Anderson functions describe the projection of a magnetic dipole field in a given direction at points along an arbitrary line. They are useful in the study of magnetic anomaly detection, with historical applications in submarine hunting and underwater mine detection. [1] They approximately describe the signal detected by a total field sensor as the sensor passes by a target (assuming the targets signature is small compared to the Earth's magnetic field).
The magnetic field from a magnetic dipole along a given line, and in any given direction can be described by the following basis functions:
which are known as Anderson functions. [1]
Definitions:
The total magnetic field along the line is given by
where is the magnetic constant, and are the Anderson coefficients, which depend on the geometry of the system. These are [2]
where and are unit vectors (given by and , respectively).
Note, the antisymmetric portion of the function is represented by the second function. Correspondingly, the sign of depends on how is defined (e.g. direction is 'forward').
The total field measurement resulting from a dipole field in the presence of a background field (such as earth magnetic field) is
The last line is an approximation that is accurate if the background field is much larger than contributions from the dipole. In such a case the total field reduces to the sum of the background field, and the projection of the dipole field onto the background field. This means that the total field can be accurately described as an Anderson function with an offset.
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Anderson functions describe the projection of a magnetic dipole field in a given direction at points along an arbitrary line. They are useful in the study of magnetic anomaly detection, with historical applications in submarine hunting and underwater mine detection. [1] They approximately describe the signal detected by a total field sensor as the sensor passes by a target (assuming the targets signature is small compared to the Earth's magnetic field).
The magnetic field from a magnetic dipole along a given line, and in any given direction can be described by the following basis functions:
which are known as Anderson functions. [1]
Definitions:
The total magnetic field along the line is given by
where is the magnetic constant, and are the Anderson coefficients, which depend on the geometry of the system. These are [2]
where and are unit vectors (given by and , respectively).
Note, the antisymmetric portion of the function is represented by the second function. Correspondingly, the sign of depends on how is defined (e.g. direction is 'forward').
The total field measurement resulting from a dipole field in the presence of a background field (such as earth magnetic field) is
The last line is an approximation that is accurate if the background field is much larger than contributions from the dipole. In such a case the total field reduces to the sum of the background field, and the projection of the dipole field onto the background field. This means that the total field can be accurately described as an Anderson function with an offset.
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cite journal}}
: Cite journal requires |journal=
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help)