The crust as the possible seat of earth's magnetism

Abstract: The characteristics of several long magnetic total field intensity profiles have been determined. Only track lines which were nearly straight and longer than 2000 miles were considered. First, the centered dipole field total intensity was subtracted from the measured total intensity to obtain a real nondipole field. A smooth curve was then drawn through this nondipole field using a stiff spline curve. The distance between crossover points of the smooth field and the nondipole field was determined and a histogram of the results plotted. The results confirm the earlier results of Serson and Hannaford that most of the anomalies have a very short wavelength. Ninety-three per cent of the cases had crossover distances less than 60 nautical miles. The simple form of the smooth curves indicated a nearly sinusoidal departure from a dipole field having crossover points between 2100 and 5200 nautical miles. The most natural unforced explanation of the above results is that short-wavelength anomalies are due to crustal effects and the long-wavelength anomalies are due to causes within the core of the earth. The large gap between the short- and long-wavelength groupings supports the hypothesis that the mantle is a forbidden region for magnetic sources. This conclusion is illustrated by calculations based on simple models.

Abstract: The following comments may be made on the communication by Oster and Philip concerning my article in Nature1 and note in the Journal of Atmospheric and Terrestrial Physics2.

Abstract: The Earth's magnetic field underwent hundreds of reversals during its history. But within a ~40 Myr span (84-125 Ma) during the Cretaceous no reversal happened. For comparison, the second longest chron length during the last 167 Ma is ~5 Myr. Thus, the ~40 Myr long chron is known as a superchron and is called Cretaceous Normal Superchron (CNS). Two other superchrons are now established: the Permian-Carboniferous Reversed Superchron and the Ordovician Reversed Superchron. Why do these superchrons exist? Are they an extreme chron duration of the same statistical distribution? Or, do superchrons reflect a distinct dynamo regime separate from an oft-reversing regime. Are the onset and end of superchrons triggered by changes in the physical conditions of outer core convection? For example, instabilities within the convection in the outer core are suspected to trigger reversals. A `low energy' geodynamo during the superchron could stem from less turbulent convection. But also the concept of a `high energy' geodynamo during a superchron is conceivable: stronger convection would stabilize the field and increase the field intensity. These different dynamo regimes could be be triggered by changing the temperature conditions at the core mantle boundary (CMB), for example with the eruption of deep mantle plumes or the descent of cold material such as subducted slabs. Insights into past geodynamo regimes can be learned primarily from two paleomagnetic methods: paleosecular variation (variation in field directions) and paleointensity. For the former, we collected 534 samples for a paleosecular variation study from a 1400 m-long, paleontologically well-described section in northern Peru. Thermal demagnetization isolates stable magnetization directions carried by greigite. Arguments are equivocal whether this remanence is syn-diagenetic, acquired during the Cretaceous normal superchron, or a secondary overprint, acquired during a chron of solely normal polarity in the upper Cenozoic, yet pre-Bruhnes (>800 kyr). We explore the ramifications on the S value, which quantifies paleosecular variation, that arises from directional analysis, sun compass correction, bedding correction, sampling frequency, outlying directions and different recording media. The sum of these affects can readily raise the S value by more than 20%. S values from northern Peru are indistinguishable from other S values for the Cretaceous normal superchron as well as those for the last 5 Ma. Summing over all the potential uncertainties, we come to the pessimistic conclusion that the S value is an unsuitable parameter to constrain geodynamo models. Alternatively, no statistical difference in paleosecular variation exists during much of the Cretaceous normal superchron and during the last 5 Ma. Even though the S value might be unsuitable, we wanted to understand why the S value is latitude dependent. The origin of this latitude dependency is widely attributed to a combination of time-varying dipole and non-dipole components. The slope and magnitude of S are taken as a basis to understand the geomagnetic field and its evolution. Here we show that S stems from a mathematical aberration of the conversion from directions to poles, hence directional populations better quantify local estimates of paleosecular variation. Of the various options, k is likely the best choice, and the uncertainty on k(N) was already worked out. As we came to the pessimistic conclusion that the S value might not be the best parameter to quantify the `energy state' of the geodynamo during a superchron, we also carried out a paleointensity study on 128 samples from volcanic rocks in Northern Peru and Ecuador. Oxidation of the remanence carriers was a problem. Only one site gave reliable results. Two methods of paleointensity determination were applied to these rocks. The results of both methods agree quite well with each other and also with previous studies from other sites. Our results suggest that the field intensity towards the end of the superchron seems to quite similar to today's magnetic moment. Thus, it can be concluded that the `energy state' of the geodynamo was not substantially different during the Cretaceous Normal Superchron compared to reversing times. Why do superchrons exist? One possible explanation is that paleomagnetism is not able to resolve different energy states of the geodynamo, neither with paleosecular variation nor with paleointensity. This was suggested by some dynamo simulations in which the heat flux across the core-mantle boundary was kept the same, but the resulting paleosecular variation, paleointensity and frequency of reversals differed a lot. Another possible explanation is that a superchron is an intrinsic feature of the distribution of magnetic polarity chron lengths. Thus, no changes of the convection in the outer core are needed to trigger a superchron.

Abstract: An examination is made of J. S. Chatterjee's recent suggestion that the earth's magnetic field has been gradually built up by magnetic storms which induce unidirectional current in the highly conducting core because the semiconducting mantle acts as a rectifier. It is shown that, even if rectification of current in the mantle does occur, it is most unlikely that magnetic storms or other transient variations have any lasting effect on the earth's main field. Some comments are made on Chatterjee's arguments and on a note by T. Rikitake.

Abstract: The Becker-Kersten treatment of domain boundary movements is widely applicable in the interpretation of magnetization curves, but it does not account satisfactorily for the higher coercivities obtained, for example, in permanent magnet alloys. It is suggested that in many ferromagnetic materials there may occur ‘particles’ (this term including atomic segregates or ‘islands’ in alloys), distinct in magnetic character from the general matrix, and below the critical size, depending on shape, for which domain boundary formation is energetically possible. For such single-domain particles, change of magnetization can take place only by rotation of the magnetization vector, I O . As the field changes continuously, the resolved magnetization, I H , may change discontinuously at critical values, H O , of the field. The character of the magnetization curves depends on the degree of magnetic anisotropy of the particle, and on the orientation of ‘easy axes’ with respect to the field. The magnetic anisotropy may arise from the shape of the particle, from magneto-crystalline effects, and from strain. A detailed quantitative treatment is given of the effect of shape anisotropy when the particles have the form of ellipsoids of revolution (§§ 2, 3, 4), and a less detailed treatment for the general ellipsoidal form (§ 5). For the first it is convenient to use the non-dimensional parameter such that h = H /(| N a - N b |) I O , N a and N b being the demagnetization coefficients along the polar and equatorial axes. The results are presented in tables and diagrams giving the variation with h of I H / I O . For the special limiting form of the oblate spheroid there is no hysteresis. For the prolate spheroid, as the orientation angle, θ , varies from 0 to 90°, the cyclic magnetization curves change from a rectangular form with | h O | = 1, to a linear non-hysteretic form, with an interesting sequence of intermediate forms. Exact expressions are obtained for the dependence of h θ on θ , and curves for random distribution are computed. All the numerical results are applicable when the anisotropy is due to longitudinal stress, when h = HI 0 /3λδ, where λ is the saturation magnetostriction coefficient, and δ the stress. The results also apply to magneto-crystalline anisotropy in the important and representative case in which there is a unique axis of easy magnetization as for hexagonal cobalt. Estimates are made of the magnitude of the effect of the various types of anisotropy. For iron the maximum coercivities, for the most favourable orientation, due to the magneto-crystalline and strain effects are about 400 and 600 respectively. These values are exceeded by those due to the shape effect in prolate spheroids if the dimensional ratio, m , is greater than 1·1; for m = 10, the corresponding value would be about 10,000 (§7). A fairly precise estimate is made of the lower limit for the equatorial diameter of a particle in the form of a prolate spheroid below which boundary formation cannot occur. As m varies from 1 (the sphere) to 10, this varies from 1·5 to 6·1 x 10 -6 for iron, and from 6·2 to 25 x 10 -6 for nickel (§ 6). A discussion is given (§ 7) of the application of these results to ( a ) non-ferromagnetic metals and alloys containing ferromagnetic ‘impurities’, ( b ) powder magnets, ( e ) high coeravity alloys of the dispersion hardening type. In connexion with ( c ) the possible bearing on the effects of cooling in a magnetic field is indicated.

Abstract: The paper deals with the electromagnetic effect of motions in the earth's core, considered as a fluid metallic sphere. On the basis of simple estimates the electric conductivity of the core is assumed of the same order of magnitude as that of common metals. The mathematical treatment follows Hansen and Stratton: three independent vector solutions of the vectorial wave equation are introduced; two of these have vanishing divergence, and they are designated as toroidal and poloidal vector fields. The vector potential and electric field are toroidal, whereas the magnetic field is poloidal. These vectors, expressed in terms of spherical harmonics and Bessel functions, possess some notable properties of orthogonality which are briefly discussed. The theory of the free, exponentially decaying current modes is then given, leading to decay periods of the order of some tens of thousands of years. Next, the field equations in the presence of mechanical motions of the conducting fluid are set up. The field is developed in a series of the fundamental, orthogonal vectors, and the field equations are transformed into a system of ordinary differential equations for the coefficients of this development. The behavior of the solutions depends on the symmetry of the "coupling matrix" that arises from the term of the field equations expressing the induction effects. In order to evaluate this matrix the velocity field is developed into a series of the fundamental vectors similar to the series for the electromagnetic field. It is then shown that when the velocity is a toroidal vector field the coupling matrix is antisymmetrical. When the velocity field is poloidal, the coupling matrix is neither purely symmetrical nor purely antisymmetrical. For stationary fluid motion the linear differential equations can be integrated in closed form by a transformation to new normal modes, whenever the matrix of the system is either symmetrical or antisymmetrical. In the latter case the eigenvalues are purely imaginary and the coefficients of the new normal modes are harmonic functions of time, representing oscillatory changes in amplitude of the field components. For a symmetrical matrix the eigenvalues are real and the time factors of the new normal modes are real exponentials representing amplification or de-amplification as the case may be, depending on the sign of the velocity. For a matrix without specific symmetry, normal modes do not, as a rule, exist but similar, somewhat less stringent results can be derived in special cases. In the case of toroidal flow, in particular, the oscillatory changes of the field components are superposed upon the slow exponential decay characteristic of the free modes.

Abstract: In Part I a method has been developed for the integration of the electromagnetic field equations in the presence of fluid motions in a spherical conductor. This analysis is here applied to an interpretation of the secular geomagnetic variations. A very brief survey of some of the observed features of the secular variation is first given. It is pointed out that not only the phases but also the magnitudes of the harmonic components, including the main dipole, are subject to large changes at the present time. There follows a brief study of the skin effect which indicates that the observed variations of the dipole terms originate in a layer adjacent to the core's boundary several hundred kilometers deep; those of the higher terms originate in a layer no more than 200 km deep. Next, the "coupling matrix" introduced in Part I is evaluated in form of a table of all matrix elements that contain vectors of dipole and quadrupole type but no higher harmonics. It is shown that a zonal fluid motion (zonal toroidal flow in the terminology adopted here) produces rotation of the tesseral magnetic dipole terms and also oscillatory changes in amplitude of these terms. There is one and only one type of matrix element that represents an interaction of the main magnetic dipole with itself; the corresponding fluid motion is a meridional flow (poloidal flow) of quadrupole symmetry. With this term amplification or de-amplification occurs, depending on the sign of the velocity. The theory thus can account for all the observed components of the secular variation.

Abstract: It can be shown that the currents in the earth's core which give rise to the externally observable magnetic field do not form a complete set of solutions of the field equations. There exists a second set of solutions composed of the modes of the electric type which produce a magnetic field inside the metallic sphere, but appear at the outside only through an electric field too weak to be measured. For reasons of symmetry the most important terms among the electric modes are the quadrupoles. The theory of inductive coupling by fluid motion, developed previously, is here applied to the interaction of the magnetic and electric modes. The system again is non-conservative, and work is done on the field by the fluid, or vice versa. It is shown that the interaction between the magnetic dipole and electric quadrupole modes constitutes a basic amplifier mechanism which amplifies the quadrupole mode until the magneto-mechanical forces exerted by the field upon the fluid begin to slow down the motion, thus prohibiting further increase of the field. This internal quadrupole field is likely to be much larger than the ordinary magnetic dipole field. Further analysis leads one to interpret the couplings between the magnetic and electric modes as a feed-back amplifier whereby the field can be maintained through the power delivered to it by the fluid motion. A survey of possible sources of power for this process indicates that the power for the maintenance of the field is provided from the rotational energy lost by the earth as it is slowed down through the action of the lunar tide.

Abstract: The earth's core may be assumed to consist of fluid metal surrounding a solid inner core which probably contains a source of heat to drive convection, but it is not possible at present to select between various possible types of convective motion in the fluid core. Types considered are characterized by some sort of radial flow streams and a tendency for the fluid to rotate on the average more rapidly near the axis to conserve angular momentum during the circulation. Though the actual flow may be quite complicated, proposed mechanisms for generating a terrestrial magnetic field are considered for some oversimplified flow patterns in an attempt to indicate what features of the flow may provide the most important possibilities for field generation. It is suggested that, without a field to absorb the energy, the flow would be accelerated indefinitely and would evolve through a succession of flow patterns, some of which would be expected to have the properties to generate a field capable of preventing further acceleration and prolonging the status quo, thus making it likely that the earth should have a field.The generating mechanisms discussed include two induction theories, the dynamo theory of Elsasser and Bullard, which is discussed at length both in terms of velocity-current systems portrayed by elaborate models and in hydromagnetic terms, and the "twisted-kink" theory of Alv\`en which is discussed only hydromagnetically. Each of these theories depends on amplifying an initial stray magnetic field up to a point where it dissipates all of the available energy, and is at least in this respect analogous to a conventional electrical generator but without a ferromagnetic core. Other mechanisms discussed depend either on the thermoelectric effect with junctions at the core-mantle interface or on a combination of thermoelectric and Hall effects in the core and mantle.If the convective flow is rather irregular, the observed slow westward drift of the detailed pattern of the earth's field is attributed to the vanishing of the total torque on the core by the magnetic field threading through the core and mantle, as a result of an eastward drag on the outer part of the core rotating more slowly in space and a westward drag on the more rapidly rotating part of the core near the axis, with the presumption that the observed magnetic pattern is characteristic of the westward-drifting outer part. If the flow instead involves a jet stream, the flow in the jet may under some circumstances be expected to be eastward for reasons comparable to temperate-zone meteorology, so the magnetic field should exert a westward drag on it leading to the westward drift of the flow pattern.