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  • Magnetotellurics  (5)
  • Electrical resistivity structure  (2)
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  • 1
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    Oxford University Press on behalf of The Royal Astronomical Society
    Publication Date: 2022-05-25
    Description: Author Posting. © The Author(s), 2014. This article is posted here by permission of The Royal Astronomical Society for personal use, not for redistribution. The definitive version was published in Geophysical Journal International 196 (2014): 1365-1374, doi:10.1093/gji/ggt484.
    Description: A robust magnetotelluric (MT) inversion algorithm has been developed on the basis of quantile-quantile (q-q) plotting with confidence band and statistical modelling of inversion residuals for the MT response function (apparent resistivity and phase). Once outliers in the inversion residuals are detected in the q-q plot with the confidence band and the statistical modelling with the Akaike information criterion, they are excluded from the inversion data set and a subsequent inversion is implemented with the culled data set. The exclusion of outliers and the subsequent inversion is repeated until the q-q plot is substantially linear within the confidence band, outliers predicted by the statistical modelling are unchanged from the prior inversion, and the misfit statistic is unchanged at a target level. The robust inversion algorithm was applied to synthetic data generated from a simple 2-D model and observational data from a 2-D transect in southern Africa. Outliers in the synthetic data, which come from extreme values added to the synthetic responses, produced spurious features in inversion models, but were detected by the robust algorithm and excluded to retrieve the true model. An application of the robust inversion algorithm to the field data demonstrates that the method is useful for data clean-up of outliers, which could include model as well as data inconsistency (for example, inability to fit a 2-D model to a 3-D data set), during inversion and for objectively obtaining a robust and optimal model. The present statistical method is available irrespective of the dimensionality of target structures (hence 2-D and 3-D structures) and of isotropy or anisotropy, and can operate as an external process to any inversion algorithm without modifications to the inversion program.
    Description: TM was supported by the scientific program of TAIGA (trans-crustal advection and in-situ reaction of global sub-seafloor aquifer) sponsored by the MEXT of Japan, and is supported by the NIPR project KP-7. ADC is supported by US National Science Foundation (NSF) grant EAR1015185.
    Keywords: Inverse theory ; Probability distributions ; Magnetotellurics
    Repository Name: Woods Hole Open Access Server
    Type: Article
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  • 2
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    Oxford University Press on behalf of The Royal Astronomical Society
    Publication Date: 2022-05-25
    Description: Author Posting. © Author, 2013. This article is posted here by permission of Oxford University Press on behalf of The Royal Astronomical Society for personal use, not for redistribution. The definitive version was published in Geophysical Journal International 196 (2014): 111-130, doi:10.1093/gji/ggt366.
    Description: The statistical properties of the Swift skew, the phase-sensitive skew and the WAL invariants I1−I7 and Q are examined through analytic derivation of their probability density functions and/or simulation based on a Gaussian model for the magnetotelluric response tensor. The WAL invariants I1−I2 are shown to be distributed as a folded Gaussian, and are statistically well behaved in the sense that all of their moments are defined. The probability density functions for Swift skew, phase-sensitive skew and the WAL invariants I3−I4, I7 and Q are derived analytically or by simulation, and are shown to have no moments of order 2 or more. Since their support is semi-infinite or infinite, they cannot be represented trigonometrically, and hence are inconsistent with a Mohr circle interpretation. By contrast, the WAL invariants I5−I6 are supported on [ − 1, 1], and are inferred to have a beta distribution based on analysis and simulation. Estimation of rotational invariants from data is described using two approaches: as the ratio of magnetotelluric responses that are themselves averages, and as averages of section-by-section estimates of the invariant. Confidence intervals on the former utilize either Fieller's theorem, which is preferred because it is capable of yielding semi-infinite or infinite confidence intervals, or the less accurate delta method. Because section-by-section averages of most of the rotational invariants are drawn from distributions with infinite variance, the classical central limit theorem does not pertain. Instead, their averaging is accomplished using the median in place of the mean for location and an order statistic model to bound the confidence interval of the median. An example using real data demonstrates that the ratio of averages approach has serious systematic bias issues that render the result physically inconsistent, while the average of ratios result is a smooth, physically interpretable function of period, and is the preferred approach.
    Description: Supported by NSF grant EAR1015185
    Keywords: Probability distributions ; Electromagnetic theory ; Magnetotellurics
    Repository Name: Woods Hole Open Access Server
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  • 3
    Publication Date: 2022-05-25
    Description: Author Posting. © The Authors, 2007. This article is posted here by permission of John Wiley & Sons for personal use, not for redistribution. The definitive version was published in Geophysical Journal International 171 (2007): 127-132, doi:10.1111/j.1365-246X.2007.03523.x.
    Description: The marginal distributions for the magnetotelluric (MT) magnitude squared response function (and hence apparent resistivity) and phase are derived from the bivariate complex normal distribution that describes the distribution of response function estimates when the Gauss–Markov theorem is satisfied and the regression random errors are normally distributed. The distribution of the magnitude squared response function is shown to be non-central chi-squared with 2 degrees of freedom, with the non-centrality parameter given by the squared magnitude of the true MT response. The standard estimate for the magnitude squared response function is biased, with the bias proportional to the variance and hence important when the uncertainty is large. The distribution reduces to the exponential when the expected value of the MT response function is zero. The distribution for the phase is also obtained in closed form. It reduces to the uniform distribution when the squared magnitude of the true MT response function is zero or its variance is very large. The phase distribution is symmetric and becomes increasingly concentrated as the variance decreases, although it is shorter-tailed than the Gaussian. The standard estimate for phase is unbiased. Confidence limits are derived from the distributions for magnitude squared response function and phase. Using a data set taken from the 2003 Kaapvaal transect, it is shown that the bias in the apparent resistivity is small and that confidence intervals obtained using the non-parametric delta method are very close to the true values obtained from the distributions. Thus, it appears that the computationally simple delta approximation provides accurate estimates for the confidence intervals, provided that the MT response function is obtained using an estimator that bounds the influence of extreme data.
    Description: This work was supported by NSF grant EAR0309584.
    Keywords: Electromagnetic induction ; Geostatistics ; Magnetotellurics ; Statistical methods
    Repository Name: Woods Hole Open Access Server
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  • 4
    Publication Date: 2022-05-25
    Description: Author Posting. © American Geophysical Union, 2006. This article is posted here by permission of American Geophysical Union for personal use, not for redistribution. The definitive version was published in Geophysical Research Letters 33 (2006): L22301, doi:10.1029/2006GL027528.
    Description: The electrical structure of the upper mantle beneath the East Pacific Rise (EPR) at 15°45′S is imaged by inverting seafloor magnetotelluric data obtained during the Mantle ELectromagnetic and Tomography (MELT) experiment. The electrical conductivity model shows no evidence for a conductive region immediately beneath the ridge, in contrast to the model previously obtained beneath the EPR at 17°S. This observation can be explained by differences in current melt production along the ridge, consistent with other observations. The mantle to the east of the ridge at 60 –100 km depth is anisotropic, with higher conductivity in the spreading direction compared to the along-strike direction, similar to the 17°S region. The high conductivity in the spreading direction can be explained by a hydrated mantle with strain-induced lattice preferred orientation of olivine or by partial melt preferentially connected in the spreading direction.
    Description: This work was supported by NSF grant OCE0118254.
    Keywords: Electrical conductivity ; Magnetotellurics ; Partial melting
    Repository Name: Woods Hole Open Access Server
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  • 5
    Publication Date: 2022-05-26
    Description: Author Posting. © American Geophysical Union, 2012. This article is posted here by permission of American Geophysical Union for personal use, not for redistribution. The definitive version was published in Geochemistry Geophysics Geosystems 13 (2012): Q10017, doi:10.1029/2012GC004326.
    Description: An electrical resistivity profile across the central Mariana subduction system shows high resistivity in the upper mantle beneath the back-arc spreading ridge where melt might be expected to exist. Although seismic data are equivocal on the extent of a possible melt region, the question arises as to why a 2-D magnetotelluric (MT) survey apparently failed to image any melt. We have run forward models and inversions that test possible 3-D melt geometries that are consistent with the MT data and results of other studies from the region, and that we use to place upper bounds on the possible extent of 3-D melt region beneath the spreading center. Our study suggests that the largest melt region that was not directly imaged by the 2-D MT data, but that is compatible with the observations as well as the likely effects of melt focusing, has a 3-D shape on a ridge-segment scale focused toward the spreading center and a resistivity of 100 Ω-m that corresponds to ∼0.1–∼1% interconnected silicate melt embedded in a background resistivity of ∼500 Ω-m. In contrast to the superfast spreading southern East Pacific Rise, the 3-D melt region suggests that buoyant mantle upwelling on a ridge-segment scale is the dominant process beneath the slow-spreading central Mariana back-arc. A final test considers whether the inability to image a 3-D melt region was a result of the 2-D survey geometry. The result reveals that the 2-D transect completed is useful to elucidate a broad range of 3-D melt bodies.
    Description: TM and NS are supported by the scientific program of “TAIGA” (Trans-crustal Advection and In situ reaction of Global sub-seafloor Aquifer)” sponsored by the MEXT of Japan, and are also supported by the JSPS for Grant-In-Aid for Scientific Research (21244070). Participation in the Marianas experiment by RLE and ADC was supported by NSF grant OCE0405641.
    Description: 2013-04-25
    Keywords: Back-arc spreading ridge ; Central Mariana Trough ; Electrical resistivity structure ; Upper mantle melting
    Repository Name: Woods Hole Open Access Server
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  • 6
    Publication Date: 2022-05-26
    Description: Author Posting. © Author, 2014. This article is posted here by permission of The Royal Astronomical Society for personal use, not for redistribution. The definitive version was published in Geophysical Journal International 198 (2014): 622-636, doi: 10.1093/gji/ggu121.
    Description: The robust statistical model of a Gaussian core contaminated by outlying data that underlies robust estimation of the magnetotelluric (MT) response function has been re-examined. The residuals from robust estimators are systematically long tailed compared to a distribution based on the Gaussian, and hence are inconsistent with the robust model. Instead, MT data are pervasively described by the alpha stable distribution family whose variance and sometimes mean are undefined. A maximum likelihood estimator (MLE) that exploits the stable nature of MT data is formulated, and its two-stage implementation in which stable parameters are first fit to the data and then the MT responses are solved for is described. The MLE is shown to be inherently robust, but differs from the conventional robust estimator because it is based on a model derived from the data, while robust estimators are ad hoc, being based on the robust model that is inconsistent with actual data. Propriety versus impropriety of the complex MT response was investigated, and a likelihood ratio test for propriety and its null distribution was established. The Cramér-Rao lower bounds for the covariance matrix of proper and improper MT responses were specified. The MLE was applied to exemplar long period and broad-band data sets from South Africa. Both are shown to be significantly stably distributed using the Kolmogorov–Smirnov goodness of fit and Ansari-Bradley non-parametric dispersion tests. Impropriety of the MT responses at both sites is pervasive, hence the improper Cramér-Rao bound was used to estimate the MLE covariance. The MLE is shown to be nearly unbiased and well described by a Gaussian distribution based on bootstrap simulation. The MLE was compared to a conventional robust estimator, establishing that the standard errors of the former are systematically smaller than for the latter and that the standardized differences between them exhibit excursions that are both too frequent and too large to be described by a Gaussian model. This is ascribed to pervasive bias of the robust estimator that is to some degree obscured by their systematically large confidence bounds. Finally, a series of topics for further investigation is proposed.
    Description: This work was supported by NSF grant EAR0809074.
    Keywords: Time series analysis ; Numerical approximations and analysis ; Fractals and multifractals ; Probability distributions ; Magnetotellurics
    Repository Name: Woods Hole Open Access Server
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  • 7
    Publication Date: 2022-05-26
    Description: Author Posting. © American Geophysical Union, 2010. This article is posted here by permission of American Geophysical Union for personal use, not for redistribution. The definitive version was published in Geochemistry Geophysics Geosystems 11 (2010): Q09003, doi:10.1029/2010GC003101.
    Description: This paper reports on a magnetotelluric (MT) survey across the central Mariana subduction system, providing a comprehensive electrical resistivity image of the upper mantle to address issues of mantle dynamics in the mantle wedge and beneath the slow back-arc spreading ridge. After calculation of MT response functions and their correction for topographic distortion, two-dimensional electrical resistivity structures were generated using an inversion algorithm with a smoothness constraint and with additional restrictions imposed by the subducting slab. The resultant isotropic electrical resistivity structure contains several key features. There is an uppermost resistive layer with a thickness of up to 150 km beneath the Pacific Ocean Basin, 80–100 km beneath the Mariana Trough, and 60 km beneath the Parece Vela Basin along with a conductive mantle beneath the resistive layer. A resistive region down to 60 km depth and a conductive region at greater depth are inferred beneath the volcanic arc in the mantle wedge. There is no evidence for a conductive feature beneath the back-arc spreading center. Sensitivity tests were applied to these features through inversion of synthetic data. The uppermost resistive layer is the cool, dry residual from the plate accretion process. Its thickness beneath the Pacific Ocean Basin is controlled mainly by temperature, whereas the roughly constant thickness beneath the Mariana Trough and beneath the Parece Vela Basin regardless of seafloor age is controlled by composition. The conductive mantle beneath the uppermost resistive layer requires hydration of olivine and/or melting of the mantle. The resistive region beneath the volcanic arc down to 60 km suggests that fluids such as melt or free water are not well connected or are highly three-dimensional and of limited size. In contrast, the conductive region beneath the volcanic arc below 60 km depth reflects melting and hydration driven by water release from the subducting slab. The resistive region beneath the back-arc spreading center can be explained by dry mantle with typical temperatures, suggesting that any melt present is either poorly connected or distributed discontinuously along the strike of the ridge. Evidence for electrical anisotropy in the central Mariana upper mantle is weak.
    Description: Japanese participation in the Marianas experiment was supported by Japan Society for the Promotion of Science for Grant-In-Aid for Scientific Research (15340149 and 12440116), Japan-U.S. Integrated Action Program and the 21st Century COE Program of Origin and Evolution of Planetary Systems, and by the Ministry of Education, Culture, Sports, Science, and Technology for the Stagnant Slab Project, Grant-in Aid for Scientific Research on Priority Areas (17037003 and 16075204). U.S. participation was supported by NSF grant OCE0405641. Australian support came from Flinders University. T. M. is supported by the Postdoctoral Scholar Program at the Woods Hole Oceanographic Institution, with funding provided by the Deep Ocean Exploration Institute.
    Keywords: Electrical resistivity structure ; Upper mantle structure ; Mariana ; Subduction zone ; Back-arc spreading system ; Marine magnetotellurics
    Repository Name: Woods Hole Open Access Server
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