Deep Schlumberger sounding and the crustal resistivity structure of central Australia

Summary. 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.     

Generalized thin sheet analysis in magnetotellurics: an extension of Price's analysis

Summary. Price's thin sheet analysis for electromagnetic fields has been extended in order to model the effects of crustal resistivity and conductivity variations on magnetotelluric fields. These extensions allow for a general layered medium below the crust and also account for the vertical resistance of the crust as well as its horizontal conductance. An important parameter emerges from the analysis which determines the distance it takes for the crustal current levels to readjust to changes in the crustal conductance. This adjustment distance is given by the square root of the conductivity thickness product multiplied by the resistivity thickness product. Approximate analytical solutions were developed for two-dimensional geometries in order to demonstrate these effects as well as the modifications produced by finite source wavelengths.     

Magnetometer array studies and deep Schlumberger soundings in the Damara orogenic belt, South West Africa

Summary. A zone of concentrated induced electric currents crossing parts of Zimbabwe, Botswana and South West Africa was discovered during a magnetovariational study conducted in 1972. In 1977, a second study was made with 27 recording magnetometers distributed across the width of South West Africa between latitudes 19 and 22°S. Several geomagnetic disturbances were recorded with high recording efficiencies. Three of these time sequences were digitized for analysis. Magnetograms and Fourier transform amplitude and phase maps in the period range 22–128min were used to delineate the westward continuation of the conductive structure revealed by the earlier investigation. The conductive zone runs approximately east-west from the Botswana border (21°E) to 17°E longitude. From here to the Atlantic coast it trends in a NE—SW direction. Anomalous fields, normalized to the horizontal field at a station recording the normal field, were used to obtain maximum depth estimates of around 45 km for the induced currents. Several deep Schlumberger soundings were done over the anomalous zone and the results showed that the conductive structure is, in places, only 3 km from the surface and that it has a resistivity of less than 20 Ωm. The resistivity of the upper crust outside the structure ranges from 5000 to more than 20000 Ωm. Some 14 post-Karoo alkaline igneous complexes occur along the course of the resistivity anomaly. These intrusive complexes represent the youngest igneous activity in the Damara Orogenic Belt and were most probably emplaced along a line of weakness in the lithosphere. The resistivity anomaly would seem to delineate this line of weakness.     

B-polarization induction in two generalized thin sheets at the surface of a conducting half-space

Summary. A new closed-form solution is obtained analytically for a B- polarization induction problem of geophysical interest, in which a local region of the Earth is represented by a generalized thin sheet at the surface of and in electrical contact with a uniformly conducting half-space. The generalized sheet, first introduced by Ranganayaki & Madden, is a mathematical idealization of a double layer which consists, in this problem, of two adjacent half-planes with distinct conductances representing a surface conductivity discontinuity such as an ocean—coast boundary, underlain by a uniform sheet of finite integrated resistivity representing the lower crust. The resistive sheet exerts a considerable mathematical influence on the solution causing, under certain conditions, an additional pole to appear in one of the forms of contour integral by which the solution can be expressed; it also weakens or eliminates field singularities that would otherwise occur at the conductance discontinuity. A numerical calculation is made for model parameters typifying an ocean—coast boundary underlain by a highly resistive crust. It is found that the residue of the pole associated with the resistive sheet dominates the solution for this example, the main consequence of which is a huge increase in the horizontal range over which the induced currents adjust themselves between the different 'skin-effect' distributions at infinity on either side of the model. Moreover the solution shows that this 'adjustment distance' has a more complicated dependence on the conductance and integrated resistivity of the sheet than that given simply by the square root of their product which was the length parameter proposed by Ranganayaki & Madden.     

Magnetotelluric interpretation of crustal and mantle structure in the Grenville Province

Summary Accurate determinations of depths and conductivities of electrical structures in shield regions are often difficult because of the inhomogeneity of the uppermost crust. A magnetotelluric (MT) station (BAT) in the Grenville Province of the Precambrian Shield in eastern Canada has been in operation since 1975 for time-dependency studies of electrical resistivity changes related to earthquakes. The MT response of the station displays low skew with small to moderate anisotropy. One-dimensional inversion of the apparent resistivity and phase reveals two well-defined conductors in the crust, one at 10 km and the second at the base of the crust. The latter has a resistivity less than 50 Ω m. These results are substantiated by three additional MT stations located up to 40 km distant.
Data from other new MT stations and from stations previously published in the literature are compared with two-dimensional computer model results and with the three-dimensional analogue scale model results of Dosso et al. While additional data for periods less than 100 s would be desirable the results from a number of the MT stations are not inconsistent with a widespread occurrence of a conducting zone at the base of the crust in the Grenville. The inversion analysis also indicates the existence of a conductor at some depth greater than 100 km with a resistivity less than 30 Ω m. This may coincide with a seismic low-velocity zone observed in the mantle under the Canadian Shield.     

Interpretation of transient electromagnetic soundings over three-dimensional structures for the central-loop configuration

Summary. An assessment is made of the bias of fitting constrained layered-earth models to transient electromagnetic data obtained over 3-D structures. In this assessment we use the central-loop configuration and show that accurate estimates of the depth of burial of 3-D structures can be obtained with layered-earth model fitting. However, layered-earth interpretations are not reliable for estimating depth extents and resistivities of 3-D structures. When layered earths are used for interpretation, it is advantageous in some cases to use data based on the magnetic field instead of the voltage. A magnetic-field definition of apparent resistivity, in contrast to a definition based on the voltage, eliminates apparent-resistivity overshoots and undershoots in the data. A resistivity undershoot in the data can produce an extraneous and misleading layer in an interpretation of a 3-D resistive structure. Due to 3-D effects, apparent-resistivity soundings (magnetic field and voltage) may rise so steeply at late times that it may not be possible to fit a sounding to a reasonable layered-earth model. Truncating such a sounding, over a buried conductor, allows for a reasonable layered-earth fit and an accurate estimate of the depth to the conductor. However, the resistivity of the conductor is overestimated.
Measurements of the horizontal field in the central-loop configuration can map 3-D structures, provided the sensor is located accurately at the centre of the transmitting loop. Horizontal-field calculations show that the transients peak on the flanks of a 3-D structure, but are depressed over the structure's centre. Weak transient responses flanked by two large transient responses, which are opposite in sign, locate the structure. The sign reversal is caused by a corresponding reversal in the currents that are channelled through or deflected away from conductive or resistive structures, respectively.     

Forward modelling of direct current and low-frequency electromagnetic fields using integral equations

We present a semi-analytical, unifying approach for modelling the electromagnetic response of 3-D bodies excited by low-frequency electric and magnetic sources. We write the electric and magnetic fields in terms of power series of angular frequency, and show that to obey Maxwell's equations, the fields must be real when the exponent is even, and imaginary when it is odd. This leads to the result that the scattering equations for direct current fields and for fields proportional to frequency can both be explicitly formulated using a single, real dyadic Green's function. Although the underground current flow in each case is due to different physical phenomena, the interaction of the scattering currents is of the same type in both cases. This implies that direct current resistivity, magnetometric resistivity and electric and magnetic measurements at low induction numbers can all be modelled in parallel using basically the same algorithm. We make a systematic derivation of the quantities required and show that for these cases they can all be expressed analytically. The problem is finally formulated as the solution of a system of linear equations. The matrix of the system is real and does not depend on the type of source or receiver. We present modelling results for different arrays and apply the algorithm to the interpretation of field data. We assume the standard dipoledipole resistivity array for the direct current case, and vertical and horizontal magnetic dipoles for induction measurements. In the case of magnetometric resistivity we introduce a moving array composed of an electric dipole and a directional magnetometer. The array has multiple separations for depth discrimination and can operate in two modes. The mode where the predominant current flow runs along the profile is called MMR-TM. This mode is more sensitive to lateral variations in resistivity than its counterpart, MMR-TE, where the mode of conduction is predominantly perpendicular to the profile.     

Transient electromagnetic responses in seafloor with triaxial anisotropy

Electrical anisotropy of young oceanic crust at mid-ocean ridges is detectable by observation of the rate and geometry of the diffusion of electromagnetic fields. The anisotropy in electrical properties arises from the presence of conductive seawater in an interconnected network of mostly ridge-parallel cracks. In this paper, we first justify the choice of a triaxial model to represent young oceanic crust, with three distinct electrical conductivities in the vertical, strike and spreading directions. We then present an algorithm to calculate the transient electromagnetic responses generated by an electric dipole source over such a triaxially anisotropic seafloor. We show that if the transient passages are measured with three distinct electric dipole-dipole configurations, it is possible to discern all three unknown conductivities independently of each other.     

The determination of resistivity and porosity of the sediment and fractured basalt layers near the Juan de Fuca Ridge

Summary. In the summer of 1984 an electrical survey using magnetometric off-shore electrical sounding (MOSES) was conducted at two sites in Middle Valley, part of the northern Juan de Fuca Ridge complex. MOSES has been designed to minimize the difficulties inherent in electrical surveys of the crust below the electrically conductive sea layer. Site 1, at 48°32N, 128°42W, is in the central part of the turbidite-filled basin. Using a two-layer model of conductive sediments overlying a fractured basalt basement, the sediment resistivity and thickness were found to be 0.82 ± 0.06 Ωm and 1800 ± 300 m, respectively. The basement resistivity, although not well constrained by the data is consistent with the results obtained at site 2.
Site 2, located at 48°10N, 128°50W, has a thinner sediment layer, which appears to vary with position. The sediment conductivity—thickness product is the parameter determined by the data. If the sediment resistivity were the same as at site 1, the sediment thickness would be 140 ± 30 m to the SE of site 2, and 240 ± 55 m to the NW. The fractured basalt basement has a resistivity of 8.5 ± 3.4 Ωm and is at least 1000 m thick.
Using temperature-corrected pore fluid resistivity, the calculated porosity is found to vary from 62 per cent at the top to 21 per cent at the base of the sediments and is 8 per cent in the basement. These values are in good agreement with estimates from seismic velocities for a thick turbidite sequence in a nearby sediment-filled basin and determined for layer 2A/B basalts in DSDP hole 504B, respectively.     

The use of equivalent current systems in the interpretation of Geomagnetic Deep Sounding data

Summary. Many geomagnetic variation anomalies are probably caused by the channelling, through small-scale bodies, of electric currents induced in much larger conductors elsewhere. Consequently, the direct interpretation of anomalous magnetic fields by modelling the electromagnetic response of conductive structures may give misleading results. It is suggested that, rather than attempting to proceed directly from the electromagnetic fields to conductivity models, we should instead take the intermediate step of determining the distribution of anomalous current flow.
Maps of the anomalous fields over a conductive structure can be generated from inter-station transfer functions. If it is assumed that the internal currents are concentrated in a thin sheet at a specified depth, the equivalent current system in the sheet can be computed directly from the vertical magnetic field. The most straightforward method of performing this calculation is to compute the Fast Fourier Transform of the magnetic field data, and then to apply a wavenumber filter.
The presence of any vertical currents invalidates the thin sheet model. However, if the spatial distribution of a horizontal component of the anomalous magnetic field is also known, the presence of any vertical currents can be detected directly, and their position determined. The value of the methods is illustrated by applying them to the interpretation of a Geomagnetic Deep Sounding survey of the Kenya rift valley.     

A geomagnetic scattering theory for evaluation of earth structure

Summary. Structural features of the Earth's lower crust and upper mantle can be mapped by the analysis of temporal geomagnetic fluctuations using the electromagnetic scattering theory developed in this paper. Decomposing geomagnetic field fluctuations at the Earth's surface into an excitation part and a scattered part forms the basis of a power series development. The vertical field component is interpreted as a scattering of the excitation field. The horizontal gradient and geomagnetic depth sounding methods are special cases of the theory developed. The horizontal gradient sounding method has a tensorial aspect which has not been recognized before; it should be included to obtain correct penetration depth parameter evaluations from field data.     

Bimodal electromagnetic induction in non-uniform thin sheets with an application to the northern Pyrenean induction anomaly

In order to handle the distortion of large-scale induced electric currents by local conductivity anomalies, the problem of electromagnetic induction in non-uniform thin sheets has been reformulated in terms of an integral equation over the anomalous domain. This formulation considers in the layered substratum in addition to toroidal currents also the poloidal current mode (vertical current loops), at the expense that two scalar functions have to be determined. Simple formulas for the required kernels are derived. The algorithm is applied to model the gross features of the northern Pyrenean induction anomaly. It is suggested that this pronounced anomaly results from a conductive channel between the Atlantic Ocean and the Mediterranean Sea.     

The instantaneous apparent resistivity tensor: a visualization scheme for LOTEM electric field measurements

Long-offset transient electromagnetic (LOTEM) data have traditionally been represented as early- and late-time apparent resistivities. Time-varying electric field data recorded in a LOTEM survey made with multiple sources can be represented by an 'instantaneous apparent resistivity tensor'. Three independent, coordinate-invariant, time-varying apparent resistivities can be derived from this tensor. For dipolar sources, the invariants are also independent of source orientation. In a uniform-resistivity half-space, the invariant given by the square root of the tensor determinant remains almost constant with time, deviating from the half-space resistivity by a maximum of 6 per cent. For a layered half-space, a distance–time pseudo-section of the determinant apparent resistivity produces an image of the layering beneath the measurement profile. As time increases, the instantaneous apparent resistivity tensor approaches the direct current apparent resistivity tensor. An approximate time-to-depth conversion can be achieved by integrating the diffusion depth formula with time, using the determinant apparent resistivity at each instant to represent the resistivity of the conductive medium. Localized near-surface inhomogeneities produce shifts in the time-domain apparent resistivity sounding curves that preserve the gradient, analogous to static shifts seen in magnetotelluric soundings. Instantaneous apparent resistivity tensors calculated for 3-D resistivity models suggest that profiles of LOTEM measurements across a simple 3-D structure can be used to create an image that reproduces the main features of the subsurface resistivity. Where measurements are distributed over an area, maps of the tensor invariants can be made into a sequence of images, which provides a way of 'time slicing' down through the target structure.     

Geomagnetic variation anomalies and deflection of telluric currents

Summary. We show that most of the abnormal variations of the transient magnetic field have deflection and canalization of telluric currents as main sources. In order to do so, we develop a formalism which is valid in a limited frequency range which satisfies the following hypotheses: (a) the thickness of the laterally inhomogeneous upper layer is small with respect to the penetration depth of the transient field; (b) self-induction of the heterogeneities of conductivity can be neglected. Theoretical results and observations performed at mid-latitudes are in good agreement.
The main result we establish is that deviation and canalization of the current responsible for the transient abnormal field do not affect their temporal variations. The study of temporal variations of the abnormal field thus provides us with information about the structure of the crust in the region where the deviated and canalized currents are induced.     

Modelling of electromagnetic fields in thin heterogeneous layers with application to field generation by volcanoes—theory and example

When interpreting electromagnetic fields observed at the Earth's surface in a realistic geophysical environment it is often necessary to pay special attention to the effects caused by inhomogeneities of the subsurface sedimentary and/or water layer and by inhomogeneities of the Earth's crust. The inhomogeneities of the Earth's crust are expected to be especially important when the electromagnetic field is generated by a source located in a magma chamber of a volcano. The simulation of such effects can be carried out using generalized thin-sheet models, which were independently introduced by Dmitriev (1969 ) and Ranganayaki & Madden (1980 ). In the first part of the paper, a system of integral equations is derived for the horizontal current that flows in the subsurface inhomogeneous conductive layer and for the vertical current crossing the inhomogeneous resistive layer representing the Earth's mantle. The terms relating to the finite thickness of the laterally inhomogeneous part of the model are retained in the equations. This only marginally complicates the equations, whilst allowing for a significant expansion of the approximation limits.
  The system of integral equations is solved using the iterative dissipative method developed by the authors in the period from 1978 to 1988. The method can be applied to the simulation of the electromagnetic field in an arbitrary inhomogeneous medium that dissipates the electromagnetic energy. When considered on a finite numerical grid, the integral equations are reduced to a system of linear equations that possess the same contraction properties as the original equations. As a result, the rate at which the iterative-perturbation sequence converges to the solution remains independent of the numerical grid used for the calculations. In contrast to previous publications on the method, aspects of the algorithm implementation that guarantee its effectiveness and robustness are discussed here.     

Lithology-derived structure classification from the joint interpretation of magnetotelluric and seismic models

Magnetotelluric and seismic methods provide complementary information about the resistivity and velocity structure of the subsurface on similar scales and resolutions. No global relation, however, exists between these parameters, and correlations are often valid for only a limited target area. Independently derived inverse models from these methods can be combined using a classification approach to map geologic structure. The method employed is based solely on the statistical correlation of physical properties in a joint parameter space and is independent of theoretical or empirical relations linking electrical and seismic parameters. Regions of high correlation (classes) between resistivity and velocity can in turn be mapped back and re-examined in depth section. The spatial distribution of these classes, and the boundaries between them, provide structural information not evident in the individual models. This method is applied to a 10 km long profile crossing the Dead Sea Transform in Jordan. Several prominent classes are identified with specific lithologies in accordance with local geology. An abrupt change in lithology across the fault, together with vertical uplift of the basement suggest the fault is sub-vertical within the upper crust.     

Crustal thickening under the palaeo-meso-Proterozoic Delhi Fold Belt in northwestern India: evidence from deep reflection profiling

The results of deep reflection profiling studies carried out across the palaeo-meso-Proterozoic Delhi Fold Belt (DFB) and the Archaean Bhilwara Gneissic Complex (BGC) in the northwest Indian platform are discussed in this paper. This region is a zone of Proterozoic collision. The collision appears to be responsible for listric faults in the upper crust, which represent the boundaries of the Delhi exposures. In these blocks the lower crust appears to lie NW of the respective surface exposures and the reflectivity pattern does not correspond to the exposed blocks. A fairly reflective lower crust northwest of the DFB exposures appears to be the downward continuation of the DFB upper crust. The poorly reflective lower crust under the exposed DFB may be the westward extension of the BGC upper crust at depth. Thus, the lower crust in this region can be divided into the fairly reflective Marwar Basin (MB)-DFB crust and a poorly reflective BGC crust. Vertically oriented igneous intrusions may have disturbed the lamellar lower-crustal structure of the BGC, resulting in a dome-shaped poorly reflective lower crust whose base, not traceable in the reflection data, may have a maximum depth of about 50 km, as indicated by the gravity modelling.
The DFB appears to be a zone of thick (45-50 km) crust where the lower crust has doubled in width. This has resulted in three Moho reflection bands, two of which are dipping SE from 12.5 to 15.0 s two-way time (TWT) and from 14.5 to 16.0 s TWT. Another band of subhorizontal Moho reflections, at ≈ 12.5 s TWT, may have developed during the crustal perturbations related to a post-Delhi tectonic orogeny. The signatures of the Proterozoic collision, in the form of strong SE-dipping reflections in the lower crust and Moho, have been preserved in the DFB, indicating that the crust here has not undergone any significant ductile deformation since at least after the Delhi rifting event.     

Crustal thickness variations in the margins of the Gulf of California from receiver functions

Receiver functions (RFs) from teleseismic events recorded by the NARS-Baja array were used to map crustal thickness in the continental margins of the Gulf of California, a newly forming ocean basin. Although the upper crust is known to have split apart simultaneously along the entire length of the Gulf, little is known about the behaviour of the lower crust in this region. The RFs show clear P -to- S wave conversions from the Moho beneath the stations. The delay times between the direct P and P -to- S waves indicate thinner crust closer to the Gulf along the entire Baja California peninsula. The thinner crust is associated with the eastern Peninsular Ranges batholith (PRB). Crustal thickness is uncorrelated with topography in the PRB and the Moho is not flat, suggesting mantle compensation by a weaker than normal mantle based on seismological evidence. The approximately W–E shallowing in Moho depths is significant with extremes in crustal thickness of ∼21 and 37 km. Similar results have been obtained at the northern end of the Gulf by Lewis et al., who proposed a mechanism of lower crustal flow associated with rifting in the Gulf Extensional Province for thinning of the crust. Based on the amount of pre-Pliocene extension possible in the continental margins, if the lower crust did thin in concert with the upper crust, it is possible that the crust was thinned during the early stages of rifting before the opening of the ocean basin. In this case, we suggest that when breakup occurred, the lower crust in the margins of the Gulf was still behaving ductilely. Alternatively, the lower crust may have thinned after the Gulf opened. The implications of these mechanisms are discussed.     

Structural effects of the crust on the geoid modelled using deep seismic sounding interpretations

According to the theory of isostasy, the Earth has a tendency to deform its surface in order to reach an equilibrium state. The land-uplift phenomenon in the area of the Fennoscandian Shield is thought to be a process of this kind. The geoid, as an equipotential surface of the Earth's gravity field, contains information on how much the Earth's surface departs from the equilibrium state. In order to study the isostatic process through geoidal undulations, the structural effects of the crust on the geoid have to be investigated.
  The structure of the crust of the Fennoscandian Shield has been extensively explored by means of deep seismic sounding (DSS). The data obtained from DSS are used to construct a 3-D seismic-velocity structure model of the area's crust. The velocity model is converted to a 3-D density model using the empirical relationship that holds between seismic velocities and crustal mass densities. Structural effects are then estimated from the 3-D density model.
  The structural effects computed from the crustal model show that the mass deficiency of the crust in Fennoscandia has caused a geoidal depression twice as deep as that observed from the gravimetric geoid. It proves again that the crust has been isostatically compensated by the upper mantle. In other words, an anomalously high-density upper mantle must exist beneath Fennoscandia.     

H-polarization induction over an ocean edge coupled to the mantle by a conducting crust

Summary. The Wiener—Hopf technique is used to obtain an exact analytical solution for the problem of H -polarization induction over the edge of a perfectly conducting thin sheet, representing an ocean, electrically connected to a perfectly conducting mantle through a slab of finite conductivity and thickness, which represents the Earths crust. It is shown that the induced currents resulting from this type of induction process are drawn up into the sea from the cust and mantle with the greatest concentration of current near the ocean edge. The surface impedance over the land surface, is calculated for various mantle depths and is shown to increase sharply as the coastline is approached. The magnetic field along the ocean floor is also plotted as a function of distance from the coastline, and the results are found to agree very well with those calculated previously by approximate and numerical methods.