# Identifying variations of magnetic anomalies using geomagnetic monitoring

## TL;DR

This paper rigorously proves that geomagnetic monitoring can uniquely identify the locations, variation rates, and material properties of magnetic anomalies beneath the Earth, extending previous results to include anomalies with changing parameters.

## Contribution

It introduces a rigorous mathematical framework for uniquely recovering both static and varying magnetic anomalies using geomagnetic data.

## Key findings

- Unique recovery of anomaly locations and parameters
- Extension of previous results to dynamic anomalies
- Mathematical proof of identifiability in inverse problems

## Abstract

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.