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.

Reversals of the Earth's magnetic field and temporal variations of the dynamo families

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.

Lengths of geomagnetic polarity intervals

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).

/pdf/geomagnetic-secular-variation-and-the-statistics-of-1d8d04dho3.pdf

Geomagnetic secular variation and the statistics of palaeomagnetic directions

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.

/pdf/confidence-limits-for-the-precision-parameter-k-1vd6rhl6ng.pdf

Confidence Limits for the Precision Parameter k

The magnetic inclinations and inten sities of about 650 samples from seven deepsea cores taken in the Antarctic were measured on a spinner magnetometer. This series of measurements provided a magnetic stratigraphy, based on zones of normally or reversally polar ized specimens for each core, which was then correlated with the magnetic stra tigraphy of Cox et al. (1). One core (V16-134) gave a continuous record of the paleomagnetic field back to about 3.5 million years. When selected samples were subject ed to alternatingfield demagnetization, most were found to have an unstable component that was removed by fields of 150 oersteds; all samples from two cores were partially demagnetized in a field of 150 oersteds. The average inclination in these two cores was then in good agreement with the average inclination of the ambient field for the latitude of the core site. It was also found that the intensities of the samples decreased at the points of reversal; this finding is to be expected if, as has been postulated by the dynamo theory, the intensity of the dipole field decreases to zero and builds again with opposite polarity. We believe that the magnetiza tion of the cores results from the pres ence of detrital magnetite, although other magnetic minerals also may be present. Four faunal zones (, X, , and ) have been recognized in these Antarctic cores on the basis of upward sequential disappearance of Radiolaria. The faunal boundaries and reversals consistently have the same relations to one another, indicating that they are both timedependent phenomena. Using previously determined times of reversal, one may date the following events in the cores: 1) Radiolarian faunal boundaries:-X, 2 million years; X-, 0.7 million years; -, 0.4 to 0.5 million years. These dates are in good agreement with ages previously extrapolated from radio metric dates. 2) Initiation of Antarctic diatom ooze deposition, approximately 2.0 mil-lion years ago. 3) First occurrence of ice- rafted detritus, approximately 2.5 million years ago. One can also calculate rates of sedi mentation, which vary in the cores studied from 1.1 to about 8.0 millimeters per 1000 years. Sedimentation rates for the Indian Ocean cores are higher than for the Bellingshausen Sea cores. The near coincidence of faunal changes and reversals in the cores suggests but does not prove a causal relation. We conclude from this study that paleomagnetic stratigraphy is a unique method for correlating and dating deep sea cores, and that future work with such cores may provide a complete or nearly complete record of the history of the earth9s magnetic field beyond 4 million years.

https://science.sciencemag.org/content/sci/154/3747/349.full.pdf

Paleomagnetic study of antarctic deep-sea cores.

In studies of the paleosecular variation the situation often arises that, although a number of spot readings of the paleogeomagnetic field have been deduced from the fossil magnetization of a rock formation, their stratigraphic sequence is unknown. Hence, in this paper, methods are discussed of deducing the amount of dispersion produced by the paleosecular variation in the magnetization of a rock formation against the background of noise due to experimental errors, partial remagnetization, subsequent tectonic movement, etc. The secular variation recorded at observatories and field stations during the past few centuries does not cover the full range of dispersion of the geomagnetic field in time, and models are considered by means of which this may be estimated. Angular dispersion factors are defined and have been calculated for three models and found to be of the same magnitude as those calculated from various rock formations. Other calculations for these models predict that the secular variation dispersion depends on latitude, and data from a number of igneous rock formations appear to confirm this prediction. It is not possible, however, to calculate the dispersion due to the paleosecular variation from the large body of paleomagnetic data tabulated by various authors, since these data have been computed in different ways.

K. M. Creer

Papers

The dispersion of the geomagnetic field due to secular variation and its determination for remote times from paleomagnetic data