Magnetic dipole moment of a spherical shell with TRM acquired in a field of internal origin

The acquisition of thermoremanent magnetization (TRM) by a cooling spherical shell is studied for internal magnetizing dipole fields, using Runcorn's new theorems on magnetostatics. If the shell cools progressively inward, inner regions acquire TRM in a net field composed of the dipole source term plus a uniform field due to the outer magnetized layers. In this case the global dipole moment and thus external remanent field are non-zero when the whole shell has cooled below the Curie point and the source dipole has disappeared. The remanent field outside the shell is found to depend on the thickness, radii, and cooling rate of the shell, as well as the coefficient of TRM and the intensity of the magnetizing field. Some implications for the Moon's remanent dipole moment are discussed.     

Magnetism of the Moon - a lunar core dynamo or impact magnetization?

Surface and satellite observations of lunar crustal magnetization and the remanent magnetization of the lunar samples returned by the Apollo missions of 1969–72 provide evidence for past magnetic fields on the Moon. During the more than twenty years in which research has been carried out there has been controversy concerning the origin of the field, with two possible processes of major interest. Dynamo generation of the field in a molten, electrically-conducting core is consistent with most of the observations, but encounters theoretical difficulties associated with the deduced magnitude of the ancient field and lack of positive evidence for a lunar core. The most likely alternative process is the generation of a transient magnetic field during meteorite impacts followed by thermoremanent or shock magnetization of debris and adjacent crust. This paper reviews the evidence and compares the observations with characteristics of lunar magnetism expected as a result of each of the two possible processes. It is concluded that the evidence very strongly favours the past existence of a dynamo-generated lunar magnetic field, with impact magnetization playing a minor role.     

Past and present magnetism of the Moon

The characteristics of the remanent magnetism of lunar samples suggests that it was acquired in a magnetic field on the Moon. The most likely origin of the field is a dynamo process in a molten, electricallyconducting core, but generation of a transient magnetic field during large meteorite impacts cannot be entirely ruled out. The magnetizing process may be thermoremanence, acquired when the rocks cooled through, the Curie point of the constituent iron grains which carry the remanent magnetization, or it may involve shock at the time of a meteorite impact, with or without a partial thermoremanence arising from heating.Evidence from absolute and relative determinations of the ancient field strength from the sample magnetizations strongly favours a global lunar field. This is implied by a trend which shows the field rising to a maximum value of 100 T between about 3.9–3.7 by ago and then decaying to 5–10 T until3.1 by. Such a systematic variation of field with time is not expected to be derived from magnetizations acquired in transient, impact-generated fields varying randomly in intensity.Contributory evidence for a dynamo field is provided by measurements of present lunar surface fields, the present very small dipole moment of the Moon and accumulating evidence of variation of the axis of the lunar field with time. Although there is no direct evidence for the existence of a lunar core the relevant observations are consistent with the presence of a core of up to 400 km, in radius. There are some difficulties associated with the lunar dynamo mechanism and its energy source but the evidence for a lunar dynamo is accumulating, with important implications for the structure and thermal history of the Moon.     

Lunar magnetic anomalies detected by the Apollo substatellite magnetometers

Properties of lunar crustal magnetization thus far deduced from Apollo subsatellite magnetometer data are reviewed using two of the most accurate presently available magnetic anomaly maps — one covering a portion of the lunar near side and the other a part of the far side.

The largest single anomaly found within the region of coverage on the near-side map correlates exactly with a conspicuous, light-colored marking in western Oceanus Procellarum called Reiner Gamma. This feature is interpreted as an unusual deposit of ejecta from secondary craters of the large nearby primary impact crater Cavalerius. An age for Cavalerius (and, by implication, for Reiner Gamma) of 3.2 ± 0.2 × 10⁹ y is estimated. The main (30 × 60 km) Reiner Gamma deposit is nearly uniformly magnetized in a single direction, with a minimum mean magnetization intensity of 7 × 10⁻² G cm³/g (assuming a density of 3 g/cm³), or about 700 times the stable magnetization component of the most magnetic returned samples. Additional medium-amplitude anomalies exist over the Fra Mauro Formation (Imbrium basin ejecta emplaced 3.9 × 10⁹ y ago) where it has not been flooded by mare basalt flows, but are nearly absent over the maria and over the craters Copernicus, Kepler, and Reiner and their encircling ejecta mantles.

The mean altitude of the far-side anomaly gap is much higher than that of the near-side map and the surface geology is more complex, so individual anomaly sources have not yet been identified. However, it is clear that a concentration of especially strong sources exists in the vicinity of the craters Van de Graaff and Aitken. Numerical modeling of the associated fields reveals that the source locations do not correspond with the larger primary impact craters of the region and, by analogy with Reiner Gamma, may be less conspicuous secondary crater ejecta deposits. The reason for a special concentration of strong sources in the Van de Graaff-Aitken region is unknown, but may be indirectly related to the existence of strongly modified crustal terrain which also occurs in the same region. The inferred directions of magnetization for the several sources of the largest anomalies are highly inclined with respect to one another, but are generally depleted in the north-south direction. The north-south depletion of magnetization intensity appears to continue across the far-side within the region of coverage.

The mechanism of magnetization and the origin of the magnetizing field remain unresolved, but the uniformity with which the Reiner Gamma deposit is apparently magnetized, and the north-south depletion of magnetization intensity across a substantial portion of the far side, seem to require the existence of an ambient field, perhaps of global or larger extent. The very different inferred directions of magnetization possessed by nearly adjacent sources of the Van de Graaff-Aitken anomalies, and the depletion in their north-south component of magnetization, do not favor an internally generated dipolar field oriented parallel to the present spin axis. A variably oriented interplanetary magnetizing field that was intrinsically strong or locally amplified by unknown surface processes is least inconsistent with the data.     

A study of the Rima Sirsalis lunar magnetic anomaly

The source of the lunar magnetic anomaly associated with the Rima Sirsalis linear rille has been modelled using the vector field intensities due to arbitrary uniform magnetization in a rectangular prism. It is shown that in order to match the Apollo 16 subsatellite data, the lunar surface near the rille must have a vertical magnetization of 6–9 × 10⁻³ G if the anomaly is due to flux leakage from a gap in the crust with the dimensions of the rille. This is more than one order of magnitude larger than the magnetization of any lunar sample, but is comparable with the high magnetization recently deduced for the Reiner γ formation in Oceanus Procellarum. An alternative explanation is that Rima Sirsalis and its surroundings are the site of a vertical magnetization contrast of 10⁻⁵ – 10⁻⁴ G which is at least as wide as the rille and extends to a depth of tens of kilometers in the crust. A wider magnetic source reduces the required magnetization (or depth) proportionately, since to first order the field at high altitude is proportional to the magnetic dipole moment per unit length.     

On deducing the magnetization of the lunar surface from orbital surveys

A combination of orbital photographic, selenochemical and magnetic surveys may elucidate the mechanism by which the lunar surface became magnetized and possibly yield an estimate of the intensity of the ancient magnetizing field and its time variation. The determination of the size and shape of the magnetized regions requires the measurement of the altitude dependence of field, especially at low altitudes (< 100 km) and with a high enough sampling rate to resolve the profile at the edges of magnetized bodies. The planned Lunar Polar Orbiter may well provide the necessary data.     

Magnetic properties of the Olivenza meteorite—possible implications for its evolution and an early solar system magnetic field

The magnetic properties of samples of the Olivenza chondrite (LL5) obtained from four collections have been investigated. The natural remanent magnetization (NRM) consists of a very stable primary component, which is randomly scattered in direction on a scale of 1 mm³ or less within the samples, and a secondary magnetization widely varying in intensity, and probably also in direction. The origin of the secondary NRM is not clear, and may be of terrestrial origin. It is concluded that the NRM is carried by the ordered nickel-iron mineral, tetrataenite. The origin of the primary NRM could be a magnetic field associated with the solar nebula, out of which the metal grains condensed and acquired a thermo-remanent magnetization (TRM), or Olivenza could be a fine-grained breccia, the constituent fragments possessing randomly directed magnetization. The implications for the origin and evolution of Olivenza and its parent body if the former magnetizing process has occurred are discussed.     

磁化岩石层球面各向同性统计模型

磁化岩石层产生的磁场是利用磁场观测研究地球发电机过程的最主要障碍之一。基于对球面各向同性随机矢量场及其空间两点关联张量的认识,建立了球面各向同性磁化岩石层的统计模型。结果表明,如果岩石层的剩余磁化强度和磁化率均为球面各向同性,那么在地表观测到的岩石层磁场由球面各向同性和准各向同性两个部分组成。因此,即使统计性质最简单的磁化岩石层,其产生的磁场的统计性质也要复杂得多。     

Constraints on the origins of lunar magnetism from electron reflection measurements of surface magnetic fields

Apollo 15 and 16 subsatellite measurements of lunar surface magnetic fields by the electron reflection method are summarized. Patches of strong surface fields ranging from less than $\text{1}\text{4}$° to tens of degrees in size are found distributed over the lunar surface, but in general no obvious correlation is observed between field anomalies and surface geology. In lunar mare regions a positive statistical correlation is found between the surface field strength and the geologic age of the surface as determined from crater erosion studies. However, there is a lack of correlation of surface field with impact craters in the mare, implying that mare do not have a strong large-scale uniform magnetization as might be expected from an ancient lunar dynamo. This lack of correlation also indicates that mare impact processes do not generate strong magnetization coherent over ～ 10 km scale size. In the lunar highlands fields of >100 nT are found in a region of order 10 km wide and >300 km long centered on and paralleling the long linear rille, Rima Sirsalis. These fields imply that the rille has a strong magnetization (>5 × 10^?6 gauss cm³ gm^?1 associated with it, either in the form of intrusive, magnetized rock or as a gap in a uniformly magnetic layer of rock. However, a survey of seven lunar farside magnetic anomalies observed by the Apollo 16 subsatellite suggests a correlation with inner ejecta material from large impact basins. The implications of these results for the origin of lunar magnetism are discussed.     

Global electromagnetic induction in the Moon and planets

A summary of experiments and analyses concerning electromagnetic induction in the Moon and other extraterrestrial bodies is presented. Magnetic step-transient measurements made on the lunar dark side show the eddy current response to be the dominant induction mode of the Moon. Analysis of the poloidal field decay of the eddy currents has yielded a range of monotonic conductivity profiles for the lunar interior: the conductivity rises from 3·10^?4 mho/m at a depth of 170 km to 10^?2 mho/m at 1000 km depth. The static magnetization field induction has been measured and the whole-Moon relative magnetic permeability has been calculated to be $\text{μ}\text{μ}{}_0\text{= 1.01 ± 0.06}$. The remanent magnetic fields, measured at Apollo landing sites, range from 3 to 327 γ. Simultaneous magnetometer and solar wind spectrometer measurements show that the 38-γ remanent field at the Apollo 12 site is compressed to 54 γ by a solar wind pressure increase of 7·10^?8 dyn/cm². The solar wind confines the induced lunar poloidal field; the field is compressed to the surface on the lunar subsolar side and extends out into a cylindrical cavity on the lunar antisolar side. This solar wind confinement is modeled in the laboratory by a magnetic dipole enclosed in a superconducting lead cylinder; results show that the induced poloidal field geometry is modified in a manner similar to that measured on the Moon. Induction concepts developed for the Moon are extended to estimate the electromagnetic response of other bodies in the solar system.     

带电月尘活动对月球磁场的影响

本文介绍了基于月尘扬起机制的"动态喷泉模型",分析了月尘扬起的过程;最后提出了"带电月尘活动电磁感应模型",计算得到月面明暗交界处带电月尘活动产生的感应磁场强度小于0.0064nT.本文证明带电月尘的活动对月球磁场的影响微小,可以忽略.     

Determination of rock magnetization in a horizontal layer from the external magnetic field

The inverse problem of magnetometry is solved for a horizontal layer. Model masses are magnetized nonuniformly. The magnetization vector is a function of two horizontal coordinates. The components of this vector are determined from data on the external magnetic field.     

Linear magnetization feature associated with Rima Sirsalis

Measurements of the magnetic fields by the electron reflection method in the neighborhood of the long structural rille Rima Sirsalis show that a magnetic field of strength ? 100 nT (100 γ) is present over a region on the order of 10 km in width and at least 300 km long. The center of the magnetized region closely parallels and is centered on the rille. The linear magnetization feature extends at least to latitude 8°S, 60 km beyond the place where the rille disappears at the edge of Oceanus Procellarum. This extension is coincident with the extrapolation of the rille based on photographs. However, the magnetization is much weaker or entirely absent at 5°S and has vanished at 0° latitude. These results suggest that the rille is indeed a structural feature and has associated with it magnetization, either in the form of intrusive, magnetized rock, or else in the form of a gap in an otherwise more or less uniformly magnetized layer of rock of large extent in two dimensions. Furthermore, the rille structure evidently is present for some distance beneath the lava flows of the Oceanus Procellarum basin.     

Grain size dependent potential for self generation of magnetic anomalies on Mars via thermoremanent magnetic acquisition and magnetic interaction of hematite and magnetite

Early in the history of planetary evolution portions of Martian crust became magnetized by dynamo-generated magnetic field. A lateral distribution of the secondary magnetic field generated by crustal remanent sources containing magnetic carriers of certain grain size and mineralogy is able to produce an ambient magnetic field of larger intensity than preexisting dynamo. This ambient field is capable of magnetizing portions of deeper crust that cools through its blocking temperatures in an absence of dynamo. We consider both magnetite (Fe₃O₄) and hematite (α-Fe₂O₃) as minerals contributing to the overall magnetization. Analysis of magnetization of magnetic minerals of various grain size and concentration reveals that magnetite grains less than 0.01 mm in size, and hematite grains larger than 0.01 mm in size can become effective magnetic source capable of magnetizing magnetic minerals contained in surrounding volume. Preexisting crustal remanence (for example ∼250 A/m relates to 25% of multi-domain hematite) can trigger a self-magnetizing process that can continue in the absence of magnetic dynamo and continue strengthening and/or weakening magnetic anomalies on Mars. Thickness of the primary magnetic layer and concentration of magnetic carriers allow specification of the temperature gradient required to trigger a self-magnetization process.     

Paleointensity determinations of lunar samples

Evidence for the existence of an ancient lunar field comes from the NRM of lunar rocks and from measurements of local lunar surface magnetic fields. Even when the Fe particles present in the rocks possess enough magnetic stability to preserve a record of the original magnetizing field, there are considerable difficulties in estimating the strength of the field, primarily because of the chemical changes which take place on heating in the laboratory. These difficulties are discussed together with a paleointensity method involving heating in a more indirect way. A tentative interpretation of the results of paleointensity-age measurements is given.     

A NOTE ON MAGNETIZED SPHERES*

The interpretation of total field anomalies becomes somewhat complicated, especially when an arbitrarily magnetized spherical ore mass happens to be the causative body. Even though some attempts have been made to analyze total field anomaly maps, they are often too complicated and their underlying assumptions in respect of permanent and induced components of magnetism are far from realistic. In this note, an attempt has been made to show that vertical magnetic anomalies are capable of yielding interpretation with ease and precision as far as magnetized spheres are concerned. An empirical method has been outlined for computing the magnetization inclination in the plane of the profile using the measured distances between principal maximum, principal minimum, and zero anomaly positions on a magnetic anomaly profile.     

强磁性三度体内部磁化强度的分布

本文讨论稳定磁化场中强磁性三度体内部磁化强度的数值解法。展示了由于退磁作用而造成的不均匀性,并以长方体内一些典型截面为例,较详细地讨论了磁化强度的特征,作了分布图;推导了较均匀磁化体磁化强度分布的近似公式,并计算了一组长方体的视退磁系数。     

Theories for the origin of lunar magnetism

This paper reviews the major theories which have been proposed to explain the remanent magnetism found in the lunar crust. A total of nine different mechanisms for lunar magnetism are discussed and evaluated in the light of the theoretical and experimental constraints pertinent to lunar magnetism. We conclude that none of these theories in their present state of development satisfy all the known constraints. However, the theories which agree best with our present understanding of the Moon are meteorite impact magnetization, thermoelectric dynamo field generation, and an early solar wind field.     

Magnetic properties of Antarctic shergottite meteorites EETA 79001 and ALHA 77005: possible relevance to a Martian magnetic field

The possibility that the parent body of the SNC meteorites is Mars implies that the magnetic properties of these meteorites may provide evidence concerning ancient Martian magnetic fields. EETA 79001 possesses a weak, very stable primary magnetization, the properties of which are consistent with its acquisition in an ambient magnetic field either during the meteorite's formation or during the severe shock event later in its history. The samples of ALHA 77005 studied possessed no measurable primary magnetization: the observed remanence appears to be a viscous magnetization acquired in local laboratory fields. The magnetic carriers in the meteorites are fine-grained magnetite and a lower Curie point mineral, probably titanomagnetite or pyrrhotite, present to the extent of less than 0.1% by weight. Estimates of the strength of the magnetizing field for EETA 79001 are in the range 1–10 μT.     

Primeval displacements of the lunar pole

The hypothesis that the magnetic field which magnetized the lunar crust was generated by the dynamo process in a small fluid iron core can now be tested. Because the Coriolis force was a dominant term in the equations of motion in this core, the mean lunar field was aligned along the ancient axis of rotation. From Hood's modelling of the magnetic anomalies in the lunar crust, mapped by the Apollo 15 and 16 subsatellites, the palaeo-directions of this field have been determined. From them, palaeopole positions have been determined and are found to be grouped with respect to age. The palaeoequators corresponding to ages 4 Ga and 3.85 Ga show close relationships with the circular maria or mascons on the near side and multi-ring basins of corresponding age on the far side. The polar displacements indicated from lunar palaeomagnetism can be explained by the changes in the moment of inertia tensor consequent on the excavation and later flooding of these circular mare. Small moons in the primeval Earth-Moon system are inferred to be the impacting bodies.