1. Institute of Geophysics and Planetary Physics, University of California, Los Angeles. California 90024
2. Department of Planetary and Space Science, University of California, Los Angeles. California 90024
Originally published in:
Proc. Lunar Sci Conf. 6th (1975), p. 2955-2969 Geochimica et Cosmochemica Acta Supplement 6
These single site measurements provided only weak constraints on the scale size or coherency length of the observed fields. The absence of a detectable gradient across the Apollo 12 magnetometer plus the absence of a detectable field at the 840-km altitude of Explorer 35 led Dyal et al. (1970) to conclude that the dipole source must be between 0.2 and 200 km from the Apollo 12 site and have a moment of between 1.4 10 and 1 10 gauss-cm. On Apollo 14 a portable magnetometer was used at two sites giving a gradient of 54 nT-km and field magnitudes of 43 and 103 nT (Dyal et al., 1971).
If the lunar magnetic field had such a small scale size everywhere, then the lunar field would not be detectable al an altitude of 100 km even above regions such as the Apollo 16 site with its 300 nT field. However. The Apollo 15 subsatellite measurements clearly showed that the lunar field was detectable at 100 km (Coleman et al., 1972a) and, therefore, that there were remanent magnetic fields in some regions of the moon which were coherent over dimensions greater than 1 km.
Since that time there has been much activity in mapping the lunar magnetic field from orbit and it is the purpose of this paper first to review the mapping procedure used in producing the field maps shown in the frontispieces of the Proceedings of the Fifth and Sixth Lunar Science Conferences and second to examine the altitude dependence of the lunar magnetic field which significantly affects these maps. We will not repeat the details of the instrumentation. For that we refer the reader to papers by Coleman et al. (1972a,b,c). However, we will review early lunar field maps to place the present results in their proper perspective. The reader wishing more general information on lunar magnetism is referred to the recent reviews by Fuller (1974), Dyal et al. (1974), and Schubert and Lichtenstein (1974).
The first attempt to map the lunar surface field consisted of simply superposing measurements on successive orbit tracks when the moon was in the geomagnetic tail. Since the data were not available in machine-readable format until many months after launch. and since the orientation of the spin-axis of the subsatellite was not known until well after that, the early maps were constructed from data on quick-look computer listings of the raw data obtained from the control center computer in real time. The raw data consisted of the field component parallel to the spin axis, the magnitude in the spin plane and the time that the magnetic field in the spin plane crossed the zero field reading going positive. This latter measurement only has meaning when referenced to the sun pulse. Hence, it was not used in the early mapping studies. Such superposed epoch plots were presented by Coleman et al. (1972a,b,c.d) and Russell et al. (1973a) for Apollo 15 data and by Coleman et al. (1972e) for Apollo 16 data.
While these plots clearly demonstrated that the field variations seen by the subsatellite were correlated with selenographic position, it was highly desirable to attempt to derive information about the lateral extent of these surface fields. Thus, surface contour maps of the raw data were constructed. The first such map using the magnitude of the field in the spin plane was made by subtracting the minimum field strength observed on each orbit near Van de Graaff from each of the readings on that orbit, and then scaling the resulting residuals by the altitude to 2.5 power (Coleman et al. 1972c,d).
The next field map covered only the Van de Graaff-Aitken region (Russell et al., 1973b: Coleman et al., 1972e; Lichtenstein et al., 1974) and was produced from 10 successive orbits of data at an altitude of roughly 70km. This map utilized the vector information reduced from the raw data listings. First, the three field components in spacecraft coordinates were computed from the transverse magnitude, the zero crossing delay, the sun pulse delay and the component parallel to the spin axis. Next, the average field for each orbit was subtracted and the residuals contoured. No altitude-dependent corrections were applied, nor were the data rotated into local lunar coordinates.
When digital tapes became available more data could be incorporated into the maps and a greater portion of the lunar surface covered. The first such map for only the radial component was published by Sharp et al. (1973). Again the average field in inertial space was removed for each orbit and the altitude dependence empirically removed with an altitude to the 1.5-power correction. Superposed epoch plots of each of the field components were also shown, together with a map of the Van de Graaff region at 130-km altitude, in addition to the 70-km map.
When all the data from the Apollo 15 mission became available the next generation field map was attempted. For these maps, the average and linear slope were removed from each of the components in inertial space (solar ecliptic coordinates) and then the residuals rotated into radial, east, and north selenographic components. These residuals were not altitude corrected. The data were then sorted and averaged in 1o 1o boxes, and the resulting averages smoothed with a two-dimensional filter (full width half maximum 2o 2o). These maps were not completed in time for presentation at the Fourth Lunar Science Conference but the radial component map was completed in time for inclusion in the frontispiece of the Proceedings. A map of all three components produced in this manner but covering only the Van de Graaff-Aitken region was published by Russell et al. (1974a) and Schubert and Lichtenstein (1974). These maps portray the lunar field at the altitude of the subsatellites over all scales from global to approximately 1o with some attenuation of the quadrupole field and nearby harmonics (Russell et al., 1974a).
One of the most serious limitations of the above mapping studies is the assumption that the magnetic field of the geomagnetic tail, in which the moon is immersed during the mapping passes, remains constant (in the cases where the average is removed) or varies linearly with time (in the cases where the average and trend are removed). In short, the natural power spectrum of fluctuations in the tail from periods of roughly 1 hr to 24 sec is converted to surface correlated features with wavelengths of from 180o to 1o. Over some of the mapped tracks there is sufficient redundant coverage that such noise fluctuations are attenuated in the averaging process. In other regions. the lunar field itself is so large that it clearly dominates over the background noise. However, there are several regions on these maps which display the signature of contamination by the natural fluctuations, that is, elongated contours parallel to the orbit track. Thus, when the Apollo 16 data became available for addition to these maps, the mapping procedure was refined once more.
From our previous maps and from our attempts to measure the global lunar field (Russell et al., 1973b; 1974a,b.c; 1975) it was apparent that there is little or no detectable global field and that any large-scale field pattern is well below the contour levels of our maps. The most striking feature of all our maps was the small-scale size of even the largest anomalies (~ 10o maximum). Therefore, we restricted the bandwidth of the data being used in the mapping studies, and thereby reduced the power in the natural fluctuations affecting the accuracy of the map. To affect this bandwidth limitation the raw data were passed through a high pass filter with a corner frequency corresponding to wavelengths of 20o. Then, they were rotated into the local lunar coordinate system of radial, east and north components, and sorted into 1o 1o bins, averaged, and then further filtered by a two-dimensional Gaussian filter, as in past studies.
While previous maps were accurate in most regions only above the 0.4 nT-level, we have contoured these latest maps to the 1/8-nT level and they appear to be quite reliable at this level. The simplest method of cross-checking the maps is to ascertain whether the fields on the east and north maps agree with that predicted from the radial component. For example, if a negative radial anomaly lies to the east of a positive radial anomaly, then the field should be eastward between them.
Radial, east and north component maps have been constructed for the entire subsatellite ground track using all the Apollo 15 and 16 geomagnetic tail data within the altitude range from 60 to 170 km. These are presented in the frontispiece of the Fifth Lunar Science Conference together with contour maps of the average altitude, coverage and the total field magnitude. The magnitude is computed from the maps of the three components.
While we feel these maps quite accurately portray the fine-scale lunar magnetic field we should caution the user about two points. First, there is possibly some noise still left in these maps and certain of the smaller features could conceivably be due to this noise. The most probable such features are those appearing on only one of the maps of the three components. However, we cannot unambiguously identify which ones are due to noise. Second, we have forced the field to average to zero along the orbit track over a scale size of 20o. This effectively attenuates large-scale features such as that apparently present from 40o E to 120o E as seen in Fig. 2 of Russell et al. (1974c).
The brief lifespan of the Apollo 16 subsatellite included two passes through the geomagnetic tail suitable for mapping. The low-altitude portions of the orbits during both tail passes were over the far side lunar highlands from ~ 0o E to 180o E at about 10o N covering nearly identical suborbit tracks. The average altitude in this region during the first pass was roughly 75 km, and during the second pass was roughly 30 km. Figure 1 shows the altitude versus longitude for two typical orbits used in the mapping procedure, one from each tail pass. We note that the positions of the sub satellites were determined to better than 1o in longitude and latitude and 3 km in altitude by S-band tracking.
|Fig. 1. Altitude versus longitude for the low-altitude portion of two orbits used in the Apollo 16 magnetic field maps, one from each tail pass.|
The fine-scale lunar field has been mapped for each of these two passes separately. These maps can be found in the frontispiece of Volume 3 of the Proceedings of the Sixth Lunar Science Conference. They clearly illustrate the strong altitude dependence of the lunar magnetic field. The first pass revealed several discrete magnetized regions with field strengths of up to ~1/3 nT and scale sizes of the order of 100 km, but none the strength of the Van de Graaff anomaly at similar altitudes. However, during the second pass the complexion of the magnetic variations changed markedly. The field magnitude often exceeded 1 nT, and the field components were constantly changing with scale sizes of roughly 30km, revealing a clearly discernible pattern of magnetization over the entire low-altitude ground track. This pattern is consistent with the results obtained during the high-altitude pass in that all features of the high-altitude pass have counterparts at low altitudes. The converse, however, is not true. Most of the low-altitude detail is attenuated at high altitudes.
The altitude dependence of the lunar field is more quantitatively displayed in Figs.# 2, 3, 4, 5, 6, 7, which show the variation of each of the field components in each of the four lunar quadrants for the Apollo 15 and 16 data separately. The data have been separated by satellite and by quadrant because of the quite different ground tracks of the two satellites, and because the strength of the lunar magnetic field is apparently highly dependent on selenographic position. Even with this division, we see evidence of non-monotonic altitude dependences traceable presumably to the fact that some strong regions are overflown at high altitudes but not at low altitudes, with the low-altitude coverage being over weaker field regions. This is apparently the cause of the simultaneous decrease in BR, BE, and BN with altitude in the Apollo 15 270-360 E quadrant data. However, this mechanism cannot explain why BE and BN decrease with altitude in the Apollo 16 data from 0o E to 90o E while the radial component increases. Nor does it explain the much more rapid increase with decreasing altitude of BR than of BE and BN from 90o to 180o E in the Apollo 16 data. In these regions the field is becoming more vertical with decreasing altitude. This would be the case if the crust were magnetized in the vertical direction in these regions. We note that a discontinuity in a layer of horizontal magnetization will result in a vertical field near the discontinuity. However, averaged over the entire slab, the net altitude dependence is an increase in the strength of the horizontal field relative to the radial field at altitudes less than the length of the slab.
|Fig. 2. The altitude dependence of the radial component of the fine-scale magnetic field for the four selenographic quadrants as observed by the Apollo 15 subsatellite. The magnetic field is given in nT.|
|Fig. 3. The altitude dependence of the Apollo 15 east component.|
Fig. 4. The altitude dependence of the Apollo 15 north component.
|Fig. 5. The altitude dependence of the radial component of the fine-scale magnetic field for the four selenographic quadrants as observed by the Apollo 16 subsatellite.|
|Fig. 6. The altitude dependence of the Apollo 16 east component.|
|Fig. 7. The altitude dependence of the Apollo 16 north component.|
To illustrate the altitude dependence expected for vertical magnetization we have examined the sample model shown in Fig. 8. The crust is magnetized to a depth D parallel to the vertical direction. A planar discontinuity in the magnetization extends to infinity in both directions. At an altitude A and a displacement X from the discontinuity the subsatellite is making observations.
|Fig. 8. Sketch of simple model used to mimic observed altitude variation.|
|Fig. 9. Altitude profiles for four different pairs of depths and displacements together with two sets of observations. The horizontal component is the square root of the sum of the squares of the average east and north components.|
Figure 9 shows altitude profiles for two different depths and two different displacements. At a displacement of 10 km from the discontinuity the horizontal and radial curves cross below 20 km, whereas at a displacement of 50 km the curves cross from 60- to 100-km altitude in closer accord with the data shown in the right-hand panels. If 50km were the mean displacement, then the typical separation between discontinuities would be 200 km, which is in accord with the scale sizes seen in the lunar field maps. We note that, while there is a tendency for the data in the 180-270o E quadrant to behave as our model, there is much scatter, suggesting that the magnetization is not vertical over the entire ground track of the subsatellite. Gauging the depth of magnetization from these data is not as easy. We see that the behavior of the model horizontal component at low altitude more closely resembles the behavior of the observations for a 100 km-thick layer than for a 10 km-thick layer. However, our model is only two-dimensional and if a third dimension were added, the altitude dependence would be expected to change. To distinguish between the magnetized crater-fill hypothesis of Strangway et al. (1973, 1975) and a thick magnetized crust from the altitude dependence data requires more extensive modeling including an examination of the altitude dependence of the Strangway et al. model. On the other hand, the offset of the observed magnetic field contours from the hypothesized "magnetized" craters appears to rule out this model, at least in its simplest form.
The combination of the returned lunar samples and the subsatellite measurements indicate that the lunar crust is extensively magnetized both in areal extent and in depth. Yet, there is no significant magnetic dipole moment (Russell et al., 1974b,c; 1975). There are two possible explanations of this behavior: one, that the moon was magnetized by an external field which reversed several times as the crust cooled, and two, that the moon was magnetized by an internal source all traces of which have since disappeared. While an internal uniform magnetic field or a dynamo-driven current would produce a dipolar field external to the moon, the magnetization impressed by this field in a cooling lunar crust has recently been shown by Runcorn (1975a,b) to produce no external field. Figure 10 shows the magnetization, M, and magnetic field, B, for such a magnetized shell. This is the three-dimensional analog of the uniformly magnetized infinite sheet which also produces no external field. In either of the above two models the observed features are simply due to contrasts in the magnetization caused by changes in the magnetization efficiency; i.e. the mineral properties due to subsequent demagnetization, or due to magnetization at different epochs in different field strengths and/or orientations.
|Fig. 10. The magnetization (left panel) and magnetic induction (right panel) for a dipolar shell of magnetization illustrating that there is no magnetic field exterior to the shell.|
As can be seen in Figs. 2 , 3 , and 4, the field in the Van de Graaff region changes from being predominantly horizontal at high altitudes to becoming predominately radial at low altitudes. At 65 km the radial component is equal in size to the square root of the sum of the squares of both the east and north components. In the Apollo 16 data at more northerly latitudes with coverage down to 15 km, the radial field becomes 50% greater than the total horizontal component.
In an attempt to quantify the magnetization of the surface material in this region, we have approximated the Van de Graaff anomaly with a single magnetic dipole, and solved for the best-fit moment. By inspection of the contour maps, we can see that the fields in the neighborhood of Van de Graaff are far more complex than a simple dipole. Thus, we have limited the analysis to the longitude band from 168.5o to 174o. where the behavior of the field is rather simple. The inversion procedure consisted of initially assuming the location of the source to obtain a least-squares estimate of the moment. Subsequently, the method of steepest descent was used to obtain corrections for the estimate of the moment vector and the originally assumed locations vector (Ioannidis , 1975).
|Fig. 11. The fine-scale magnetic field projected into the east-west vertical plane for all subsatellite passes between 20o S and 21o S latitude over the Van de Graaff region. The field lines shown correspond to a buried dipole moment with the properties listed in the text.|
The best-fit moment thus obtained was not well determined, even with this restriction in latitude. The location and moment were sensitive to the initially assumed source location. and the residuals from the best fit were generally only about 20% lower than the residuals assuming no source at all. Figure 11 shows the subsatellite magnetic field measurements together with field lines of a typical best-fit moment in the vertical east-west plane. This moment is located 94 km beneath the surface at a latitude of 20.5o S and a longitude of 172.8o E, and has components of (1.7, 0.1, 0.7) 10 gauss-cm in selenographic coordinates (X toward the earth; Z along the lunar rotation axis). It is clear that the data agree with the model only over a limited interval and that an accurate representation of the field variations requires a more complex model. Finally, we note that the best-fit moments were all directed inward and were principally in the vertical east-west plane, in accord with the observation that the north-south field is generally weaker than the east-west field. The depth of the source locations was only weakly determined, however, and no great significance should be attached to the particular depth quoted above.
If the moon were magnetized by an external field, only the component parallel to the lunar rotation axis would have been effective in magnetizing the lunar crust. Thus, we would have expected a predominantly north-south magnetization of the crust. Similarly, if the source were an internal dynamo, based on our terrestrial and Jovian experiences. we would have expected an orientation of the moment close to the rotation axis. Again the magnetization of the crust should be predominantly in the north-south direction. However, observationally it is not in this direction. While there are areas of strong localized north-south field, there is no large-scale area of the region mapped in which north-south fields predominate.
Thus, our simple models of lunar magnetism must become more sophisticated. Perhaps, this sophistication is the inclusion of temporal variations of the magnetizing source, wandering of the magnetic pole relative to the crust, or possible non-dipolar dynamo mechanism. Whatever the mechanism, the measurement of more large features such as Van de Graaff and of more low-altitude fields such as on the last Apollo 16 pass is vital to our unfolding the global pattern of magnetization upon which an unambiguous identification rests.
The maps of the fine-scale lunar magnetic field at approximately 100-km altitude above the lunar surface accurately measure magnetic fields with scale sizes of 20o or less to an accuracy of better than 1/8 nT. While in the Apollo 15 data strong fields were seen only in the vicinity of the Van de Graaff crater, in the Apollo 16 data below about 50-km significant fields were measured everywhere along a 100o swath above the far side highlands. On the other hand, two independent. semiquantitative techniques for detecting lunar surface remanent magnetic fields, limb compression occurrence statistics (Russell and Lichtenstein, 1975) and the reflection of energetic electrons (McCoy et al., 1975) indicate that there are some regions of the lunar surface which are only weakly magnetized.
The strong altitude dependence evident in these records is different for the three components. In several of the regions mapped the field becomes more vertical with decreasing altitude, in contrast to simple models that would predict a stronger north-south field. Clearly these simple models need to be refined and clearly a more complete magnetic mapping of the lunar surface is required. At present, the maps of the lunar magnetic field more resemble maps of the solar photospheric magnetic field than of any of the planetary fields we have investigated.
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