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2013
Cromwell, G, Tauxe L, Staudigel H, Constable CG, Koppers AAP, Pedersen RB.  2013.  In search of long-term hemispheric asymmetry in the geomagnetic field : Results from high northern latitudes. Geochemistry Geophysics Geosystems. 14:3234-3249.   10.1002/ggge.20174   AbstractWebsite

Investigations of the behavior of the geomagnetic field on geological timescales rely on globally distributed data sets from dated lava flows. We present the first suitable data from the Arctic region, comprising 37 paleomagnetic directions from Jan Mayen (71 degrees N, 0.2-461 ka) and Spitsbergen (79 degrees N, 1-9.2 Ma) and five paleointensity results. Dispersion of the Arctic virtual geomagnetic poles over the last 2 Ma (27.34.0 degrees) is significantly lower than that from published Antarctic data sets (32.15.0 degrees). Arctic average virtual axial dipole moment (76.824.3 ZAm(2)) is high in comparison to Antarctica over the same time interval (34.88.2 ZAm(2)), although the data are still too sparse in the Arctic to be definitive. These data support a long-lived hemispheric asymmetry of the magnetic field, contrasting higher, more stable fields in the north with lower average strength and more variable field directions in the south. Such features require significant non-axial-dipole contributions over 10(5)-10(6) years.

2011
Constable, CG.  2011.  Modelling the geomagnetic field from syntheses of paleomagnetic data. Physics of the Earth and Planetary Interiors. 187:109-117.   10.1016/j.pepi.2011.05.004   AbstractWebsite

This review examines results from time-varying geomagnetic field models that span several thousand years, and from variations in dipole moment strength up to million year time scales. For the past 400 years, twin magnetic flux lobes bordering the inner core tangent cylinder in both northern and southern hemispheres dominate the geomagnetic field and appear more or less fixed in location. In contrast, the millennial scale view shows that such features are quite mobile and subject to morphological changes on time scales of a few centuries to a thousand years, possibly reflecting large scale reorganization of core flow. The lobes rarely venture into the Pacific hemisphere, and average fields over various time scales generally reveal two or three sets of lobes, of diminished amplitude. Thus millennial scale models are suggestive of thermal core-mantle coupling generating a weak bias in the average field rather than a strong inhibition of large scale field changes. The recovery of variations in dipole moment on million year time scales allows frequency domain analyses to search for characteristic time scales for core dynamics that might be associated with excursion and reversal rate, time taken for reversals, or any signs of control by Earth's orbital parameters. The spectrum is characteristically red for the time interval 0-160 Ma, suggesting non-stationarity associated with average reversal rate changes, probably reflecting the impact of superchrons and a continually evolving core. Distinct regimes of power law decay with frequency may reflect different physical processes contributing to the secular variation. Evidence for non-stationarity at shorter time-scales is also present in dipole moment variations over 0-2 Ma with average growth rate faster than the decay process. Rates of change of dipole moment and rapid local field variations found in the paleomagnetic record are evaluated in the context of the 400 year historical record and the spectrum of geomagnetic variations for 0-160 Ma. (C) 2011 Elsevier B.V. All rights reserved.

2006
Constable, C, Korte M.  2006.  Is Earth's magnetic field reversing? Earth and Planetary Science Letters. 246:1-16.   10.1016/j.epsl.2006.03.038   AbstractWebsite

Earth's dipole field has been diminishing in strength since the first systematic observations of field intensity were made in the mid nineteenth century. This has led to speculation that the geomagnetic field might now be in the early stages of a reversal. In the longer term context of paleomagnetic observations it is found that for the current reversal rate and expected statistical variability in polarity interval length an interval as long as the ongoing 0.78 Myr Brunhes polarity interval is to be expected with a probability of less than 0.15, and the preferred probability estimates range from 0.06 to 0.08. These rather low odds might be used to infer that the next reversal is overdue, but the assessment is limited by the statistical treatment of reversals as point processes. Recent paleofield observations combined with insights derived from field modeling and numerical geodynamo simulations suggest that a reversal is not imminent. The current value of the dipole moment remains high compared with the average throughout the ongoing 0.78 Myr Brunhes polarity interval; the present rate of change in Earth's dipole strength is not anomalous compared with rates of change for the past 7 kyr; furthermore there is evidence that the field has been stronger on average during the Brunhes than for the past 160 Ma, and that high average field values are associated with longer polarity chrons. There is no evidence from recent millennial scale time-varying paleofield models to indicate that the field is entering a polarity transition. Nevertheless, it remains a reasonable supposition that the magnetic field will eventually reverse even though the time scale is unpredictable. A more immediate concern is that ongoing secular variation in the magnetic field may be expected to moderate the current high dipole strength on centennial to millennial time scales: it would not be surprising if it dropped substantially, returning closer to the average without necessarily reversing. This could have important consequences for space weather, and also highlights the need for improved understanding of the impact of geomagnetic field strength on the production rates of cosmogenic isotopes that are used to estimate past solar variability. (c) 2006 Elsevier B.V. All rights reserved.

2003
Tauxe, L, Constable C, Johnson CL, Koppers AAP, Miller WR, Staudigel H.  2003.  Paleomagnetism of the southwestern USA recorded by 0-5 Ma igneous rocks. Geochemistry Geophysics Geosystems. 4   10.1029/2002gc000343   AbstractWebsite

The issue of permanent nondipole contributions to the time-averaged field lies at the very heart of paleomagnetism and the study of the ancient geomagnetic field. In this paper we focus on paleomagnetic directional results from igneous rocks of the southwestern U. S. A. in the age range 0-5 Ma and investigate both the time-averaged field and its variability about the mean value. Several decades of work in the southwestern United States have resulted in the publication of paleomagnetic data from over 800 individual paleomagnetic sites. As part of a new investigation of the San Francisco Volcanics, we collected paleomagnetic samples from 47 lava flows, many of which have been previously dated. The new data combined with published data are highly scattered. Contributions to the scatter were considered, and we find that removal of data sets from tectonically active areas and judicious selection according to Fisher's [1953] precision parameter results in an axially symmetric data distribution with normal and reverse modes that are indistinguishable from antipodal. Monte Carlo simulations suggest that a minimum of 5 samples per site are needed to estimate the precision parameter sufficiently accurately to allow its use as a determinant of data quality. Numerical simulations from statistical paleosecular variation models indicate the need for several hundred paleomagnetic sites to get an accurate determination of the average field direction and are also used to investigate the directional bias that results from averaging unit vectors rather than using the full field vector. Average directions for the southwestern U. S. A. show small deviations from a geocentric axial dipole field, but these cannot be considered statistically significant. Virtual geomagnetic pole (VGP) dispersions are consistent with those from globally distributed observations analyzed by McElhinny and McFadden [1997]. However, a systematic investigation of the effect of imposing a cutoff on VGPs with large deviations from the geographic axis indicates that while it may reduce bias in calculating the average direction, such a procedure can result in severe underestimates of the variance in the geomagnetic field. A more satisfactory solution would be to use an unbiased technique for joint estimation of the mean direction and variance of the field distribution.

2000
Constable, CG, Johnson CL, Lund SP.  2000.  Global geomagnetic field models for the past 3000 years: transient or permanent flux lobes? Philosophical Transactions of the Royal Society of London Series a-Mathematical Physical and Engineering Sciences. 358:991-1008. AbstractWebsite

PSVMOD1.0 is a compilation of globally distributed palaeodirectional data from archaeomagnetic artefacts, lava flows, and lake sediments at 24 sites evaluated at 100 year intervals from 1000 BC to AD 1800. We estimate uncertainty in these measures of declination and inclination by comparison with predictions from standard historical models in time-intervals of overlap, and use the 100-year samples and their associated uncertainties to construct a sequence of minimum structure global geomagnetic field models. Global predictions of radial magnetic field at the core mantle boundary (CMB), as well as inclination and declination anomalies at the Earth's surface, provide an unprecedented view of geomagnetic secular variations over the past 3000 years, and demonstrate a consistent evolution of the field with time. Resolution of the models is poorest in the Southern Hemisphere, where only six of the 24 sites are located, several with incomplete temporal coverage. Low-flux regions seen in the historical field near the North Pole are poorly resolved, but the Northern Hemisphere flux lobes are clearly visible in the models. These lobes are not fixed in position and intensity, but they only rarely venture into the Pacific hemisphere. The Pacific region is seen to have experienced significant secular variation: a strong negative inclination anomaly in the region, like that seen in 0-5 Ma models, persists from 1000 BC until AD 1000 and then gradually evolves into the smaller positive anomaly seen today. On average bt tween 1000 BC and AD 1800, the non-axial-dipole contribution to the radial magnetic field at the core-mantle boundary is largest in the north-central Pacific, and beneath Central Asia, with clear non-zonal contributions. At the Earth's surface, average inclination anomalies are large and negative in the central Pacific, and most positive slightly to the east of Central Africa. Inclination anomalies decrease with increasing latitude. Average declinations are smallest in equatorial regions, again with strong longitudinal variations, largest negative departures are centred over Australia and Eastern Asia. Secular variation at the Earth's surface is quantified by standard deviation of inclination and declination about their average values, and at the CMB by standard deviation in radial magnetic field. All three show significant geographical variations, but appear incompatible with the idea that secular variation in the Pacific hemisphere is permanently attenuated by greatly enhanced conductivity in D " beneath the region.

1993
Constable, CG, Parker RL, Stark PB.  1993.  Geomagnetic-Field Models Incorporating Frozen-Flux Constraints. Geophysical Journal International. 113:419-433.   10.1111/j.1365-246X.1993.tb00897.x   AbstractWebsite

Techniques for modelling the geomagnetic field at the surface of Earth's core often penalize contributions at high spherical harmonic degrees to reduce the effect of mapping crustal fields into the resulting field model at the core-mantle boundary (CMB). Ambiguity in separating the observed field into crustal and core contributions makes it difficult to assign error bounds to core field models, and this makes it hard to test hypotheses that involve pointwise values of the core field. The frozen-flux hypothesis, namely that convective terms dominate diffusive terms in the magnetic-induction equation, requires that the magnetic flux through every patch on the core surrounded by a zero contour of the radial magnetic field remains constant, although the shapes, areas and locations (but not the topology) of these patches may change with time. Field models exactly satisfying the conditions necessary for the hypothesis have not yet been constructed for the early part of this century. We show that such models must exist, so testing the frozen-flux hypothesis becomes the question of whether the models satisfying it are geophysically unsatisfactory on other grounds, for example because they are implausibly rough or complicated. We introduce an algorithm to construct plausible fleld models satisfying the hypothesis, and present such models for epochs 1945.5 and 1980. Our algorithm is based on a new parametrization of the field in terms of its radial component B(r) at the CMB. The model consists of values of B(r) at a finite set of points on the CMB, together with a rule for interpolating the values to other points. The interpolation rule takes the specified points to be the vertices of a spherical triangle tessellation of the CMB, with B(r) varying linearly in the gnomonic projections of the spherical triangles onto planar triangles in the planes tangent to the centroids of the spherical triangles. This parametrization of B(r) provides a direct means of constraining the integral invariants required by the frozen-flux hypothesis. Using this parametrization, we have constructed field models satisfying the frozen-flux hypothesis for epochs 1945.5 and 1980, while fitting observatory and survey data for 1945.5 and Magsat data for 1980. We use the better constrained 1980 CMB field model as a reference for 1945.5: we minimize the departure of the 1945.5 CMB field model from a regularized 1980 CMB field model, while constraining the 1945.5 model to have the same null-flux curves and flux through those curves as the 1980 model. The locations, areas and shapes of the curves are allowed to change. The resulting 1945.5 CMB field model is nearly as smooth as that for 1980, fits the data adequately, and satisfies the conditions necessary for the frozen-flux hypothesis.