Frequency Characteristics Analysis for Magnetic Anomaly Detection
Jiazeng Wang, Zekun Jiang, Junqi Gao, Shuxiang Zhao, Wenmin Zhai, Ying Shen
Abstract
This letter presents a frequency characteristics analysis for a magnetic anomaly detection (MAD) study. A magnetic dipole model is developed to study the energy distribution of the obtained MAD signal in the frequency domain, where <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$f_{h}$ </tex-math></inline-formula> is proposed to define the signal high-frequency boundary. The relations between <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$f_{h}$ </tex-math></inline-formula> and other parameters, such as the velocity of the target (or platform), closest path approach (CPA), magnetic moment strength, magnetic moment orientation (MMO), and sensor orientation, are analyzed. We find that the frequency response is independent of the moment strength. The combined effects of the MMO and sensor orientation on <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$f_{h}$ </tex-math></inline-formula> are defined by the functio <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$n g(\alpha $ </tex-math></inline-formula> , <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$\beta $ </tex-math></inline-formula> , <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$\theta $ </tex-math></inline-formula> , <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$\phi$ </tex-math></inline-formula> ), which is studied by the Monte Carlo method, yielding a maximum value of max( <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$g) \approx ~0.85$ </tex-math></inline-formula> . Thus, the function <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$f_{h} = 0.85v$ </tex-math></inline-formula> /CPA is advanced for frequency boundary estimation. The proposed theoretical analysis is examined in an experiment to aid in extracting the magnetic anomaly signal effectively.