Chave Alan D.

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  • Technical Report
    Time series analysis programs
    (Woods Hole Oceanographic Institution, 1980-05) Chave, Alan D.
    This report documents a set of Fortran subroutines for manipulating one dimensional, complex-valued time series information . The programs are divided into two libraries: TSLIB for ordinary Fourier analysis and ACLIB for more specialized applications. The latter includes interpolation routines, maximum entropy spectral analysis programs , and subroutines for advanced mathematical operations. The programs are designed for efficiency and speed with a minimum of hidden operations and memory accesses. These subroutines have been used extensively in the analysis of magnetotelluric and other geophysical data .
  • Preprint
    Geophysical evidence from the MELT area for compositional controls on oceanic plates
    ( 2005-06-29) Evans, Rob L. ; Hirth, Greg ; Baba, Kiyoshi ; Forsyth, Donald W. ; Chave, Alan D. ; Mackie, Randall L.
    Magnetotelluric (MT) and seismic data, collected during the MELT experiment at the Southern East Pacific Rise (SEPR) constrain the distribution of melt beneath this mid-ocean-ridge spreading center and also the evolution of the oceanic lithosphere during its early cooling history. In this paper, we focus on structure imaged at distances ~100 to 350 km east of the ridge crest, corresponding to seafloor ages of ~1.3 to 4.5 Ma, where the seismic and electrical conductivity structure is nearly constant, independent of age. Beginning at a depth of about 60 km, there is a large increase in electrical conductivity and a change from isotropic to transversely anisotropic electrical structure with higher conductivity in the direction of fast propagation for seismic waves. Because conductive cooling models predict structure that increases in depth with age, extending to about 30 km at 4.5 Ma, we infer that the structure of young oceanic plates is instead controlled by a decrease in water content above 60 km induced by the melting process beneath the spreading center.
  • Article
    Bounded influence magnetotelluric response function estimation
    (Blackwell Publishing, 2004-05-13) Chave, Alan D. ; Thomson, David J.
    Robust magnetotelluric response function estimators are now in standard use in electromagnetic induction research. Properly devised and applied, these have the ability to reduce the influence of unusual data (outliers) in the response (electric field) variables, but are often not sensitive to exceptional predictor (magnetic field) data, which are termed leverage points. A bounded influence estimator is described which simultaneously limits the influence of both outliers and leverage points, and has proven to consistently yield more reliable magnetotelluric response function estimates than conventional robust approaches. The bounded influence estimator combines a standard robust M-estimator with leverage weighting based on the statistics of the hat matrix diagonal, which is a standard statistical measure of unusual predictors. Further extensions to magnetotelluric data analysis are proposed, including a generalization of the remote reference method which utilizes multiple sites instead of a single one and a two-stage bounded influence estimator which effectively removes correlated noise in the local electric and magnetic field variables using one or more uncontaminated remote references. These developments are illustrated using a variety of magnetotelluric data.
  • Article
    Constraints on the resistivity of the oceanic lithosphere and asthenosphere from seafloor ocean tidal electromagnetic measurements
    (Oxford University Press, 2019-07-11) Zhang, Huiqian ; Egbert, Gary D. ; Chave, Alan D. ; Huang, Qinghua ; Kelbert, Anna ; Erofeeva, Svetlana Y.
    The electromagnetic (EM) field generated by ocean tidal flow is readily detectable in both satellite magnetic field data, and in ocean-bottom measurements of electric and magnetic fields. The availability of accurate charts of tidal currents, constrained by assimilation of modern satellite altimetry data, opens the possibility of using tidal EM fields as a source to image mantle electrical resistivity beneath the ocean basins, as highlighted by the recent success in defining the globally averaged lithosphere–asthenosphere boundary (LAB) with satellite data. In fact, seafloor EM data would be expected to provide better constraints on the structure of resistive oceanic lithosphere, since the toroidal magnetic mode, which can constrain resistive features, is a significant component of the tidal EM field within the ocean, but is absent above the surface (in particular in satellite data). Here we consider this issue in more detail, using a combination of simplified theoretical analysis and 1-D and 3-D numerical modelling to provide a thorough discussion of the sensitivity of satellite and seafloor data to subsurface electrical structure. As part of this effort, and as a step toward 3-D inversion of seafloor tidal data, we have developed a new flexible 3-D spherical-coordinate finite difference scheme for both global and regional scale modelling, with higher resolution models nested in larger scale solutions. We use the new 3-D model, together with Monte Carlo simulations of errors in tidal current estimates, to provide a quantitative assessment of errors in the computed tidal EM signal caused by uncertainty in the tidal source. Over the open ocean this component of error is below 0.01 nT in Bz at satellite height and 0.05 nT in Bx on the seafloor, well below typical signal levels. However, as coastlines are approached error levels can increase substantially. Both analytical and 3-D modelling demonstrate that the seafloor magnetic field is most sensitive to the lithospheric resistance (the product of resistivity and thickness), and is more weakly influenced (primarily in the phase) by resistivity of the underlying asthenosphere. Satellite data, which contain only the poloidal magnetic mode, are more sensitive to the conductive asthenosphere, but have little sensitivity to lithospheric resistance. For both seafloor and satellite data’s changes due to plausible variations in Earth parameters are well above error levels associated with source uncertainty, at least in the ocean interior. Although the 3-D modelling results are qualitatively consistent with theoretical analysis, the presence of coastlines and bathymetric variations generates a complex response, confirming that quantitative interpretation of ocean tidal EM fields will require a 3-D treatment. As an illustration of the nested 3-D scheme, seafloor data at five magnetic and seven electric stations in the northeastern Pacific (41○N, 165○W) are fit with trial-and-error forward modelling of a local domain. The simulation results indicate that the lithospheric resistance is roughly 7 × 108 Ωm2. The phase of the seafloor data in this region are inconsistent with a sharp transition between the resistive lithosphere and conductive asthenosphere.
  • Article
    Correction of seafloor magnetotelluric data for topographic effects during inversion
    (American Geophysical Union, 2005-12-14) Baba, Kiyoshi ; Chave, Alan D.
    The large contrast in electrical conductivity between seawater and the underlying seafloor accumulates boundary electric charges which can severely distort observed electric and magnetic fields. For marine magnetotelluric (MT) studies, correcting this topographic effect is critical to obtaining accurate conductivity models for the mantle. Previously, correction for topography was based on the thin sheet approximation which breaks down at periods under ∼1000 s in the deep ocean. This paper introduces an analysis method for seafloor MT data which combines removal of three-dimensional (3-D) topographic effects with inversion of the data for 2-D structure. The observed MT impedance is first corrected to a flat-lying seafloor datum using the observed bathymetry without invoking the thin sheet approximation. The corrected MT response is then inverted in a flat seafloor model space. Because of coupling between topographic effects and deeper structure, the correction and inversion steps are iterated until changes in each become small. The procedure is verified using synthetic and real data. Tests for synthetic 3-D topography over a half-space show that the method closely recovers the true half-space model after a few iterations. The procedure is also applied to real data collected in the Mantle Electromagnetic and Tomography (MELT) experiment on the East Pacific Rise at 17°S.
  • Article
    A note about Gaussian statistics on a sphere
    (Oxford University Press, 2015-07) Chave, Alan D.
    The statistics of directional data on a sphere can be modelled either using the Fisher distribution that is conditioned on the magnitude being unity, in which case the sample space is confined to the unit sphere, or using the latitude–longitude marginal distribution derived from a trivariate Gaussian model that places no constraint on the magnitude. These two distributions are derived from first principles and compared. The Fisher distribution more closely approximates the uniform distribution on a sphere for a given small value of the concentration parameter, while the latitude–longitude marginal distribution is always slightly larger than the Fisher distribution at small off-axis angles for large values of the concentration parameter. Asymptotic analysis shows that the two distributions only become equivalent in the limit of large concentration parameter and very small off-axis angle.
  • Article
    On the statistics of magnetotelluric rotational invariants
    (Oxford University Press on behalf of The Royal Astronomical Society, 2013-10-25) Chave, Alan D.
    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.
  • Article
    The statistical distribution of magnetotelluric apparent resistivity and phase
    (John Wiley & Sons, 2007-07-29) Chave, Alan D. ; Lezaeta, Pamela F.
    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.
  • Thesis
    Applications of time series analysis to geophysical data
    (Massachusetts Institute of Technology and Woods Hole Oceanographic Institution, 1980-06) Chave, Alan D.
    This thesis consists of three papers applying the techniques of time series analysis to geophysical data. Surface wave dispersion along the Walvis Ridge, South Atlantic Ocean, is obtained by bandpass filtering the recorded seismogram in the frequency domain. The group velocity is anomalously low in the period range of 15-50 s, and formal inversion of the data indicates both crustal thickening to 12.5 km and low shear velocity (4.25-4.35 km/s) to depths of 40-50 km. The electromagnetic induction fields at a deep ocean site northeast of Hawaii were used to determine the electrical conductivity of the earth to 400 km depth. Singular value decomposition of the data matrix indicates three degrees of freedom, suggesting source field complications and a two dimensional conductive structure. Inversion of one of the principal terms in the response function shows an abrupt rise in electrical conductivity to 0.05 mho/m near 160 km with no resolvable decrease below this. A model study suggests that moving source fields influence the induction appreciably in the other principal response tunction. A set of piston cores from the northeast Atlantic Ocean are used to construct paleomagnetic time series covering the interval 25-127 kybp. Stratigraphic control is provided by counts of planktonic toraminifera, and empirical orthogonal function analysis shows a significant decrease in sedimentation rate at the interglaciai/glacial transition. The sediments are magnetically stable and reliable relative paleointensity measurements could be obtained. Spectral analysis of the directions reveals a predominant 10 ky periodicity and no dominant looping direction.
  • Article
    On the physics of frequency-domain controlled source electromagnetics in shallow water. 1: isotropic conductivity
    (Oxford University Press, 2017-11-17) Chave, Alan D. ; Everett, Mark E. ; Mattsson, Johan ; Boon, James ; Midgley, Jonathan
    In recent years, marine controlled source electromagnetics (CSEM) has found increasing use in hydrocarbon exploration due to its ability to detect thin resistive zones beneath the seafloor. It is the purpose of this paper to evaluate the physics of CSEM for an ocean whose electrical thickness is comparable to or much thinner than that of the overburden using the in-line configuration through examination of the elliptically polarized seafloor electric field, the time-averaged energy flow depicted by the real part of the complex Poynting vector, energy dissipation through Joule heating and the Fréchet derivatives of the seafloor field with respect to the subseafloor conductivity that is assumed to be isotropic. The deep water (ocean layer electrically much thicker than the overburden) seafloor EM response for a model containing a resistive reservoir layer has a greater amplitude and reduced phase as a function of offset compared to that for a half-space, or a stronger and faster response. For an ocean whose electrical thickness is comparable to or much smaller than that of the overburden, the electric field displays a greater amplitude and reduced phase at small offsets, shifting to a stronger amplitude and increased phase at intermediate offsets and a weaker amplitude and enhanced phase at long offsets, or a stronger and faster response that first changes to stronger and slower, and then transitions to weaker and slower. These transitions can be understood by visualizing the energy flow throughout the structure caused by the competing influences of the dipole source and guided energy flow in the reservoir layer, and the air interaction caused by coupling of the entire subseafloor resistivity structure with the sea surface. A stronger and faster response occurs when guided energy flow is dominant, while a weaker and slower response occurs when the air interaction is dominant. However, at intermediate offsets for some models, the air interaction can partially or fully reverse the direction of energy flux in the reservoir layer toward rather than away from the source, resulting in a stronger and slower response. The Fréchet derivatives are dominated by preferential sensitivity to the reservoir layer conductivity for all water depths except at high frequencies, but also display a shift with offset from the galvanic to the inductive mode in the underburden and overburden due to the interplay of guided energy flow and the air interaction. This means that the sensitivity to the horizontal conductivity is almost as strong as to the vertical component in the shallow parts of the subsurface, and in fact is stronger than the vertical sensitivity deeper down. However, the sensitivity to horizontal conductivity is still weak compared to the vertical component within thin resistive regions. The horizontal sensitivity is gradually decreased when the water becomes deep. These observations in part explain the success of shallow towed CSEM using only measurements of the in-line component of the electric field.
  • Technical Report
    Report of a workshop on technical approaches to construction of a seafloor geomagnetic observatory
    (Woods Hole Oceanographic Institution, 1995-09) Chave, Alan D. ; Green, Arthur W. ; Filloux, Jean H. ; Law, Lawrie K. ; Petitt, Robert A. ; Rasson, Jean L. ; Schultz, Adam ; Spiess, Fred N. ; Tarits, Pascal ; Tivey, Maurice A. ; Webb, Spahr C.
    This report considers the technical issues on sensors, data recording and transmission, control and timing, power, and packaging associated with constricting a seafloor geomagnetic observatory. Existing technologies either already in use for oceanographic purposes or adapted from terrestral geomagnetic observatories could be applied to measure the vector magnetic field components and absolute intensity with minimal development. The major technical challenge arises in measuring absolute direction on the seafloor because terrestral techniques are not transferrable to the deep ocean. Two solutions to this problem were identified. The first requires the development of an instrument which measures the instantaneous declination and inclination of the magnetic field relative to a north-seeking gyroscope and the local vertical. The second is a straightforward extension of a precision acoustic method for determining absolute position on the seafloor.
  • Article
    Seasonal variation of ocean bottom pressure derived from Gravity Recovery and Climate Experiment (GRACE) : local validation and global patterns
    (American Geophysical Union, 2005-09-02) Kanzow, Torsten ; Flechtner, Frank ; Chave, Alan D. ; Schmidt, Roland ; Schwintzer, Peter ; Send, Uwe
    The Gravity Recovery and Climate Experiment (GRACE) processing centers at the GeoForschungsZentrum Potsdam (GFZ) and the University of Texas Center for Space Research (UTCSR) provide time series of monthly gravity field solutions covering the period since mission launch in March 2002. Although the achieved accuracy still remains an order of magnitude below the mission's baseline goal, these time series have successfully been used to study terrestrial phenomena such as water storage variations. Over the oceans, the monthly gravity field solutions can be converted into estimates of the fluctuating ocean bottom pressure (OBP), which is the sum of atmospheric and oceanic mass variations. The GRACE products may be validated against in situ OBP observations which are available from a ground truth site in the tropical northwest Atlantic Ocean. Large differences are observed between the in situ and GRACE-derived OBP which are investigated by comparing the tidal and nontidal ocean models used at GFZ and UTCSR for dealiasing short-term (<2 months) mass variations from satellite measurements. Results show that the barotropic nontidal and tide models need improvement at periods shorter than 1 day and longer than 2 weeks. On a global scale the monthly OBP fields from GRACE generally overestimate the variability compared to ocean general circulation models, especially in tropical regions. This may be attributed to continuing deficiencies in GRACE data processing. Nevertheless, there is some initial evidence that GRACE possesses the potential to observe large-scale averages of bottom pressure fluctuations.
  • Article
    High-Q spectral peaks and nonstationarity in the deep ocean infragravity wave band: Tidal harmonics and solar normal modes
    (American Geophysical Union, 2019-02-20) Chave, Alan D. ; Luther, Douglas S. ; Thomson, David J.
    Infragravity waves have received the least study of any class of waves in the deep ocean. This paper analyzes a 389‐day‐long deep ocean pressure record from the Hawaii Ocean Mixing Experiment for the presence of narrowband (≲2 μHz) components and nonstationarity over 400–4,000 μHz using a combination of fitting a mixture noncentral/central χ2 model to spectral estimates, high‐resolution multitaper spectral estimation, and computation of the offset coherence between distinct frequencies for a given data segment. In the frequency band 400–1,000 μHz there is a noncentral fraction of 0.67 ± 0.07 that decreases with increasing frequency. Evidence is presented for the presence of tidal harmonics in the data over the 400‐ to 1,400‐μHz bands. Above ~2,000 μHz the noncentral fraction rises with frequency, comprising about one third of the spectral estimates over 3,000–4,000 μHz. The power spectrum exhibits frequent narrowband peaks at 6–11 standard deviations above the noise level. The widths of the peaks correspond to a Q of at least 1,000, vastly exceeding that of any oceanic or atmospheric process. The offset coherence shows that the spectral peaks have substantial (p = 0.99–0.9999) interfrequency correlation, both locally and between distinct peaks within a given analysis band. Many of the peak frequencies correspond to the known values for solar pressure modes that have previously been observed in solar wind and terrestrial data, while others are the result of nonstationarity that distributes power across frequency. Overall, this paper documents the existence of two previously unrecognized sources of infragravity wave variability in the deep ocean.
  • Article
    Electrical structure beneath the northern MELT line on the East Pacific Rise at 15°45′S
    (American Geophysical Union, 2006-11-16) Baba, Kiyoshi ; Tarits, Pascal ; Chave, Alan D. ; Evans, Rob L. ; Hirth, Greg ; Mackie, Randall L.
    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.
  • Article
    A multitaper spectral estimator for time-series with missing data
    (Oxford University Press, 2019-06-14) Chave, Alan D.
    A multitaper estimator is proposed that accommodates time-series containing gaps without using any form of interpolation. In contrast with prior missing-data multitaper estimators that force standard Slepian sequences to be zero at gaps, the proposed missing-data Slepian sequences are defined only where data are present. The missing-data Slepian sequences are frequency independent, as are the eigenvalues that define the energy concentration within the resolution bandwidth, when the process bandwidth is [−1/2,1/2) for unit sampling and the sampling scheme comprises integer multiples of unity. As a consequence, one need only compute the ensuing missing-data Slepian sequences for a given sampling scheme once, and then the spectrum at an arbitrary set of frequencies can be computed using them. It is also shown that the resulting missing-data multitaper estimator can incorporate all of the optimality features (i.e. adaptive-weighting, F-test and reshaping) of the standard multitaper estimator, and can be applied to bivariate or multivariate situations in similar ways. Performance of the missing-data multitaper estimator is illustrated using length of day, seafloor pressure and Nile River low stand time-series.
  • Article
    On the electromagnetic fields produced by marine frequency domain controlled sources
    (John Wiley & Sons, 2009-10-14) Chave, Alan D.
    In recent years, marine controlled source electromagnetics (CSEM) has found increasing use in hydrocarbon exploration due to its ability to detect thin resistive zones beneath the seafloor. Although it must be recognized that the quantitative interpretation of marine CSEM data over petroleum-bearing formations will typically require 2-D surveys and 2-D or 3-D modelling, the use of the 1-D approximation is useful under some circumstances and provides considerable insight into the physics of marine CSEM. It is the purpose of this paper to thoroughly explore the 1-D solutions for all four fundamental source types—vertical and horizontal, electric and magnetic dipole (VED, HED, VMD and HMD)—using a set of canonical reservoir models that encompass brine to weak to strong hydrocarbon types. The paper introduces the formalism to solve the Maxwell equations for a 1-D structure in terms of independent and unique toroidal and poloidal magnetic modes that circumscribe the salient diffusion physics. Green's functions for the two modes from which solutions for arbitrary source current distributions can be constructed are derived and used to obtain the electromagnetic (EM) fields produced by finite VED, HED, VMD and HMD sources overlying an arbitrary 1-D electrical structure. Field behaviour is analysed using the Poynting vector that represents the time-averaged flow of energy through the structure and a polarization ellipse decomposition of the triaxial seafloor EM field that is a complete field description. The behaviour of the two EM modes using unimodal VED and VMD sources is presented. The paper closes by extending these results to the bimodal HED and HMD sources.
  • Preprint
    Area selection for diamonds using magnetotellurics : examples from southern Africa
    ( 2009-06-05) Jones, Alan G. ; Evans, Rob L. ; Muller, Mark R. ; Hamilton, Mark P. ; Miensopust, Marion P. ; Garcia, Xavier ; Cole, Patrick ; Ngwisanyi, Tiyapo ; Hutchins, David A. ; Fourie, C. J. S. ; Jelsma, Hielke ; Aravanis, Theo ; Pettit, Wayne ; Webb, Susan J. ; Webb, Jan ; Collins, Louise ; Hogg, Colin ; Horan, Clare ; Spratt, Jessica ; Wallace, Gerry ; Chave, Alan D. ; Cole, Janine ; Stettler, Raimund ; Tshoso, G. ; Mountford, Andy ; Cunion, Ed ; Khoza, T. David ; Share, Pieter-Ewald ; SAMTEX Team
    Southern Africa, particularly the Kaapvaal Craton, is one of the world’s best natural laboratories for studying the lithospheric mantle given the wealth of xenolith and seismic data that exist for it. The Southern African Magnetotelluric Experiment (SAMTEX) was launched to complement these databases and provide further constraints on physical parameters and conditions by obtaining information about electrical conductivity variations laterally and with depth. Initially it was planned to acquire magnetotelluric data on profiles spatially coincident with the Kaapvaal Seismic Experiment, however with the addition of seven more partners to the original four through the course of the experiment, SAMTEX was enlarged from two to four phases of acquisition, and extended to cover much of Botswana and Namibia. The complete SAMTEX dataset now comprises MT data from over 675 distinct locations in an area of over one million square kilometres, making SAMTEX the largest regional-scale MT experiment conducted to date. Preliminary images of electrical resistivity and electrical resistivity anisotropy at 100 km and 200 km, constructed through approximate one-dimensional methods, map resistive regions spatially correlated with the Kaapvaal, Zimbabwe and Angola Cratons, and more conductive regions spatially associated with the neighbouring mobile belts and the Rehoboth Terrain. Known diamondiferous kimberlites occur primarily on the boundaries between the resistive or isotropic regions and conductive or anisotropic regions. Comparisons between the resistivity image maps and seismic velocities from models constructed through surface wave and body wave tomography show spatial correlations between high velocity regions that are resistive, and low velocity regions that are conductive. In particular, the electrical resistivity of the sub-continental lithospheric mantle of the Kaapvaal Craton is determined by its bulk parameters, so is controlled by a bulk matrix property, namely temperature, and to a lesser degree by iron content and composition, and is not controlled by contributions from interconnected conducting minor phases, such as graphite, sulphides, iron oxides, hydrous minerals, etc. This makes quantitative correlations between velocity and resistivity valid, and a robust regression between the two gives an approximate relationship of Vs [m/s] = 0.045*log(resistivity [ohm.m]).
  • Article
    Magnetotelluric data, stable distributions and impropriety: an existential combination
    (Oxford University Press, 2014-05-30) Chave, Alan D.
    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.
  • Article
    A characterization of periodicity in the voltage time series of a riometer
    (American Geophysical Union, 2020-04-20) Marshall, François ; Thomson, David J. ; Chave, Alan D. ; Fiori, Robyn ; Danskin, Donald
    This paper reveals unprecedented periodicity in the voltage series of relative ionospheric opacity meters (riometers) of the Canadian Riometer Array (CRA). In quiet times, the riometer voltage series is accurately modeled by a stochastic process whose components include both a six term expansion in harmonic functions and some amplitude modulated modes of lower signal to noise ratio (SNR). In units of cycles per sidereal day (cpsd), the frequencies of the six harmonic functions lie within 0.01 cpsd of an integer. Earth's rotation induces a splitting of the low SNR components, resulting in the appearance of nine multiplets in standardized power spectrum estimates of the considered CRA voltage series. A second feature of these spectrum estimates is a 6 min periodic element appearing in both the CRA voltage series and the proton mass density series of the Advanced Composition Explorer (ACE). Spectral peak frequencies have been detected, which lie near established solar mode frequency estimates. In addition, some of these peak frequency estimates are coincident with peak frequency estimates of the standardized power spectra for the time series of proton mass density and interplanetary magnetic field strength (IMF) at ACE.
  • Article
    Mantle dynamics beneath the East Pacific Rise at 17°S : insights from the Mantle Electromagnetic and Tomography (MELT) experiment
    (American Geophysical Union, 2006-02-17) Baba, Kiyoshi ; Chave, Alan D. ; Evans, Rob L. ; Hirth, Greg ; Mackie, Randall L.
    The electromagnetic data from the Mantle Electromagnetic and Tomography (MELT) experiment are inverted for a two-dimensional transversely anisotropic conductivity structure that incorporates a correction for three-dimensional topographic effects on the magnetotelluric responses. The model space allows for different conductivity values in the along-strike, cross-strike, and vertical directions, along with imposed constraints of model smoothness and closeness among the three directions. Anisotropic models provide a slightly better fit to the data for a given level of model smoothness and are more consistent with other geophysical and laboratory data. The preferred anisotropic model displays a resistive uppermost 60-km-thick mantle independent of plate age, except in the vicinity of the ridge crest. In most inversions, a vertically aligned sheet-like conductor at the ridge crest is especially prominent in the vertical conductivity. Its presence suggests that the melt is more highly concentrated and connected in the vertical direction immediately beneath the rise axis. The melt zone is at least 100 km wide and is asymmetric, having a greater extent to the west. Off-axis, and to the east of the ridge, the mantle is more conductive in the direction of plate spreading at depths greater than 60 km. The flat resistive-conductive boundary at 60 km agrees well with the inferred depth of the dry solidus of peridotite, and the deeper conductive region is consistent with the preferred orientation of olivine inferred from seismic observations. This suggests that the uppermost 60 km represents the region of mantle that has undergone melting at the ridge and has been depleted of water (dissolved hydrogen). By contrast, the underlying mantle has retained a significant amount of water.