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Shure, L, Parker RL.  1981.  An alternative explanation for intermediate-wavelength magnetic anomalies. Journal of Geophysical Research. 86:1600-1608.   10.1029/JB086iB12p11600   AbstractWebsite

Harrison and Carle [this issue] and others have examined very long profiles of the magnetic field and have calculated one-dimensional power spectra. In these they expect to see, but do not find, a minimum in power at intermediate wavelengths, between 65 and 150 km. Conventional one-dimensional models of the field predict very little power in this band, which lies between the spectral peaks arising from sources in the crust and the core. Mantle sources or high-intensity, long-wavelength magnetizations have been proposed to account for the observations. An alternative, more plausible explanation is that one-dimensional spectra of two-dimensional fields contain contributions from wavenumbers in the perpendicular (i.e., nonsampled) direction. Unless the seafloor spreading anomalies are perfectly lineated at right angles to the profile, some low-wavenumber energy must be attributed to this effect; we propose that such directional aliasing is a major factor in the power spectra. To support this idea, we discuss theoretical models and analyze a large-scale marine survey.

Constable, CG, Tauxe L, Parker RL.  1998.  Analysis of 11 Myr of geomagnetic intensity variation. Journal of Geophysical Research-Solid Earth. 103:17735-17748.   10.1029/98jb01519   AbstractWebsite

We have conducted a detailed exploratory analysis of an II million year long almost continuous record of relative geomagnetic paleointensity from a sediment core acquired on Deep Sea Drilling Project Leg 73, at Site 522 in the South Atlantic. We assess the quality of the paleointensity record using spectral methods and conclude that the relative intensity record is minimally influenced by climate variations. Isothermal remanence is shown to be the most effective normalizer for these data, although both susceptibility and anhysteretic remanence are also adequate. Statistical analysis shows that the paleointensity variations follow a gamma distribution, and are compatible with predictions from modified paleosecular variation models and global absolute paleointensity data. When subdivided by polarity interval, the variability in paleointensity is proportional to the average, and further, the average is weakly correlated with interval length. Spectral estimates for times from 28.77 until 22.74 Ma, when the reversal rate is about 4 Myr(-1), are compatible with a Poisson model in which the spectrum of intensity variations is dominated by the reversal process in the frequency range 1-50 Mgr(-1) In contrast, between 34.7 and 29.4 Ma, when the reversal rate is about 1.6 Myr(-1), the spectra indicate a different secular variation regime. The magnetic field is stronger, and more variable, and a strong peak in the spectrum occurs at about 8 Myr(-1). This peak magi be a reflection of the same signal as recorded by the small variations known as tiny wiggles seen in marine magnetic anomaly profiles.

Parker, RL, Zumberge MA.  1989.  An Analysis of geophysical experiments to test Newton's law of gravity. Nature. 342:29-32.   10.1038/342029a0   AbstractWebsite

Signals reported as evidence for a non-newtonian 'fifth' force at a North Carolina television tower and elsewhere can be explained in a conventional way by postulating small density variations underground. The assumptions employed in earlier analyses which pointed to a failure of the inverse square law are examined and found to be difficult to justify.

Klitgord†, KD, Mudie JD, Huestis SP, Parker RL.  1975.  An analysis of near-bottom magnetic anomalies: Sea-floor spreading and the magnetized layer. Geophysical Journal of the Royal Astronomical Society. 43:387-424.: Blackwell Publishing Ltd   10.1111/j.1365-246X.1975.tb00641.x   AbstractWebsite

Near-bottom magnetic data over six oceanic ridge segments in the East Pacific are inverted, giving magnetization solutions with alternate positive and negative bands which correspond to geomagnetic field reversals. We estimate the average half-width of the crustal formation zone to be 2–3 km, based on the transition widths between these bands. The solutions show a narrow region of high magnetization centred directly over the centre of spreading, superimposed on a more gradual decrease of magnetization amplitudes with age. Both features are attributed to weathering of highly magnetized pillow lavas. We demonstrate that the short wavelength (<3km) anomalies are largely due to topography. Distances to reversal boundaries give distance vs age curves for each ridge which show that spreading changes occur as sudden accelerations typically separated by several million years of very constant motion. These rate changes are probably accompanied by shifts in the locations of poles of relative motion, which are necessary in a system of more than two interacting plates. Palaeomagnetic data and reversal boundary locations from near-bottom and surface data are combined to give spreading half-rates and a refined time scale for the past 6 My. Widespread spreading rate variations occurred at 2–3 MyBP and about 5 MyBP, possibly as a response to large scale changes in the plate pattern.

Parker, RL.  2014.  Anomalous phases in TE-mode magnetotellurics. Geophysics. 79:E75-E79.   10.1190/geo2013-0325.1   AbstractWebsite

We examined the transverse electric mode of 2D magnetotelluric sounding for a simple system comprising a laterally variable thin sheet over an insulator terminated by a perfectly conducting base. We found, by asymptotic analysis and a numerical example, that the phase of the c response, or that of the corresponding entry in the impedance tensor, is completely unrestricted. This behavior is unlike that of 1D systems or transverse magnetic mode induction, where the phase is confined to a single quadrant.

Parker, RL, Shure L, Hildebrand JA.  1987.  The application of inverse theory to seamount magnetism. Reviews of Geophysics. 25:17-40.   10.1029/RG025i001p00017   AbstractWebsite

The traditional least squares method for modeling seamount magnetism is often unsatisfactory because the models fail to reproduce the observations accurately. We describe an alternative approach permitting a more complex internal structure, guaranteed to generate an external field in close agreement with the observed anomaly. Potential field inverse problems like this one are fundamentally incapable of a unique solution, and some criterion is mandatory for picking a plausible representative from the infinite-dimensional space of models all satisfying the data. Most of the candidates are unacceptable geologically because they contain huge magnetic intensities or rapid variations of magnetization on fine scales. To avoid such undesirable attributes, we construct the simplest type of model: the one closest to a uniform solution as measured by the norm in a specially chosen Hilbert space of magnetization functions found by a procedure called seminorm minimization. Because our solution is the most nearly uniform one we can say with certainty that any other magnetization satisfying the data must be at least as complex as ours. The theory accounts for the complicated shape of seamounts, representing the body by a covering of triangular facets. We show that the special choice of Hilbert space allows the necessary volume integrals to be reduced to surface integrals over the seamount surface, and we present numerical techniques for their evaluation. Exact agreement with the magnetic data cannot be expected because of the error of approximating the shape and because the measured fields contain noise of crustal, ionospheric, and magnetospheric origin. We examine the potential size of the various error terms and find that those caused by approximation of the shape are generally much smaller than the rest. The mean magnetization is a vector that can in principle be discovered from exact knowledge of the external field of the seamount; this vector is of primary importance for paleomagnetic work. We study the question of how large the uncertainty in the mean vector may be, based on actual noise, as opposed to exact, data; the uncertainty can be limited only by further assumptions about the internal magnetization. We choose to bound the rms intensity. In an application to a young seamount in the Louisville Ridge chain we find that remarkably little nonuniformity is required to obtain excellent agreement with the observed anomaly while the uniform magnetization gives a poor fit. The paleopole position of ordinary least squares solution lies over 30° away from the geographic north, but the pole derived from our seminorm minimizing model is very near the north pole as it should be. A calculation of the sensitivity of the mean magnetization vector to the location of the magnetic observations shows that the data on the perimeter of the survey were given the greatest weight and suggests that enlargement of the survey area might further improve the reliability of the results.

McMillan, DG, Constable CG, Parker RL.  2004.  Assessing the dipolar signal in stacked paleointensity records using a statistical error model and geodynamo simulations. Physics of the Earth and Planetary Interiors. 145:37-54.   10.1016/j.pepi.2004.02.011   AbstractWebsite

Stacks of globally distributed relative paleointensity records from sediment cores are used to study temporal variations in the strength of the geomagnetic dipole. We assess the intrinsic accuracy and resolution of such stacks, which may be limited by errors in paleointensity, non-dipole field contributions, and the age scales assigned to each sediment core. Our approach employs two types of simulations. Numerical geodynamo models generate accurate predictions of time series of magnetic variations anywhere in the world. The predicted variations are then degraded using an appropriate statistical model to simulate expected age and paleointensity errors. A series of experiments identify the major contributors to error and loss of resolution in the resulting stacks. The statistical model simulates rock magnetic and measurement errors in paleointensity, and age errors due to finite sampling and approximations inherent in interpolation, incomplete or inaccurate tie point information, and sedimentation rate variations. Data sampling and interpolation to a designated age scale cause substantial decorrelation, and control the maximum level of agreement attainable between completely accurate records. The particular method of interpolation appears to have little effect on the coherence between accurate records, but denser tie point data improve the agreement. Age errors decorrelate geomagnetic signals, usually at shorter periods, although they can destroy coherence over a broad range of periods. The poor correlation between neighboring paleomagnetic records often observed in real data can be accounted for by age errors of moderate magnitude. In a global dataset of 20 records, modeled after the SINT800 compilation and spanning 300 kyr, our results show that dipole variations with periods longer than about 20 kyr can be recovered by the stacking process. Reasonable contributions to error in the paleointensity itself have a modest influence on the result, as do non-dipole field contributions whose effect is minor at periods longer than 10 kyr. Modest errors in the ages of tie points probably account for most of the degradation in geomagnetic signal. Stacked sedimentary paleomagnetic records can be improved by denser temporal sampling and careful selection of independent high-quality tie points. (C) 2004 Elsevier B.V. All rights reserved.

Parker, RL, Song YQ.  2005.  Assigning uncertainties in the inversion of NMR relaxation data. Journal of Magnetic Resonance. 174:314-324.   10.1016/j.jmr.2005.03.002   AbstractWebsite

Recovering the relaxation-time density function (or distribution) from NMR decay records requires inverting a Laplace transform based on noisy data, an ill-posed inverse problem. An important objective in the face of the consequent ambiguity in the solutions is to establish what reliable information is contained in the measurements. To this end we describe how upper and lower bounds on linear functionals of the density function, and ratios of linear functionals, can be calculated using optimization theory. Those bounded quantities cover most of those commonly used in the geophysical NMR, such as porosity, T-2 log-mean, and bound fluid volume fraction, and include averages over any finite interval of the density function itself. In the theory presented statistical considerations enter to account for the presence of significant noise in the signal, but not in a prior characterization of density models. Our characterization of the uncertainties is conservative and informative; it will have wide application in geophysical NMR and elsewhere. © 2005 Elsevier Inc. All rights reserved.