Conductivity Depth Profiles Research Articles

Quiet-day ionospheric currents and their application to upper mantle conductivity in Australia

This study concerns the use of selected geomagnetic field records to establish the 1990 quiet-day current system (Sq) for Australia and to use the ionospheric current source of Sq for a determination of the Earth’s deep electrical conductivity. The primary data set came from a chain of eight, three-component magnetometer stations that was operated along a north-south line in central Australia. Additional records, necessary for boundary conditions, were added to the data set. A regional spherical harmonic analysis (SHA) allowed the separation of the internal and external field contributions to the Sq variations. Mapping of the equivalent ionospheric current from the external field showed that the Sq contour focus passed near the —30° geomagnetic latitude of central Australia with a 5° latitude variation between winter and summer and a corresponding change from about 80 to 200 kA in strength. A special transfer function allowed the computation of an equivalent conductivity-depth profile of central Australia from the paired external and internal coefficients of the SHA. A regression line through the conductivity estimates gives a profile that starts at 0.025 S/m for a depth of 130 km, rising gradually to about 0.045 S/m at 250 km, then steepens to 0.11 S/m at 360 km and rises moderately to 0.13 S/m at 470 km near the base of the upper mantle. No data were obtained through the mantle transition zone. Computations gave 0.18 S/m in the region of 800 km depth. Previous conductivity models for the upper mantle beneath central Australia, although less specific in values, are consistent with our profile. At depths greater than 500 km, the regression profile is in agreement with the conductivity distribution beneath the Tasman Sea determined from seafloor magnetotellurics, although both measurements lack high resolution at such depths.

Tikhonov Regularization of Electrical Conductivity Depth Profiles in Field Soils

AbstractElectromagneetic induction is an established, noninvasive technique for measuring the apparent electrical conductivity of soils and contaminants in soils and aquifers. Nevertheless, the noninvasive determination of electrical conductivity depth profiles using only aboveground electromagnetic induction measurements remains difficult since it involves ill‐posed inverse problems. Tikhonov regularization is an established technique for the solution of ill‐posed linear inverse problems. We used Tikhonov regularization for estimating the electrical conductivity depth profile of the soil from aboveground electromagnetic induction measurements. Results from the inversion of sets of Geonics EM‐38 measurements are reported. It was found that this technique is superior to other inverse techniques previously reported in the literature.

Boundary undercurrent and water mass changes in the Lincoln Sea

Oceanographic measurements taken between 1989 and 1994 in the Lincoln Sea describe the currents and water mass structure along the continental slope of the Arctic Basin between the Canadian and Eurasian Basins. The measurements included periodic conductivity and temperature versus depth (CTD) profiles from ice camps, CTD cross sections normal to the slope, and year‐round current measurements. Analysis of this data describes the hydrographic structure of the waters over the continental slope and identifies some significant interannual variations. An undercurrent, confined to the continental slope, with a width of about 50 km and speeds of 5–9 cm s−1 is shown in geostrophic current cross sections. The presence of this easterly flow at depth is confirmed by current meter measurements, and its existence has also been observed in the Beaufort Sea and the Barents Sea [Aagaard, 1989]. The waters within this undercurrent exhibit temperature‐salinity (TS) characteristics similar to Canadian Basin waters, suggesting a boundary current system which is continuous along the continental slope north of Alaska and Canada. Significant interannual variations in temperature and salinity profiles may be related to variations in the large‐scale circulation of the Arctic. Examination of the upper pycnocline waters over the slope between 1991 and 1994 indicated a relative temperature maximum overlying a minimum, TS characteristics similar to waters attributed to Bering Sea origin found in the Canadian Basin. These characteristics were not seen, however, during 1989 and 1990, suggesting a recent increase in the transport of surface waters from the Canadian Basin into the Eurasian Basin.

On the derivation of the Earth's conductivity structure by means of spherical cap harmonic analysis

SUMMARY After Haines & Torta (1994) applied spherical cap harmonic analysis (SCHA) to deduce the formulation of equivalent currents in terms of spherical cap harmonic coefficients, it seemed appropriate to extend the same scheme that relates global spherical harmonics with the Earth's conductivity structure to regional modelling of geomagnetic-field variations. From the considerations made in this paper it seems difficult or even impossible to obtain either a conductivity-depth profile (by assuming a homogeneous mantle conductivity within the region) or a 3-D structure, from a regional analysis of global-scale phenomena such as the regular daily variation, by using the same formulations as employed in global analyses. There exist, in addition, some intrinsic limits of SCHA itself, which, although in general do not decrease its potential in regional geomagnetic modelling, can affect the derivation of a proper conductivity estimation.

Depth Profiles of Electrical Conductivity from Linear Combinations of Electromagnetic Induction Measurements

AbstractWithin the past 10 yr, frequency‐domain electromagnetic (FEM) induction techniques have become more and more widely used in soil science and hydrology. Each measurement of apparent electrical conductivity represents a depth‐weighted average of soil electrical conductivity. However, the depth weighting corresponding to each measurement may be very different from that required by the user. The simultaneous use of multiple measurements (with different depth weightings) should allow some aspects of the depth distribution of electrical conductivity to be inferred. We illustrate a method for obtaining linear combinations of FEM measurements to estimate the soil electrical conductivity within the depth interval of interest. The method relies on the simple fact that the measurement‐system response is linear, so that a linear combination of apparent‐conductivity readings corresponds to a linear combination of response functions. One can seek a linear combination of response functions that has desirable characteristics. This sets up an optimization problem that can be solved by standard methods, which avoids difficulties encountered with layered inversions to resolve nonlayered systems. The approach was applied to GEONICS EM31, EM34, and EM38 instruments in three examples: (i) single frequency measurements at vertical and horizontal dipole configurations, (ii) frequency measurements using the EM34 at all six possible configurations, and (iii) frequency measurements using the EM38 held at varying heights above the ground. The derived linear combinations were applied to field data from southern Australia. Soil conductivity profiles predicted using linear combinations showed good agreement with profiles measured with a conductivity probe.

Fresh‐Water/Sea‐Water Relationship Within a Ground‐Water Flow System, Northeastern Coast of the Yucatan Peninsula

AbstractGround‐water velocities within fractures and boreholes, hydraulic heads, and depth profiles of conductivity were measured along a 70 km section of the northeastern coast of the Yucatan Peninsula, Mexico. Hydraulic heads ranged from 40 to 60 cm above mean sea level between 2 and 4 km from the coast. Fluid velocities estimated from point‐dilution tests, in the dual‐porosity rock in a borehole several kilometers from the coast, were 0.021 cm/sec in the fresh‐water lens and 0.082 cm/sec near a fracture in the underlying sea‐water zone. Velocities in large fractures increased from 1 cm/sec 10 kilometers inland to 12 cm/sec near discharge points along the coast. This increase is attributed to the decrease in thickness of the fresh‐water lens.The thickness of the fresh‐water lens is approximately 40% less than the Ghyben‐Herzberg relation predicts for a static system, providing the potential to drive fresh water through fractures into the sea‐water zone below the halocline. Overall, the halocline appears to be in a steady‐state position due to the rapid flow of fresh water and brackish water towards the coast combined with rising sea water in corivectional flow.

Analyzing electromagnetic induction data: Suggestions from laboratory measurements

Recent inversions of electrical profiles of the upper mantle beneath the oceans permit a variety of conductivity-depth profiles ranging from models with monotonically increasing conductivity to layered models having decreases of conductivity with depth. Laboratory data on possible mantle materials can physically explain high mantle conductivities in terms of a fluid phase (partial melt, hydrous fluid) or a good solid conductor (amorphous or graphitic carbon) and favor a profile having a high conductivity layer (HCL) underlain by a more resistive layer.

Global electromagnetic induction

Methods of analysis of long period geomagnetic variations (periods over a few hours), the available electromagnetic response function estimates, and the effect of lateral inhomogeneity within the Earth are reviewed. Recent advances in the inversion of response function data to produce conductivitydepth profiles are mentioned, and aspects of the inverse problem specific to global (spherical Earth) induction are discussed. There is a rapid rise in electrical conductivity between about 400 km and 800 km, but whether this is a gradual change or consists of one or several steps is not resolvable with the presently available data and naive inversion algorithm used here. At the greatest depths to which presently analysed variations penetrate (1000–1500 km), available data have some difficulty in resolving finer structure, but there are indications that the electrical structure of the continents becomes more laterally homogeneous as depth increases. Previously published inversions see lateral variations in electrical structure down to at least 500 km, and at shallower depths these variations are unambiguously resolved.

An integral equation method for inversion of electromagnetic soundings

The analogy of the problem of electromagnetic induction sounding of the earth's conductivity-depth profile using a two perpendicular-loop system to the general remote sensing problem of the atmosphere is pointed out. The induction sounding problem has been reduced to the solution of a new integral equation of Fredholm type. Kernels of the integral equation are evaluated, and their characteristics are investigated. A nonlinear relaxation inversion technique is suggested for the solution. Convergence of the solution, information content of measurements, and the range of possible retrieval of the conductivity profile are discussed.

Anomalies in Daily Variation Magnetic Fields and Structure Under North-western United States and South-western Canada

Summary Thirty-one magnetometers of a large array secured records through a magnetically quiet 5-day period in July 1969, between latitudes 44 and 51 N and longitudes 100 and 121 W. The North American Central Plains variation anomaly persists in the Z component at periods 8 and 12 hr, but not in Y. Even qualitative explanation requires a channelled current of complicated geometry. Induction by Y is dominant at periods less than 2 hr but induction by 2 appears significant at daily-variation periods. The northern end of the conductive ridge in the upper mantle under the Wasatch Front produces prominent induction anomalies in Y and Z at periods 8 and 12 hr. At period 24 hr the amplitude maps show complex patterns of anomalies with features which do not correspond to those at shorter periods. The phase of 2 shows a steep gradient to the south-south-west and approaches that of X. This phase shift of over 5 hr is attributed to induction by X of currents in the highly conductive upper mantle under the Basin and Range Province, south of the array. The anomalies in 2 and Y amplitudes then arise from variable transmission of fields due to these currents through the electrically heterogeneous upper mantle and crust to the stations of the array. The use of a phase-difference test shows that anomalies in Z and Y amplitudes at period 24 hr, near the Northern Rockies, are such variable transmission (vartran) anomalies, whereas those at periods less than 2 hr are induction anomalies. West of the Northern Rockies the conductivity-depth profile which best fits the normal fields differs from the Great Plains profile by the addition of a conductive layer 15 km thick, in the depth range 50-100 km. The top of the ultimate mantle conductor is at depth 350 km. Small local anomalies near the Northern Rockies are modelled by elaborating on the conductive layer.

Gross Estimates of the Conductivity, Dielectric Constant, and Magnetic Permeability Distributions in the Moon

Sources of direct information on the electrical parameters of the moon include earth‐based astatic radar, earth‐satellite bistatic radar, lunar‐lander astatic radar, earth‐based radiothermic measurements, lunar orbital magnetic field measurements, and lunar‐lander magnetic attraction experiments. These pieces of information, when fitted to a reasonable geological model of the moon, permit estimation of the depth profiles of electrical conductivity, dielectric constant, and magnetic permeability. At lunar surface dc conductivities as low as 10‐12 mho/m may occur, and conductivities as high as 10 mhos/m appear possible for the deep lunar interior. It is demonstrated that interpretation of the Explorer 35 lunar satellite magnetometer data is at present based on such inadequate theory that the above range of values of conductivity could be quite consistent with the orbital magnetic field data. Anomalous ‘dc’ dielectric constants as high as 1010 could exist in the lunar interior if pore water and metallic minerals are present in juxtaposition. Magnetic permeabilities as large as 1.7 can be present in the lunar surface rocks. Typical depth profiles of conductivity and dielectic constant that fall within the extremes noted above are presented.

The effect of flow above the water-table on tile drain design in Murrumbidgee Irrigation Area soils

Most tile drainage systems in the Murrumbidgee Irrigation Areas are installed in soils that are relatively impermeable at a short distance below the drain level, and these systems are designed to discharge excess water at a rate much less than the average hydraulic conductivity of the soil profile. The contribution of unsaturated flow above the water-table under these conditions may be considerable, and the effect of ignoring this contribution upon drainage design is therefore investigated. Capillary conductivity-suction relationships of Murrumbidgee Irrigation Area sods are characterized by the absence of a critical suction value, above which capillary conductivity declines rapidly from the saturated hydraulic conductivity. The presence of a critical suction value, however, is a basic assumption in acceptable analyses of capillary flow and immediate application of these analyses in our case is not justified. An approximate analysis is therefore presented, dividing flow above the water-table into a saturated capillary fringe as conventionally defined and a region above this fringe, where flow is in the unsaturated state and mainly vertical. The latter region is evaluated from the capillary conductivity-depth profile during vertical infiltration from the soil surface to the water-table. It is found that flow above the water-table is accounted for by adding a layer of 10 cm or less to the saturated flow region. The maximum error in design spacing, resulting from neglect of flow above the water-table, is about 6%. Capillary flow may therefore be safely ignored for practical design purposes. If necessary, more accurate solutions may be obtained numerically by solving the Laplace equation for the stream function rather than for the potential function.

Geomagnetic induction in a concentrically stratified Earth

The ratios of the internal to external source terms of the earth's surface potential for certain geomagnetic fluctuations are indicative of the electrical conductivity of the earth's interior. A nonlinear first-order differential equation is derived for these ratios as functions of depth and conductivity in a spherically symmetric earth. This equation may be solved numerically to match an observable surface ratio with a conductivity-depth profile, or it may be solved analytically for a few of the infinite number of possible profiles. This approach provides a good qualitative insight into the problem of geomagnetic induction in a concentrically stratified earth.