Regional mapping of the lunar magnetic anomalies at the surface: Method and its application to strong and weak magnetic anomaly regions
Introduction
The origin of the lunar magnetic anomalies is one of the most important issues for the lunar science and has been debated (e.g. Dyal et al., 1974, Fuller, 1974, Lin et al., 1988, Hood and Artemieva, 2008, Garric-Bethell et al., 2009, Gattacceca et al., 2010, Wieczorek et al., 2012, Purucker et al., 2012, Hood et al., 2013). For the global mapping of vector fields, the Lunar Prospector observations at low altitudes were corrected and normalized to 30 km altitude (Richmond and Hood, 2008, Purucker and Nicholas, 2010), while the Kaguya observation during the nominal phase were normalized to 100 km altitude (Tsunakawa et al., 2010). In general, the magnetic fields of short wavelength components are rapidly attenuated at the higher altitude. This attenuation may result in lack of fine and possibly important structures of the lunar magnetic anomalies. Although the near-surface total intensity has been mapped by the electron reflectometry (e.g. Halekas et al., 2001, Mitchell et al., 2008), three components of the magnetic field are more useful for the study of the magnetic anomaly source in comparison with other maps of the topography, geology and so on. Thus the mapping altitude of the vector field is required to be as low as possible.
Distribution of the magnetic field above the surface is attributed to the boundary value distribution if the magnetic field can be expressed in terms of the magnetic potential. One of the boundary values is the radial component of the magnetic field at the surface. The magnetic field of the lunar crust above the surface can be described if the boundary value distribution is given. As an inverse boundary value problem, we can estimate the radial component of the magnetic field at the surface (Tsunakawa et al., 2010).
In the inverse problem, signals of the crustal magnetic field should carefully be separated from noise and bias mainly due to the external field, since the noise and bias are usually amplified via downward continuation. Effects of these amplifications on the surface mapping depends mainly on the strength and wavelength of magnetic anomalies and the three dimensional distribution of observation points. Since these factors vary with respect to the observed region, the regional analysis is suitable for detailed surface mapping of the lunar magnetic anomalies. In the present study, we have developed a statistical method for regional mapping of three components of the crustal magnetic field at the surface from the satellite observation. This method has been applied to two regions: the northwest region of the South Pole-Aitken basin as a strong magnetic anomaly region, and the southeast region of the lunar near side as a weak magnetic anomaly region. We will show the mapping results and discuss characteristic features of the lunar magnetic anomalies on the basis of three components of the magnetic field at the lunar surface.
Section snippets
Datasets
The Kaguya spacecraft, which is a three-axis stabilized spacecraft, observed the magnetic field around the Moon with nearly polar orbit at low altitudes of 6–80 km from December, 2008 to June, 2009, after the high altitude observation. The altitude was gradually lowered with periapsis near the South Pole-Aitken (SPA) basin because strong magnetic anomalies are widely distributed around the SPA basin (e.g. Richmond and Hood, 2008, Mitchell et al., 2008). In particular, the observation was carried
Theory
Previous maps of the vector field of the lunar magnetic anomaly have been provided at a certain altitude, for example, 30 km altitude. Those mapping methods are based on the altitude correction applied to the observations at various altitudes. Tsunakawa et al. (2010) point out that the altitude correction of the magnetic anomaly is attributed to the boundary value problem at the surface by the magnetic potential theory. In this section, we briefly review previous mapping methods with respect to
Method of the surface vector mapping (SVM)
We propose a method for estimating three components of the magnetic field at a spherical surface, together with procedures to reduce effects of noise and bias, in this section.
Results of regional mapping
Two regions were analyzed with the SVM: (1) northwest region of the South Pole-Aitken basin on the lunar far side as a strong magnetic anomaly region, and (2) southeast region of the lunar near side as a weak magnetic anomaly region. These regions show relatively clear elongation of the lunar magnetic anomalies on previous maps (e.g. Purucker and Nicholas, 2010, Tsunakawa et al., 2010). Since the used data consist of 4 s averaged data for the KG dataset and 5 s averaged data for the LP dataset,
Surface vector mapping with the combined dataset
The surface mapping results from the KG and LP datasets are similar in the northwest region of the SPA basin as shown in Section 5.1. If the datasets are combined, density of the pass is nearly twice of the individual datasets, and the altitude distribution is more uniform. Thus it is expected to improve the mapping in this region using the combined dataset.
The SVM was applied to the combined dataset of the KG and LP observations in the northwest region of the SPA basin: Npass = 216, Ndata =
Conclusions
The method of the surface vector mapping (SVM) has been developed for regional mapping of the magnetic anomaly at the surface using the satellite observation. The SVM is based on the inverse boundary value problem with a spherical boundary surface. Using first derivatives along the pass, the bias effect of remaining components of the external field after de-trending is successfully reduced. The effect of the observation noise is decreased by the Bayesian statistical procedure using ABIC. The
Acknowledgments
The authors thank all the staff of the SELENE/Kaguya project, especially, Satoru Nakazawa, Hisashi Otake, and the late Yuichi Iijima. We also thank Lon Hood for his constructive comments on the manuscript. The Kaguya dataset is available from the SELENE data archive (http://l2db.selene.darts.isas.jaxa.jp/index.html.en).
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