  We are concerned with the inverse problem of identifying magnetic anomalies
with varing parameters beneath the Earth using geomagnetic monitoring.
Observations of the change in Earth's magnetic field--the secular
variation--provide information about the anomalies as well as their variations.
In this paper, we rigorously establish the unique recovery results for this
magnetic anomaly detection problem. We show that one can uniquely recover the
locations, the variation parameters including the growth or decaying rates as
well as their material parameters of the anomalies. This paper extends the
existing results in [8] by two of the authors to varying anomalies.
