Graphical methods for investigating the fit of a Fisher distribution to spherical data

Lewis, T.; Fisher, N. I.

doi:10.1111/j.1365-246x.1982.tb04931.x

Cited by 45 publications

(25 citation statements)

References 5 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…In the FC/ZFC low-temperature experiments, both SC14-7 and SC18-3 experienced a change in the rate of remanence loss during warming through the interval 110-120 K, which is diagnostic of the Verwey transition in magnetite (Figures 6a and 6b) [Muxworthy and McClelland, 2000]. (c) Quantile-Quantile plots of tilt-corrected sitelevel virtual geomagnetic poles (VGPs) [Lewis and Fisher, 1982]. The suppressed appearance of the transition in sample SC14-7, as well as the gradual remanence loss with warming exhibited results shows 95% confidence bounds that extend from 105 to 138% untilting; the optimal value is 121.5%.…”

Section: Magnetic Mineralogymentioning

confidence: 99%

New Late Permian paleomagnetic data from Argentina: Refinement of the apparent polar wander path of Gondwana

Domeier

Voo

Tohver

et al. 2011

Geochem. Geophys. Geosyst.

View full text Add to dashboard Cite

The Late Paleozoic–Early Mesozoic apparent polar wander path of Gondwana is largely constructed from relatively old paleomagnetic results, many of which are considered unreliable by modern standards. Paleomagnetic results derived from sedimentary sequences, which are generally poorly dated and prone to inclination shallowing, are especially common. Here we report the results of a joint paleomagnetic‐geochronologic study of a volcanic complex in central Argentina. U‐Pb dating of zircons has yielded a robust age estimate of 263.0 +1.6/−2.0 Ma for the complex. Paleomagnetic analysis has revealed a pretilting (primary Permian) magnetization with dual polarities. Rock magnetic experiments have identified pseudo‐single domain (titano)magnetite and hematite as the mineralogic carriers of the magnetization. Lightning‐induced isothermal remagnetizations are widespread in the low‐coercivity magnetic carriers. The resulting paleomagnetic pole is 80.1°S, 349.0°E, A95 = 3.3°, N = 35, and it improves a Late Permian mean pole calculated from a filtered South American paleomagnetic data set. More broadly, this new, high‐quality, igneous‐based paleomagnetic pole falls between the previously distinct Late Permian segments of the Laurussian and Gondwanan apparent polar wander paths, suggesting that the long‐recognized disparity between these large paleomagnetic data sets may be primarily due to the inclusion of low‐quality or systemically biased data.

show abstract

Section: Magnetic Mineralogymentioning

confidence: 99%

New Late Permian paleomagnetic data from Argentina: Refinement of the apparent polar wander path of Gondwana

Domeier

Voo

Tohver

et al. 2011

Geochem. Geophys. Geosyst.

View full text Add to dashboard Cite

show abstract

“…In such a plot, Gaussian‐distributed data are expected to fit a straight line whose slope is the standard deviation, and the intercept the mean (Lewis & Fisher 1982; Shaw & Cande 1990). In order to detect any systematic bias in the data (and to sort the residuals r i consistently), we choose to orient all the normals η i to the great‐circle segments towards the young side of the isochron.…”

Section: Examplesmentioning

confidence: 99%

Statistical tools for estimating and combining finite rotations and their uncertainties

Kirkwood¹,

Royer²,

Chang³

et al. 2002

Geophysical Journal International

View full text Add to dashboard Cite

Plate reconstructions are a key tool in the study of plate tectonics. Although many methods have been proposed to calculate the finite rotations that describe plate motions, only a few address the problem of the uncertainties in plate reconstructions. This information is critical for a meaningful comparison of rates and directions of motion, predicted by a rotation, with geological field observations at plate boundaries. Similarly, uncertainties of a product of uncertain rotations through a plate circuit are crucial for testing plate geometry or for comparing reference frames. Here we present a method that allows the propagation of the uncertainties in the marine data (magnetic‐anomaly and fracture‐zone crossings), used to derive the finite rotations, to the uncertainties in the rotation parameters (latitude and longitude of pole, and angle of rotation). The rotation parameters are estimated by minimizing a quadratic objective function. A Taylor series approximation, centred at the true (and unknown) rotation parameters, is used to approximate the non‐linear least squares by a linear regression problem. From the design matrix estimated from the data, a covariance matrix describing the uncertainties in the rotation can be estimated. The covariance matrix depends upon the geometry of the plate boundary, the number of data, and the uncertainties in the data. Using a heuristic description of non‐linear least squares, we show how the methodology is analogous to standard linear regression. We generalize the method for reconstructing a single plate boundary to solve for the closure of a triple junction, and we present a simple way to combine the covariance matrices of individual rotations to estimate the uncertainties in their product, and show how to derive the uncertainties in the reconstructed points. Since any statistical analysis depends upon assumptions about the errors in the data, we discuss the assumptions inherent in the proposed methodology, and the limitations which result from these assumptions. One of them (referred to as the ‘equal‐kappas’ assumption) is especially troublesome when two or more rotations, based on different data distributions, are combined. From similar problems arising in linear regression, we propose a method to solve the plate reconstruction problem when the equal‐kappas assumption is not tenable. Finally, we briefly review the sources of error in the magnetic anomaly and fracture‐zone crossings that are inverted to derive plate reconstructions, and show how their uncertainties can be evaluated. A series of examples illustrates how these tools, implemented in software, can be used to solve or to test various plate geometries involving a single plate boundary, a triple junction and a combination of both.

show abstract

“…However, instrumentation problems, such as stuck bits, often appear as plateaus or staircases in q-q plots of the raw data. For a lucid discussion of q-q plots and their use, see Kleiner and Graedel [1980] or Lewis and Fisher [1982].…”

Section: Diagnosticsmentioning

confidence: 99%

On the robust estimation of power spectra, coherences, and transfer functions

Chave¹,

Thomson²,

Ander³

1987

J. Geophys. Res.

321

188

View full text Add to dashboard Cite

Robust estimation of power spectra, coherences, and transfer functions is investigated in the context of geophysical data processing. The methods described are frequency-domain extensions of current techniques from the statistical literature and are applicable in cases where section-averaging methods would be used with data that are contaminated by local nonstationarity or isolated outliers. The paper begins with a review of robust estimation theory, emphasizing statistical principles and the maximum likelihood or M-estimators. These are combined with section-averaging spectral techniques to obtain robust estimates of power spectra, coherences, and transfer functions in an automatic, data-adaptive fashion. Because robust methods implicitly identify abnormal data, methods for monitoring the statistical behavior of the estimation process using quantile-quantile plots are also discussed. The results are illustrated using a variety of examples from electromagnetic geophysics. INTRODUCTIONReliable estimation of power spectra for single data sequences or of transfer functions and coherences between multiple time series is of central importance in many areas of geophysics and engineering. While the effects of the underlying Gaussian distributional assumptions on such estimates are generally understood, the ability of a small fraction of non-Gaussian noise or localized nonstationarity to affect them is not. These phenomena can destroy conventional estimates, often in a manner that is difficult to detect.Problems with conventional (i.e., nonrobust) time series procedures arise because they are essentially copies of classical statistical procedures parameterized by frequency. Once Fourier transforms are taken, estimating a spectrum is the same process as computing a variance, and estimating a transfer function is a similar procedure to linear regression. Because these methods are based on the least squares or Gaussian maximum likelihood approaches to statistical inference, their advantages include simplicity and the optimality properties established by the Gauss- Paper number 5B5911 0148-0227/87/005B-5911505.00 residuals are drawn from a multivariate normal probability distribution, then the least squares result is also a maximum likelihood, fully efficient, minimum variance estimate. In practice, the regression model is rarely an accurate description due to departures of the data from the model requirements. Most data contain a small fraction of unusual observations or "outliers" that do not fit the model distribution or share the characteristics of the bulk of the sample. These can often be described by a probability distribution which has a nearly Gaussian shape in the center and tails which are heavier than would be expected for a normal one, or by mixtures of Gaussian distributions with different variances.Two forms of data outliers are common: point defects and local nonstationarity. Point defects are isolated outliers that exist independent of the structure of the process under study. In this paper the principles o...

show abstract

Graphical methods for investigating the fit of a Fisher distribution to spherical data

Cited by 45 publications

References 5 publications

New Late Permian paleomagnetic data from Argentina: Refinement of the apparent polar wander path of Gondwana

New Late Permian paleomagnetic data from Argentina: Refinement of the apparent polar wander path of Gondwana

Statistical tools for estimating and combining finite rotations and their uncertainties

On the robust estimation of power spectra, coherences, and transfer functions

Contact Info

Product

Resources

About