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2017
Avery, MS, Gee JS, Constable CG.  2017.  Asymmetry in growth and decay of the geomagnetic dipole revealed in seafloor magnetization. Earth and Planetary Science Letters. 467:79-88.   10.1016/j.epsl.2017.03.020   AbstractWebsite

Geomagnetic intensity fluctuations provide important constraints on time-scales associated with dynamical processes in the outer core. PADM2M is a reconstructed time series of the 0-2 Ma axial dipole moment (ADM). After smoothing to reject high frequency variations PADM2M's average growth rate is larger than its decay rate. The observed asymmetry in rates of change is compatible with longer term diffusive decay of the ADM balanced by advective growth on shorter time scales, and provides a potentially useful diagnostic for evaluating numerical geodynamo simulations. We re-analyze the PADM2M record using improved low-pass filtering to identify asymmetry and quantify its uncertainty via bootstrap methods before applying the new methodology to other kinds of records. Asymmetry in distribution of axial dipole moment derivatives is quantified using the geomagnetic skewness coefficient, sg. A positive value indicates the distribution has a longer positive tail and the average growth rate is greater than the average decay rate. The original asymmetry noted by Ziegler and Constable (2011) is significant and does not depend on the specifics of the analysis. A long-term record of geomagnetic intensity should also be preserved in the thermoremanent magnetization of oceanic crust recovered by inversion of stacked profiles of marine magnetic anomalies. These provide an independent means of verifying the asymmetry seen in PADM2M. We examine three near bottom surveys: a 0 to 780 ka record from the East Pacific Rise at 19 degrees S, a 0 to 5.2 Ma record from the Pacific Antarctic Ridge at 51 degrees S, and a chron C4Ar-C5r (9.3-11.2 Ma) record from the NE Pacific. All three records show an asymmetry similar in sense to PADM2M with geomagnetic skewness coefficients, s(g) > 0. Results from PADM2M and C4Ar-C5r are most robust, reflecting the higher quality of these geomagnetic records. Our results confirm that marine magnetic anomalies can carry a record of the asymmetric geomagnetic field behavior first found for 0-2 Ma in PADM2M, and show that it was also present during the earlier time interval from 9.3-11.2 Ma. (C) 2017 The Authors. Published by Elsevier B.V.

Panovska, S, Constable CG.  2017.  An activity index for geomagnetic paleosecular variation, excursions, and reversals. Geochemistry Geophysics Geosystems. 18:1366-1375.   10.1002/2016gc006668   AbstractWebsite

Magnetic indices provide quantitative measures of space weather phenomena that are widely used by researchers in geomagnetism. We introduce an index focused on the internally generated field that can be used to evaluate long term variations or climatology of modern and paleomagnetic secular variation, including geomagnetic excursions, polarity reversals, and changes in reversal rate. The paleosecular variation index, P-i, represents instantaneous or average deviation from a geocentric axial dipole field using normalized ratios of virtual geomagnetic pole colatitude and virtual dipole moment. The activity level of the index, sigma P-i, provides a measure of field stability through the temporal standard deviation of P-i. P-i can be calculated on a global grid from geomagnetic field models to reveal large scale geographic variations in field structure. It can be determined for individual time series, or averaged at local, regional, and global scales to detect long term changes in geomagnetic activity, identify excursions, and transitional field behavior. For recent field models, P-i ranges from less than 0.05 to 0.30. Conventional definitions for geomagnetic excursions are characterized by P-i exceeding 0.5. Strong field intensities are associated with low P-i unless they are accompanied by large deviations from axial dipole field directions. sigma P-i provides a measure of geomagnetic stability that is modulated by the level of PSV or frequency of excursional activity and reversal rate. We demonstrate uses of P-i for paleomagnetic observations and field models and show how it could be used to assess whether numerical simulations of the geodynamo exhibit Earth-like properties.

2011
Ziegler, LB, Constable CG.  2011.  Asymmetry in growth and decay of the geomagnetic dipole. Earth and Planetary Science Letters. 312:300-304.   10.1016/j.epsl.2011.10.019   AbstractWebsite

The geodynamo in Earth's core is responsible for magnetic field changes on diverse timescales, including numerous enigmatic reversals of the dipole field polarity. Understanding the physical processes driving them is an active area of investigation via both paleomagnetic work and numerical simulations of the geodynamo. Some previous studies on geomagnetic field intensity detected a sawtooth pattern of intensity around reversals: a gradual decay in field strength preceding a reversal followed by rapid growth afterwards. Here we characterize distinct statistical properties for increasing and decreasing dipole strength over the past two million years. Examining the geomagnetic field and its time derivative on a range of time scales reveals that for periods longer than about 25 ky there is a clear asymmetry in the statistical distributions for growth versus decay rates of the dipole strength. At 36 ky period, average growth rate is about 20% larger than the decay rate, and the field spends 54% of its time decaying, but only 46% growing. These differences are not limited to times when the field is reversing, suggesting that the asymmetry is controlled by fundamental physical processes underlying all paleosecular variation. The longer decay cycle might suggest the possibility of episodic periods of subcritical dynamo activity where the field is dominated by diffusive processes, followed by transient episodes of strong growth of the axial dipole. However, our work finds no clear separation of timescales for the influence of diffusive and convective processes on dipole moment: both seem to play an important but asymmetric role on the 25-150 ky timescale. (C) 2011 Elsevier B.V. All rights reserved.

2008
Ziegler, LB, Constable CG, Johnson CL.  2008.  Testing the robustness and limitations of 0-1 Ma absolute paleointensity data. Physics of the Earth and Planetary Interiors. 170:34-45.   10.1016/j.pepi.2008.07.027   AbstractWebsite

Absolute paleomagnetic field intensity data derived from thermally magnetized lavas and archeological objects provide information about past geomagnetic field behavior, but the average field strength, its variability, and the expected statistical distribution of these observations remain uncertain despite growing data sets. We investigate these issues for the 0-1 Ma field using data compiled in Perrin and Schnepp [Perrin, M., Schnepp, E., 2004. IAGA paleointensity database: distribution and quality of the data set. Phys. Earth Planet. Int. 147, 255-267], 1124 samples of heterogeneous quality and with restricted temporal and spatial coverage. We accommodate variable spatial sampling by using virtual axial dipole moments (VADM) in our analyses. Uneven temporal sampling results in biased estimates for the mean field and its statistical distribution. We correct for these effects using a bootstrap technique, and find an average VADM of 7.26 +/- 0.14 x 10(22) A m(2). The associated statistical distribution appears bimodal with a subsidiary peak at approximately 5 x 10(22) A m(2). We evaluate a range of potential sources for this behavior. We find no visible evidence for contamination by poor quality data when considering author-supplied uncertainties in the 0-1 Ma data set. The influence of material type is assessed using independent data compilations to compare Holocene data from lava flows, submarine basaltic glass (SBG), and archeological objects. The comparison to SBG is inconclusive because of dating issues, but paleointensity estimates from lavas are on average about 10% higher than for archeological materials and show greater dispersion. Only limited tests of geographic sampling bias are possible. We compare the large number of 0-0.55 Ma Hawaiian data to the global data set with no definitive results. The possibility of over-representation of typically low intensity excursional data is discounted because exclusion of transitional data still leaves a bimodal distribution. No direct test has allowed us to rule out the idea that the observed pdf results from a mixture of two distinct distributions corresponding to two identifiable intensity states for the magnetic field. We investigate an alternative possibility that we were simply unable to recover a hypothetically smoother underlying distribution with a time span of only 1 Myr and the resolution of the current data set. Simulations from a stochastic model based on the geomagnetic field spectrum demonstrate that long period intensity variations can have a strong impact on the observed distributions and could plausibly explain the apparent bimodality. Our 0-1 Ma distribution of VADMs is consistent with that obtained for average relative paleointensity records derived from sediments. (C) 2008 Elsevier B.V. All rights reserved.

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.

Korte, M, Constable CG.  2005.  Continuous geomagnetic field models for the past 7 millennia: 2. CALS7K. Geochemistry Geophysics Geosystems. 6   10.1029/2004gc000801   AbstractWebsite

We present two continuous global geomagnetic field models for recent millennia: CALS3K.2, covering the past 3000 years, and CALS7K.2, covering 7000 years from 5000 BC to 1950 AD. The models were determined by regularized least squares inversion of archeomagnetic and paleomagnetic data using spherical harmonics in space and cubic B splines in time. They are derived from a greatly increased number of paleomagnetic directional data, compared to previous efforts, and for the first time a significant amount of archeointensity data is used in this kind of global model, allowing the determination of evolution of geomagnetic dipole strength. While data accuracy and dating uncertainties remain a limitation, reliable low-resolution global models can be obtained. The results agree well with previous results from virtual axial dipole moment (VADM) studies from archeomagnetic intensity data apart from a systematic offset in strength. A comparison of model predictions with the previous 3000 year model, CALS3K.1, gives general agreement but also some significant differences particularly for the early epochs. The new models suggest that the prominent two northern hemisphere flux lobes are more stationary than CALS3K.1 implied, extending considerably the time span of stationary flux lobes observed in historical models. Between 5000 BC and 2000 BC there are time intervals of weak dipole moment where dipole power is exceeded by low-degree nondipole power at the core-mantle boundary.

2002
McMillan, DG, Constable CG, Parker RL.  2002.  Limitations on stratigraphic analyses due to incomplete age control and their relevance to sedimentary paleomagnetism. Earth and Planetary Science Letters. 201:509-523.   10.1016/s0012-821x(02)00747-1   AbstractWebsite

A major limitation in the analysis of physical quantities measured from a stratigraphic core is incomplete knowledge of the depth to age relationship for the core. Records derived from diverse locations are often compared or combined to construct records that represent a global signal. Time series analysis of individual or combined records is commonly employed to seek quasi-periodic components or characterize the timescales of relevant physical processes. Assumptions that are frequently made in the approximation of depth to age relationships can have a dramatic and harmful effect on the spectral content of records from stratigraphic cores. A common procedure for estimating ages in a set of samples from a stratigraphic core is to assign, based on complementary data, the ages at a number of depths (tie points) and then assume a uniform accumulation rate between the tie points. Imprecisely dated or misidentified tie points and naturally varying accumulation rates give rise to discrepancies between the inferred and the actual ages of a sample. We develop a statistical model for age uncertainties in stratigraphic cores that treats the true, but in practice unknown, ages of core samples as random variables. For inaccuracies in the ages of tie points, we draw the error from a zero-mean normal distribution. For a variable accumulation rate, we require the actual ages of a sequence of samples to be monotonically increasing and the age errors to have the form of a Brownian bridge. That is, the errors are zero at the tie points. The actual ages are modeled by integrating a piecewise constant, randomly varying accumulation rate. In each case, our analysis yields closed form expressions for the expected value and variance of resulting errors in age at any depth in the core. By Monte Carlo simulation with plausible parameters, we find that age errors across a paleomagnetic record due to misdated tie points are likely of the same order as the tie point discrepancies. Those due to accumulation rate variations can be as large as 30 kyr, but are probably less than 10 kyr. We provide a method by which error estimates like these can be made for similar stratigraphic dating problems and apply our statistical model to an idealized marine sedimentary paleomagnetic record. Both types of errors severely degrade the spectral content of the inferred record. We quantify these effects using realistic tie point ages, their uncertainties and depositional parameters. (C) 2002 Elsevier Science B.V. All rights reserved.

1999
Constable, CG, Johnson CL.  1999.  Anisotropic paleosecular variation models: implications for geomagnetic field observables. Physics of the Earth and Planetary Interiors. 115:35-51.   10.1016/s0031-9201(99)00065-5   AbstractWebsite

We present a family of statistical models for paleosecular variation (PSV) of the geomagnetic field that are compatible with paleodirectional and paleointensity variations in lava flows sampling the last 5 Ma, and explore what paleomagnetic observables might be used to discriminate among the various family members. We distinguish statistical models with axial anisotropy, which provide a suitable description for an earth with homogeneous boundary conditions at the core-mantle interface from those with more general anisotropy corresponding to geographically heterogeneous boundary conditions. The models revise and extend earlier ones, which are themselves descendants of CP88, devised by Constable and Parker [Constable, C.G., Parker, R.L., 1988. Statistics of the geomagnetic secular variation for the past 5 m.y. J. Geophys, Res. 93, 11569-11581]. In CP88, secular variation is described by statistical variability of each Gauss coefficient in a spherical harmonic description of the geomagnetic field, with each coefficient treated as a normally distributed random variable: the Gauss coefficients of the non-dipole part of the field exhibit isotropic variability, and the variances are derived from the present field spatial power spectrum. The dipole terms have a special status in CP88, with a non-zero mean for the axial-dipole, and lower variance than predicted from the spatial power spectrum. All non-dipole terms have zero mean except the axial-quadrupole. CP88 is untenable for two reasons: it fails to predict the observed geographic dependence of directional variability in the magnetic field, and it grossly underpredicts the variance in paleointensity data. The new models incorporate large variance in the axial-dipole, and in the non-axial-quadrupole Gauss coefficients, g1/2: and h1/2:. The resulting variance in paleomagnetic observables depends only on latitude (zonal models), unless the variance in h1/2: is different from that in g1/2 (non-zonal models). Non-zonal (longitudinal) variations in PSV, such as the flux lobes seen in the historical magnetic field, are simulated using the non-zonal models. Both the zonal and non-zonal models fit summary statistics of the present dataset. We investigate the influence of persistent non-zonal influences in PSV on various paleomagnetic observables. It is shown that virtual geomagnetic pole (VGP) dispersion is rather insensitive to longitudinal variations in structure of PSV, and that inclination dispersion has the potential to be more informative given the right site distribution. There is also the possibility of using paleointensity and geographic variations in the frequency of occurrence of excursional directions to identify appropriate PSV models. (C) 1999 Elsevier Science B.V. All rights reserved.