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Constable, CG.  2003.  Geomagnetic Reversals: Rates, Timescales, Preferred Paths, Statistical Models, and Simulations. Earth's core and lower mantle: Fluid mechanics of astrophysics and geophysics. ( Jones CA, Soward AM, Zhang K, Eds.).:77-99., London ; New York: Taylor & Francis Abstract
Constable, C, Parker R.  1991.  Deconvolution of Long-Core Paleomagnetic Measurements - Spline Therapy for the Linear Problem. Geophysical Journal International. 104:453-468.   10.1111/j.1365-246X.1991.tb05693.x   AbstractWebsite

The magnetization of long cores of sedimentary material is often measured in a pass-through magnetometer, whose output is the convolution of the desired function with the broad impulse response of the system. Because of inevitable measurement noise and the inherent poor conditioning of the inverse problem, any attempt to estimate the true magnetization function from the observations must avoid unnecessary amplification of small-scale features which would otherwise dominate the model with deceptively large undulations. We propose the construction of the smoothest possible magnetization model satisfying the measured data to within the observational error. By means of a cubic spline basis in the representations of both the unknown magnetization and the empirically measured response, we facilitate the imposition of maximum smoothness on the unknown magnetization. For our purposes, the smoothest model is the one with the smallest 2-norm of the second derivative, the same criterion used in the construction of cubic spline interpolators. The approach is tested on a marine core that was subsequently sectioned and measured in centimetre-sized individual specimens, with highly satisfactory results. An empirical estimate of the resolution of the method indicates a three-fold improvement in the processed record over the original signal. We illuminate the behaviour of the numerical scheme by showing the relation between our smoothness-maximizing procedure and a more conventional filtering approach. Our solution can indeed be approximated by convolution with a special set of weights, although the approximation may be poor near the ends of the core. In an idealized system we study the question of convergence of the deconvolution process, by whether the model magnetization approaches the true one when the experimental error and other system parameters are held constant, while the spacing between observations is allowed to become arbitrarily small. We find our procedure does in fact converge (under certain conditions) but only at a logarithmic rate. This suggests that further significant improvement in resolution cannot be achieved by increased measurement density or enhanced observational accuracy.

Constable, CG.  1985.  Eastern Australian Geomagnetic-Field Intensity Over the Past 14000 yr. Geophysical Journal of the Royal Astronomical Society. 81:121-130.   10.1111/j.1365-246X.1985.tb01354.x   AbstractWebsite

Two north-eastern Australian volcanic crater lake cores have been used to obtain relative intensity estimates for the geomagnetic field. ARM imparted in a low DC bias field has been used as a normalizing parameter. The intensity fluctuations in the two lakes are in excellent agreement with each other and with south-eastern Australian archaeointensity data over their coeval time spans. This strongly suggests that the same sources are influencing the geomagnetic secular variation throughout eastern Australia at this time. The relative intensity records go back to about 14000yr BP thereby extending currently available recent Australian intensity records by some 7000 yr.

Constable, C.  2007.  Geomagnetic temporal spectrum. Encyclopedia of geomagnetism and paleomagnetism. ( Gubbins D, Herrero-Bervera E, Eds.).:353-355., Dordrecht: Springer Abstract
Constable, C.  2000.  On rates of occurrence of geomagnetic reversals. Physics of the Earth and Planetary Interiors. 118:181-193.   10.1016/s0031-9201(99)00139-9   AbstractWebsite

The magnetostratigraphic time scale provides a record of the occurrence of geomagnetic reversals. The temporal distribution of reversals may be modelled as the realization of an inhomogeneous renewal process; i.e., one in which the intensity, lambda(t), or reversal rate is a function of time. Variations in reversal rate occurring on time scales of tens of millions of years an believed to reflect changes in core-mantle boundary conditions influencing the structure of core flow and the field produced by the geodynamo. We present a new estimate for reversal rate variations as a function of time using nonparametric adaptive kernel density estimation and discuss the difficulties in making inferences on the basis of such estimates. Using a technique proposed by Hengartner and Stark (1992a; b; 1995), it is possible to compute confidence bounds on the temporal probability density function for geomagnetic reversals. The method allows the computation of a lower bound on the number of modes required by the observations, thus enabling a test of whether "bumps" are required features of the reversal rate function. Conservative 95% confidence intervals can then be calculated for the temporal location of a single mode or antimode of the probability density function. Using observations from the time interval 0-158 Ma, it is found that the derivative of the rate function must have changed sign at least once. The timing of this sign change is constrained to be between 152.56 and 22.46 Ma the 95% confidence level. Confidence bounds are computed for the reversal rate under the assumption that the observed reversals are a realization of an inhomogenous Poisson or other renewal process with an arbitrary monotonically increasing rate function from the end of the Cretaceous Normal Superchron (CNS) to the present, a zero rate during the CNS, and a monotonically decreasing rate function from M29R at 158 Ma to the onset of the CNS. It is unnecessary to invoke more than one sign change in the derivative of the rare function to fit the observations. There is no incompatibility between our results and a recent assertion that there is an asymmetry in average reversal rate prior to and after the CNS, when the CNS is assumed to be a period of zero reversal rate. Neither can we use our results to reject an alternative hypothesis that rates are essentially constant from 158 to 130 Ma, and from 25 Ma to the present. with an intermediate nonstationary segment. (C) 2000 Elsevier Science B.V. All rights reserved.

Constable, C.  1990.  A Simple Statistical-Model For Geomagnetic Reversals. Journal of Geophysical Research-Solid Earth and Planets. 95:4587-4596.   10.1029/JB095iB04p04587   AbstractWebsite

The diversity of paleomagnetic records of geomagnetic reversals now available indicate that the field configuration during transitions cannot be adequtely described by simple zonal or standing field models. A new model described here is based on statistical properties inferred from the present field and is capable of simulating field transitions like those observed. Some insight is obtained into what one can hope to learn from paleomagnetic records. In particular, it is crucial that the effects of smoothing in the remanence acquisition process be separated from true geomagnetic field behavior. This might enable us to determine the time constants associated with the dominant field configuration during a reversal.

Cromwell, G, Johnson CL, Tauxe L, Constable CG, Jarboe NA.  2018.  PSV10: A global data set for 0-10 Ma time-averaged field and paleosecular variation studies. Geochemistry Geophysics Geosystems. 19:1533-1558.   10.1002/2017gc007318   AbstractWebsite

Globally distributed paleomagnetic data from discrete volcanic sites have previously been used for statistical studies of paleosecular variation and the structure of the time-averaged field. We present a new data compilation, PSV10, selected from high-quality paleodirections recorded over the past 10 Ma and comprising 2,401 sites from 81 studies. We require the use of modern laboratory and processing methods, a minimum of four samples per site, and within-site Fisher precision parameter, k(w), 50. Studies that identify significant tectonic effects or explicitly target transitional field states are excluded, thereby reducing oversampling of transitional time intervals. Additionally, we apply two approaches using geological evidence to minimize effects of short-term serial correlation. PSV10 is suitable for use in new global geomagnetic and paleomagnetic studies as it has greatly improved spatial coverage of sites, especially at equatorial and high latitudes. VGP dispersion is latitudinally dependent, with substantially higher values in the Southern Hemisphere than at corresponding northern latitudes when no VGP cutoff is imposed. Average inclination anomalies for 10 degrees latitude bins range from about +32 degrees to -7.52 degrees for the entire data set, with the largest negative values occurring at equatorial and mid-northern latitudes. New 0-5 Ma TAF models (LN3 and LN3-SC) based on selections of normal polarity data from PSV10 indicate a Non-zonal variations in field structure are observed near the magnetic equator and in regions of increased radial flux at high latitudes over the Americas, the Indian Ocean, and Asia.

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.

Cromwell, G, Constable CG, Staudigel H, Tauxe L, Gans P.  2013.  Revised and updated paleomagnetic results from Costa Rica. Geochemistry Geophysics Geosystems. 14:3379-3388.   10.1002/ggge.20199   AbstractWebsite

Paleomagnetic results from globally distributed lava flows have been collected and analyzed under the time-averaged field initiative (TAFI), a multi-institutional collaboration started in 1996 and designed to improve the geographic and temporal coverage of the 0-5 Ma paleomagnetic database for studying both the time-averaged field and its very long-term secular variations. Paleomagnetic samples were collected from 35 volcanic units, either lava flows or ignimbrites, in Costa Rica in December 1998 and February 2000 from the Cordilleras Central and Guanacaste, the underlying Canas, Liberia and Bagaces formations and from Volcano Arenal. Age estimates range from approximately 40 ka to slightly over 6 Ma. Although initial results from these sites were used in a global synthesis of TAFI data by Johnson et al. (2008), a full description of methodology was not presented. This paper documents the definitive collection of results comprising 28 paleomagnetic directions (24 normal, 4 reversed), with enhanced precision and new geological interpretations, adding two paleointensity estimates and 19 correlated Ar-40/Ar-39 radiometric ages. The average field direction is consistent with that of a geocentric axial dipole and dispersion of virtual geomagnetic poles (17.34.6 degrees) is in general agreement with predictions from several statistical paleosecular variation models. Paleointensity estimates from two sites give an average field strength of 26.3 T and a virtual axial dipole moment of 65 ZAm(2). The definitive results provide a useful augmentation of the global database for the longer term goal of developing new statistical descriptions of paleomagnetic field behavior.

Cronin, M, Tauxe L, Constable C, Selkin P, Pick T.  2001.  Noise in the quiet zone. Earth and Planetary Science Letters. 190:13-30.   10.1016/s0012-821x(01)00354-5   AbstractWebsite

We have carried out a detailed paleomagnetic investigation of two stratigraphically overlapping sections from the Scaglia Bianca Formation (similar to 85-89.5 Ma) in the Umbria-Marche area in central Italy. Sampling was conducted over 32 in and 7 in intervals at La Roccaccia and Furlo respectively. After AF cleaning the majority of specimens show the expected normal magnetic field orientation, however a number of specimens are directionally anomalous. Some of these deviant specimens are accompanied by apparent spikes or dips in normalized intensity. A detailed investigation of rock magnetics shows that most of these deviations are not a sign of excursionary geomagnetic field behavior, but rather correspond to specimens with distinct rock magnetic characteristics and are therefore rock magnetic 'noise'. Such specimens should not be interpreted as records of the geomagnetic field. Our experience suggests that detailed rock magnetic and magnetic fabric analysis should be done on all anomalous directions prior to interpreting them as geomagnetic field behavior. After elimination of rock magnetic noise in the Scaglia Bianca data sets, there is a high degree of agreement in direction and to a lesser extent relative intensity between correlative portions of the two sections. We therefore offer this data set as a robust record of geomagnetic field behavior during the 4.5 Myr interval represented by the La Roccaccia section. A statistical analysis of the relative intensity observations suggests that this period of the Cretaceous Normal Superchron is characterized by a normalized variability in paleointensity (standard deviation about 28% of the mean value) that is significantly lower than seen during the Oligocene over intervals in which reversals or tiny wiggles occur (typically about 50%). The directional stability results in virtual geomagnetic pole dispersion compatible with that found in volcanic rocks from around the same latitude and ranging in age from 80 to 110 Ma. (C) 2001 Elsevier Science B.V. All rights reserved.