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Parker, RL, Shure L.  1982.  Efficient modeling of the Earth's magnetic field with harmonic splines. Geophysical Research Letters. 9:812-815.   10.1029/GL009i008p00812   AbstractWebsite

The construction of smooth potential field models has many geophysical applications. The recently-developed method of harmonic splines produces magnetic field models at the core surface which are maximally smooth in the sense of minimization of certain special norms. They do not exhibit the highly oscillatory fields produced by models derived from a least-squares analysis with a truncated spherical harmonic series. Modeling the data by harmonic splines requires solving a square system of equations with dimension equal to the number of data. Too many data have been collected since the 1960s for this method to be practical. We produce almost optimally smooth models by the following method. Since each spline function for the optimal model corresponds to an observation location (called a knot), we select a subset of these splines with knots well-distributed around the Earth’s surface. In this depleted basis we then find the smoothest model subject to an appropriate fit to all of the data. This reduces the computational problem to one comparable to least-squares analysis while nearly preserving the optimality inherent in the original harmonic spline models.

Parker, RL.  1967.  Electromagnetic induction in a thin strip. Geophysical Journal of the Royal Astronomical Society. 14:487-495.: Blackwell Publishing Ltd   10.1111/j.1365-246X.1967.tb06268.x   AbstractWebsite

Electromagnetic induction in a thin strip is investigated to provide further understanding of the geomagnetic effects at an ocean edge. A solution to the equations is found by an analytic technique. It is shown that even in the case where the integrated conductivity is finite, infinite field strengths occur at the edges accompanied by rapid changes in phase.

Bullard, EC, Parker RL.  1970.  Electromagnetic induction in a thin strip. The sea Pt. 1, Vol. 4, New concepts of sea floor evolution. Regional observations concepts. :695-730., New York: Interscience Publ. Abstract
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Lowe, DAJ, Parker RL, Purucker ME, Constable CG.  2001.  Estimating the crustal power spectrum from vector Magsat data. Journal of Geophysical Research-Solid Earth. 106:8589-8598.   10.1029/2000jb900437   AbstractWebsite

The Earth's magnetic field can be subdivided into core and crustal components and we seek to characterize the crustal part through its spatial power spectrum, R-1. We process vector Magsat data to isolate the crustal field and then invert power spectral densities of flight-local components along-track for R-1 following O'Brien et al. [1999]. Our model, designated LPPC, is accurate up to approximately spherical harmonic degree 45 (lambda = 900 km): this is the resolution limit of our data and suggests that global crustal anomaly maps constructed from vector Magsat data should not contain features with wavelengths less than 900 km. We find continental power spectra to be greater than oceanic ones and attribute this to the relative thicknesses of continental and oceanic crust.

Parker, RL.  1982.  The existence of a region inaccessible to magnetotelluric sounding. Geophysical Journal of the Royal Astronomical Society. 68:165-170.: Blackwell Publishing Ltd   10.1111/j.1365-246X.1982.tb06967.x   AbstractWebsite

Summary. The exponential attenuation of fluctuating electromagnetic fields suggests that practical magneto telluric measurements may be uninformative about the electrical conductivity at sufficiently great depths. This notion can be made precise for one-dimensional systems. Below a critical depth the conductivity function may be chosen freely without affecting the consistency of the model with the data. This depth is readily computable with quadratic or linear programming techniques and does not rely upon linearization of the equations.