PARAMETER SENSITIVITY MAPS OF SURFACE GEOELECTRIC ARRAYS II. NONLINEAR AND FOCUSSED ARRAYS

In this paper we present, at first time in a geophysical journal, parameter sensitivity maps of nonlinear and focussed electrode arrays. We present them as anomalies due to electric dipoles forming on opposing surfaces of an elementary cube within the subsurface at three different depths, and not only the total effect of the dipole, but also of its components are shown. Parameter sensitivity maps of non-linear arrays, compared to those of linear arrays, have in general 1. more equal sensitivity values in x and y directions, 2. more chances for antisymmetry axes, 3. smoother lateral distribution of sensitivity values. We recommend a systematic use of parameter sensitivity maps in geoelectric prospecting, both in planning and interpretation of field measurements

Classification of Surface Geoelectric Arrays

We have found in the geophysical literature more than ninety different surface geoelectric arrays, fulfilling an updated definition (specifying the current feeding, the potential difference measurement and the geometry of the electrodes). Several composite configurations, with widely varying geometry, have also been collected. We have presented the geoelectric arrays in a systematic way and with a unified notation. The classification is based on three divalent parameters: “superposition” of measurements, “focusing” of currents and “colinearity” of the array, creating 8 groups of geoelectric arrays. For the simplest group (the group of nonfocused, nonsuperposed, colinear arrays) we cover all theoretically possible arrays. For the other groups – due to the infinite variety – we collected only the already existing arrays, but it is easy to create further example arrays. The proposed classification may facilitate a systematic comparison of properties of different arrays and inspire testing new arrays, to find optimal configurations for actual field problems. Finally, the classification certainly helps to avoid rediscovering already published arrays

Auxiliary Results of Collection and Classification of Surface Geoelectric Arrays

Recently, we have made a classification of more than one hundred various surface geoelectric arrays ever published in geophysical literature (Szalai and Szarka 2007a, 2007b). The classification is based on three divalent parameters (as “superposition” of measurements, “focusing” of currents and “colinearity” of the array), thus we set up eight groups of geoelectric arrays. One further group was separated for about 10 socalled “composite” arrays, which cannot be classified in the aforementioned way. Here we present some application examples of the classification results. Namely, we call the attention to some hidden relationships among geoelectric arrays: (1) we give an illustration how various arrays can be derived from their root array (besides the Schlumberger-related arrays several other examples will also be given in the presentation); (2) we provide a summary of arrays, capable to measure various partial derivatives of the electric potential. Among the 21 arrays 14 are already published arrays, but there are seven possible, but not-yet-applied arrays. In this way, such missing links in the genealogic trees may lead to creation of reasonable and purposeful new arrays

A Review on the Resource Curse

Natural wealth is generally considered as one of the fundamental sources of economic growth. However, a vast majority of the related empirical research verified that resource-rich countries tend to underperform their resource-deficient counterparts. This paradox is known as the resource curse. During the past two decades more sophisticated analyses have revealed that the presence of the curse is conditional and its growth effects are non-monotonic. Recent efforts concentrate on understanding the transmission channels and identifying the decisive conditions on the fulfillment of the curse. This article gives an overview on the progress and depicts the current state of the research

Effect of positional inaccuracies on multielectrode results

This paper investigates the effect of electrode positioning errors on the inverted pseudosection. Instead of random spacing errors (as usually assumed in geoelectrics) we exactly measured this effect among field conditions. In the field, in spite of the greatest possible care, the electrode positions contain some inaccuracy: either in case of dense undergrowth, or varied topography, or very rocky field. In all these cases, it is not possible to put the electrodes in their theoretical position. As a consequence, the position data will contain some error. The inaccuracies were exactly determined by using a laser distance meter. The geometrical data from real field conditions and by using Wenner-α, Wenner-β, pole-dipole and pole-pole arrays were then considered over homogeneous half space. As we have found, the positioning errors can be regarded as insignificant, even in case of relatively uncomfortable field conditions. However, in case of very rocky surface the distortions are more significant, but it is still possible to make some corrections: either by neglecting a few electrode positions with the greatest positioning error, or to minimize the inline errors, even on the price that offline deviations are high

Depth of Investigation of Dipole-dipole, Noncolinear and Focused Geoelectric Arrays

Investigation depth of various DC geoelectric arrays has always been in the focus of interest of geoelectricians. According to its classical definition (Roy and Apparao 1971), the depth of investigation is the depth of the maximum response due to a horizontal thin-sheet embedded in a half-space, by using a given geoelectric array. On basis of the graph of the thin-sheet response as a function of the depth (from the so-called „depth of investigation characteristics” or DIC function) Edwards (1977) found more realistic to compute the medium depth than the depth of the maximum response. DIC functions have been known so far only for simple colinear arrays, the dipole equatorial array and two focused arrays. Here we provide a summary about the depth of investigation values of various dipole-dipole arrays (for parallel, perpendicular, radial, azimuthal ones), and for the most important noncolinear and focused arrays. Depth of investigation values are computed from both approaches. DIC functions (obtained by a new analytical formula) are also presented, as illustrations. The analytical formula can be used to compute DIC function of any surface geoelectric array. A systematic interpretation of the resulting depth of investigation values provides simple but useful thumb-rules for practical applications

Effect of Positional Inaccuracies on Multielectrode Results

We have started to investigate the consequences of various noises o the interpreted results for various multielectrode arrays. We expect, it will be possible to find out, what kinds of noise have the most effect on the resulting data. Such an investigation may lead to a better elimination of potential errors due to noises. In the first step (presented in this paper) we studied the appearance of false anomalies due to positioning errors of the electrodes. In realistic field conditions, in spite of the greatest possible care, the electrode positions contain some inaccuracy: either in case of dense undergrowth, or varied topography, or very rocky field. In all these cases, it is not possible to put the electrodes in their theoretical position. As a consequence, the position data will contain some error. The extent of such inaccuracies was exactly determined by using a laser distance meter. Then, we computed their effect on the resulting apparent- and inverted resistivity data. We carried out such a study for Wenner, Wenner-beta, pole-dipole and pole-pole arrays. In the light of our conclusions, the usual assumption about random noise seems to be an oversimplification

Expanding the possibilities of two-dimensional multielectrode systems, with consideration to earlier geoelectric arrays

Recent two-dimensional multielectrode measurements are restricted to only a few geoelectric arrays. Realizing that specific features of nearly 90 other arrays are totally ignored, all original intentions as published about the development of new geoelectric arrays were reviewed. Apart from arrays, either already applied in two-dimensional geoelectric arrays or impossible to be applied in such systems, 61 forgotten once-developed arrays were found. These provide altogether 102 various solutions, which would be able to increase the efficiency of two-dimensional multielectrode measurements in some respect. 46 array solutions are able to enhance the depth of investigation; 9/11 array solutions give better vertical/horizontal resolution; 17 array solutions provide better planview images; 8 array solutions are worth applying in areas with limited access; 11 array solutions may reduce the effect of near-surface inhomogeneities. By reviving these forgotten arrays, it will be possible to develop versatile multielectrode systems, which are more adaptive to the diverse field needs

Report of review of St Stephen’s Children’s Centre, Newham: services for children aged up to 3 years

Formation of surface depressions is a significant geological hazard. Prediction of future sinkholes in buried karstic areas needs knowledge about the subsurface. In order to determine the varying topography of the karstifiable bedrock we carried out multielectrode measurements. Due to the hard field conditions, the bedrock depth could not be detected. The resistivity anomalies in some places had a seasonal variation (low-resistivity in springtime, high-resistivity in the end of summer); therefore we interpreted the springtime resistivity lows as indicators of locations with high water content, that is as high porosity, saturated with water. At the same time, when pushing the current- and potential electrodes into the ground, we discovered a regularity in the areal distribution of the soil's rock debris content. Therefore we carried out a systematic electrode-pricking experiment, and categorized the soil's "toughness" corresponding to soft penetration, scratching or blockage within the upper 30 cm. We have found a close relationship between the locations of resistivity- and the soil's toughness extremes. From some epikarstic features we think that high "pricking probe" values indicate smaller depths of the bedrock. The corresponding (springtime) resistivity minima may indirectly indicate more or less collapsed horsts of the carbonate rock

Parameter sensitivity maps of surface geoelectric arrays

Parameter sensitivity maps allow a better understanding of various geoelectric responses, and they are also helpful in designing optimal new arrays for specific problems. We constructed systematic parameter sensitivity maps for various geoelectric arrays, and in this paper several examples are presented, among others for non-linear and focussed arrays. Our parameter sensitivity values are computed from the response of a small-size cube in a homogeneous subsurface at three different depths. Instead of 3D numerical modelling results we consider the small cube as a superposition of three electric dipoles, corresponding to the electric charge accumulation at the opposite cube faces. We apply simple analytical formulas and we present the parameter sensitivity values separately for the individual dipoles. Several theoretical and practical aspects are discussed. We recommend a methodical use of parameter sensitivity maps in geoelectric prospecting