Phillip L. McFadden

The Magnetic Field of the Earth: Paleomagnetism, the Core, and the Deep Mantle

History of Geomagnetism and Paleomagnetism: Discovery of the Main Magnetic Elements. Fossil Magnetism and the Magnetic Field in the Past. Investigations of the External Magnetic Field. Origin of the Earths Magnetic Field. The Present Geomagnetic Field: Analysis and Description from Historical Observations: Magnetic Elements and Charts. Spherical Harmonic Description of the Earths Magnetic Field. Uniqueness and Other Mathematical Problems. Geomagnetic Secular Variation. The External Magnetic Field. Foundations of Paleomagnetism: Rock Magnetism. Magnetic Mineralogy. Paleomagnetic Directions and Poles. Paleointensity Methods. Age Determinations. The Recent Geomagnetic Field: Paleomagnetic Observations: Archeomagnetic Results. Analysis of Recent Lake Sediments. Geomagnetic Excursions. The Geomagnetic Power Spectrum. Reversals of the Earths Magnetic Field: Evidence for Field Reversal. Marine Magnetic Anomalies. Analysis of Reversal Sequences. Polarity Transitions. The Time-Averaged Paleomagnetic Field: Geocentric Axial Dipole Hypothesis. Second-Order Terms. Variation in the Earths Dipole Moment. Paleosecular Variation from Lavas (PSVL). Processes and Properties of the Earths Deep Interior: Basic Principles: Seismic Properties of the Earths Interior. Chemical and Physical Properties. Thermodynamic Properties of the Earths Deep Interior. Thermal History Models. Non-dynamo Models for the Earths Magnetic Field. Fluid Mechanics Fundamentals. Energy Sources. Introduction to Dynamo Theory: The Dynamo Problem. The Magnetic Induction Equation. The a and w Effects of Dynamo Theory. Waves in Dynamo Theory. Symmetries in Dynamo Theory. Theories for Geomagnetic Secular Variations and magnetic Field Reversals. Dynamo Theory: Vector Spherical Harmonics. Kinematic Dynamos. Cowlings Theorem and Other Constraints. Turbulence in the Core. Dynamo Waves. Dynamics of the Geodynamo. The Magnetic Fields of the Sun, Moon, and Planets: Origin of the Solar System. The Sun. The Moon. Meteorites. Magnetic Fields of the Planets. Geomagnetic Relevance. Examples of Synthesis: Fluid Velocities in the Core. Core-Mantle Coupling: Length of Day. Paleomagnetism and Dynamo Theory. Variations at the Core-Mantle Boundary and the Earths Surface. Appendices. References. Subject Index.

Geomagnetic polarity transitions

The top of Earths liquid outer core is nearly 2900 km beneath Earths surface, so we will never be able to observe it directly. This hot, dense, molten iron-rich body is continuously in motion and is the source of Earths magnetic field. One of the most dynamic manifestations at Earths surface of this fluid body is, perhaps, a reversal of the geomagnetic field. Unfortunately, the most recent polarity transition occurred at about 780 ka, so we have never observed a transition directly. It seems that a polarity transition spans many human lifetimes, so no human will ever witness the phenomenon in its entirety. Thus we are left with the tantalizing prospect that paleomagnetic records of polarity transitions may betray some of the secrets of the deep Earth. Certainly, if there are systematics in the reversal process and they can be documented, then this will reveal substantial information about the nature of the lowermost mantle and of the outer core. Despite their slowness on a human timescale, polarity transitions occur almost instantaneously on a geological timescale. This rapidity, together with limitations in the paleomagnetic recording process, prohibits a comprehensive description of any reversal transition both now and into the foreseeable future, which limits the questions that may at this stage be sensibly asked. The natural model for the geomagnetic field is a set of spherical harmonic components, and we are not able to obtain a reliable model for even the first few harmonic terms during a transition. Nevertheless, it is possible, in principle, to make statements about the harmonic character of a geomagnetic polarity transition without having a rigorous spherical harmonic description of one. For example, harmonic descriptions of recent geomagnetic polarity transitions that are purely zonal can be ruled out (a zonal harmonic does not change along a line of latitude). Gleaning information about transitions has proven to be difficult, but it does seem reasonable to draw the following conclusions with varying degrees of confidence. There appears to be a substantial decrease in the mean intensity of the dipole field during a transition to ∼25% of its usual value. The duration of an average geomagnetic polarity transition is not well known but probably lies between 1000 and 8000 years. Values outside these bounds have been reported, but we give reasons as to why such outliers are likely to be artifacts. The reversal process is probably longer than the manifestation of the reversal at Earths surface as recorded in paleomagnetic directional data. Convection hiatus during a geomagnetic polarity transition seems unlikely, and free-decay models for reversals appear to be generally incompatible with the data. This implies that certain theorems in dynamo theory, such as Cowlings theorem, should not be invoked to explain the origin of reversals. Unfortunately, the detailed description of directional changes during transitions remains controversial. Contrary to common belief, certain low-degree nondipole fields can produce significant longitudinal confinement of virtual geomagnetic poles (VGP) during a transition. The data are currently inadequate to refute or verify claims of longitudinal dipole confinement, VGP clustering, or other systematics during polarity transitions.

The time‐averaged paleomagnetic field 0–5 Ma

Persistent departures from the geocentric axial dipole field model of the time-averaged paleomagnetic field over the past 5 Myr have been analyzed using oceanic data from deep-sea cores and continental data from igneous rocks and sediments. The data set comprises the equivalent of 9490 spot readings of the field (5831 normal and 3659 reverse) from 930 groups of data. Variations in declination anomalies between groups of data strongly suggest the existence of second-order tectonic effects (small rotations) that make it difficult, if not impossible, to identify any nonzonal terms that might exist. Inclination anomalies have therefore been modeled in terms of low-degree zonal harmonics. The calculated inclination anomalies within 10° latitude bands are widely scattered (for both oceanic and continental data) and do not appear to have been drawn from distributions with common means. We attribute this large scatter to previously undetected or uncorrected second-order tectonic effects in the continental data or, in the oceanic data, to small departures from the vertical in deep-sea cores. If it is assumed that these effects are random between groups of data and without a systematic bias, they can be averaged out to a large extent if there are sufficient numbers of groups within each latitude band. This method also has the major advantage that it maximizes time averaging of the field. When this is done, an acceptable fit to the inclination anomaly data is found using a zonal harmonic model. Although the point estimates for the reverse polarity zonal quadrupole term are consistently larger than those for the normal polarity zonal quadrupole term, the difference is not significant and is likely due to contamination effects. This finding is true for a combination of all the data or for separate combinations of continental igneous rocks and ocean sediments. This conclusion differs from all previous analyses. The major differences occur in model estimates of the zonal octupole term, the estimates varying widely depending on the particular data combination. We show that false octupole terms can be introduced by several factors, including inclination errors in sediments and lavas, the use of unit vectors in the analyses, and incomplete magnetic cleaning, particularly of reversely magnetized rocks. Thus we cannot impute a geomagnetic significance to the estimates of a zonal octupole term. We suggest that the best estimates for the zonal quadrupole G2 = g20 / g10 are obtained from the combined Brunhes age igneous rocks and oceanic normal data (0.033 ± 0.019) and for the combined Matuyama age igneous rocks and oceanic reverse data (0.042 ± 0.022). When these two sets are combined, the overall best estimate of G2 is 0.038 ± 0.012.

The variation of intensity of earth’s magnetic field with time

Abstract A new and larger database is established to assess the variation of paleointensity with time. It is shown that submarine basaltic glass probably contains a grain-growth chemical remanent magnetization in magnetite. Intensity estimates from these samples are used to establish a lower bound estimate on intensities. Statistical tests on various subsets of the database are used to establish a more reliable database for finding long-term trends of the paleointensity. We can obtain a reasonable estimate for intensity versus time for the Cenozoic but not for the Mesozoic or late Paleozoic. The distributions of data as a function of time also provide valuable information. In particular, the two well-documented superchrons exhibit different intensity properties, which suggests that there is not a simple correlation between reversal rate and intensity.

The myth of the Pacific dipole window

The angular dispersion of virtual geomagnetic poles (VGP) from lava flows is often cited as having been anomalously low in the Pacific during the Brunhes epoch because the dispersion from Hawaiian lavas is said to be much lower than measured elsewhere. This led to the concept of the Pacific dipole window or Pacific non-dipole low. Because lavas tend to be erupted in bursts of activity, many of the Hawaiian data are serially correlated and thus cannot necessarily be treated as independent observations. Geochronological controls, as are available for Hawaii, have been used in a previous analysis to thin the data to try to avoid repeated sampling of the same geomagnetic field. Unfortunately, in that analysis the angular dispersion of VGPs was calculated about the mean VGP instead of about the spin axis, and thus underestimated the dispersion. We have therefore reanalyzed the relevant data using the following criteria. (1) Only those lavas with α95 < 10° have been considered. (2) A latitude-dependent cut-off angle is used to eliminate those vectors that are not part of the normal secular variation. (3) We have developed a statistical method to rationalise those flows that have repeatedly sampled the same geomagnetic field vector, because suitable geochronological controls are rarely available. Application of this new method to the Hawaiian data shows excellent agreement with the results from using geochronological controls. Where possible we have therefore included this method in our overall analysis. As expected, the resulting global data are compatible with a Fisher distribution about the spin axis. Brunhes age data from Hawaii (N = 96 independent measurements) give a VGP angular dispersion about the spin axis of SF = 12.4°, and for the Pacific region as a whole SF = 12.5° (N = 190) between latitudes 15° and 30° (north or south). These values are the same as SF = 12.4° (N = 160) calculated for the rest of the world in the same latitude range. This clearly demonstrates that the hypothesis of the Pacific dipole window may confidently be rejected.

History of Earth's magnetic field and possible connections to core-mantle boundary processes

The core-mantle boundary (CMB) sets boundary conditions for processes occurring within the core. Thus the history of the geomagnetic field is intimately connected with the history of the CMB: information about one can often provide information about the other. It is a simple matter to separate sources of external origin from those of internal origin, but there is no unique way to specify the location of the internal sources. Indirect arguments suggest that sources within Earths outer core strongly dominate the field for spherical harmonic terms with degree less than about 14 and that crustal sources play an increasing role in harmonics with higher degrees. Building on the pioneering studies of Roberts and Scott and of Backus in the 1960s, the velocity field of the core fluid at the top of the outer core can be estimated from geomagnetic secular variation data. However, even with appropriate assumptions about location of the magnetic field source, there is a serious nonuniqueness in inversion of the secular variation data to velocity field because magnetic field lines are not changed by movement of conductive fluid parallel to those field lines. Additional assumptions about the flow are therefore required, sometimes leading to quite different estimates in the pattern of fluid flow. The resulting velocity field estimates appear to be sensitive to conditions (e.g., small lateral variations in temperature) at the CMB. Consideration of mantle dynamics suggests that large changes in the CMB conditions probably occur on a 10- to 100-m.y. timescale. Secular variations with periods shorter than a million years, but longer than several years, almost certainly originate from processes operating in the outer core; unfortunately, there is not yet consensus as to what those processes are. Longer-period variations in the paleomagnetic record, including nonstationarities in the rates of magnetic field reversals, in paleointensities, and in paleosecular variation, may reflect changes in CMB conditions. Because these boundary conditions are controlled primarily by mantle dynamics, there have been several speculations regarding causal links between changes in Earths lithosphere and changes in Earths magnetic field. Finally, the evidence linking lateral variations at the CMB to perceived systematics in polarity transition data is found to be intriguing, but insufficient.

Dynamo theory and paleomagnetism

For more than 200 years the origin of Earths magnetic field was attributed to permanent magnetization. Even today no single argument (e.g., that Earths deep interior is too hot to sustain permanent magnetization) conclusively rules out the permanent magnetization hypothesis. Nevertheless, when all the evidence is considered, this hypothesis can be safely discarded and replaced with an electric current (dynamo) hypothesis. Surprisingly, this can be done even though there is no adequate dynamo model for Earth. The development of geodynamo models began with the disk dynamo of Larmor in 1919 and expanded to include many classes of models, such as αω, α2, α2ω, Taylor state, and Model Z dynamos. Because of mathematical difficulties associated with solving the many coupled partial differential equations of dynamo theory, numerous simplifying assumptions are made. The majority of numerical dynamo models assume a three-dimensional velocity field in an inviscid fluid and use mean field theory to solve for axisymmetric magnetic fields. There is also an increasing number of intermediate and strong field models emerging, in which feedback from the magnetic field to the velocity field is permitted. Nevertheless, these models still require several simplifying assumptions and there are many additional problems. For instance, many core parameters are difficult to estimate; there is debate on whether the top of the core is stably stratified and on the effects such stratification might have; what effects the presence of an inner core have; and whether the coupling across the coremantle boundary significantly affects the geodynamo. Perhaps it is not surprising that dynamo theoreticians, faced with large difficulties in mathematics and many uncertainties in physics, essentially choose to ignore input from fields such as paleomagnetism. However, it is precisely because of such difficulties that paleomagnetism can provide valuable constraints to narrow the range of viable dynamo models. For example, paleomagnetism ultimately should provide constraints on the velocity and magnetic field symmetries of dynamos; determine whether the geodynamo is in the weak, intermediate, or strong field regime; determine if there is a fundamental difference in dynamo processes during superchrons when reversals of the magnetic field essentially cease; and provide valuable information on the growth of the inner core and its possible stabilizing effects on geodynamo processes.

Paleomagnetic tomography of the core-mantle boundary

Abstract Analysis of updated global paleomagnetic data indicates that over the last 5 million years the normal and reverse polarity states are discernibly different. This difference, which can be characterized by a higher ratio of the axial quadrupole to dipole field for the reverse polarity relative to the normal polarity, is attributed to lateral variations in temperature or composition at or near the core-mantle boundary. Although several mechanisms are considered, thermal electric effects associated with core-mantle topography and/or with chemical variations in D″, the seismic layer (approximately 150 km thick) at the base of the mantle, are judged to be the most likely sources of the observed polarity asymmetry. This asymmetry should not necessarily be expected to give rise to systematic trends in polarity transitions.