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.     

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.     

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.     

Preferential flow: first results of a full-scale flow model

The main goal of a joint project undertaken by the geophysical and hydrological research units of Kiel University is to study preferential flow in a large open-air, full-scale model, looking in particular at near-surface penetration and flow of water through the unsaturated vadose zone. An artificial irrigation device is installed in place of natural rain, and a homogeneous sand body is used instead of natural soil. This provides a reference model for future field experiments. Inside the sand body there are a large number of geophysical and hydrological sensors to measure DC resistivity (using various electrode configurations), water content and water potential (using TDR and tensiometer instruments, respectively). A ground-penetrating radar (GPR) system is installed at the surface, whereas at the bottom several containers and a thin gravel layer are embedded to measure the flow arrival and the discharge of water. Irrigation is varied in intensity, time, area, and salt content (tracer).
  Results of the first six experiments show that the percolation of intruding water can be followed by all techniques and percolation is finally controlled by the discharge measurements. These display some undulations and variations of the water 'front' and agree with the measurements of all other sensors. The redundancy achieved by the use of multiple methods was intended to enable an assessment of the reliability of the techniques used. The true values of electrical resistivity before and after irrigation reflect the distribution of water saturation within the sand body. A numerical 3-D inversion of the apparent resistivity provides information regarding future field experiments, in which it will be possible to install only some of the sensors in order to preserve the natural structure of the soil.     

Joint Inversion of Geophysical Data

Summary. By jointly inverting several different kinds of geophysical measurements at a site we avoid some of the ambiguity inherent in the individual methods. We show how this can be done for the combination of DC resistivity and magnetotelluric measurements on a layered medium by considering a simple 3-layer model. The combination resolves the resistivity of the thin resistive second layer, even though neither of the two methods can do so alone.
The method is then applied to field data from a shallow sedimentary basin. A blind zone occurs beneath a thick near-surface conductive shale. By a study of the eigenvalue structure of the model it can be seen that resolution in this zone would be slightly enhanced by higher frequency magnetotelluric data, but additional DC data at larger spacing would yield no improvement.     

Investigation of mountain permafrost in the Kozia Dolinka valley,Tatra Mountains,Poland

The Kozia Dolinka valley lies at an altitude above 1900 m a.s.l. on the northern slope of the main ridge of the High Tatra Mountains. Mountain permafrost occurrences were studied with the use of BTS, infrared imaging, water and ground temperature measurements and DC resistivity soundings. The data suggest the existence of isolated patches of permafrost. The lowest observed bottom temperature of winter snow values was in the order of-10C. DC soundings revealed the existence of a high resistivity layer of limited extent. Permafrost seasonal monitoring was conducted with resistivity soundings. Measurements were carried out in spring-autumn 1999, when a distinct change in permafrost thickness was observed.     

MUDBOIL AND ICE‐WEDGE DYNAMICS INVESTIGATED BY ELECTRICAL RESISTIVITY TOMOGRAPHY,GROUND TEMPERATURES AND SURFACE MOVEMENTS IN SVALBARD

Arctic tundra surfaces are dominated by a variety of patterned ground forms. Whereas a large number of studies have described morphology, structure and processes of patterned ground, few have monitored detailed patterned ground dynamics and subsurface environments continuously. We applied electrical resistivity tomography (ERT) to understand near‐surface conditions of two types of patterned ground, ice‐wedge polygons and mudboils in Svalbard, where periglacial processes associated with permafrost are intensively monitored. Automated monitoring shows surface movement characterized by annual cycles of frost heave and thaw settlement, the amounts and rates of which are influenced by the intensity of ice segregation. A time series of ERT shows (1) a distinct resistivity boundary delimiting the active‐layer depth, (2) seasonal variation in resistivity controlled by thermo‐hydrological dynamics and (3) spatial variation in resistivity reflecting desiccation in summer and intensive ice segregation in winter. These results demonstrate ERT as a useful complementary technique for monitoring active‐layer depths and near‐surface hydrological conditions at periglacial patterned ground sites, where automated soil thermal and moisture measurements are limited.     

Internal Structure and Permafrost Characteristics of the Rock Glaciers of Southern Carpathians (Romania) Assessed by Geoelectrical Soundings and Thermal Monitoring

Six rock glaciers in the Southern Carpathians have been investigated by means of geoelectrical soundings in order to detect their internal stratigraphy and the existence of frozen sediments. In the case of three relict rock glaciers, the electrical resistivity measurements indicated a typical internal structure. Low resistivity values (<10 kΩm) which are typical of unfrozen fine‐grained materials were obtained, but high resistivity values (25–240 kΩm) measured in the Pietroasa, Ie?u and Pietrele rock glaciers denote the presence of sediments cemented by interstitial ice and ice lenses. Based on the moderate resistivity values, the ice content is probably low to medium in the upper portion of these rock glaciers, that is, above 2040 m. At two sites (Pietroasa and V?iuga rock glaciers), ground surface temperature (GST) evolution was monitored using digital dataloggers. Mean annual ground surface temperature and GST regime throughout the winter were extracted from the recordings and confirmed the probability of permafrost occurrence in Pietroasa rock glacier. In the Ie?u and Pietrele rock glaciers, measurements of bottom temperatures of the winter snow cover were performed in March 2012. Considering the thick active layer, the reduced ice content and the presence of scarce vegetation on their surface it could be assumed that the permafrost exists in marginal conditions in the Southern Carpathians. The ground ice in permafrost is produced by the groundwater freezing or by snow banks buried by coarse angular boulders following large rockfalls.     

雷州半岛九斗洋干玛珥湖火山机构与第四系空间展布——基于高密度电阻率法勘测和钻孔研究

为查明雷琼火山群中九斗洋干玛珥湖的第四纪地层空间展布,以及埋藏古火山形态,为后续研究提供地质背景资料,采用高效、便捷的高密度电阻率法对九斗洋干玛珥湖湖盆区进行勘测,并结合钻孔岩芯的研究进行验证。得出的主要结论为：1）盆地深部地层最高电阻率可达到300 Ω?m以上,盆地中央基岩以下存在高阻地质体,推测为岩浆通道位置。岩浆经过通道溢出后横向展布,覆于沉积地层上,随后在火山口内形成湖泊,堆积第四纪湖相沉积,其火山机构与玛珥湖型火山一致;2）九斗洋干玛珥湖第四纪松散沉积地层的电阻率通常＜60 Ω?m,泥炭层电阻率最低;3）第四纪沉积总厚度为25~50 m,盆地松散沉积的岩浆岩基底总体平整,但尚有波状起伏。研究结果表明,高密度电阻率法结合钻孔验证是研究火山机构形态及火山口湖第四纪沉积空间展布的有效方法。     

Resolution potential of surface wave phase velocity measurements at small arrays

The deployment of temporary arrays of broadband seismological stations over dedicated targets is common practice. Measurement of surface wave phase velocity across a small array and its depth-inversion gives us information about the structure below the array which is complementary to the information obtained from body-wave analysis. The question is however: what do we actually measure when the array is much smaller than the wave length, and how does the measured phase velocity relates to the real structure below the array? We quantify this relationship by performing a series of numerical simulations of surface wave propagation in 3-D structures and by measuring the apparent phase velocity across the array on the synthetics. A principal conclusion is that heterogeneities located outside the array can map in a complex way onto the phase velocities measured by the array. In order to minimize this effect, it is necessary to have a large number of events and to average measurements from events well-distributed in backazimuth. A second observation is that the period of the wave has a remarkably small influence on the lateral resolution of the measurement, which is dominantly controlled by the size of the array. We analyse if the artefacts created by heterogeneities can be mistaken for azimuthal variations caused by anisotropy. We also show that if the amplitude of the surface waves can be measured precisely enough, phase velocities can be corrected and the artefacts which occur due to reflections and diffractions in 3-D structures greatly reduced.     

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.     

Hydrogeologic Characterization of a Fault-Related Dome Using Outcrop,Borehole and Electrical Resistivity Data

Geological structures introduce heterogeneity along deformed strata, which in turn exert a strong control on regional groundwater occurrences and water flow. We developed and applied procedures of structural, borehole and direct current resistivity (DCR) data to (1) figure out a reliable structural model of a fault-related dome, (2) visualize the relationship between structural complexity and aquifers geometry and (3) characterize the fault damage zones and its related sealing potentialities. The present approach was applied at the northern Eastern Desert, Egypt, considering its complex deformation history. To alleviate the uncertainties and artifacts in solving the DCR inverse problem, advanced and non-conventional inversion schemes were applied. Moreover, fault seal potentialities were assessed by applying the shale gouge ratio (SGR) estimation to predict the groundwater pathway flow. The main findings include: (a) The DCR measurements can be considered as a complementary tool to visualize the relationship between subsurface structures and aquifers geometry at highly deformed areas; (b) detailed surface structural data analysis combined with sophisticated inversion algorithms application can increase the reliability of the constructed geo-electrical cross sections for deep and large-scale geological surveys; and (c) the structural modeling of geological units and faults distribution contributes to clarify hydrogeological settings and aquifers connectivity. The approach can be readily applied elsewhere, as long as detailed structural analysis, geometric parameters and high-resolution DCR resistivity data are available.

     

Magnetotelluric Soundings In the Canadian Rocky Mountains

Summary. Magnetotelluric soundings have been made at 25 stations in the Rocky Mountain Trench (RMT) and Main Ranges near 53° N, close to the centre of a major conductivity anomaly which had been mapped in a magnetovariation array study. Most stations covered the frequency range 0.01–500 Hz and three stations 0.0002–500 Hz. the resistivity tensor shows low to moderate anisotropy in the RMT, but is strongly 2-D or 3-D in the Rocky Mountains. Apparent resistivities as a function of frequency are displayed in pseudosections along the Trench and along a transverse profile across the RMT and into the Main Ranges. In preparation for 2-D modelling, 1-D inversions have been used to construct resistivity-depth sections satisfying both magnitudes and phases of the MT responses. These show very low resistivities, in the range 1—10Ωm, in the upper crust under the RMT and even lower values under the Main Ranges. the latter values give strong confirmation of the Northern Rockies conductor reported by Bingham, Cough & Ingham and are in agreement with models of the conductors fitted to long-period magnetovariation fields by Ingham, Gough & Parkinson. the MT results here reported add some essential depth and resistivity information. It is suggested that the conductors beneath the Rocky Mountains Main Ranges and Trench constitute a thickening at the edge of the Canadian Cordilleran Regional (CCR) conductor. Gough has argued that a wide variety of geophysical and geological parameters indicate high temperatures and partial melting in the mantle under the CCR conductor. At the upper crustal depths penetrated in this magnetotelluric study, it is considered more probable that the high conductivity is caused by hot, saline water of mantle origin rather than silicate melt. the CCR in general may have two layers of fluid producing its high conductivity, silicate melt below and saline hot water above.     

RECONNAISSANCE SURVEYS OF CONTEMPORARY PERMAFROST ENVIRONMENTS IN CENTRAL ICELAND USING GEOELECTRICAL METHODS: IMPLICATIONS FOR PERMAFROST DEGRADATION AND SEDIMENT FLUXES

Four different sites in the highlands of central Iceland have been investigated for permafrost occurrence using two‐dimensional resistivity imaging. The results of the surveys indicate the presence of shallow permafrost of low to medium resistivity. The distribution pattern is spatially heterogeneous which is consistent with permafrost at the fringe of seasonal frost. These sites are likely to react rapidly to changes of the environmental boundary conditions, therefore future research should include monitoring for detecting the early impact of climate change on permafrost degradation. The extent to which periglacial morphodynamics and sediment fluxes are influenced by permafrost and/or seasonal frost and potential permafrost degradation is hard to determine. Hence, long‐term monitoring approaches for both permafrost and sediment dynamics are essential.     

Two years of magnetotelluric measurements in Abitibi, western Québec, using a telephone line

Continuous magnetotelluric measurements were made over a period of 600 days, with 100-m-, 30-km- and 100-km-long dipoles and a period range of 40–4000 s. Data analysis for different dipole lengths indicates the presence of static shift at various scales. It is shown that the longer the telluric dipole, the less statically shifted the resistivity curves; nevertheless, static shifts can still be present due to geological structures causing anomalies exhibiting wavelengths comparable to the dipole length. Also, a relationship is observed between the coherence and the main impedance components. This relation is explained in terms of signal-to-noise ratio. A way to reduce the bias on the impedance estimates is suggested. The apparent resistivities and phases computed from three different impedance estimates using 100-km-long dipoles are then compared to those observed in similar studies made near our observation region.     

Application of Magnetotelluric (MT) Resistivity to Imaging of Regional Three-Dimensional Geologic Structures and Groundwater Systems

Widespread definition of a groundwater system in three dimensions is necessary for the management and maintenance of groundwater resources. A magnetotelluric (MT) survey can be an effective geophysical prospecting method for imaging regional geological structures by measuring both shallow and deep resistivity. To demonstrate the capability of an MT survey to characterize a groundwater system, the Kumamoto area of central Kyushu in southwestern Japan was selected as a case study site because of its rich groundwater resources. Three-dimensional (3D) MT resistivity structure to a depth of 5?km was modeled by 1D inversion analysis of raw MT data and 3D interpolation of the resultant resistivity column data by the optimization principle method. Consequently, both deep and shallow aquifers were detected. A high-resistivity zone appears at depths between 500 and 2,000?m between the Futagawa?CHinagu faults and the Usuki?CYatsushiro tectonic line, which supports the existence of an aquiclude under the aquifer. The most important characteristic inferred from the 3D resistivity model is that the deep groundwater system below a depth of 1,000?m has two main flow paths. One path is likely to be through porous rocks because the low resistivity zone is regarded as tuff with sand and gravel, and the other flow path is interpreted to be through fractured zones along the Hinagu faults. Hence, the path and direction of the groundwater flows are probably controlled by geologic structures and the configuration of the active faults. These findings support the effectiveness of the MT method for investigating groundwater systems.     

A study of the physics of telluric current flow at very low frequencies in the Earth's crust

Summary. Interpretation of the effects of natural electromagnetic induction is often in terms of models in which changes in resistivity at great distances from the point of measurement are not taken into account. In this paper we will try to show that this is not a valid approximation for very low-frequency telluric currents, flowing near the surface in the Earth's crust, when the material separating the crust from the mantle has a sufficiently high electrical resistance. In this case the shape and dimensions of the circuit, as well as the resistivity distribution along the whole length of the path followed by the currents, play a part in determining the induced electromagnetic field. A number of experimentally verifiable consequences follow from this.     

Stable Iterative Methods for the Inversion of Geophysical Data

Summary. Interpretation of earth electrical measurements can often be assisted by inversion, which is a non-linear model-fitting problem in these cases. Iterative methods are normally used, and the solution is defined by' best fit'in the sense of generalized least-squares.
The inverse problems we describe are ill-posed. That is, small changes in the data can lead to large changes in both the solution and in the iterative process that finds the solution. Through an analysis of the problem, based on local linearization, we define a class of methods that stabilize the iteration, and provide a robust solution. These methods are seen as generalizations of the well-known Singular Value Truncation and Marquardt Methods of iterative inversion.
Here, and in a companion paper, we give examples illustrating the successful application of the method to ill-posed problems relating to the resistivity of the Earth.     

Seismic vertical array analysis for phase decomposition

We propose a vertical array analysis method that decomposes complex seismograms into body and surface wave time histories by using a velocity structure at the vertical array site. We assume that the vertical array records are the sum of vertically incident plane P and S waves, and laterally incident Love and Rayleigh waves. Each phase at the surface is related to that at a certain depth by the transfer function in the frequency domain; the transfer function is obtained by Haskell's matrix method, assuming a 1-D velocity structure. Decomposed P , S and surface waves at the surface are estimated from the vertical array records and the transfer functions by using a least-squares method in the frequency domain; their time histories are obtained by the inverse Fourier transform. We carried out numerical tests of this method based on synthetic vertical array records consisting of vertically incident plane P and S waves and laterally incident plane Love and Rayleigh waves. Perfect results of the decomposed P , S , Love and Rayleigh waves were obtained for synthetic records without noise. A test of the synthetic records in which a small amount of white noise was added yielded a reasonable result for the decomposed P , S and surface waves. We applied this method to real vertical array records from the Ashigara valley, a moderate-sized sedimentary valley. The array records from two earthquakes occurring at depths of 123 and 148 km near the array (epicentral distance of about 31 km) exhibited long-duration later phases. The analysis showed that duration of the decomposed S waves was a few seconds and that the decomposed surface waves appeared a few seconds after the direct S -wave arrival and had very long duration. This result indicated that the long-duration later phases were generated not by multireflected S waves, but by basin-induced surface waves.     

Hydrogeological and ground-water resource analysis using a geotechnical database

An application of a geotechnical database system for primary evaluation of ground-water resources in a sedimentary basin is proposed. The database consists of 1200 borehole logs including geologic columns,in situ test results, ground-water level, water quality data, and resistivity logs. The Kumamoto plain, situated in southwest Japan, is chosen as a study area. The evaluation process consists of two steps: (1) modeling of shapes of water-bearing strata, and (2) modeling of distribution of physical quantity which has some relationship with the porosity of those strata. In step (1), the shapes of upper and/or lower surface of the pyroclastic flow deposits and the andesitic lava were determined, whereas the three-dimensional distribution model of resistivity was constructed from resistivity logging data obtained from 100 boreholes and using the proposed interpolation method in the step (2). An empirical equation between the porosity and the resistivity of the lava was also identified. The integration of two types of model and the empirical equation contributed to an estimate of the total volume of the ground-water under the study area.