The purpose of this research is to investigate the internal origin hypothesis by assuming that the crustal lunar magnetic field was generated by a paleo-dynamo process. The study is focused on four comparatively high intensity magnetic anomalies associated with high marked swirl albedo. These four formations: Reiner Gamma, Descartes Formation, Mare Marginis and Mare Ingenii, all having a similar Imbrian age, can also be fairly well modeled using simple magnetized disks at depth. Using these simple assumptions, the paleomagnetic pole positions have been determined. The modeling of these anomalies shows a cluster of paleomagnetic pole positions within a radius of about 35 degrees centered at (30S, 215E). These preliminary results are consistent with the hypothesis of a now extinct paleo-dynamo being responsible for magnetization of lunar crust. However, a more statistical analysis remains to be done over regions of weaker magnetic anomalies to be fully conclusive.
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It has been established that the Moon is lacking a global magnetic field (Ness, 1971) since the Explorer 35 mission at the end of 60's. However, the observations of solar wind interactions with the Moon revealed the existence of weak localized fields, which were later confirmed by in situ measurements (Dyal et al., 1974). In particular, a remnant magnetization could be estimated from the returned samples of the Apollo and Luna missions (Fuller, 1974). These measurements also suggested the existence of a past magnetizing field of about 100 μT around 3.9 Ga that decreased after 3.6 Ga (Cisowski et al., 1983; Collinson, 1993). Despite these informations, we do not have a clear idea concerning the internal or external origin of this past magnetizing field (Hood et al., 2001; Hood and Artemieva, 2008). The most straightforward analogy with the Earth's magnetic field is that the Moon once possessed a main magnetic field generated by a planetary dynamo that is now extinct (Fuller and Cisowski, 1987; Collinson, 1993). However, according to Hood and Huang (1991), the small size of the lunar core as derived from seismic data (Khan et al., 2004) and electromagnetic studies (Hood et al., 1999) would not be able to generate a dynamo sustaining a magnetic field with 100 μT amplitude. Instead, they invoke meteoric impacts in order to account for the relatively random nature of the lunar magnetic field (Hood and Huang, 1991), like over the Fra Mauro in the nearside (Hood et al., 1981), for instance. More recently, the hypothesis of magnetization acquired in the presence of transient fields generated by cometary impacts (Schultz and Snrka, 1980) has been revived by Richmond et al. (2005) who correlated strong anomalies with zones of high swirl albedo. However, this hypothesis seems to also be deficient for regions like Reiner Gamma (Nicholas et al., 2007) and Descartes Formation, for instance. For this latter zone, an albedo spectral analysis concluded that the material was not of exotic composition (Blewett et al., 2005). The debate is thus still open. Despite the random nature of the Moon magnetic field, recent measurements showed some disparities. Lunar Prospector (LP) reflectometer data have pointed out that the crustal rocks of the Moon were strongly demagnetized by meteoric impacts (Halekas et al., 2002), which makes it difficult to determine the origin of these magnetic anomalies. However, since the Apollo era, it has also been established that some lunar formations, like those located at the antipodes of the impact generated young basins, acquired relatively strong magnetization (Lin et al., 1998; Halekas et al., 2001; Hood et al., 2001). In addition, it has been noticed that high albedo features such as Reiner Gamma, Mare Ingenii, Mare Marginis and Descartes Formation are associated with strong magnetic anomalies (Hood and Schubert, 1980; Hood et al., 1981). This is confirmed by the accurate LP data (Hood et al., 2001; Richmond et al., 2003, 2005).
In this research, we take the opportunity of such clear and comparatively strong signals to test the existence of a former lunar dynamo. We focus our study on the strong magnetic anomalies associated with very marked albedo zones such as Reiner Gamma, Descartes Formation, Mare Marginis (located in the nearside of Moon) and Mare Ingenii (located in the farside of the Moon). These four regions are of similar Imbrian age of about 3.8 Ga (Richmond et al., 2003). Using an equivalent source method, we evaluate the magnetic signal generated by disks uniformly magnetized and we estimated the corresponding paleo-pole positions. We then discuss our obtained result and their limits.
DATA SELECTION AND PROCESSING
During the Apollo era only small regions within about 30 degrees of the lunar equator were magnetically mapped from orbit. In the Apollo 15 case, mainly two areas above Gerasimovich and Van de Graaff-Aitken in the farside were surveyed (Hood et al., 1981) while the Apollo 16 mission operated only over a very narrow nearside equatorial band. In contrast, the aim of the Lunar Prospector (LP) mission, whose lifetime was extended from January 1998 to the end of July 1999, was to globally map geophysical and geochemical properties of the Moon. Instruments and orbital parameters were chosen accordingly (Binder, 1998). A comprehensive description of the LP mission can be found in Andolz et al. (1998).
The data sets used in this study are the level 1 refined magnetometer data of the LP mission. However, the proximity of the solar maximum made it challenging to select the most undisturbed data. In order to maximize the signal to noise ratio, we only consider low altitude measurements, below 35 km, when the Moon is in the Earth's magnetic tail. This situation happened only 4 days per month during the LP's 19-month lifetime. High altitude data, acquired between 110 to 80 km during the year 1998, were discarded as they showed a signal that was comparatively too weak and of low resolution. This initial data selection drastically decreased the amount of usable data to about 7% of the whole database. The selected magnetometer data given in selenographic centered cartesian coordinate, were projected into spherical North, East and Radial components.
Despite the great care taken to select the data, high frequency external signals remain. A low-pass filter, based on Discrete Wavelet Transform (DWT) algorithms, was used to clean magnetic variations smaller than 10 km along the satellite tracks. This transformation method is described by Daubechies (1992) and has been previously applied to terrestrial magnetometer measurements (Fedi and Quarta, 1998; Leblanc and Morris, 2001). The anomaly field direction is not influenced much by these transformations. An example of the filtering is shown in Fig. 1.
The satellite data also contains a low frequency external signal, which is further filtered out (detrended) using a low degree polynomial fit in the spherical reference frame.
|Fig. 1:||Example of denoising magnetometer data using Daubechies orthogonal wavelets. Denoised data are plotted in red while initial raw data are in blue. The anomalies are superimposed to show the effectiveness of denoising to eliminate external field using wavelets. We use 20 coefficients (D20) of Daubechies wavelets|
|Fig. 2:||Example of lunar magnetic anomalies. Lunar magnetic anomalies are repeated in adjacent tracks. (Top) Magnetic total components data over Reiner Gamma on January 27th 1999. (Bottom) Magnetic total components data over Descartes formations on April 13th 1999|
This detrending is a common procedure in satellite magnetism. It was formerly used to reduce Apollo subsatellite magnetometer data (Hood et al., 1981), LP magnetometer data (Hood et al., 2001) and Mars Global Surveyor (MGS) magnetometer data (Hood et al., 2005). It is worth stressing that this empirical method generates long scale spurious effects (Thébault et al., 2008), but the obtained results in the lunar case may still be used with confidence as we focus on spatial scales smaller than the created artifacts.
The processing methods described earlier are applied to the whole selected half-orbits. A systematic visual inspection was carried out and the lunar remnant magnetic fields over a given area were considered to be genuine if they were repeatedly detected in close adjacent profiles. Figure 2 shows an example of the selected lunar magnetic field over Reiner Gamma and Descartes Formation. This processing was applied over the four regions of very high albedo: Reiner Gamma, Descartes Formation, Mare Marginis and Mare Ingenii. Corresponding results are plotted in Fig. 3 to 6. Table 1 and 2 compare some statistics between raw and processed data.
|Fig. 3:||Magnetic anomalies over Descartes Formation. (Top-Left) Data distribution. (Top-right) The altitude of the LP satellite expressed in km. (Middle-left) Radial component of the observed field. (Middle-right) Radial component of the modeled field. (Bottom-left) Total component of the observed field. (Bottom-right) Total component of the modeled field. The contour map of magnetic field is in nT. The projection system is the equidistant cylindrical centered on 16.5E|
|Fig. 4:||Magnetic anomalies over Reiner Gamma Formation. (Top-Left) Data distribution. (Top-right) The altitude of the LP satellite expressed in km. (Middle-left) Radial component of the observed field. (Middle-right) Radial component of the modeled field. (Bottom-left) Total component of the observed field. (Bottom-right) Total component of the modeled field. The contour map of magnetic field is in nT. The projection system is the equidistant cylindrical centered on 302E|
|Fig. 5:||Magnetic anomalies over Mare Marginis Formation. (Top-Left) Data distribution. (Top-right) The altitude of the LP satellite expressed in km. (Middle-left) Radial component of the observed field. (Middle-right) Radial component of the modeled field. (Bottom-left) Total component of the observed field. (Bottom-right) Total component of the modeled field. The contour map of magnetic field is in nT. The projection system is the equidistant cylindrical centered on 86E|
|Fig. 6:||Magnetic anomalies over Mare Ingenii Formation. (Top-Left) Data distribution. (Top-right) The altitude of the LP satellite expressed in km. (Middle-left) Radial component of the observed field. (Middle-right) Radial component of the modeled field. (Bottom-left) Total component of the observed field. (Bottom-right) Total component of the modeled field. The contour map of magnetic field is in nT. The projection system is the equidistant cylindrical centered on 168E|
|Table 1:||Magnetic field anomalies statistics: Raw data|
|Table 2:||Magnetic field anomalies statistics: Processed data|
The radial component of the anomaly field over Reiner Gamma and Mare Ingenii shows a mainly NE-SW direction, whereas the Descartes and Mare Marginis anomalies are principally E-W (Fig. 3-6). The magnetic anomaly of the total field over Descartes Formation (Fig. 3) shows a maximum magnitude of 22 nT at (11S, 15.5E) that is in good agreement with the study of Richmond et al. (2003). This maximum intensity coincides with the area of highly marked albedo. Considering the radial component of the anomaly field, this marked albedo closely correlates with the negative lobe of the magnetic anomaly (Fig. 3). The Reiner Gamma total field anomaly shows two anomalies (Fig. 4): the strongest, about 16 nT, is centered over (7.5N, 301E) in the southern region and the weakest, of about 6 nT, lies in the northern part of the map. When comparing these results with those given by Hood et al. (2001) they are consistent for the anomaly direction but the magnitudes are lower. We explain this difference by the altitude variation between both data sets: altitude in this study varies from 30 to 35 km while it varies from 18 to 20 km in the study of Hood et al. (2001). Previous works, based on Apollo 15 and 16 subsatellite magnetometric data with almost the same altitude range (Hood et al., 1981), are more coherent with our processed data. The radial component of Reiner Gamma mapped in this research varies from -8 nT to +8 nT, which is slightly different from that mapped by Hood et al. (1981) using Apollo 16 (-3 to +10 nT), but both have the same direction. This is due firstly to the incomplete coverage of Apollo data over the same region compared to that of LP and secondly to the different high-pass filters used in each study. Similarly, Fig. 5 shows the magnetic anomaly over Mare Marginis which has a maximum about 7nT and is centered on (16N, 83E). This relatively strong anomaly has been previously reported by Hood and Schubert (1980) using the electron reflectance technique. At last, present results obtained for Mare Ingenii on the farside (Fig. 6) are coherent with those of Hood et al. (2001). Both total magnetic field maps reveal a maximum magnitude centered at (37.5S, 163.5E) coinciding also with the marked high albedo feature. This high albedo zone is completely included in the positive part of the dipole field (Fig. 6). These four high albedo regions, either in nearside or farside, also bear a comparatively strong magnetization with a mainly dipolar geometry at satellite altitude.
METHOD OF INVERSION
The dipolar geometry of the magnetic signal is adapted to a source modeling using an equivalent source of very simple geometry, like a disk uniformly magnetized at depth. In order to test the former dynamo hypothesis, we assume that the four major magnetic anomalies discussed above were acquired in an ambient global dipole magnetic field. In general, we may use different approaches to determine the physical parameters of a magnetized body. The first one considers the forward method, which consists of setting an equivalent layer of dipoles within the crust (Hood et al., 2005, for MGS magnetic data). The parameters are then found by consecutive trials and comparisons between the magnetic field generated by the equivalent layer and the satellite data. In this research, considering the isolated and rather dipolar nature of the magnetic anomalies under study, we may use an inverse method as we assume unique sources for each of the four regions. The geometry and depths of sources are shown in Table 2. Moreover, the Lunar magnetic field is being assumed to be of remnant origin and the magnetization of rocks is assumed to be aligned with the now extinct dipolar magnetic field that was imprinted in rocks 3.8 Ga ago (Imbrian age for the four structures under study). Present purpose is thus to estimate in order to obtain an estimate of the angular location of the corresponding paleomagnetic poles. The method can be summarized as follows (Parker et al., 1987; Parker, 1991):
A source with magnetization generates a magnetic field at any space location through the equation (Blakely, 1996):
where, is the gradient operator with respect to the observation coordinates, is the gradient operator with respect to the source coordinates, v is the volume of the magnetized body, μ0 is the magnetic permeability of free space and (r0, θ0, φ0) are the spherical coordinates of the elementary point source. We may express the total magnetic anomaly at any point rj as a scalar product:
where, is the unit vector in the direction of is the vector-valued Green's function given by Parker (1991):
Comparisons between the observed and the modeled fields in the studied area may be achieved in the least-square sense by minimizing the Euclidean norm Q2:
Solution non uniqueness is a ubiquitous problem in geomagnetism. A further constraint is then added to the inverse problem and we assume the magnitude of magnetization to be higher than the minimum value given by Parker (2003):
where, ||Bmax|| is the maximum total magnetic anomaly observed, h1 is the altitude and h2 is the altitude plus layer thickness. This equation was first established by Parker (2003) in the case of crustal remnant magnetization on Mars and was recently applied by Nicholas et al. (2007) on the Moon.
From the least-squares estimation of the magnetization vector parameter (Mr, Mθ, Mφ) we deduce the selenographic angular location of the paleomagnetic poles. The latitude of paleo-pole λp is given by Butler (1992):
where, λ0 is the source latitude, D is the declination angle derived from D = tan-1 (-Mθ/Mφ) and I is the dip angle given by
and the co-latitude β is given by β = tan-1 (2/tan I). The longitudinal difference between the pole and the source location is positive toward the east and is given by:
If cosβ≥sin λ0 sin λp then the longitude of the paleo-pole is evaluated using φp = φ0+Δφ where φ0 is the source longitude, otherwise, φp = φ0+180°+Δφ.
Following Butler (1992), present results are determined with the semi-axes confidence ellipse error in paleo-pole locations given by:
where, α95 is the 95% confidence error taken to be equal to the standard deviation.
RESULTS AND DISCUSSION
Using the source geometry parameters in Table 3, we find computed magnetic fields rather similar to the observed ones. For the Reiner Gamma, Descartes Formation, Mare Marginis and Mare Ingenii, the iterative procedure described above shows residual mean square misfits between the computed and measured field equal to 2.45, 3.02, 2.25 and 2.95 nT, respectively. The depth of the sources ranges between 10 and 20 km, which is in accordance with earlier study (Hood et al., 2001; Nicholas et al., 2007). Source anomaly is assumed to be near the surface. The estimated magnetization value of Reiner Gamma, 0.12 Am-1, is close to the corresponding value given by Nicholas et al. (2007) using also an ideal body as given by Eq. 5. Magnetization intensity values obtained for Descartes Formation and Mare Marginis are close to each other. The Mare Ingenii feature shows a small value compared to the others. This may be related to the demagnetizing effects of the more heavily cratered farside to which it belongs and to the large extension of the formation.
The pole positions of the hypothetical global field are derived from the magnetization vectors of the source using Eq. 6 and 7. The results are given in Table 4 and are shown in Fig. 7. This figure shows that the pole positions are located in the farside and are clustered around the position (30S, 215E). However, Mare Ingenii exhibits an equatorial pole position slightly further from the cluster center. In addition, the inverse modeling result showed a higher sensitivity to the initial priory information. This singular behavior may be related to its location within the farside of the Moon or to the fact that the simple assumptions used in this study are less reasonable for Mare Ingenii. It is worth stressing that the magnetized crustal material or Mare Ingenii may have been reworked by heavy meteoric bombardment during geological history. Moreover, it is generally accepted that Mare Ingenii is associated with an antipodal young basin impact (Hood et al., 2001). Conversely, Reiner Gamma, Descartes Formation and Mare Marginis, belonging to the nearside of the Moon, are not close to each other. The physical conditions are thus rather different, although the common parameter for these four formations is their Imbrian age. Taking the above results with the necessary caution, a cluster of paleomagnetic positions is a good indicator that the Moon once had in its early age a global dipolar core field.
|Table 3:||Magnetization properties deduced from equivalent source|
|Table 4:||Directional properties of paleo-poles. All units are in degrees|
|Fig. 7:||The location of lunar paleomagnetic poles mapped in the equidistant cylindrical projection centred at 180E. The projection shows adjacent locations of the paleomagnetic poles for the formations computed according to Eq. 6 and 7. RG: for Reiner Gamma, D for Descartes Formation, M for Mare Marginis and I for Mare Ingenii. The 95% confident ellipse is computed using Eq. 8 and 9|
We have mapped magnetic anomalies over four lunar regions of high albedo using selected orbits with low noise. The mapping field is consistent and presents real lunar crustal sources. The study of the lunar magnetic pole positions of these selected high albedo formations of a similar age uses an inversion method based on simple uniformly magnetized circular disks. This inversion is slightly sensitive to source position, especially when the anomaly shape is far from being dipolar. However, our results show a clustering of poles as determined by the magnetization vectors associated to these strong lunar magnetic anomalies. Moreover, these pole positions belonging to southern part of the farside are partially in favor of a magnetization acquired in the presence of a lunar magnetic field generated by a global paleo-dynamo. However, it currently remains difficult to expand our conclusions to the global Moon's crustal magnetization. We intend in the future to generalize the modeling and to investigate the magnetization of all significant lunar magnetic anomalies using a more complex geometry form for the causative sources. In order to process the data at global scales, we will need to consider a more extensive set of LP data, like those at low altitudes and acquired in different Moon environments. This will help us assessing the correlation between albedo, geological age and magnetization in a more statistical sense. In addition, a re-examination of returned samples from the Apollo mission will also help in better understanding the magnetic evolution that took place during the Moon's early history.
We are grateful to anonymous referees for their very constructive comments. Steven Joy (Institute of Geophysics and Planetary Physics IGPP/UCLA) is greatly acknowledged for making Lunar Prospector magnetic data available to us. For IPGP, this is contribution number 2345.
- Halekas, J.S., D.L. Mitchell, R.P. Lin, S. Frey, L.L. Hood, M.H. Acuña and A.B. Binder, 2001. Mapping of crustal magnetic anomalies on the lunar near side by lunar prospector electron reflectometer. J. Geophys. Res., 106: 27,481-27,852.
- Halekas, J.S., D.L. Mitchell, R.P. Lin, L.L. Hood, M.H. Acuna and A.B. Binder, 2002. Demagnetization signatures of lunar impact craters. Geophys. Res. Lett., 29: 13,1645-13,1645.
- Parker, R.L., 2003. Ideal bodies for Mars magnetics. J. Geophys. Res., 108: 5006-5006.
- Richmond, N.C., L.L. Hood, J.S. Halekas, D.L. Mitchell, R.P. Lin, M.H. Acuña and A.B. Binder, 2003. Correlation of a strong lunar magnetic anomalies with high-albedo region of descartes mountains. Geophys. Res. Lett., 30: 1395-1395.