Latitude Dependence of the Angular Dispersion of the Geomagnetic Field
TL;DR: In this paper, a method is presented for isolating the contribution due to variation with latitude of the average intensity of the non-dipole field to the main geomagnetic field.
Abstract: Summary Changes in the direction of the Earth's magnetic field at a given site are produced in part by wobble of the main geomagnetic dipole, in part by fluctuations in the intensity and direction of the non-dipole field, and in part by changes in the intensity of the main dipole field. These three processes combine to produce an angular variance that is strongly latitude dependent. A method is presented for isolating the contribution due to variation with latitude of the average intensity of the non-dipole field. The aspect of geomagnetic secular variation most accessible to palaeomagnetic measurement is the angular dispersion of the field over long periods of time. The amount of the angular dispersion is determined by two factors. One is the angular wobble of the main geomagnetic field. The other is the time average of the ratio flF of the non-dipole field to the dipole field. This time average is of general geophysical interest because it provides a measure of the time average of the magnetohydrodynamic processes in the region of the Earth's core beneath the site where the palaeomagnetic samples were collected. The time average of the nondipole field may exhibit a longitude dependence and a latitude (or zonal) dependence. Existence of the former implies that lateral differences exist in the boundary conditions at the core-mantle interface. Lateral temperature variations (Cox & Doell 1964) or lateral differences in relief along the core-mantle interface (Hide 1966) may lead to longitudinal differences in the operation of the geomagnetic dynamo and hence to longitudinal differences in the time average of the non-dipole field. Even if the core-mantle boundary conditions were completely uniform, however, the angular dispersion of the geomagnetic field would still vary with latitude for two reasons. The first is that the Coriolis forces of the geomagnetic dynamo vary with latitude, hence it is reasonable that the nondipole field may also vary. The second is that because of the geometry of the vector addition of dipole and nondipole fields on a sphere, the geomagnetic angular dispersion will vary with latitude even if the non-dipole field is the same at all latitudes. The objective of the present study is to develop models that describe the latitude dependence of geomagnetic
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TL;DR: In this paper, the ages of basaltic lava flows on the island of Hawaii were investigated using the Thelliers' method in vacuum and the results showed that the dispersion of virtual geomagnetic poles for the eight lavas is 15.5°, appreciably larger than the average for older lava flows.
Abstract: Radiocarbon ages have been published for nine basaltic lava flows on the island of Hawaii; the ages range from 2600 to somewhat older than 17,900 years B.P. By using the Thelliers' method in vacuum, geomagnetic paleointensity values were obtained from eight of the lavas; the ninth proved unsuitable. The paleointensities for the four youngest flows (2600–4600 years B.P.) yield virtual dipole moments (VDM's) that are 20% greater to more than twice the worldwide values for those times obtained by V. Bucha from archeomagnetic data. The dispersion of virtual geomagnetic poles for the eight lavas is 15.5°, appreciably larger than the average for older lava flows on Hawaii. These results contrast with the historic magnetic field in the region of Hawaii, in which both secular variation and nondipole components are very low. At about 10,000 years B.P. the measured VDM is not very different from the long-term worldwide average but differs considerably from a smooth extrapolation of Bucha's average curve. At about 18,000 years B.P. the measured VDM is very low and is associated with an unusually shallow paleomagnetic inclination for the latitude of Hawaii. These new paleointensity and paleodirectional data strongly suggest that sizable nondipole geomagnetic fields have existed in the vicinity of Hawaii at various times during the Holocene epoch and perhaps earlier.
707 citations
TL;DR: P paleomagnetic and radiometric age data from samples recovered by ocean drilling define an age-progressive paleolatitude history, indicating that the Emperor Seamount trend was principally formed by the rapid motion of the Hawaiian hotspot plume during Late Cretaceous to early-Tertiary times.
Abstract: The Hawaiian-Emperor hotspot track has a prominent bend, which has served as the basis for the theory that the Hawaiian hotspot, fixed in the deep mantle, traced a change in plate motion. However, paleomagnetic and radiometric age data from samples recovered by ocean drilling define an age-progressive paleolatitude history, indicating that the Emperor Seamount trend was principally formed by the rapid motion (over 40 millimeters per year) of the Hawaiian hotspot plume during Late Cretaceous to early-Tertiary times (81 to 47 million years ago). Evidence for motion of the Hawaiian plume affects models of mantle convection and plate tectonics, changing our understanding of terrestrial dynamics.
379 citations
TL;DR: In this paper, it is suggested that the rotation of blocks and the strike-slip displacement are two qualitative and quantitative contemporaneous aspects of a single deformation process, and the agreement between paleomagnetic rotation data and those inferred from offset and spacing data in northern Israel is excellent, suggesting that the faults and intervening blocks were rotated with progressive deformation along the levant transform.
Abstract: The magnitude and sense of block rotations depicted from such structural data as fault spacing and slip are noted to agree with values obtained from independent paleomagnetic determinations. The agreement between paleomagnetic rotation data and those inferred from offset and spacing data in northern Israel is excellent, suggesting that the faults and intervening blocks were rotated with progressive deformation along the levant transform. It is suggested that the rotation of blocks and the strike-slip displacement are two qualitative and quantitative contemporaneous aspects of a single deformation process.
342 citations
Cites methods from "Latitude Dependence of the Angular ..."
...In the Cretaceous the angular standard deviation expected in northern Israel, using SV model D [Cox, 1970] is about 13....
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TL;DR: In this article, a recent model for polarity reversals suggested that reversals involve critical interactions between the primary (dipole) and secondary (quadrupole) dynamo families.
Abstract: A recent model for polarity reversals suggested that reversals involve critical interactions between the primary (dipole) and secondary (quadrupole) dynamo families. This model predicted that the relative secondary family contribution to the field would be smaller when the reversal rate is low than when the reversal rate is high. In particular, therefore, it was predicted that the contribution from the secondary family would have been low during the Cretaceous Normal Superchron. This prediction is tested using model G for the paleosecular variation of lavas to estimate the relative contributions of the two families back through time. It is found that the data support the prediction. It is also found that a decrease in the contribution from the secondary family is associated with an increase in the contribution from the primary family, and vice versa.
328 citations
TL;DR: In this paper, the role of palaeosecular variation (PSV) in the use of statistics for palaeomagnetic studies is examined and new reliability criteria for the reliability of a data set are provided.
Abstract: In this study, we examine the role of palaeosecular variation (PSV) in the use of statistics for
palaeomagnetic studies, and we provide new reliability criteria for palaeomagnetic poles or
directions.We first conclude that Fisher statistics should not be applied to average palaeomagnetic
directions but to virtual geomagnetic pole (VGP) distributions instead.
Secondly, we strongly advocate that typical properties of geomagnetic field behaviour are
taken into account in the assessment of palaeomagnetic data sets. The latitude-dependent
properties (E, S, k) provide useful guidelines for the reliability of a palaeomagnetic data set. A
reliable assessment of these properties depends on the (sufficient) number of palaeomagnetic
samples being taken. Therefore, as an additional instrument of assessing data sets, we provide
a N-dependent A95 envelope, bounded by an upper limit A95max, and a lower limit A95min
that helps to ascertain whether or not a distribution has sufficiently well-sampled PSV and
therefore geomagnetic field behaviour. Applying these criteria is indispensable for studies
of geomagnetic behaviour, or for studies aiming at using TK03.GAD for inclination error
correction through the elongation/inclination (E/I) method. For palaeomagnetic studies aimed
at geological reconstructions, they form helpful guidelines and increase the confidence in the
rocks having faithfully recorded the field.
An analysis of published Eastern Mediterranean data shows that the vast majority of studies
do not conform to the Van der Voo criteria, in particular with respect to N and A95. We have
provided criteria that are on the one hand more lenient (lower N may still provide relevant
information), and on the other hand more strict (for high N the criterion of A95 < 16° should
be adapted to a requirement of lower A95, e.g. A95 80).
297 citations
Cites background or methods from "Latitude Dependence of the Angular ..."
...These are Cox (1970): ks K p = 2(1 + 3 sin 2 λ)2 (5 + 3 sin2 λ) ; (5) Creer (1962): ks K p = 2(1 + 3 sin 2 λ) (5 − 3 sin2 λ) ....
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...(6) Cox (1970) also provides a conversion in the case of Fisherian distributions of directions....
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...5(A), we show the curves for Fisherian VGPs and Fisherian directions (Cox 1970) together with the A95/α95 ratios derived from the TK03....
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...Both Creer (1962) and Cox (1970) introduced a conversion equation (assuming Fisherian VGPs) between k and K, and hence α95 and A95....
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...As was already noted more than 40 yr ago (Creer et al. 1959; Creer 1962; Cox 1970), and more recently emphasized again by Beck (1999) and Tauxe & Kent (2004), distributions of palaeomagnetic directions at any location on the globe are elongated in a N–...
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TL;DR: In this article, the authors developed a form of theory which appears to be appropriate to measurements of position on a sphere and demonstrated the simultaneous distribution of the amplitude and direction of the vector sum of a number of random unit vectors of given precision.
Abstract: Any topological framework requires the development of a theory of errors of characteristic and appropriate mathematical form. The paper develops a form of theory which appears to be appropriate to measurements of position on a sphere. The primary problems of estimation as applied to the true direction, and the precision of observations, are discussed in the subcases which arise. The simultaneous distribution of the amplitude and direction of the vector sum of a number of random unit vectors of given precision, is demonstrated. From this is derived the test of significance appropriate to a worker whose knowledge of precision lies entirely in the internal evidence of the sample. This is the analogue of ‘Student’s’ test in the Gaussian theory of errors. The general formulae obtained are illustrated using measurements of the direction of remanent magnetization in the directly and inversely magnetized lava flows obtained in Iceland by Mr J. Hospers.
5,482 citations
TL;DR: In this article, free hydromagnetic oscillations of a rotating spherical shell of an incompressible fluid are investigated by means of a simple theoretical model for each spatial harmonic, rotation gives rise to two distinct modes of oscillation, "magnetic" and "inertial" which propagate with different velocities.
Abstract: Free hydromagnetic oscillations of a rotating spherical shell of an incompressible fluid are investigated by means of a simple theoretical model For each spatial harmonic, rotation gives rise to two distinct modes of oscillation, ‘magnetic’ and ‘inertial’, which propagate with different velocities As an application of the theory, it is shown that if the strength of the toroidal magnetic field in the Earth’s core is 100 Oe, then many of the properties of the observed secular changes, including the slow westward drift, of the main geomagnetic field at the Earth’s surface can be accounted for in terms of the interaction of magnetic modes in the core with the Earth’s poloidal magnetic field Concomitant magnetic variations due to inertial modes in the core would, owing to their relatively short periods (several days), fail to penetrate to the surface of the Earth, although the eddy currents induced in the lower mantle by these modes might affect the mechanical coupling between the mantle and the core
353 citations
321 citations
TL;DR: In this article, a probability model based on the theory of Bernouli trials was proposed to analyze variations in the lengths of geomagnetic polarity, intervals are analyzed by means of the probability that a polarity inversion will occur during one cycle of change in the geOMagnetic dipole moment.
Abstract: Variations in the lengths of geomagnetic polarity, intervals are analyzed by means of a probability model based on the theory of Bernouli trials. Polarity reversals are assumed to occur as the result of the interaction between steady oscillations of the geomagnetic dipole and secular variations of the nondipole field. The particular cycle on which a polarity inversion occurs is determined by the magnitude of the nondipole field, which is assumed to vary randomly and independently of dipole variations. The reversal properties of the geomagnetic dynamo are characterized by the single parameter p, the probability that a polarity inversion will occur during one cycle of change in the geomagnetic dipole moment. From an analysis of polarity changes during the past 10 m.y., the value of p is estimated to be 0.05. During the Permian period, it was at least two orders of magnitude smaller. The analysis suggests that within the past 10 m.y. there have occurred hitherto undiscovered short geomagnetic polarity events with durations shorter than 0.05 m.y.
312 citations
TL;DR: In this article, confidence limits for the precision parameter k used in the analysis of palaeomagnetic data and for the angular standard deviation σ were calculated for 95 per cent and 99 per cent confidence limits.
Abstract: Summary
Confidence limits are calculated for the precision parameter k used in the analysis of palaeomagnetic data and for the angular standard deviation σ.
A set of tables for 95 per cent and 99 per cent confidence limits is presented.
286 citations