priori. Hence, one cannot naively reduce the current study to the one considered in [8,9], where the knowledge of the free geomagnetic field is a critical ingredient. Finally, we would like to point out that our uniqueness argument is constructive, and it actually implies a construction procedure for the anomaly detection.…”