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Ander, ME, Zumberge MA, Lautzenhiser T, Parker RL, Aiken CLV, Gorman MR, Nieto MM, Cooper APR, Ferguson JF, Fisher E, McMechan GA, Sasagawa G, Stevenson JM, Backus G, Chave AD, Greer J, Hammer P, Hansen BL, Hildebrand JA, Kelty JR, Sidles C, Wirtz J.  1989.  Test of Newton's inverse-square law in the Greenland Ice Cap. Physical Review Letters. 62:985-988.   10.1103/PhysRevLett.62.985   AbstractWebsite

An Airy-type geophysical experiment was conducted in a 2-km-deep hole in the Greenland ice cap at depths between 213 and 1673 m to test for possible violations of Newton’s inverse-square law. An anomalous gravity gradient was observed. We cannot unambiguously attribute it to a breakdown of Newtonian gravity because we have shown that it might be due to unexpected geological features in the rock below the ice.

Chapman, DC, Parker RL.  1981.  A theoretical analysis of the diffusion porometer: Steady diffusion through two finite cylinders of different radii. Agricultural Meteorology. 23:9-20.   10.1016/0002-1571(81)90088-1   AbstractWebsite

Calibration and use of the diffusion porometer are imprecise because of imperfect understanding of steady diffusion through a porous material. The case of a flat plate with uniformly distributed right circular cylindrical holes is approximated by diffusion through two finite right circular cylinders: one representing the pore, and one representing the area into which vapor diffuses — its size determined by the mutual interference with neighboring pores. An exact three-dimensional solution is presented. It is found that for large pore spacing the empirical result of Holcomb and Cooke is excellent, but for close pore spacing some error occurs. A method for calculation of true calibration plate resistance is described as well as a method for estimating pore size for an unknown plate or membrane.

Parker, RL.  1975.  The theory of ideal bodies for gravity interpretation. Geophysical Journal of the Royal Astronomical Society. 42:315-334..: Blackwell Publishing Ltd   10.1111/j.1365-246X.1975.tb05864.x   AbstractWebsite

Ambiguity in gravity interpretation is inevitable because of the fundamental incompleteness of real observations; it is, however, possible to provide rigorous limits on possible solutions even with incomplete data. In this paper a systematic theory is developed for finding such bounds, including an upper bound on depth of burial; the bounds are discovered by constructing the unique body achieving the extreme parameter, e.g. depth; such a body is called the 'ideal' one associated with the given data. Ideal bodies can also be constructed for bounding density, thickness of layer and lateral extent. General properties of ideal bodies are derived and numerical methods for modest numbers of observations are discussed. Some artificial examples, where the buried system is exactly known, are given and it is shown how relatively good bounds can be reached with only a few measurements. A Bouguer anomaly from the Swiss Alps is then considered and it is concluded that the mountain roots are unusually shallow there.

Parker, RL.  1991.  A theory of ideal bodies for seamount magnetism. Journal of Geophysical Research-Solid Earth. 96:16101-16112.   10.1029/91jb01497   AbstractWebsite

Recent studies of samples from seamounts indicate that the distribution of magnetic intensity is approximately lognormal, which implies that the commonly adopted models of interior magnetization based upon a constant vector with an isotropic perturbation are inappropriate. We develop a unidirectional model in which the direction of magnetization is fixed and the intensity is of one sign, with no upper limit on magnitude, which, if the seamount is built during a period of single magnetic polarity, is likely to be a better approximation. We show that models of this class fitting the data best in the two-norm sense conform to the ideal-body pattern comprising unidirectional, point dipoles in the surface of the seamount. Practical methods are developed for discovering the best data misfit associated with paleopole position. The methods are first tested on simple artificial magnetic anomalies and are found to be capable of recovering the true pole position with high accuracy when such a solution is possible; also when a mixed polarity artificial model is analyzed, it is found that there are no unidirectional solutions, just as would be hoped. The method is next applied to three seamount surveys. In the first it is found that every direction of magnetization is in accord with the data, so that apparently nothing useful can be learned from the survey without a stronger assumption; this result is in contrast with the results of an earlier solution based upon a statistical model, which yielded a high accuracy in the position of the paleopole. The second investigation provides a reasonably compact location of the paleopole of the seamount. The third magnetic anomaly is complex and earlier studies concluded this was necessarily the product of mixed polarity magnetization. We find that in fact unidirectional magnetizations can satisfy observation.

Parker, RL, Oldenburg DW.  1973.  Thermal model of ocean ridges. Nature Physical Science. 242:137-139.   10.1038/physci242137a0   AbstractWebsite

McKenzie's model of crustal creation at the ocean ridges1,2 and its derivatives3,4 predicts such features as the topography and high heat flow of the ridges. In spite of this success there are some unsatisfactory aspects of the model; for example, the arbitrary temperature distribution in the intrusive zone gives rise to infinite heat generation and the lithospheric thickness is a free parameter not determined by the physics. We offer here a simple refinement of McKenzie's model that overcomes these difficulties. The essential difference stems from the inclusion of terms in the boundary conditions to account for the evolution of latent heat in places where the plate is growing. We first describe the physical basis of the model.

Garmany, J, Orcutt JA, Parker RL.  1979.  Travel time inversion: A geometrical approach. Journal of Geophysical Research. 84:3615-3622.   10.1029/JB084iB07p03615   AbstractWebsite

A geometric formulation of the seismic travel time problem is given based upon the use of slowness as an independent variable. Many of the difficulties in the conventional treatment (e.g., singular kernels) are thereby, avoided. Furthermore, it is shown that the inverse problem possesses an inherently linear formulation. In this formalism we are able to provide extremal solutions giving upper and lower depth bounds using linear programing. This approach has been compared with two well-known nonlinear extremal inversions. We find our technique to be easier to implement and find that it often generates superior results.

Malinverno, A, Parker RL.  2006.  Two ways to quantify uncertainty in geophysical inverse problems. Geophysics. 71:W15-W27.   10.1190/1.2194516   AbstractWebsite

We present two approaches to invert geophysical measurements and estimate subsurface properties and their uncertainties when little is known a priori about the size of the errors associated with the data. We illustrate these approaches by inverting first-arrival traveltimes of seismic waves measured in a vertical well to infer the variation of compressional slowness in depth. First, we describe a Baye-Sian formulation based on probability distributions that define prior knowledge about the slowness and the data errors. We use an empirical Bayes approach, where hyperparameters are not well known ahead of time (e.g., the variance of the data errors) and are estimated from their most probable value. given the data. The second approach is a non-Bayesian formulation that we call spectral, in the sense that it uses the power spectral density of the traveltime data to constrain the inversion (e.g., to estimate the variance of the data errors). In the spectral approach, we vary assumptions made about the characteristics of the slowness signal and evaluate the resulting slowness estimates and their uncertainties. This approach is computationally simple and starts from a few assumptions. These assumptions can be checked during the analysis. On the other hand, it requires evenly spaced traveltime measurements, and it cannot be extended easily (e.g., to data that have gaps). In contrast, the Bayesian framework is based on a general theory that can be generalized immediately, but it is more involved computationally. Despite the conceptual and practical differences, we find that the two approaches give the same results when they start from the same assumptions: The allegiance to a Bayesian or non-Bayesian formulation matters less than what one is willing to assume when solving the inverse problem.