Statistics of the estimate of the magnitute-coherence function

Carter, G.; Knapp, C.; Nuttall, Albert H.

doi:10.1109/tau.1973.1162487

Cited by 64 publications

(43 citation statements)

References 7 publications

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“…[74] Munk and Cartwright [1966] and Bendat [1978] do not agree on the expression for equation (B16), but as we state it, equation (B16) constitutes the best approximation of the exact expressions of Carter et al [1973] and Touzi et al [1999] (see Figures B1a and B1b). Equation (B16) implies the estimate is positively biased.…”

Section: B4 Statistics Of Multiwindow Coherence Estimatesmentioning

confidence: 84%

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Spatiospectral localization of isostatic coherence anisotropy in Australia and its relation to seismic anisotropy: Implications for lithospheric deformation

2003

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[1] We investigate the two-dimensional (2-D) nature of the coherence between Bouguer gravity anomalies and topography on the Australian continent. The coherence function or isostatic response is commonly assumed to be isotropic. However, the fossilized strain field recorded by gravity anomalies and their relation to topography is manifest in a degree of isostatic compensation or coherence which does depend on direction. We have developed a method that enables a robust and unbiased estimation of spatially, directionally, and wavelength-dependent coherence functions between two 2-D fields in a computationally efficient way. Our new multispectrogram method uses orthonormalized Hermite functions as data tapers, which are optimal for spectral localization of nonstationary, spatially dependent processes, and do not require solving an eigenvalue problem. We discuss the properties and advantages of this method with respect to other techniques. We identify regions on the continent marked by preferential directions of isostatic compensation in two wavelength regimes. With few exceptions, the short-wavelength coherence anisotropy is nearly perpendicular to the major trends of the suture zones between stable continental domains, supporting the geological observation that such zones are mechanically weak. Mechanical anisotropy reflects lithospheric strain accumulation, and its presence must be related to the deformational processes affecting the lithosphere integrated over time. Threedimensional models of seismic anisotropy obtained from surface wave inversions provide an independent estimate of the lithospheric fossil strain field, and simple models have been proposed to relate seismic anisotropy to continental deformation. We compare our measurements of mechanical anisotropy with our own model of the azimuthally anisotropic seismic wave speed structure of the Australian lithosphere. The correlation of isostatic anisotropy with directions of fast wave propagation gleaned from the azimuthal anisotropy of surface waves decays with depth. This may support claims that above $200 km, internally coherent deformation of the entire lithosphere is responsible for the anisotropy present in surface wave speeds or split shear waves.

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Section: B4 Statistics Of Multiwindow Coherence Estimatesmentioning

confidence: 84%

“…Exact expressions for bias and variance are based on distribution theory [Carter et al, 1973;Touzi et al, 1996]. The distribution functions for the coherence square estimator of two Gaussian processes are complicated expressions involving gamma functions and generalized hypergeometric functions.…”

Section: B4 Statistics Of Multiwindow Coherence Estimatesmentioning

confidence: 99%

Spatiospectral localization of isostatic coherence anisotropy in Australia and its relation to seismic anisotropy: Implications for lithospheric deformation

2003

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“…The coherence estimate is asymptotically Gaussian (Carter et al, 1973;Touzi and Lopes, 1996;Walden, 1990). The grand average is the constant denoted γ 2 .…”

Section: Anisotropy Tests For Coherence and T Ementioning

confidence: 99%

On the robustness of estimates of mechanical anisotropy in the continental lithosphere: A North American case study and global reanalysis

Kalnins

Simons

Kirby

et al. 2015

Earth and Planetary Science Letters

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Publisher's copyright statement: NOTICE: this is the author's version of a work that was accepted for publication in Earth and Planetary Science Letters. Changes resulting from the publishing process, such as peer review, editing, corrections, structural formatting, and other quality control mechanisms may not be reected in this document. Changes may have been made to this work since it was submitted for publication. Use policyThe full-text may be used and/or reproduced, and given to third parties in any format or medium, without prior permission or charge, for personal research or study, educational, or not-for-prot purposes provided that:• a full bibliographic reference is made to the original source • a link is made to the metadata record in DRO • the full-text is not changed in any way The full-text must not be sold in any format or medium without the formal permission of the copyright holders.Please consult the full DRO policy for further details. AbstractLithospheric strength variations both influence and are influenced by many tectonic processes, including orogenesis and rifting cycles. The long, complex, and highly anisotropic histories of the continental lithosphere might lead to a natural expectation of widespread mechanical anisotropy. Anisotropy in the coherence between topography and gravity anomalies is indeed often observed, but whether it corresponds to an elastic thickness that is anisotropic remains in question. If coherence is used to estimate flexural strength of the lithosphere, the null-hypothesis of elastic isotropy can only be rejected when there is significant anisotropy in both the coherence and the elastic strengths derived from it, and if interference from anisotropy in the data themselves can be plausibly excluded. We consider coherence estimates made using multitaper and wavelet methods, from which estimates of effective elastic thickness are derived. We develop a series of statistical and geophysical tests for anisotropy, and specifically evaluate the potential for spurious results with synthetically generated data. Our primary case study, the North American continent, does not exhibit meaningful anisotropy in its mechanical strength. Similarly, a global reanalysis of continental gravity and topography using multitaper methods produces only scant evidence for lithospheric flexural anisotropy.

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“…The approximate equations used in the calculation include evaluation of the standardized normal distribution at the 100α point, and specify the (1-α) * 100 % confidence bounds. The second method, presented by Carter, Nutall & Knapp, 27 and utilized (or perhaps developed independently) by Touzi etal 28 …”

Section: Coherence Uncertainty Analysismentioning

confidence: 99%

System identification and uncertainty quantification using orthogonal excitations and the Semispan Supersonic Transport (S4T) model

Heeg¹,

Wieseman²

2012

53rd AIAA/ASME/ASCE/AHS/ASC Structures, Structural Dynamics and Materials Conference

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Orthogonal harmonic multisine excitations were utilized in a wind tunnel test and in simulation of the SemiSpan Supersonic Transport model to assess aeroservoelastic characteristics. Fundamental issues associated with analyzing sinusoidal signals were examined, including spectral leakage, excitation truncation, and uncertainties on frequency response functions and mean-square coherence. Simulation allowed for evaluation of these issues relative to a truth model, while wind tunnel data introduced real-world implementation issues.

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Statistics of the estimate of the magnitute-coherence function

Cited by 64 publications

References 7 publications

Spatiospectral localization of isostatic coherence anisotropy in Australia and its relation to seismic anisotropy: Implications for lithospheric deformation

Spatiospectral localization of isostatic coherence anisotropy in Australia and its relation to seismic anisotropy: Implications for lithospheric deformation

On the robustness of estimates of mechanical anisotropy in the continental lithosphere: A North American case study and global reanalysis

System identification and uncertainty quantification using orthogonal excitations and the Semispan Supersonic Transport (S4T) model

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