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2013
Buffett, BA, Ziegler L, Constable CG.  2013.  A stochastic model for palaeomagnetic field variations. Geophysical Journal International. 195:86-97.   10.1093/gji/ggt218   AbstractWebsite

Regeneration of the Earth's magnetic field by convection in the liquid core produces a broad spectrum of time variation. Relative palaeointensity measurements in marine sediments provide a detailed record over the past 2 Myr, but an explicit reconstruction of the underlying dynamics is not feasible. A more practical alternative is to construct a stochastic model from estimates of the virtual axial dipole moment. The deterministic part of the model (drift term) describes time-averaged behaviour, whereas the random part (diffusion term) characterizes complex interactions over convective timescales. We recover estimates of the drift and diffusion terms from the SINT2000 model of Valet et al. and the PADM2M model of Ziegler et al. The results are used in numerical solutions of the Fokker-Planck equation to predict statistical properties of the palaeomagnetic field, including the average rates of magnetic reversals and excursions. A physical interpretation of the stochastic model suggests that the timescale for adjustments in the axial dipole moment is set by the dipole decay time tau(d). We obtain tau(d) = 29 kyr from the stochastic models, which falls within the expected range for the Earth's core. We also predict the amplitude of convective fluctuations in the core, and establish a physical connection to the rates of magnetic reversals and excursions. Chrons lasting longer than 10 Myr are unlikely under present-day conditions. However, long chrons become more likely if the diffusion term is reduced by a factor of 2. Such a change is accomplished by reducing the velocity fluctuations in the core by a factor of root 2, which could be attributed to a shift in the spatial pattern of heat flux from the core or a reduction in the total core heat flow.

2009
Lawrence, KP, Tauxe L, Staudigel H, Constable CG, Koppers A, McIntosh W, Johnson CL.  2009.  Paleomagnetic field properties at high southern latitude. Geochemistry Geophysics Geosystems. 10   10.1029/2008gc002072   AbstractWebsite

Statistical analyses of paleomagnetic data from lava flows are used to study geomagnetic field behavior on million year timescales. Previous paleomagnetic studies have lacked high-latitude measurements necessary to investigate the persistence of geomagnetic anomalies observed in the recent and historical field and replicated in some numerical geodynamo simulations. These simulations suggest that reduced convective flow inside the tangent cylinder may affect the magnetic field at high latitude, whereas lower-latitude observations are expressions of columnar/helical flow outside the tangent cylinder. This paper presents new paleointensity and paleodirectional data from 100 volcanic sites in the Erebus Volcanic Province (EVP), Antarctica, and 21 new age determinations by the (40)Ar/(39)Ar incremental heating method. The new EVP data are combined with previously published paleomagnetic and geochronological results, providing 133 sites, 91 having radioisotopic dates. Modified Thellier-Thellier paleointensity estimates are reported for 47 sites (37 have dates). Ages for the combined data set span 0.03 to 13.42 Ma. The 125 high-quality EVP directional data selected from the merged data set have a non-Fisherian distribution and a mean direction with an inclination anomaly of similar to 3 degrees, but 95% confidence limits include the prediction from a geocentric axial dipole. Virtual geomagnetic pole (VGP) dispersions for Brunhes, Matuyama, and the combined 0-5 Ma data set are consistently high compared with values from middle-to low-latitude regions regardless of the criterion used to determine transitional fields. With VGP latitude cut off at 45 degrees, the dispersion (23.9 +/-2.1 degrees) for the combined 0-5 Ma EVP data set is consistent with earlier high-latitude data and paleosecular variation (PSV) in Model G but not with some more recent statistical PSV models. Mean EVP paleointensity of 31.5 +/-2.4 mu T, derived from 41 high-quality sites, is about half the current value at McMurdo (similar to 63 mu T). The result is essentially independent of data selection criteria. High VGP dispersion and low-intensity values support the global observation of anticorrelation between directional variability and field strength. Simulations of time-varying dipole strength show that uneven temporal sampling may bias the mean EVP intensity estimate, but the possibility of persistently anomalous field behavior at high latitude cannot be excluded.

2008
Johnson, CL, Constable CG, Tauxe L, Barendregt R, Brown LL, Coe RS, Layer P, Mejia V, Opdyke ND, Singer BS, Staudigel H, Stone DB.  2008.  Recent investigations of the 0-5 Ma geomagnetic field recorded by lava flows. Geochemistry Geophysics Geosystems. 9   10.1029/2007gc001696   AbstractWebsite

We present a synthesis of 0 - 5 Ma paleomagnetic directional data collected from 17 different locations under the collaborative Time Averaged geomagnetic Field Initiative ( TAFI). When combined with regional compilations from the northwest United States, the southwest United States, Japan, New Zealand, Hawaii, Mexico, South Pacific, and the Indian Ocean, a data set of over 2000 sites with high quality, stable polarity, and declination and inclination measurements is obtained. This is a more than sevenfold increase over similar quality data in the existing Paleosecular Variation of Recent Lavas (PSVRL) data set, and has greatly improved spatial sampling. The new data set spans 78 degrees S to 53 degrees N, and has sufficient temporal and spatial sampling to allow characterization of latitudinal variations in the time-averaged field (TAF) and paleosecular variation (PSV) for the Brunhes and Matuyama chrons, and for the 0 - 5 Ma interval combined. The Brunhes and Matuyama chrons exhibit different TAF geometries, notably smaller departures from a geocentric axial dipole field during the Brunhes, consistent with higher dipole strength observed from paleointensity data. Geographical variations in PSV are also different for the Brunhes and Matuyama. Given the high quality of our data set, polarity asymmetries in PSV and the TAF cannot be attributed to viscous overprints, but suggest different underlying field behavior, perhaps related to the influence of long-lived core-mantle boundary conditions on core flow. PSV, as measured by dispersion of virtual geomagnetic poles, shows less latitudinal variation than predicted by current statistical PSV models, or by previous data sets. In particular, the Brunhes data reported here are compatible with a wide range of models, from those that predict constant dispersion as a function of latitude to those that predict an increase in dispersion with latitude. Discriminating among such models could be helped by increased numbers of low-latitude data and new high northern latitude sites. Tests with other data sets, and with simulations, indicate that some of the latitudinal signature previously observed in VGP dispersion can be attributed to the inclusion of low-quality, insufficiently cleaned data with too few samples per site. Our Matuyama data show a stronger dependence of dispersion on latitude than the Brunhes data. The TAF is examined using the variation of inclination anomaly with latitude. Best fit two- parameter models have axial quadrupole contributions of 2 - 4% of the axial dipole term, and axial octupole contributions of 1 - 5%. Approximately 2% of the octupole signature is likely the result of bias incurred by averaging unit vectors.

2005
Constable, C, Johnson C.  2005.  A paleomagnetic power spectrum. Physics of the Earth and Planetary Interiors. 153:61-73.   10.1016/j.pepi.2005.03.015   AbstractWebsite

We construct a power spectrum of geomagnetic dipole moment variations or their proxies that spans the period range from some tens of million down to about 100 years. Empirical estimates of the spectrum are derived from the magnetostratigraphic time scale, from marine sediment relative paleointensity records, and from a time varying paleomagnetic field model for the past 7 kyr. The spectrum has the most power at long periods, reflecting the influence of geomagnetic reversals and in general decreases with increasing frequency (decreasing period). The empirical spectrum is compared with predictions from simple models. Discrepancies between the observed and predicted spectra are discussed in the context of: (i) changes in reversal rate, (ii) overall average reversal rate, (iii) cryptochrons, (iv) the time taken for a reversal to occur, and (v) long term paleosecular variations and average estimates of the field strength and variance from other sources. (c) 2005 Elsevier B.V. All rights reserved.

1996
Johnson, CL, Constable CG.  1996.  Palaeosecular variation recorded by lava flows over the past five million years. Philosophical Transactions of the Royal Society of London Series a-Mathematical Physical and Engineering Sciences. 354:89-141.   10.1098/rsta.1996.0004   AbstractWebsite

We present a new global palaeomagnetic database, comprising lava flows and thin intrusive bodies, suitable for studying palaeosecular variation and the time-averaged field. The database is presented in some detail in the appendix and is available oil-line from the authors. We review palaeosecular variation models to date, emphasizing the assumptions required and the rather arbitrary construction of many of these models, Preliminary studies of the statistical properties of the new database suggest that existing palaeosecular variation models are inadequate to explain the long-term temporal variations in the field. It is increasingly apparent that data distribution and duality are pivotal in determining the characteristics of the secular variation. The work presented here demonstrates the need for revised models of the time-averaged field structure for both normal and reverse polarities before reliable models for palaeosecular variation can be made.