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Parker, RL.  1973.  The rapid calculation of potential anomalies. Geophysical Journal of the Royal Astronomical Society. 31:447-455.   10.1111/j.1365-246X.1973.tb06513.x   AbstractWebsite

It is shown how a series of Fourier transforms can be used to calculate the magnetic or gravitational anomaly caused by an uneven, non-uniform layer of material. Modern methods for finding Fourier transforms numerically are very fast and make this approach attractive in situations where large quantities of observations are available.

Parker, RL.  1966.  Reconnexion of lines of force in rotating spheres and cylinders. Proceedings of the Royal Society of London Series a-Mathematical and Physical Sciences. 291:60-72.   10.1098/rspa.1966.0078   AbstractWebsite

A solid conducting sphere or cylinder begins to rotate suddenly from rest in an initially uniform magnetic field. An analytic solution for this problem is obtained and it is shown that lines of magnetic force reconnect to form closed loops during the transient phase. The general behaviour of the system is investigated for all conductivities. Numerical examples are given and approximate expressions derived in the limiting cases of large conductivity and time.

Prieto, GA, Parker RL, Thomson DJ, Vernon FL, Graham RL.  2007.  Reducing the bias of multitaper spectrum estimates. Geophysical Journal International. 171:1269-1281.   10.1111/j.1365-246X.2007.03592.x   AbstractWebsite

The power spectral density of geophysical signals provides information about the processes that generated them. We present a new approach to determine power spectra based on Thomson's multitaper analysis method. Our method reduces the bias due to the curvature of the spectrum close to the frequency of interest. Even while maintaining the same resolution bandwidth, bias is reduced in areas where the power spectrum is significantly quadratic. No additional sidelobe leakage is introduced. In addition, our methodology reliably estimates the derivatives (slope and curvature) of the spectrum. The extra information gleaned from the signal is useful for parameter estimation or to compare different signals.

O'Brien, MS, Parker RL.  1993.  Regularized geomagnetic field modelling using monopoles. Geophysical Journal International. 118:566-578.   10.1111/j.1365-246X.1994.tb03985.x   AbstractWebsite

There are many techniques for modelling the geomagnetic field, any one of which may be suitable for a particular application depending on its associated modelling goals. Each method combines a choice of functions and an approach to fitting data so that, in general, it is best suited to a particular type of field modelling, e.g. core versus crustal, regional versus global, downward continuation versus interpolation. Those few approaches such as spherical cap harmonic analysis (Haines 1985a) that possess any true flexibility in this respect suffer from mathematical and computational complexity. In addition, regularization is still a somewhat overlooked issue. Regularization is essential for downward continuing geomagnetic data because shorter wavelength field components and their errors blow up in this process. Approaches such as harmonic spline modelling (Shure, Parker and Backus 1982) which include regularization do so while significantly complicating the task of inversion. We present a new regularized modelling scheme which employs magnetic monopoles as representing functions. We apply regularizing norms of the type introduced by Shure et al. (1982). Owing to the mathematical simplicity of the monopoles, the expressions for the norms are themselves very simple and flexible, and the monopole models very easy to compute. Moreover, the conceptual simplicity of this representation allows for easy modification to accommodate most geomagnetic modelling problems. We apply the technique to problems on three different length scales, each application having distinctly different modelling goals: globally we model the radial core field at the core-mantle boundary (CMB) from satellite data; on a large regional scale we model the radial crustal field at the earth's surface from satellite data; on a small regional scale we model the radial crustal field at the earth's surface from surface data. For each of these varied applications we are able to generate monopole models which produce smooth, plausible fields that fit the data.

Zumberge, MA, Berger J, Dzieciuch MA, Parker RL.  2004.  Resolving quadrature fringes in real time. Applied Optics. 43:771-775.   10.1364/ao.43.000771   AbstractWebsite

In many interferometers, two fringe signals can be generated in quadrature. The relative phase of the two fringe signals depends on whether the optical path length is increasing or decreasing. A system is developed in which two quadrature fringe signals are digitized and analyzed in real time with a digital signal processor to yield a linear, high-resolution, wide-dynamic-range displacement transducer. The resolution in a simple Michelson interferometer with inexpensive components is 5 X 10(-13) m Hz(-1/2) at 2 Hz. (C) 2004 Optical Society of America.

Korte, M, Constable CG, Parker RL.  2002.  Revised magnetic power spectrum of the oceanic crust. Journal of Geophysical Research-Solid Earth. 107   10.1029/2001jb001389   AbstractWebsite

[1] The magnetic field originating within the Earth can be divided into core and crustal components, which can be characterized by the geomagnetic power spectrum. While the core spectrum is determined quite well by satellite studies, models of the shorter wavelength crustal spectrum disagree considerably. We reexamine aeromagnetic data used by O'Brien et al. [1999] to obtain a new, improved estimate of the crustal geomagnetic power spectrum. O'Brien et al. 's model somewhat failed to give a satisfactory connection between the longer-wavelength satellite studies and a reliable crustal model. We show that this was caused by an inadequate processing step that aimed to remove external variations from the data. We moreover attempt to bound the long-wavelength part of the spectrum using constraints of monotonicity in the correlation of the magnetization. However, this proves to be a weak constraint. Reversing the process, though, we are able to evaluate the correlation function using the reliable part of our geomagnetic spectrum. Thus we can obtain a sensible estimate for the long-wavelength part of the spectrum that is not well constrained by the data. Our new model shows better agreement with earlier satellite studies and can be considered reliable in the spherical harmonic degree range l = 30 to 1200.