## The Lunar Magnetic Field

Unlike the Earth, the Moon currently has no core magnetic field (although it may have had one in the past). It does however have a crustal field, for which we present three models from Purucker and Nicholas (2010).

### Sequential model

The external magnetic field in the sequential, line dipole approach is
represented as a uniform field over each satellite half orbit, and the
half orbits extend from pole to pole.
The external field was determined in a least squares sense from all
three components of the vector data. Following the removal of the
external field model from each half orbit, an internal line dipole
model is developed in spherical coordinates
(Dyment and Arkani‐Hamed, 1998),
utilizing three adjacent half orbits which are separated in space by
about 1° (30 km), and in time by 1.9 h. The crust under the three
adjacent half orbits is divided into blocks, each of which is assumed
to have a magnetic dipole at its center. A horizontal dipole is located
under each observation of the center pass, on the 1737.1 km mean lunar
radius surface.

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### Coestimation model

The coestimation model utilizes a harmonic approach to
characterize the internal magnetic field, and coestimates the
internal and external magnetic fields. The external magnetic fields
are still described, as in the sequential approach, as a uniform
external field over each satellite half orbit.
This model allows for better feature recognition, but the amplitude
of the anomalies is suppressed slightly compared to the sequential
approach.

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### Correlative model

We apply a harmonic wave number correlation technique
(Langel and Hinze, 1998)
to extract common features of the two maps, retaining coefficients from
the coestimation map that differ by less than 30% phase angle from
their counterparts in the sequential map.
This technique is often applied in geomagnetic applications in order to
minimize the influence of noncrustal components in the final map.
While emphasizing the common features, it also sometimes reduces the
amplitude of the map significantly.
In this case, only minimal amplitude reduction was noted from the
coestimation map.

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