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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.

Ander, ME, Zumberge MA, Lautzenhiser T, Parker RL, Aiken CLV, Gorman MR, Nieto MM, Ferguson JF, McMechan GA.  1989.  A new field experiment in the Greenland Ice Cap to test Newton's inverse square law. Annals of the New York Academy of Sciences. 571:672-680.   10.1111/j.1749-6632.1989.tb50553.x   AbstractWebsite

Recent experimental evidence suggests that Newton’s law of gravity may not be precise. There are modern theories of quantum gravity that, in their attempts to unify gravity with other forces of nature, predict non-Newtonian gravitational forces that could have ranges on the order of 102-105 m. If they exist, these forces would be apparent as violations of Newton’s inverse square law. A geophysical experiment was carried out to search for possible finite-range, non-Newtonian gravity over depths of 213-1673 m in the glacial ice of the Greenland ice cap. The principal reason for this choice of experimental site is that a hole drilled through the ice cap already existed and the uniformity of the ice eliminates one of the major sources of uncertainty arising in the first of earlier namely, the heterogeneity of the rocks through which a mine shaft or drill hole passes. Our observations were made in the summer of 1987 at Dye 3, Greenland, in the 2033-m-deep borehole, which reached the basement rock.

Backus, G, Parker RL, Constable C.  1996.  Foundations of Geomagnetism. :xiv,369p.., Cambridge England ; New York: Cambridge University Press AbstractWebsite

The main magnetic field of the Earth is a complex phenomenon. To understand its origins in the fluid of the Earth's core, and how it changes in time requires a variety of mathematical and physical tools. This book presents the foundations of geomagnetism, in detail and developed from first principles. The book is based on George Backus' courses for graduate students at the University of California, San Diego. The material is mathematically rigorous, but is logically developed and has consistent notation, making it accessible to a broad range of readers. The book starts with an overview of the phenomena of interest in geomagnetism, and then goes on to deal with the phenomena in detail, building the necessary techniques in a thorough and consistent manner. Students and researchers will find this book to be an invaluable resource in the appreciation of the mathematical and physical foundations of geomagnetism.

Banks, RJ, Parker RL, Huestis SP.  1977.  Isostatic compensation on a continental scale: local versus regional mechanisms. Geophysical Journal of the Royal Astronomical Society. 51:431-452.: Blackwell Publishing Ltd   10.1111/j.1365-246X.1977.tb06927.x   AbstractWebsite

Summary. Using the techniques of linear and quadratic programming, it can be shown that the isostatic response function for the continental United States, computed by Lewis & Dorman (1970), is incompatible with any local compensation model that involves only negative density contrasts beneath topographic loads. We interpret the need for positive densities as indicating that compensation is regional rather than local. The regional compensation model that we investigate treats the outer shell of the Earth as a thin elastic plate, floating on the surface of a liquid. The response of such a model can be inverted to yield the absolute density gradient in the plate, provided the flexural rigidity of the plate and the density contrast between mantle and topography are specified. If only positive density gradients are allowed, such a regional model fits the United States response data provided the flexural rigidity of the plate lies between 1021 and 1022 N m. The fit of the model is insensitive to the mantle/ load density contrast, but certain bounds on the density structure can be established if the model is assumed correct. In particular, the maximum density increase within the plate at depths greater than 34 kin must not exceed 470 kg m−3; this can be regarded as an upper bound on the density contrast at the Mohorovicic discontinuity. The permitted values of the flexural rigidity correspond to plate thicknesses in the range 5–10 km, yet deformations at depths greater than 20 km are indicated by other geophysical data. We conclude that the plate cannot be perfectly elastic; its effective elastic moduli must be much smaller than the seismically determined values. Estimates of the stress-differences produced in the earth by topographic loads, that use the elastic plate model, together with seismically determined elastic parameters, will be too large by a factor of four or more.

Barbour, AJ, Parker RL.  2014.  psd: Adaptive, sine multitaper power spectral density estimation for R. Computers & Geosciences. 63:1-8.   10.1016/j.cageo.2013.09.015   AbstractWebsite

We present an R package for computing univariate power spectral density estimates with little or no tuning effort. We employ sine multitapers, allowing the number to vary with frequency in order to reduce mean square error, the sum of squared bias and variance, at each point. The approximate criterion of Riedel and Sidorenko (1995) is modified to prevent runaway averaging that otherwise occurs when the curvature of the spectrum goes to zero. An iterative procedure refines the number of tapers employed at each frequency. The resultant power spectra possess significantly lower variances than those of traditional, non-adaptive estimators. The sine tapers also provide useful spectral leakage suppression. Resolution and uncertainty can be estimated from the number of degrees of freedom (twice the number of tapers). This technique is particularly suited to long time series, because it demands only one numerical Fourier transform, and requires no costly additional computation of taper functions, like the Slepian functions. It also avoids the degradation of the low-frequency performance associated with record segmentation in Welch's method. Above all, the adaptive process relieves the user of the need to set a tuning parameter, such as time-bandwidth product or segment length, that fixes frequency resolution for the entire frequency interval; instead it provides frequency-dependent spectral resolution tailored to the shape of the spectrum itself. We demonstrate the method by applying it to continuous borehole strainmeter data from a station in the Plate Boundary Observatory, namely station B084 at the Pinon Flat Observatory in southern California. The example illustrates how pad elegantly handles spectra with large dynamic range and mixed-bandwidth features-features typically found in geophysical datasets. (C) 2013 Elsevier Ltd. All rights reserved.

Berger, J, Agnew DC, Parker RL, Farrell WE.  1979.  Seismic system calibration 2. Cross-spectral calibration using random binary signals. Bulletin of the Seismological Society of America. 69:271-288. AbstractWebsite
Bowers, NE, Cande SC, Gee JS, Hildebrand JA, Parker RL.  2001.  Fluctuations of the paleomagnetic field during chron C5 as recorded in near-bottom marine magnetic anomaly data. Journal of Geophysical Research-Solid Earth. 106:26379-26396.   10.1029/2001jb000278   AbstractWebsite

Near-bottom magnetic data contain information on paleomagnetic field fluctuations during chron C5 as observed in both the North and South Pacific. The North Pacific data include 12 survey lines collected with a spatial separation of up to 120 kin, and the South Pacific data consist of a single long line collected on the west flank of the East Pacific Rise (EPR) at 19 degreesS. The North Pacific magnetic profiles reveal a pattern of linear, short-wavelength (2 to 5 km) anomalies (tiny wiggles) that are highly correlated over the shortest (3.8 km) to longest (120 km) separations in the survey. Magnetic inversions incorporating basement topography show that these anomalies are not caused by the small topographic relief. The character of the near-bottom magnetic profile from anomaly 5 on the west flank of the EPR, formed at a spreading rate more than twice that of the North Pacific, displays a remark-able similarity to the individual and stacked lines from the North Pacific survey area, Over distances corresponding to 1 m.y., 19 lows in the magnetic anomaly profile can be correlated between the North and South Pacific lines. Modeling the lows as due to short polarity events suggests that they may be caused by rapid swings of the magnetic field between normal and reversed polarities with little or no time in the reversed state. Owing to the implausibly high number of reversals required to account for these anomalies and the lack of any time in the reversed state, we conclude that the near-bottom signal is primarily a record of pateointensity fluctuations during chron C5. Spectral analysis of the North Pacific near bottom lines shows that the signal is equivalent to a paleointensity curve with a temporal resolution of 40 to 60 kyr, while measurements of the smallest separations of correlatable dips in the field suggest a temporal resolution of 36 kyr.

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
Caress, DW, Parker RL.  1989.  Spectral interpolation and downward continuation of marine magnetic anomaly data. Journal of Geophysical Research-Solid Earth and Planets. 94:17393-17407.   10.1029/JB094iB12p17393   AbstractWebsite

A two- or three-dimensional treatment of magnetic anomaly data generally requires that the data be interpolated onto a regular grid, especially when the analysis involves transforming the data into the Fourier domain. We present an algorithm for interpolation and downward continuation of magnetic anomaly data that works within a statistical framework. We assume that the magnetic anomaly is a realization of a random stationary field whose power spectral density (PSD) we can estimate; by using the PSD the algorithm produces an array incorporating as much of the information contained in the data as possible while avoiding the introduction of unnecessary complexity. The algorithm has the added advantage of estimating the uncertainty of every interpolated value. Downward continuation is a natural extension of the statistical algorithm. We apply our method to the interpolation of magnetic anomalies from the region around the 95.5°W Galapagos propagating rift onto a regular grid and also to the downward continuation of these data to a depth of 2200 m. We also note that the observed PSD of the Galapagos magnetic anomalies has a minimum at low wave numbers and discuss how this implies that intermediate wavelength (65 km <λ < 1500 km) magnetic anomalies are weaker than suggested by one dimensional spectral analysis of single profiles.

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.

Constable, C, Parker R.  1991.  Deconvolution of long-core paleomagnetic measurements: Spline therapy for the linear problem. Geophysical Journal International. 104:453-468.   10.1111/j.1365-246X.1991.tb05693.x   AbstractWebsite

The magnetization of long cores of sedimentary material is often measured in a pass-through magnetometer, whose output is the convolution of the desired function with the broad impulse response of the system. Because of inevitable measurement noise and the inherent poor conditioning of the inverse problem, any attempt to estimate the true magnetization function from the observations must avoid unnecessary amplification of small-scale features which would otherwise dominate the model with deceptively large undulations. We propose the construction of the smoothest possible magnetization model satisfying the measured data to within the observational error. By means of a cubic spline basis in the representations of both the unknown magnetization and the empirically measured response, we facilitate the imposition of maximum smoothness on the unknown magnetization. For our purposes, the smoothest model is the one with the smallest 2-norm of the second derivative, the same criterion used in the construction of cubic spline interpolators. The approach is tested on a marine core that was subsequently sectioned and measured in centimetre-sized individual specimens, with highly satisfactory results. An empirical estimate of the resolution of the method indicates a three-fold improvement in the processed record over the original signal. We illuminate the behaviour of the numerical scheme by showing the relation between our smoothness-maximizing procedure and a more conventional filtering approach. Our solution can indeed be approximated by convolution with a special set of weights, although the approximation may be poor near the ends of the core. In an idealized system we study the question of convergence of the deconvolution process, by whether the model magnetization approaches the true one when the experimental error and other system parameters are held constant, while the spacing between observations is allowed to become arbitrarily small. We find our procedure does in fact converge (under certain conditions) but only at a logarithmic rate. This suggests that further significant improvement in resolution cannot be achieved by increased measurement density or enhanced observational accuracy.

Constable, CG, Parker RL.  1988.  Smoothing, splines and smoothing splines; Their application in geomagnetism. Journal of Computational Physics. 78:493-508.   10.1016/0021-9991(88)90062-9   AbstractWebsite

We discuss the use of smoothing splines (SS) and least squares splines (LSS) in nonparametric regression on geomagnetic data. The distinction between smoothing splines and least squares splines is outlined, and it is suggested that in most cases the smoothing spline is, a preferable function estimate. However, when large data sets are involved, the smoothing spline may require a prohibitive amount of computation; the alternative often put forward when moderate or heavy smoothing is -desired is the least squares spline. This may not be capable of modeling the data adequately since the smoothness of the resulting function can be controlled only by the number and position of the knots. The computational efficiency of the least squares spline may be retained and its principal disadvantage overcome, by adding a penalty term in the square of the second derivative to the minimized functional. We call this modified form a penalized least squares spline, (denoted by PS throughout this work), and illustrate its use in the removal of secular trends in long observatory records of geomagnetic field components. We may compare the effects of smoothing splines, least squares splines, and penalized least squares splines by treating them as equivalent variable-kernel smoothers. As Silverman has shown, the kernel associated with the smoothing spline is symmetric and is highly localized with small negative sidelobes. The kernel for the least squares spline with the same fit to the data has large oscillatory sidelobes that extend far from the central region; it can be asymmetric even in the middle of the interval. For large numbers of data the penalized least squares spline can achieve essentially identical performance to that of a smoothing spline, but at a greatly reduced computational cost. The penalized spline estimation technique has potential widespread applicability in the analysis of geomagnetic and paleomagnetic data. It may be used for the removal of long term trends in data, when either the trend or the residual is of interest.

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.

Constable, CG, Parker RL, Stark PB.  1993.  Geomagnetic field models incorporating frozen-flux constraints. Geophysical Journal International. 113:419-433.   10.1111/j.1365-246X.1993.tb00897.x   AbstractWebsite

Techniques for modelling the geomagnetic field at the surface of Earth's core often penalize contributions at high spherical harmonic degrees to reduce the effect of mapping crustal fields into the resulting field model at the core-mantle boundary (CMB). Ambiguity in separating the observed field into crustal and core contributions makes it difficult to assign error bounds to core field models, and this makes it hard to test hypotheses that involve pointwise values of the core field. The frozen-flux hypothesis, namely that convective terms dominate diffusive terms in the magnetic-induction equation, requires that the magnetic flux through every patch on the core surrounded by a zero contour of the radial magnetic field remains constant, although the shapes, areas and locations (but not the topology) of these patches may change with time. Field models exactly satisfying the conditions necessary for the hypothesis have not yet been constructed for the early part of this century. We show that such models must exist, so testing the frozen-flux hypothesis becomes the question of whether the models satisfying it are geophysically unsatisfactory on other grounds, for example because they are implausibly rough or complicated. We introduce an algorithm to construct plausible fleld models satisfying the hypothesis, and present such models for epochs 1945.5 and 1980. Our algorithm is based on a new parametrization of the field in terms of its radial component B(r) at the CMB. The model consists of values of B(r) at a finite set of points on the CMB, together with a rule for interpolating the values to other points. The interpolation rule takes the specified points to be the vertices of a spherical triangle tessellation of the CMB, with B(r) varying linearly in the gnomonic projections of the spherical triangles onto planar triangles in the planes tangent to the centroids of the spherical triangles. This parametrization of B(r) provides a direct means of constraining the integral invariants required by the frozen-flux hypothesis. Using this parametrization, we have constructed field models satisfying the frozen-flux hypothesis for epochs 1945.5 and 1980, while fitting observatory and survey data for 1945.5 and Magsat data for 1980. We use the better constrained 1980 CMB field model as a reference for 1945.5: we minimize the departure of the 1945.5 CMB field model from a regularized 1980 CMB field model, while constraining the 1945.5 model to have the same null-flux curves and flux through those curves as the 1980 model. The locations, areas and shapes of the curves are allowed to change. The resulting 1945.5 CMB field model is nearly as smooth as that for 1980, fits the data adequately, and satisfies the conditions necessary for the frozen-flux hypothesis.

Constable, CG, Parker RL.  1988.  Statistics of the geomagnetic secular variation for the past 5 m.y.. Journal of Geophysical Research-Solid Earth and Planets. 93:11569-11581.   10.1029/JB093iB10p11569   AbstractWebsite

A new statistical model is proposed for the geomagnetic secular variation over the past 5 m.y. Unlike previous models, which have concentrated upon particular kinds of paleomagnetic observables, such as VGP or field direction, the new model provides a general probability density function from which the statistical distribution of any set of paleomagnetic measurements can be deduced. The spatial power spectrum of the present-day nondipole field is consistent with a white source near the core-mantle boundary with Gaussian distribution. After a suitable scaling, the spherical harmonic coefficients may be regarded as statistical samples from a single giant Gaussian process; this is our model of the nondipole field. Assuming that this characterization holds for the fields of the past, we can combine it with an arbitrary statistical description of the dipole. We compute the corresponding probability density functions and cumulative distribution functions for declination and inclination that would be observed at any site on the surface of the Earth. Global paleomagnetic data spanning the past 5 m.y. are used to constrain the free parameters of the model, i.e., those giving the dipole part of the field. The final model has these properties: (1) with two exceptions, each Gauss coefficient is independently normally distributed with zero mean and standard deviation for the nondipole terms commensurate with a white source at the core surface; (2) the exceptions are the axial dipole g1 and axial quadrupole g2 terms; the axial dipole distribution is bimodal and symmetric, resembling a combination of two normal distributions with centers close to the present-day value and its sign-reversed counterpart; (3) the standard deviations of the nonaxial dipole terms g11 and h11 and of the magnitude of the axial dipole are all about 10% of the present-day g1 component; and (4) the axial quadrupole reverses sign with the axial dipole and has a mean magnitude of 6% of its mean magnitude. The advantage of a model specified in terms of the spherical harmonic coefficients is that it is a complete statistical description of the geomagnetic field, capable of simultaneously satisfying many known properties of the field. Predictions about any measured field elements may be made to see if they satisfy the available data.

Constable, SC, Parker RL, Constable CG.  1987.  Occam's inversion: A practical algorithm for generating smooth models from electromagnetic sounding data. Geophysics. 52:289-300.   10.1190/1.1442303   AbstractWebsite

The inversion of electromagnetic sounding data does not yield a unique solution, but inevitably a single model to interpret the observations is sought. We recommend that this model be as simple, or smooth, as possible, in order to reduce the temptation to overinterpret the data and to eliminate arbitrary discontinuities in simple layered models. To obtain smooth models, the nonlinear forward problem is linearized about a starting model in the usual way, but it is then solved explicitly for the desired model rather than for a model correction. By parameterizing the model in terms of its first or second derivative with depth, the minimum norm solution yields the smoothest possible model. Rather than fitting the experimental data as well as possible (which maximizes the roughness of the model), the smoothest model which fits the data to within an expected tolerance is sought. A practical scheme is developed which optimizes the step size at each iteration and retains the computational efficiency of layered models, resulting in a stable and rapidly convergent algorithm. The inversion of both magnetotelluric and Schlumberger sounding field data, and a joint magnetotelluric‐resistivity inversion, demonstrate the method and show it to have practical application.

Farrell, WE, McKenzie DP, Parker RL.  1969.  On the note emitted from a mug while mixing instant coffee. Proceedings of the Cambridge Philosophical Society-Mathematical and Physical Sciences. 65:365-367. AbstractWebsite
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.

Gee, JS, Cande SC, Hildebrand JA, Donnelly K, Parker RL.  2000.  Geomagnetic intensity variations over the past 780 kyr obtained from near-seafloor magnetic anomalies. Nature. 408:827-832.   10.1038/35048513   AbstractWebsite

Knowledge of past variations in the intensity of the Earth's magnetic field provides an important constraint on models of the geodynamo. A record of absolute palaeointensity for the past 50 kyr has been compiled from archaeomagnetic and volcanic materials, and relative palaeointensities over the past 800 kyr have been obtained from sedimentary sequences. But a long-term record of geomagnetic intensity should also be carried by the thermoremanence of the oceanic crust. Here we show that near-seafloor magnetic anomalies recorded over the southern East Pacific Rise are well correlated with independent estimates of geomagnetic intensity during the past 780 kyr. Moreover, the pattern of absolute palaeointensity of seafloor glass samples from the same area agrees with the well-documented dipole intensity pattern for the past 50 kyr. A comparison of palaeointensities derived from seafloor glass samples with global intensity variations thus allows us to estimate the ages of surficial lava flows in this region. The record of geomagnetic intensity preserved in the oceanic crust should provide a higher-time-resolution record of crustal accretion processes at mid-ocean ridges than has previously been obtainable.

Gill, AE, Parker RL.  1970.  Contours of “h cosec θ” for the world's oceans. Deep-Sea Research. 17:823-&.   10.1016/0011-7471(70)90044-6   AbstractWebsite

Contours of d = h cosec θ are presented for the worlds oceans, where h is the depth of the ocean and θ the latitude. This quantity is the distance between the ocean surface and the ocean floor in the direction of the axis of rotation of the earth. The inverse is proportional to 2Ω/d = f/h where Ω is the rate of rotation of the earth and f = 2Ω sinθ is the Coriolis parameter. The quantity f/h may be interpreted as the potential vorticity of the ocean in the absence of motion relative to the rotating earth.

Greenhouse, JP, Parker RL, White A.  1973.  Modelling geomagnetic variations in or near an ocean using a generalized image technique. Geophysical Journal of the Royal Astronomical Society. 32:325-338.   10.1111/j.1365-246X.1973.tb05834.x   AbstractWebsite

A generalized image technique is described for modelling electromagnetic induction in two-dimensional systems, consisting of a thin (Price-type) ocean overlying a perfect conductor in the mantle. The method constructs a Green's function for currents in the ocean by conformally mapping the perfect conductor boundary into a straight line. Examples are given that show the effects to be expected at an ocean-continent boundary with isotherms rising under the ocean, and at a mid-ocean rise where the high temperatures are believed to be quite shallow.

Hammer, PTC, Hildebrand JA, Parker RL.  1991.  Gravity inversion using seminorm minimization: Density modeling of Jasper Seamount. Geophysics. 56:68-79.   10.1190/1.1442959   AbstractWebsite

A gravity inversion algorithm for modeling discrete bodies with nonuniform density distributions is presented. The algorithm selects the maximally uniform model from the family of models which fit the data, ensuring a conservative and unprejudiced estimate of the density variation within the body. The only inputs required by the inversion are the gravity anomaly field and the body shape. Tests using gravity anomalies generated from synthetic bodies confirm that seminorm minimizing inversions successfully represent mass distribution trends but do not reconstruct sharp discontinuities. We apply the algorithm to model the density structure of seamounts. Inversion of the seasurface gravity field observed over Jasper Seamount suggests the edifice has a low average density of 2.38 g/cm3 and contains a dense body within its western flank. These results are consistent with seismic, magnetic, and petrologic studies of Jasper Seamount.

Henry, M, Orcutt JA, Parker RL.  1980.  A new method for slant stacking refraction data. Geophysical Research Letters. 7:1073-1076.   10.1029/GL007i012p01073   AbstractWebsite

We describe a method for slant stacking seismic records at a number of ranges to synthesize the τ—ρ curve. The seismograms do not have to be evenly spaced in range and the correct three-dimensional point-source geometry is retained throughout. The problem is posed as a linear inverse problem in a form that permits the construction of a special solution in a very efficient manner.

Hildebrand, JA, Parker RL.  1987.  Paleomagnetism of Cretaceous Pacific Seamounts revisited. Journal of Geophysical Research-Solid Earth and Planets. 92:12695-12712.   10.1029/JB092iB12p12695   AbstractWebsite

The paleomagnetism of Cretaceous Pacific seamounts is reexamined. Herein techniques for nonuniform magnetic modeling are applied to determine paleomagnetic pole positions and their associated confidence limits. Modeling techniques are presented for reconstruction of both uniform and nonuniform components of the seamount magnetization. The uniform component yields an estimate of the paleomagnetic pole position, and the nonuniform component accounts for irregularities in the seamount magnetization. A seminorm minimization approach constructs maximally uniform magnetizations and is used to represent seamount interiors. A statistical modeling approach constructs random nonuniform magnetizations and is used to determine the confidence limits associated with each pole position. Mean paleopoles are calculated for groups of seamounts, including their associated error bounds. The mean paleopole for seven reliably dated Upper Cretaceous seamounts is located close to the position predicted by Pacific-hotspot relative motion. The paleopole for five seamounts with Cretaceous minimum dates is located west of the hotspotpredicted apparent polar wander path and may represent a Lower Cretaceous or Upper Jurassic pole.

Hildebrand, JA, Stevenson JM, Hammer PTC, Zumberge MA, Parker RL, Fox CG, Meis PJ.  1990.  A seafloor and sea surface gravity survey of Axial Volcano. Journal of Geophysical Research-Solid Earth and Planets. 95:12751-12763.   10.1029/JB095iB08p12751   AbstractWebsite

Seafloor and sea surface gravity measurements are used to model the internal density structure of Axial Volcano. Seafloor measurements made at 53 sites within and adjacent to the Axial Volcano summit caldera provide constraints on the fine-scale density structure. Shipboard gravity measurements made along 540 km of track line above Axial Volcano and adjacent portions of the Juan de Fuca ridge provide constraints on the density over a broader region and on the isostatic compensation. The seafloor gravity anomalies give an average density of 2.7 g cm−3 for the uppermost portion of Axial Volcano, The sea surface gravity anomalies yield a local compensation parameter of 23%, significantly less than expected for a volcanic edifice built on zero age lithosphere. Three-dimensional ideal body models of the seafloor gravity measurements suggest that low-density material, with a density contrast of at least 0.15 g cm−3, may be located underneath the summit caldera. The data are consistent with low-density material at shallow depths near the southern portion of the caldera, dipping downward to the north. The correlation of shallow low-density material and surface expressions of recent volcanic activity (fresh lavas and high-temperature hydrothermal venting) suggests a zone of highly porous crust. Seminorm minimization modeling of the surface gravity measurements also suggest a low-density region under the central portion of Axial Volcano. The presence of low-density material beneath Axial caldera suggests a partially molten magma chamber at depth.