TIME-DOMAIN ELECTROMAGNETIC SOUNDING—COMPUTATION OF MULTI-LAYER RESPONSE AND THE PROBLEM OF EQUIVALENCE IN INTERPRETATION*

Computations of the time-domain electromagnetic response of a multi-layered earth have been carried out for different source-receiver coil systems. The primary excitation is a train of half-sinusoidal waveforms of alternating polarity. The conversion into the time-domain involves Fourier series summation of the matched complex mutual coupling ratios of the layered earth models computed by a digital linear filter method. As an example, the response of a perpendicular coil system on the ground surface for two source-receiver separations has been presented for a five-layer earth model. This has been compared with the responses of homogeneous, two-layer, three-layer, and four-layer models. Next, the investigations have been extended to study the problems of equivalence of three-layer models, the intermediate layer of which is either conductive or resistive. For an intermediate conductive layer (H-type), the studies show that in the early portion of the signal the interpretation of a true three-layer earth is possible to some extent, whereas the ambiguity due to equivalence persists in the late samples. On the other hand, for an intermediate resistive layer (K-type), the three-layer earth and its equivalent model cannot be distinguished from each other over the entire sampling period. On the basis of a computational approach, equivalence has been empirically established as √h/ρ=constant for H-type earth-sections, and as h²ρ=constant for K-type earth sections, where h and ρ are respectively the thickness and resistivity of the intermediate layer.     

THE APPLICATION OF LINEAR FILTER THEORY TO THE DIRECT INTERPRETATION OF GEOELECTRICAL RESISTIVITY SOUNDING MEASUREMENTS*

Koefoed has given practical procedures of obtaining the layer parameters directly from the apparent resistivity sounding measurements by using the raised kernel function H(λ) as the intermediate step. However, it is felt that the first step of his method—namely the derivation of the H curve from the apparent resistivity curve—is relatively lengthy. In this paper a method is proposed of determining the resistivity transform T(λ), a function directly related to H(λ), from the resistivity field curve. It is shown that the apparent resistivity and the resistivity transform functions are linearily related to each other such that the principle of linear electric filter theory could be applied to obtain the latter from the former. Separate sets of filter coefficients have been worked out for the Schlumberger and the Wenner form of field procedures. The practical process of deriving the T curve simply amounts to running a weighted average of the sampled apparent resistivity field data with the pre-determined coefficients. The whole process could be graphically performed within an quarter of an hour with an accuracy of about 2%.     

GRADIENT ARRAY PROFILES OVER THIN RESISTIVE VEINS1

Furness , P. 1993. Gradient Array Profiles over thin resistive veins. Geophysical Prospecting 41 , 113–130. Gradient array geoelectric surveys are commonly used to explore for buried sheet-like targets. It is demonstrated that under certain circumstances the responses of such features can become practically equivalent for a range of models differing considerably in resistivity and thickness. This is the dual of the familiar equivalence phenomenon associated with thin beds in geoelectric sounding operations. Hence the geoelectric response profiles over thin dipping resistive veins are conveniently studied by considering equivalent forms with vanishing thickness and infinite resistivity but with the same resistivity-thickness product. The effects of varying the dip, depth of burial, depth extent and resistivity–thickness product of such features on the gradient array response profiles are investigated by means of a series of numerical experiments. These demonstrate several effects of significance to survey design and data interpretation. In particular it is found that while the resistivity–thickness product influences the amplitude of the response profiles it has little effect on their form. A similar behaviour is found to be exhibited by veins with extended depth extent when the dip is varied. A complete quantitative interpretation of gradient array profiles over thin dipping resistive veins is thus only possible for veins of limited depth extent. For veins with an extended depth dimension, the data is ambiguous (in a practical sense) in terms of the dip and the resistivity–thickness product. Here, the interpretation can only be expected to deduce the horizontal and vertical locations of the vein apex.     

RESISTIVITY SOUNDING ON A MULTILAYERED EARTH CONTAINING TRANSITION LAYERS*

For curves over a horizontally stratified earth where any of the layers has a conductivity variation proportional to (1 +β·z)^N, where β and N are arbitrary constants and z is the depth to the layer, expressions for apparent resistivity for Wenner and Schlumberger sounding are derived. No assumption has been made about the continuity of conductivity at the interface. It is shown that most of the previous investigations in this connection can be regarded as particular cases of the present study.     

MAGNETOTELLURIC RESPONSE ON VERTICALLY INHOMOGENEOUS EARTH HAVING CONDUCTIVITY VARYING LINEARLY WITH DEPTH*

Magnetotelluric response is studied for an inhomogeneous medium having conductivity varying linearly with depth as σ(z) =σ₁+αz. For a medium having conductivity increasing linearly with depth, the phase of the impedance approaches 60° at long periods and the apparent resistivity becomes log (ρ_a) = 2 log (1.36/α^1/3) — 1/3 log (T'). The asymptote of log (ρ_a, T'→∞) when plotted against log (T') has a constant gradient —1/3 and has an intercept on the log (T') axis, which equals 6 log (1.36/α^1/3). When a homogeneous layer with a moderate thickness overlies an inhomogeneous half-space, this layer does not affect the asymptote, but it affects the cut-off period and pushes this toward the long period direction. For a medium having conductivity decreasing linearly with depth, the impedance is equivalent to that of a Cagniard two-layer model; the intercept period related to the thickness is T'₀=σ₁(h₂/2)². Homogeneous multilayer approximations to an inhomogeneous layer are also investigated, and it is shown that the fit to the model variation depends on the number of layers and the layer parameters chosen.     

A study on directional resistivity logging-while-drilling based on self-adaptive hp-FEM

Numerical simulation of resistivity logging-while-drilling (LWD) tool response provides guidance for designing novel logging instruments and interpreting real-time logging data. In this paper, based on self-adaptive hp-finite element method (hp-FEM) algorithm, we analyze LWD tool response against model parameters and briefly illustrate geosteering capabilities of directional resistivity LWD. Numerical simulation results indicate that the change of source spacing is of obvious influence on the investigation depth and detecting precision of resistivity LWD tool; the change of frequency can improve the resolution of low-resistivity formation and high-resistivity formation. The simulation results also indicate that the self-adaptive hp-FEM algorithm has good convergence speed and calculation accuracy to guide the geologic steering drilling and it is suitable to simulate the response of resistivity LWD tools.     

Electrical resistivity characterization and defect detection on a geosynthetic clay liner (GCL) on an experimental site

In this paper we analyze the onsite characterization of a geosynthetic clay liner (GCL) that serves to ensure the impermeability of a landfill cap by DC electrical methods. The imaging of the GCL geoelectrical properties is a challenging problem because it is a very thin (between 4 and 7 mm thick) and resistive layer (from 100,000 to 2,000,000 Ω·m) depending on meteorological conditions and aging. We compare results obtained using electrical resistivity tomography (ERT) using two different kinds of arrays (dipole–dipole DD and Wenner–Schlumberger) on an experimental site with engineered defects. To confirm these results and to find the real onsite GCL resistivity we have performed sampling of the posterior distribution of this parameter using vertical electrical sounding (VES) inversions. Different VES methods were extracted from ERT with DD array and converted into a Schlumberger array.As a main conclusion the dipole–dipole array provides a better resistivity resolution of the defects than the Wenner–Schlumberger array. On ERT images, the defect detection seems to be impossible if the GCL has very high resistivity, as it happened when it was put in place. Taking into account the equivalence rules, the inversions are in both cases (ERT and VES) compatible. The GCL resistivity estimated from PSO (particle swarm optimization) varies from 3.0 10⁵ to 1.10⁶ Ω·m depending on saturation conditions during the twenty first months of its placing. Then, the resistivity dropped to 4.10⁴–9.10⁴ Ω·m, indicating a probable chemical damage of the GCL due to aging. Finally the fact that the VES inversions are solved via PSO sampling allows for the detection of a very thin and resistive layer and opens the possibility of performing micro VES surveys along the landfill to detect possible GCL defects.     

Correlation of vertical electrical sounding and electrical borehole log data for groundwater exploration

We have correlated the longitudinal unit conductance CL obtained from interpreted vertical electrical sounding data with the formation resistivity R_t and the formation resistivity factor F, obtained by carrying out electrical borehole logging. Interpreted geophysical data of eleven soundings and two electrical borehole log records are used for the analysis. The geophysical data used were acquired in a sedimentary basin. The study area is called Lower Maner Basin located in the province of Andhra Pradesh, India. Vertical electrical soundings were carried out using a Schlumberger configuration with half current electrode separation varying from 600–1000 m. For logging the two boreholes, a Widco logger‐model 3200 PLS was used. True formation resistivity R_t was calculated from a resistivity log. Formation resistivity factor F was also calculated at various depths using R_t values. An appreciable inverse relation exists between the correlated parameters. The borehole resistivity R_t and the formation resistivity factor F decrease with the increase in the longitudinal unit conductance CL. We have shown the use of such a relation in computing borehole resistivity R_t and formation resistivity factor F at sites that posses only vertical electrical sounding data, with a fair degree of accuracy. Validation of the correlation is satisfactory. Scope for updating the correlation is discussed. Significance and applications of the relation for exploration of groundwater, namely to update the vertical electrical sounding data interpretation by translating the vertical electrical sounding data into electrical borehole log parameters, to facilitate correlations studies and to estimate the porosity (φ), permeability (K) and water saturation S_w of water bearing zones are discussed.     

Gully erosion in Mangatu Forest,New Zealand,estimated from digital elevation models

The methodology and errors involved in determining the amount of sediment produced during two (19·5 and 33·2 year) periods by 11 (c. 0·01 − >0·20 km²) gullies within a 4 km² area in the headwaters of the Waipaoa River basin, New Zealand, using sequential digital elevation models are described. Sediment production from all gullies within the study area was 0·99 ± 0·03 × 10⁶ t a⁻¹ (2480 ± 80 t ha⁻¹ a⁻¹) during the period from 1939 to 1958. It declined to 0·62 ± 0·02 × 10⁶ t a⁻¹ (1550 ± 50 t ha⁻¹ a⁻¹) during the period from 1958 to 1992, when many of the smaller gullies were stabilized by a programme of afforestation, which commenced in 1960. Both figures are very high by global standards. The two largest (the Tarndale and Mangatu) gully complexes together generated 73 and 95 per cent of the sediment in the specified time periods, but the latter amount is equivalent to only c. 5 per cent of the total annual sediment load of the Waipaoa River. © 1998 John Wiley & Sons, Ltd.     

Uranium-lead abundances and isotopic studies in the chondrites Richardton and Farmington

²⁰⁷Pb/²⁰⁴Pb-²⁰⁶Pb/²⁰⁴Pb whole meteorite isochrons for Richardton (H5) and Farmington (L5) are presented and give Pb-Pb ages of 4.545 ± 0.010 and 4.620 ± 0.010 Ga respectively (errors ± 2σ). The Pb-Pb isochron for Farmington passes below the Can?on Diablo troilite composition, which may therefore not be the initial Pb composition for this meteorite.All samples show an apparent excess radiogenic lead for single-stage (closed-system) evolution when Can?on Diablo troilite is used for the initial lead composition. Evidence is presented to show that the apparent excess Pb cannot be explained by terrestrial contamination. There is no unique isotopic composition for initial lead that yields concordant ages at 4.55 Ga for all samples for either meteorite. The data likewise cannot be reconciled to Can?on Diablo initial lead through any of the conventional two- and three-stage evolution models.The apparent excess Pb, with respect to a Can?on Diablo troilite composition and a single-stage closed-system history, and the apparent inhomogeneous initial Pb isotopic compositions, appear to be real. This may be an indication that the U-Pb systems in these meteorites are disturbed, but this disturbance cannot be described consistently by any of the conventional episodic evolution models.     

RESISTIVITY MEASUREMENTS IN VALLEYS WITH ELLIPTIC CROSS-SECTION*

In this paper an idealized valley of a semi-elliptic cross-section is considered. For a Schlumberger configuration on the axis, sets of master curves are calculated for the ratio of semi-axis a/b= 1, 2, 3, 4, 5 in corresponding to various resistivity ratios of surrounding rocks and valley sediments. For small resistivity ratios, these model curves have the shape of three-layer curves for horizontal bedding and are often equivalent to them within the accuracy of measurements. The axial ratio a/b considerably affects the depth determination of valley sediments. In the special case of a circular cross-section (a/b= 1) the influence of the position of the electrodes on the sounding curve is studied in more detail. The application of the master curves in practice shows that the influence of the specific shape of the valley on soundings should not be neglected. In general, the valleys have a greater “true” depth than can be seen from the interpretation of a sounding by master curves corresponding to the horizontal bedding.     

AN ANALYSIS OF EQUIVALENCE IN RESISTIVITY SOUNDING*

A mathematical analysis is given of the phenomenon of equivalence in resistivity sounding, which is based upon the properties of the raised kernel function. Analysis of this function instead of the apparent resistivity function is justified because, as has been shown in a previous publication, variations in the apparent resistivity function lead to variations in the raised kernel function with relative values of the same order of magnitude The expression for the raised kernel function is expanded into a Mac Laurin series. Equivalence can occur only if the second order term of this series is negligible. The coefficient of the first order term depends on the resistivity and the thickness of the layer under consideration. There is an infinite set of combinations of values for these two quantities, for which the coefficient of the first order term has the same value. All these combinations represent equivalent layer distributions.     

The effect of screening of the magnetotelluric field by high resistivity layers: Three-dimensional numerical modeling constraints

A 3-D numerical modeling approach is applied to the effect of screening of the magnetotelluric (MT) field by high resistance (≥10⁶ Ω m²) layers, which up to now has mainly been studied in terms of 2-D heterogeneous models of geological sections [Berdichevsky and Yakovlev, 1990]. Three-layer models above a poorly conducting basement (ρ=10⁴ Ω m) are used. The resistance of the screening layer was generally taken equal to 2×10⁶ Ω m² and its thickness was varied from 200 to 2000 m. The resistivity of the host medium was set at 10 Ω m. Heterogeneities of a low and a high resistivity (ρ=10^?3 and 10⁴ Ω m, respectively) ranging in horizontal size from 4 to 40 km and having a height of 1–2.8 km (a protrusion on the basement) were examined. Based on calculations of these models, 2-D and 3-D screening effects were compared. The 3-D modeling determined values of model parameters at which the screening properties are preserved both in the case of a screen of limited horizontal dimensions and in the presence of a rupture in the screen comparable in horizontal size with the 3-D heterogeneity. As follows from the modeling results, the screening effect of the high resistivity model layers seriously complicates the use of MT soundings for the identification of a local heterogeneity of both a low and a high resistivity (ρ=10^?3 and 10⁴ Ω m, respectively) if its lateral size is smaller than the 4-km thickness of the studied three-layer section in question and its height is 1–1.5 km. The regular patterns of the screening effect revealed in this work are of interest in electromagnetic sounding applications.     

THE QUANTITATIVE INTERPRETATION OF DIPOLE SOUNDINGS BY MEANS OF THE RESISTIVITY TRANSFORM FUNCTION*

In this paper a theorem is demonstrated which allows—after the introduction of a suitable dipole kernel function or dipole resistivity transform function—to write the apparent resistivity function as an Hankel transformable integral expression. As a practical application of the theorem a procedure of quantitative interpretation of dipole soundings is suggested in which the dipole resistivity transform function obtained after inversion of the original dipole apparent resistivity data is used to control the goodness of the set of layering parameters which have been derived with our previous method of transformation of dipole sounding curves into equivalent Schlumberger diagrams.     

Influence of pH on the Toxicity of Phenol and its Two Derivatives Pentachlorophenol and Dinitrophenol to Some Fresh Water Teleosts

— The fish Colisa fasciatus, Saccobranchus fossilis and Notopterus notopterus were exposed to phenol, pentachlorophenol and dinitrophenol at four pH levels, i. e. 4.6 + 0.12, 6.0±0.14, 7.3 ±0.10 and 8.8 ±0.13, to evaluate the effect of pH on the toxicity of these chemicals. — A change in pH from 7.3 ± 0.10 to 6.0 ± 0.14 increased toxicity to a certain degree while a change from 7.3 ± 0.10 to 4.6 ± 0.12 potentiated the toxicity of phenol, pentachlorophenol and dinitrophenol 5.05, 19.30 and 22.33 times, respectively for Notopterus notopterus, 3.59, 4.39 and 4.73 times, tespectively for Colisa fasciatus and 3.04, 4.68 and 5.85 times, respectively for Saccobranchus fossilis. — A change in pH from 7.3 ± 0.10 to 8.8 ± 0.13 has a protective effect on the toxicities.     

电偶源频率电磁测深中磁场比值视电阻率与其相位间的频散关系及资料的联合反演

探讨了在电偶源频率电磁测深中利用磁场比值定义的视电阻率ρｚｙ的物理意义及与其相位间的频散关系,给出了在频散关系的基础上电视电阻率资料估算相位的方法,并证明所估算的相位与理论模型计算值是一致的研究了ρｚｙ与ψｚｙ联合反演问题,并研制出具有较好应用效果的实用化软件。     

Geophysical Investigation of Fresh‐Saline Water Interface: A Case Study from South Punjab,Pakistan

The importance of the study of fresh‐saline water incursion cannot be over‐emphasized. Borehole techniques have been widely used, but they are quite expensive, intrusive, and time consuming. The electrical resistivity method has proved very successful in groundwater assessment. This advanced technique uses the calculation of Dar‐Zarrouk (D‐Z) parameters, namely longitudinal unit conductance, transverse unit resistance, and longitudinal resistivity has been employed by using 50 vertical electrical sounding points to assess the groundwater and delineate the fresh‐saline water interface over 1045 km² area of Khanewal in Southern Punjab of Pakistan. The x‐y plots and maps of D‐Z parameters were produced to establish a decipherable vision for the occurrence and distribution of different water‐bearing formations of fresh‐saline water aquifers through a complicated situation of intermixing of different resistivity ranges for fresh‐saline water bodies. This technique is useful to reduce the ambiguity produced by the process of equivalence and suppression which cause intermixing in differentiating fresh, brackish, and saline aquifers during interpretation. The fresh‐saline water interface is correlated very well with the previous studies of water quality analysis carried out in Khanewal area. The results suggest that the D‐Z parameters are useful for demarcating different aquifer zones. The behavior and pattern of D‐Z parameters with respect to occurrence and distribution of different water‐bearing formations were effectively identified and delineated in the study area.     

3D upper crustal density structure of the Deccan Syneclise,Central India

A constrained 3D density model of the upper crust along a part of the Deccan Syneclise is carried out based on the complete Bouguer anomaly data. Spectral analysis of the complete Bouguer gravity anomaly map of the study region suggests two major sources: short wavelength anomalies (<100 km) caused primarily due to the density inhomogeneities at shallow crustal level and long wavelength anomalies (>100 km) produced due to the sources deeper than the upper crust. A residual map of the short wavelength anomalies is prepared from the complete Bouguer anomaly using Butterworth high‐pass filter (100 km cut‐off wavelength). Utilizing the constraints from deep resistivity sounding, magnetotellurics and deep seismic sounding studies, 2.5D density models have been generated along 39 profiles of this region. The mismatch between the calculated response of the a priori 2.5D model with the residual (short wavelength) gravity anomalies is minimized by introducing high‐density intrusive bodies (≥2.81 g/cm³) in the basement. With these 2.5D density models, the initial geometry of our 3D density model, which includes alluvium, Deccan trap, Mesozoic sediment and high‐density intrusive bodies in the basement up to a depth of 7 km (upper crust), is generated. In the final 3D model, Deccan trap extends from 200 m to nearly 1700 m below the 90–150 m thick Quaternary sediment. Further down, the sub‐trappean Mesozoic sediment is present at a depth range of 600–3000 m followed by the basement. The derived 3D density model also indicates six intrusive bodies of density 2.83 g/cm³ in the basement at an average depth of about 4–7 km that best fits the residual gravity anomaly of the study area.     

The effect of intrinsic model noise upon resistivity inversion

Model uncertainty is introduced into direct-current resistivity data by adding random changes to layer thicknesses in a ten-layer model. The resulting information is then aliased by generating a sounding curve which contains less information than the ten resistivities and nine thicknesses. These sounding curves are then inverted via the Backus-Gilbert algorithm using singular value decomposition to obtain solutions in terms of simpler two-or three-layer models. Quantitative results confirm what has been known qualitatively for many years as the principle of equivalence. An interesting result is that the geometric average of a given suite of noisy models is virtually identical to the best-fit model for the average of the noisy curves. The results show that the inversion of resistivity data by nonlinear least-squares parameter fitting is stable in the sense that noise in the data inverts to the same magnitude of noise in the model.     

Validation of joint inversion of direct current and electromagnetic measurements

One of the ways to improve the information content of a set of field data is that of combining the interpretation of disparate data sets. Electromagnetic and direct current resistivity methods suffer from inherent equivalence problem. Application of joint inversion for these measurements can overcome the problem of equivalence very well. In the present work, synthetic data from vertical electrical sounding (VES) and horizontal coplanar low-frequency induction sounding (EMHD) are inverted individually and jointly over different types of 1D earth structures. Global optimization with Monte Carlo Multistart algorithm was used in the calculations. The results obtained from the inversions of synthetic data indicate that the joint inversion significantly improves the solution reducing the ambiguity of the models.