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Van Beusekom, AE, Parker RL, Bank RE, Gill PE, Constable S.  2011.  The 2-D magnetotelluric inverse problem solved with optimization. Geophysical Journal International. 184:639-650.   10.1111/j.1365-246X.2010.04895.x   AbstractWebsite

P>The practical 2-D magnetotelluric inverse problem seeks to determine the shallow-Earth conductivity structure using finite and uncertain data collected on the ground surface. We present an approach based on using PLTMG (Piecewise Linear Triangular MultiGrid), a special-purpose code for optimization with second-order partial differential equation (PDE) constraints. At each frequency, the electromagnetic field and conductivity are treated as unknowns in an optimization problem in which the data misfit is minimized subject to constraints that include Maxwell's equations and the boundary conditions. Within this framework it is straightforward to accommodate upper and lower bounds or other conditions on the conductivity. In addition, as the underlying inverse problem is ill-posed, constraints may be used to apply various kinds of regularization. We discuss some of the advantages and difficulties associated with using PDE-constrained optimization as the basis for solving large-scale nonlinear geophysical inverse problems. Combined transverse electric and transverse magnetic complex admittances from the COPROD2 data are inverted. First, we invert penalizing size and roughness giving solutions that are similar to those found previously. In a second example, conventional regularization is replaced by a technique that imposes upper and lower bounds on the model. In both examples the data misfit is better than that obtained previously, without any increase in model complexity.

Li, Y, Constable S.  2007.  2D marine controlled-source electromagnetic modeling: Part 2 - The effect of bathymetry. Geophysics. 72:WA63-WA71.   10.1190/1.2430647   AbstractWebsite

Marine controlled-source electromagnetic (CSEM) data are strongly affected by bathymetry because of the conductivity contrast between seawater and the crust below the seafloor. We simulate the marine CSEM response to 2D bathymetry using our new finite element (FE) code, and our numerical modeling shows that all electric and magnetic components are influenced by bathymery, but to different extents. Bathymetry effects depend upon transmission frequency, seabed conductivity, seawater depth, transmitter-receiver geometry, and roughness of the seafloor topography. Bathymetry effects clearly have to be take into account to avoid the misinterpretation of marine CSEM data sets.

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Wheelock, B, Constable S, Key K.  2015.  The advantages of logarithmically scaled data for electromagnetic inversion. Geophysical Journal International. 201:1765-1780.   10.1093/gji/ggv107   AbstractWebsite

Non-linear inversion algorithms traverse a data misfit space over multiple iterations of trial models in search of either a global minimum or some target misfit contour. The success of the algorithm in reaching that objective depends upon the smoothness and predictability of the misfit space. For any given observation, there is no absolute form a datum must take, and therefore no absolute definition for the misfit space; in fact, there are many alternatives. However, not all misfit spaces are equal in terms of promoting the success of inversion. In this work, we appraise three common forms that complex data take in electromagnetic geophysical methods: real and imaginary components, a power of amplitude and phase, and logarithmic amplitude and phase. We find that the optimal form is logarithmic amplitude and phase. Single-parameter misfit curves of log-amplitude and phase data for both magnetotelluric and controlled-source electromagnetic methods are the smoothest of the three data forms and do not exhibit flattening at low model resistivities. Synthetic, multiparameter, 2-D inversions illustrate that log-amplitude and phase is the most robust data form, converging to the target misfit contour in the fewest steps regardless of starting model and the amount of noise added to the data; inversions using the other two data forms run slower or fail under various starting models and proportions of noise. It is observed that inversion with log-amplitude and phase data is nearly two times faster in converging to a solution than with other data types. We also assess the statistical consequences of transforming data in the ways discussed in this paper. With the exception of real and imaginary components, which are assumed to be Gaussian, all other data types do not produce an expected mean-squared misfit value of 1.00 at the true model (a common assumption) as the errors in the complex data become large. We recommend that real and imaginary data with errors larger than 10 per cent of the complex amplitude be withheld from a log-amplitude and phase inversion rather than retaining them with large error-bars.

Constable, S, Orange A, Key K.  2015.  And the geophysicist replied: "Which model do you want?" Geophysics. 80:E197-E212.   10.1190/geo2014-0381.1   AbstractWebsite

Marine controlled-source electromagnetic (CSEM) and magnetotelluric (MT) soundings were carried out between 1997 and 2003 over the Gemini prospect in the Gulf of Mexico during early development of marine instrumentation. The resulting data sets provide a good test bed for examining the effect of the data type and misfit choice on regularized inversion solutions. We inverted the data sets individually and jointly for isotropic and anisotropic resistivity at a variety of data misfits. We found that multifrequency CSEM inversions vastly improved structural resolution over single-frequency inversions, suggesting that variation in skin depth added significant information. Joint MT and CSEM inversion appeared to improve resolution over MT-only inversions at depths considerably deeper than the CSEM data can resolve, probably by constraining shallow structure in the parts of the model to which the MT data were sensitive. The addition of model anisotropy improved data fit, but introduced an arbitrary scaling between the regularization penalty on model roughness and the penalty on anisotropy. A small relative penalty on anisotropy produced two independent models for horizontal and vertical resistivity, whereas a large penalty reproduced the isotropic models. Intermediate penalties produced pleasing models, but there was no objective criterion to choose one particular model. Inverted models also depend significantly on the choice of target data misfit, but the optimum misfit is difficult to determine even with well-estimated errors. So-called L-curves do not provide an objective choice of misfit because they are both heuristic and depend on the choice of data that is plotted. Various measures of structure in data residuals were tested in an attempt to guide the misfit choice, with some success, but this too was somewhat heuristic. Ultimately, of the 100 or so inversions that were run, no single model could be considered "preferred," but together they provided a good understanding of the information contained in the data.

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Ray, A, Key K, Bodin T, Myer D, Constable S.  2014.  Bayesian inversion of marine CSEM data from the Scarborough gas field using a transdimensional 2-D parametrization. Geophysical Journal International. 199:1847-1860.   10.1093/gji/ggu370   AbstractWebsite

We apply a reversible-jump Markov chain Monte Carlo method to sample the Bayesian posterior model probability density function of 2-D seafloor resistivity as constrained by marine controlled source electromagnetic data. This density function of earth models conveys information on which parts of the model space are illuminated by the data. Whereas conventional gradient-based inversion approaches require subjective regularization choices to stabilize this highly non-linear and non-unique inverse problem and provide only a single solution with no model uncertainty information, the method we use entirely avoids model regularization. The result of our approach is an ensemble of models that can be visualized and queried to provide meaningful information about the sensitivity of the data to the subsurface, and the level of resolution of model parameters. We represent models in 2-D using a Voronoi cell parametrization. To make the 2-D problem practical, we use a source-receiver common midpoint approximation with 1-D forward modelling. Our algorithm is transdimensional and self-parametrizing where the number of resistivity cells within a 2-D depth section is variable, as are their positions and geometries. Two synthetic studies demonstrate the algorithm's use in the appraisal of a thin, segmented, resistive reservoir which makes for a challenging exploration target. As a demonstration example, we apply our method to survey data collected over the Scarborough gas field on the Northwest Australian shelf.

Wang, SG, Bastani M, Constable S, Kalscheuer T, Malehmir A.  2019.  Boat-towed radio-magnetotelluric and controlled source audio-magnetotelluric study to resolve fracture zones at Aspo Hard Rock Laboratory site, Sweden. Geophysical Journal International. 218:1008-1031.   10.1093/gji/ggz162   AbstractWebsite

Boat-towed radio-magnetotelluric (RMT) measurements using signals between 14 and 250 kHz have attracted increasing attention in the near-surface applications for shallow water and archipelago areas. A few large-scale underground infrastructure projects, such as the Stockholm bypass in Sweden, are planned to pass underneath such water zones. However, in cases with high water salinity, RMT signals have a penetration depth of a few metres and do not reach the geological structures of interest in the underlying sediments and bedrock. To overcome this problem, controlled source signals at lower frequencies of 1.25 to 12.5 kHz can be utilized to improve the penetration depth and to enhance the resolution for modelling deeper underwater structures. Joint utilization of boat-towed RMT and controlled source audio-magnetotellurics (CSAMT) was tested for the first time at the Aspo Hard Rock Laboratory (HRL) site in south-eastern Sweden to demonstrate acquisition efficiency and improved resolution to model fracture zones along a 600-m long profile. Pronounced galvanic distortion effects observed in 1-D inversion models of the CSAMT data as well as the predominantly 2-D geological structures at this site motivated usage of 2-D inversion. Two standard academic inversion codes, EMILIA and MARE2DEM, were used to invert the RMT and CSAMT data. EMILIA, an object-oriented Gauss-Newton inversion code with modules for 2-D finite difference and 1-D semi-analytical solutions, was used to invert the RMT and CSAMT data separately and jointly under the plane-wave approximation for 2-D models. MARE2DEM, a Gauss-Newton inversion code for controlled source electromagnetic 2.5-D finite element solution, was modified to allow for inversions of RMT and CSAMT data accounting for source effects. Results of EMILIA and MARE2DEM reveal the previously known fracture zones in the models. The 2-D joint inversions of RMT and CSAMT data carried out with EMILIA and MARE2DEM show clear improvement compared with 2-D single inversions, especially in imaging uncertain fracture zones analysed in a previous study. Our results show that boat-towed RMT and CSAMT data acquisition systems can be utilized for detailed 2-D or 3-D surveys to characterize near-surface structures underneath shallow water areas. Potential future applications may include geo-engineering, geohazard investigations and mineral exploration.

Myer, D, Constable S, Key K.  2011.  Broad-band waveforms and robust processing for marine CSEM surveys. Geophysical Journal International. 184:689-698.   10.1111/j.1365-246X.2010.04887.x   AbstractWebsite

P>In the marine controlled-source electromagnetic method, the Earth response varies in frequency; therefore, using a wide range of frequencies may better constrain geological structure than using a single frequency or only a few closely spaced frequencies. Binary waveforms, such as the square wave, provide a number of frequencies, though many are limited in usefulness because of the rapid decline of amplitude with frequency. Binary waveform design can be improved by recognizing that the class of doubly symmetric waveforms has special properties: they are compact, have controlled phase, are never polarizing and can be described by a simple closed-form mathematical solution. Using this solution, we discovered a compact waveform in which the amplitudes of the third and seventh harmonics are maximized and which has a signal-to-noise advantage at higher frequencies over several other common waveforms. Compact waveforms make possible improved methods for time-series processing. Using short time windows and a first-difference pre-whitener lessens spectral contamination from magnetotelluric signal and oceanographic noise; robust stacking reduces bias from time-series noise transients; and accurate variance estimates may be derived from averages of waveform-length Fourier transform windows of the time-series.

Key, K, Constable S.  2002.  Broadband marine MT exploration of the East Pacific Rise at 9 degrees 50 ' N. Geophysical Research Letters. 29   10.1029/2002gl016035   AbstractWebsite

[1] We present the first use at a mid-ocean ridge of a recently developed broadband marine magnetotelluric (MT) instrument. The extended high frequency performance of the instrument allows resolution of electrical resistivity structure at shallower depths than traditional marine MT sensors. Our two-dimensional inversion model from data collected at four MT sites on the East Pacific Rise (EPR) at 9degrees50'N demonstrates the viability of the method to image electrical resistivity structure in both the crust and shallow mantle. While our pilot experiment falls far short of the coverage needed to provide rigorous constraints on structure, a low resistivity zone in the crustal portion of the inversion model agrees well with seismic tomography and seafloor compliance results. Resistivities beneath the ridge imply a crustal partial melt fraction of 1-20%. A total melt volume of about 0.75 km(3) per kilometer of ridge implies an average melt residence time of about 1000 years.

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Key, K, Constable S.  2011.  Coast effect distortion of marine magnetotelluric data: Insights from a pilot study offshore northeastern Japan. Physics of the Earth and Planetary Interiors. 184:194-207.   10.1016/j.pepi.2010.11.008   AbstractWebsite

We report on strong coast effect distortions observed for broadband marine magnetotelluric (MT) data collected on the forearc offshore northeastern Japan. Eight days of horizontal electric and magnetic fields recorded at eight seafloor stations and the horizontal magnetic fields from a land remote station were processed with a robust multiple-station algorithm, yielding good MT responses and inter-station transfer functions at periods of 7-10,000 s. Transverse electric (TE) mode responses have cusps in apparent resistivity and negative phases at periods around 1000 s, while the transverse magnetic (TM) mode responses are galvanically depressed below the TE responses. An analysis of inter-station transfer functions confirms that the apparent resistivity cusps are a magnetic field, rather than electric field, phenomenon, consisting of an amplitude minimum and rapid phase change around a characteristic frequency. Poynting vectors for a TE coast effect model study illustrate that the anomalous phases are associated with energy diffusing back up to the seafloor from below, after being turned around from its usual downward propagating trajectory by inductive coupling between the conductive ocean and the resistive seafloor along the continental margin. We show that the characteristic frequency and position of the TE mode apparent resistivity cusps are determined by a relatively simple combination of the electrical resistivity of the seafloor, the depth of the ocean, and the distance from the coastline. By including coastlines and bathymetry in 2D inversion, we recover the seafloor conductivity structure along the forearc, demonstrating that broadband data can constrain the thickness of conductive forearc sediments and the underlying high resistivity associated with the mantle wedge and subducting oceanic lithosphere. (C) 2010 Elsevier B.V. All rights reserved.

Constable, S.  1993.  Conduction by mantle hydrogen. Nature. 362:704-704.   10.1038/362704a0   AbstractWebsite
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Constable, S.  2007.  Conductivity, Ocean floor measurements. Encyclopedia of Geomagnetism and Paleomagnetism. ( Gubbins D, Herrero-Bervera E, Eds.).:71-73.: Springer Abstract
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Constable, S.  1993.  Constraints on Mantle Electrical-Conductivity from Field and Laboratory Measurements. Journal of Geomagnetism and Geoelectricity. 45:707-728.   10.5636/jgg.45.707   AbstractWebsite

A global geomagnetic response function, sensitive to the average radial electrical conductivity structure of Earth's mantle to depths of at least 1800 km, is obtained by averaging published, single-site response functions estimated at periods between 10(5)-10(7) seconds from magnetic observatory records. Although the error bars on the global response function are mostly smaller than 5%, Parker's D+ algorithm demonstrates compatibility with a one-dimensional model, both in terms of magnitude and distribution of data residuals. Smooth models in the sense of minimum first and second derivatives of log(conductivity) with log(depth) show conductivities increasing from 0.01 S/m 200 km deep to 2 S/m at a depth of 2000 km. Geotherms inferred from these conductivities using a laboratory model for the temperature dependence of dry subsolidus olivine yield temperatures of 1750-degrees-C at a depth of 410 km; hotter than the 1400-degrees-C for this depth inferred from published values for the equilibrium boundary of the olivine alpha --> alpha + beta transition. Inclusion of a sharp jump in conductivity at the 660 km seismic discontinuity lowers the electrogeotherm to 1600-degrees-C at 410 km, while an explicit penalty on the conductivity at this depth demonstrates that a temperature of 1400-degrees is compatible with the global response function if 1000 S of additional conductance is included above 200 km. The electrical conductivity below the jump at 660 km is 1 S/m increasing to 2 S/m at 2000 km, in excellent agreement with recent diamond anvil measurements of lower mantle materials. Extension of the global response to higher frequencies is possible using data from magnetic satellites. One such study is shown to be in general agreement with the averaged response.

Cox, CS, Constable SC, Chave AD, Webb SC.  1986.  Controlled-Source Electromagnetic Sounding of the Oceanic Lithosphere. Nature. 320:52-54.   10.1038/320052a0   AbstractWebsite

The attenuation of ionospheric signals in the frequency range 0.06–24 Hz by sea water effectively precludes using the magnetotel-luric method to study the electrical structure of the upper oceanic lithosphere. We have carried out a dipole–dipole electromagnetic sounding in the North Pacific by injecting electromagnetic signals into the ocean and sea bed. The crust at the site is 25 Myr old and has a thin sediment cover. The technique, similar to that used in earlier work1,2, involves dragging a horizontal dipole antenna along the sea floor. The electric fields that propagated through the resistive basement were detected by seafloor receivers at ranges of 10–65 km. As the ambient electric field is very small (varying from 10−18 V2 m−2 Hz−1 at 0.1 Hz to 10−24 V2 m2 Hz−1 above 1 Hz; ref. 3), the controlled-source signals could be easily monitored. Our data are consistent with a simple one-dimensional Earth model consisting of a 3–7-km-thick crustal layer of moderate conductivity (~0.001 S m−1) underlain by a thicker region of very low conductivity (<2 × 10−5 S m−1). The results suggest an upper mantle water content of at most 0.1% by volume.

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Constable, SC, McElhinny MW, McFadden PL.  1984.  Deep Schlumberger Sounding and the Crustal Resistivity Structure of Central Australia. Geophysical Journal of the Royal Astronomical Society. 79:893-910.   10.1111/j.1365-246X.1984.tb02875.x   AbstractWebsite

Three 200 km Schlumberger resistivity soundings have been conducted over the central Australian shield, using telephone lines to obtain the large electrode spacings. These represent the first crustal scale controlled source electrical study to be carried out in this continent. A computer controlled data acquisition system was used which allowed precise measurements to be made with only modest emission currents (0.1–0.5 A).The three soundings, centred on the towns of Renner Springs, Wauchope and Aileron, showed the southern part of the study area (the Arunta Block) to be an order of magnitude more resistive than the more northerly section (the Tennant Creek Block). This difference correlates with the higher heat flow of the Tennant Creek Block. A lowering of apparent resistivity at large electrode spacings for one sounding (Wauchope) is taken to indicate the presence of a low resistivity layer in the middle crust, at a depth less than 20 km. However, the effect of the highly conductive overburden characteristic of inland Australia, combined with the large transverse resistance of the crust, prevented the other two soundings from detecting such a layer. Without support from these two soundings, it is impossible to be sure that the lowered resistivity at Wauchope is not caused merely by lateral variations in near-surface resistivity.The data also show that crustal resistivities are much lower than the expected values for dry rock, whether or not a low resistivity layer is included in the model. This implies a widespread occurrence of free water in the crust, with greater amounts occurring at depth if the low resistivity zone exists.

Constable, S, Duba A.  2002.  Diffusion and mobility of electrically conducting defects in olivine. Physics and Chemistry of Minerals. 29:446-454.   10.1007/s00269-002-0260-8   AbstractWebsite

Electrical conductivity of lherzolite (65% olivine), measured as a function of time after changes in the oxygen fugacity (f(O2)) of the surrounding CO(2)/CO atmosphere, is used to infer the diffusivity of the point defects responsible for conduction in olivine. A total of 63 equilibration runs at temperatures of 900, 1000, 1100, and 1200 degreesC were fit using nonlinear parameter estimation to recover time constants (directly related to diffusivity) and conductivity steps. An observed f(O2) dependence in the time constants associated with re-equilibration implies two defect species of fixed diffusivity but with f(O2)-dependent concentrations. Although the rate-limiting step may not necessarily be associated with a conducting defect, when time constants are converted to diffusivities, the magnitudes and activation energies agree extremely well with the model for magnesium vacancies (the slower species) and small polarons (holes localized on Fe(3+)) derived by Constable and Roberts (1997). This earlier study used an independent method of simultaneous modeling of thermopower and electrical conductivity as a function of f(O2) and temperature, on data from a different type of sample (a dunite). We observe that at high f(O2) where polarons dominate over magnesium vacancies in the defect population, re-equilibration is dominated by magnesium vacancy diffusion, and vice versa (at low f(O2) magnesium vacancies dominate and re-equilibration proceeds at the faster rate associated with polaron mobility). We interpret this to suggest association between the cation vacancies and polarons, as has been suggested by Tsai and Dieckmann (1997), making the concentration of the minority defect the rate-limiting step in the oxidation/reduction reactions.

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Everett, ME, Constable S, Constable CG.  2003.  Effects of near-surface conductance on global satellite induction responses. Geophysical Journal International. 153:277-286.   10.1046/j.1365-246X.2003.01906.x   AbstractWebsite

A 3-D finite-element simulation of global electromagnetic induction is used to evaluate satellite responses in geomagnetic dipole coordinates for harmonic ring-current excitation of a three-layer mantle overlain by a realistic near-surface conductance distribution. Induced currents are modelled for lithospheric and asthenospheric upper-mantle conductivities in the range sigma= 10(-4) -0.1 S m(-1) . The magnetic scalar intensity B is calculated at a typical satellite altitude of 300 km. At short periods, T = 2 and 12 h, the induction signal owing to the near-surface conductance is large when a resistive upper mantle is present, but drops off with increasing mantle conductivity. At longer periods, T = 2 d, the near-surface induction signal is generally much smaller and nearly independent of upper-mantle conductivity. The near-surface induction signal is very sensitive to the electrical conductivity of the lithospheric mantle, but only moderately sensitive to that of the asthenospheric mantle. Induced currents are confined to the heterogeneous surface shell at periods of less than 2 h, and flow predominantly in the mantle at periods of longer than 2 d. In the intervening period range, induced currents are partitioned between the near-surface and the upper mantle. These results indicate the importance of carrying out a full 3-D analysis in the interpretation of satellite induction observations in the period range from hours to days.

Everett, ME, Constable S.  1999.  Electric dipole fields over an anisotropic seafloor: theory and application to the structure of 40 Ma Pacific Ocean lithosphere. Geophysical Journal International. 136:41-56.   10.1046/j.1365-246X.1999.00725.x   AbstractWebsite

Seismic anisotropy has been detected in the oceanic crust and upper mantle, and likewise it is geologically reasonable to expect that a certain amount of lateral anisotropy exists in seafloor electrical properties. Anisotropy in Earth properties can often lead to surprising effects on geophysical responses that are not anticipated from simple isotropic theories. Here, we investigate the effects of lateral anisotropy on the frequency-domain, controlled-source electromagnetic (CSEM) response of a uniaxially conducting, non-magnetic seafloor excited by a horizontal electric dipole whose moment is oriented obliquely with respect to the electrical strike direction. A 'paradox of anisotropy' is observed, in which the seafloor electric field strength is enhanced in the most conductive direction of the seafloor. This enhancement is opposite to what one would expect based on naive isotropic theory. We also show that it is possible in certain circumstances to extract the along-strike electrical conductivity from marine controlled-source electromagnetic data using only isotropic modelling. The extraction of across-strike conductivity, however, requires full anisotropic modelling. The physical insight into electromagnetic induction in uniaxial media that is presented here should greatly assist the geological interpretation of marine CSEM experimental data. Applying our algorithm to the PEGASUS data set (CSEM data collected over 40 Ma Pacific Ocean lithosphere) produces a model with conductivity in the fossil spreading direction that is seven times greater than the conductivity perpendicular to spreading. Strain-aligned mineralogical fabric, as predicted by tectonic modelling, would explain our result, with enhanced conductivities caused by hydrogen conduction along the olivine a-axis or connected accumulations of trace conductors such as graphite or magnetite.

Heinson, G, Constable S, White A.  1993.  The electrical conductivity of the lithosphere and asthenosphere beneath the coastline of southern california. Bulletin of Australian society of Exploration in Geophysics. 24:194-200. Abstract
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Chave, AD, Constable S, Edwards RN.  1991.  Electrical exploration methods for the seafloor. Electromagnetic methods ub appied geophysics. 2( Nabhigian M, Ed.).:931-966., Tulsa: Society of Exploration Geophysics Abstract
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Key, K, Constable S, Liu L, Pommier A.  2013.  Electrical image of passive mantle upwelling beneath the northern East Pacific Rise. Nature. 495:499-502.: Nature Publishing Group, a division of Macmillan Publishers Limited. All Rights Reserved.   10.1038/nature11932   AbstractWebsite

Melt generated by mantle upwelling is fundamental to the production of new oceanic crust at mid-ocean ridges, yet the forces controlling this process are debated1, 2. Passive-flow models predict symmetric upwelling due to viscous drag from the diverging tectonic plates, but have been challenged by geophysical observations of asymmetric upwelling3, 4, 5 that suggest anomalous mantle pressure and temperature gradients2, 6, 7, and by observations of concentrated upwelling centres8 consistent with active models where buoyancy forces give rise to focused convective flow2. Here we use sea-floor magnetotelluric soundings at the fast-spreading northern East Pacific Rise to image mantle electrical structure to a depth of about 160 kilometres. Our data reveal a symmetric, high-conductivity region at depths of 20–90 kilometres that is consistent with partial melting of passively upwelling mantle9, 10, 11. The triangular region of conductive partial melt matches passive-flow predictions, suggesting that melt focusing to the ridge occurs in the porous melting region rather than along the shallower base of the thermal lithosphere. A deeper conductor observed east of the ridge at a depth of more than 100 kilometres is explained by asymmetric upwelling due to viscous coupling across two nearby transform faults. Significant electrical anisotropy occurs only in the shallowest mantle east of the ridge axis, where high vertical conductivity at depths of 10–20 kilometres indicates localized porous conduits. This suggests that a coincident seismic-velocity anomaly12 is evidence of shallow magma transport channels13, 14 rather than deeper off-axis upwelling. We interpret the mantle electrical structure as evidence that plate-driven passive upwelling dominates this ridge segment, with dynamic forces being negligible.

Du Frane, WL, Stern LA, Constable S, Weitemeyer KA, Smith MM, Roberts JJ.  2015.  Electrical properties of methane hydrate plus sediment mixtures. Journal of Geophysical Research-Solid Earth. 120:4773-4783.   10.1002/2015jb011940   AbstractWebsite

Knowledge of the electrical properties of multicomponent systems with gas hydrate, sediments, and pore water is needed to help relate electromagnetic (EM) measurements to specific gas hydrate concentration and distribution patterns in nature. Toward this goal, we built a pressure cell capable of measuring in situ electrical properties of multicomponent systems such that the effects of individual components and mixing relations can be assessed. We first established the temperature-dependent electrical conductivity (sigma) of pure, single-phase methane hydrate to be similar to 5 orders of magnitude lower than seawater, a substantial contrast that can help differentiate hydrate deposits from significantly more conductive water-saturated sediments in EM field surveys. Here we report sigma measurements of two-component systems in which methane hydrate is mixed with variable amounts of quartz sand or glass beads. Sand by itself has low sigma but is found to increase the overall sigma of mixtures with well-connected methane hydrate. Alternatively, the overall sigma decreases when sand concentrations are high enough to cause gas hydrate to be poorly connected, indicating that hydrate grains provide the primary conduction path. Our measurements suggest that impurities from sand induce chemical interactions and/or doping effects that result in higher electrical conductivity with lower temperature dependence. These results can be used in the modeling of massive or two-phase gas-hydrate-bearing systems devoid of conductive pore water. Further experiments that include a free water phase are the necessary next steps toward developing complex models relevant to most natural systems.

Du Frane, WL, Stern LA, Weitemeyer KA, Constable S, Pinkston JC, Roberts JJ.  2011.  Electrical properties of polycrystalline methane hydrate. Geophysical Research Letters. 38   10.1029/2011gl047243   AbstractWebsite

Electromagnetic (EM) remote-sensing techniques are demonstrated to be sensitive to gas hydrate concentration and distribution and complement other resource assessment techniques, particularly seismic methods. To fully utilize EM results requires knowledge of the electrical properties of individual phases and mixing relations, yet little is known about the electrical properties of gas hydrates. We developed a pressure cell to synthesize gas hydrate while simultaneously measuring in situ frequency-dependent electrical conductivity (sigma). Synthesis of methane (CH(4)) hydrate was verified by thermal monitoring and by post run cryogenic scanning electron microscope imaging. Impedance spectra (20 Hz to 2 MHz) were collected before and after synthesis of polycrystalline CH(4) hydrate from polycrystalline ice and used to calculate s. We determined the sigma of CH(4) hydrate to be 5 x 10(-5) S/m at 0 degrees C with activation energy (E(a)) of 30.6 kJ/mol (-15 to 15 degrees C). After dissociation back into ice, sigma measurements of samples increased by a factor of similar to 4 and E(a) increased by similar to 50%, similar to the starting ice samples. Citation: Du Frane, W. L., L. A. Stern, K. A. Weitemeyer, S. Constable, J. C. Pinkston, and J. J. Roberts (2011), Electrical properties of polycrystalline methane hydrate, Geophys. Res. Lett., 38, L09313, doi:10.1029/2011GL047243.

MacGregor, L, Sinha M, Constable S.  2001.  Electrical resistivity structure of the Valu Fa Ridge, Lau Basin, from marine controlled-source electromagnetic sounding. Geophysical Journal International. 146:217-236.   10.1046/j.1365-246X.2001.00440.x   AbstractWebsite

In December 1995 we carried out a comprehensive controlled-source electromagnetic survey of the Valu Fa Ridge at 22 degrees 25'S in the Lau Basin. The Valu Fa Ridge is a back-arc spreading centre of intermediate spreading rate and is a site of extensive hydrothermal activity. Seismic studies have imaged a melt lens at an average depth of 3.2 km below the seafloor, surrounded by a zone of lowered seismic velocity, interpreted as a region of partial melt in the crust. The electromagnetic experiment was part of a multidisciplinary study which included wide-angle and reflection seismics, bathymetry and potential field measurements. Electromagnetic signals at frequencies between 0.25 and 40 Hz were transmitted from a horizontal electric dipole towed close to the seafloor and were recorded by an array of 11 sea-bottom receivers fit ranges of up to 20 km from the source. Over 80 hr of data, consisting of the magnitude of the horizontal electric field at the seafloor, were collected. These data have extremely low scatter compared to similar data from previous surveys. The data were interpreted using a combination of 1- and 2-D forward modelling and inversion. The vertical resistivity gradient in the upper crust at the Vain Fa Ridge is abnormally low, with resistivities of less than 10 Ohm m observed throughout layer 2 of the crust to a depth of 3 km. This is significantly more conductive at depth than the axis of the slow-spreading Reykjanes Ridge at 57 degrees 45'N, and the fast-spreading East Pacific Rise at 13 degreesN, where similar data sets have been collected in the past. Although the structure of layer 2 is well constrained by the electromagnetic data, its extremely low resistivity causes rapid attennuation of electromagnetic signals diffusing through it, and hence the data are not sensitive to the structure in layer 3, in particular the structure of the melt lens or surrounding low-velocity zone. The seismic velocity structure of the Valu Fa Ridge, determined from the coincident wide-angle seismic study, is similar to that observed at other mid-ocean ridges, with a steep seismic velocity gradient through layer 2 (although overall velocities are slightly lower). The seismic velocity anomaly calculated relative to an average off-axis structure is also small. This suggests that the very low resistivities observed at the axis are not caused by an upper crust of abnormally high porosity. However, hot and/or saline fluids permeating the crust can explain the low resistivities without affecting the seismic velocity. Since the conductive region extends unbroken from 3 km depth to the seafloor, it is probable that these fluids circulate to (or close to) the magma chamber itself.

Constable, SC.  1992.  Electrical studies of the Australian lithosphere. Geological Society of Australia, Special Publication. 17:121-140. Abstract
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Constable, S, Shankland TJ, Duba A.  1992.  The Electrical-Conductivity of an Isotropic Olivine Mantle. Journal of Geophysical Research-Solid Earth. 97:3397-3404.   10.1029/91jb02453   AbstractWebsite

In order to extend the useful temperature range of interpretation of olivine electrical conductivity-sigma we have used the nonlinear iterative Marquardt technique to fit experimental data over the range 720-degrees-1500-degrees-C to the parametric form sigma = sigma-1e(-A1/kT) + sigma-2e(-A2/kT), where k is Boltzmann's constant and T is absolute temperature. The model describes conduction by migration of two different thermally activated defect populations with activation energies A1 and A2, and preexponential terms sigma-1 and sigma-2 that depend on number of charge carriers and their mobility and that may be different for each crystallographic direction. A combined interpretation of recent high (San Carlos olivine) and low (Jackson County dunite) temperature measurements has been made that demonstrates that a single activation energy A1 for all three crystallographic directions adequately fits the data. The parametric fits show that the high-temperature conduction mechanism has far greater anisotropy than the low-temperature mechanism, consistent with previous assignments to ionic and electronic conduction, respectively. The geometric mean of the conductivity in the three directions is approximately sigma-BAR 10(2.402)e-1.60eV/kT + 10(9.17)e-4.25eV/kT S/m and is presented as a model for isotropic olivine, SO2, appropriate from 720-degrees-C to above 1500-degrees-C, at oxygen fugacities near the center of the olivine stability field. It is observed that the magnitudes of sigma-1 for the three crystal directions are similar to the ratios of the inter-ionic distances between the M1 magnesium sites in olivine, to within 5%, consistent with Fe3+ preferring the M1 site below 1200-degrees-C.