Automatic interpretation of Schlumberger sounding curves, using modified Dar Zarrouk functions

Abstract

Formulas defining two types of modified Dar ^arrouk curves are used to invert Schlumberger sounding curves, using an iterative procedure. The number of layers, which is equal to the number of points on the inverted curve, is reduced by AUTOMATIC INTERPRETATION OF SCHLUMBERGER SOUNDING CURVES, USING MODIFIED DAR ZARROUK FUNCTIONSBy ADEL A. R. ZOHDY ABSTRACT For horizontally stratified media, Schlumberger VES (vertical electrical sounding) curves with slopes of greater than -1 not only resemble but commonly almost coincide with their corresponding DZ (Dar Zarrouk) curves. By considering an n-point Schlumberger VES curve to be an n-layer DZ curve, and by solving for the layering from the DZ curve, we obtain a first approximation to the actual layering in the form of an nlayer section. However, the minimum slope for DZ curves is 1, whereas on some VES curves negative slopes may be as low as 3; therefore, these VES curves cannot be considered to be a first approximation to their corresponding DZ curves. Formulas are obtained for calculating two types of MDZ (modified DZ) curves whose positive and negative slopes are not limited to +1 and 1, respectively. Therefore, for any VES curve, there exists a corresponding MDZ curve that lies close to it. The automatic interpretation is made by an iterative procedure in which, for the first approximation, the observed VES curve is assumed to be the sought MDZ curve. This MDZ curve is solved for layer thicknesses and resistivities; then, by means of a convolution technique, a VES curve is calculated for the obtained layering, and the calculated VES curve is compared with the observed one. A second approximation to the sought MDZ curve is obtained by utilizing the differences between the observed and calculated VES curves. The iteration is continued until a match, within a prescribed fitting tolerance, is obtained between observed and calculated VES curves. The number of layers in the resulting model (detailed solution) is always equal to the number of points used to define the observed VES curve. Equivalent solutions composed of a fewer number of layers are determined by automatically smoothing the DZ curve of the detailed solution and inverting it. Special equivalent solutions that are subject to certain geologic or geoelectric constraints can be found by manual adjustments of the detailed n-layer DZ curve. Excellent automatic matches were obtained when the method was tested with several theoretical VES curves and with several hundreds of field VES curves of different forms. The average processing time per VES curve (extending over more than three logarithmic cycles) on the IBM 360/65 computer is about 8 seconds. For distorted and incomplete field curves, the average processing time is approximately doubled. El E2 TECHNIQUES IN DIRECT-CURRENT RESISTIVITY EXPLORATION

Fractional Current Flow in the Subsurface Using Electrical Resistivity Method: A Laboratory Approach

“…Among the existing geophysical techniques, the resistivity method is generally and mostly used for shallow subsurface studies and groundwater exploration [20]. Four electrodes are used in this method to measure resistivity [21]. One pair of electrodes is used to penetrate the current into the ground and another pair is used to measure the potential difference of hemispheric equipotential surfaces where the ground surface is intersecting them [22].…”

“…Schlumberger array used for VES investigation [11,21], is a type of direct current resistivity survey described by its configuration. It makes use of four collinear electrodes, a pair of current electrodes as source and another pair of potential electrodes as the receivers.…”

Vertical Electrical Sounding Exploration of Groundwater in Kertajati, Majalengka, West Java, Indonesia

“…VES data interpretation aims to determine the true resistivities and thicknesses of the successive strata below the different stations, utilizing measured field curves (El-Gawad et al, 2018). The apparent resistivity (ρa) values were obtained from the voltage (mV) and current (mA) read from the resistivity meter and its calculated corresponding geometric factor (Zohdy, 1975).…”