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  Resistivity Depth Sounding, Physics tutorial

Introduction:

This method is also known as vertical electrical sounding or expanding probe. Here current and potential electrodes are maintained at same relative spacing and whole spread is increasingly expanded about fixed central point. Resistivity depth soundings investigate layering, by using arrays in which distances between some or all of electrodes are increased systematically. Apparent resistivities are plotted against expansion on log-log paper and matched against type curves.

Though introduction of multicore cables and switch selection has motivated use of simple doubling, expansion is still usually in steps which are roughly or accurately logarithmic. Half-spacing sequence 1, 1.5, 2, 3, 5, 7, 10, 15 . . . is suitable, but some interpretation programs need exact logarithmic spacing. Sequences for five and six readings to decade are 1.58, 2.51, 3.98, 6.31, 10.0, 15.8 . . . and 1.47, 2.15, 3.16, 4.64, 6.81, 10.0, 14.7 . . . respectively. Curves drawn through readings at other spacing can be re-sampled but there are obvious benefits in being able to use field results directly. Though methods have been developed for interpreting dipping layers, conventional depth-sounding works well only where interfaces are approximately horizontal. Method is widely utilized in geotechnical surveys to find out overburden thickness and also in hydrogeology to describe horizontal zones of porous strata.

Choice of array:

As depth-sounding involves expansion about centre point, instrument usually stays in one place. Instrument portability is thus less significant than in profiling. Wenner array is very popular but for speed and ease the Schlumberger array, in which only two electrodes are moved, is frequently favored. Interpretational literature, computer programs and type curves are extensively available for both arrays. Local near-surface variations in resistivity almost always initiate noise with amplitudes greater than differences between Wenner and Schlumberger curves.

Array orientation is frequently constrained by local conditions that is there may be only one direction in which electrodes can be taken adequate distance in straight line. If there is a choice, array must be expanded parallel to probable strike direction, to minimize effect of non-horizontal bedding. It is usually desirable to perform second, orthogonal expansion to check for directional effects, even if only very restricted line length can be attained. Dipole-dipole and two-electrode arrays are not utilized for ordinary DC sounding work. Dipole-dipole depth pseudo-sections are much utilized in IP surveys.

Using the Schlumberger array:

Site selection, very significant in all sounding work, is mainly critical with Schlumberger array that is very sensitive to conditions around closely spaced inner electrodes. Location where upper layer is very inhomogeneous is inappropriate for array centre and offset Wenner array may thus be preferred for land-fill sites. Apparent resistivities for Schlumberger array are generally computed from approximate equation that severely applies only if inner electrodes form ideal dipole of negligible length. Though more accurate apparent resistivities can be achieved using precise equation, interpretation isn't essentially more dependable as all the type curves are based on ideal dipole. Technically a Schlumberger array is expanded by moving outer electrodes only, but voltage will finally become very small to be correctly estimated unless inner electrodes are also moved farther apart. Sounding curve will therefore comprise of number of separate segments. Even if ground really is divided in layers which are perfectly internally homogeneous, segments won't join smoothly as approximations made in using dipole equation are different for different l/L ratios. This effect is usually less significant than effect of ground inhomogeneities around potential electrodes, and segments may be related for interpretation by moving them in their entirety parallel to resistivity axis to form continuous curve. To do this, overlap readings should be made. Preferably there must be at least three of these at each change, but two are more usual and one is unfortunately norm.

Offset Wenner depth sounding:

Schlumberger interpretation is complicated by segmentation of sounding curve and by use of the array which only approximates conditions assumed in interpretation. With Wenner array, on the other hand, near surface conditions vary at all four electrodes for each reading, risking a high noise level. A much smoother sounding curve can be generated with offset array of five equi-spaced electrodes, only four of which are utilized for any one reading. Two readings are observed at each expansion and are average to generate curve in which local effects are suppressed. Differences between two readings give a measure of significance of these effects. Use of five electrodes complicates field work, but if expansion is based on doubling previous spacing, very quick and proficient operation is possible using multicore cables designed for this purpose.

Presentation of sounding data:

There is generally time while distant electrodes are being moved to compute and plot apparent resistivities. Small delays are in any case better than returning with uninterruptable results, and field plotting must be routine. All that is required is pocket calculator and supply of log-log paper. Simple interpretation can be performed using two-layer type curves on transparent material. Generally an exact two-layer fit won't be found and rough interpretation based on segment-by-segment matching will be best which can be done in field. Ideally, this procedure is handled using auxiliary curves to describe allowable positions of origin of two-layer curve being fitted to later segments of field curve.

Pseudo-sections and depth sections:

Increasing power of small computers now permits effects of lateral changes in resistivity to be separated from changes with depth. For this to be done, data should be collected along whole length of traverse at number of different spacings which are multiples of fundamental spacing. Results can be shown as contoured pseudosections which give rough visual impressions of way in which resistivity differs with depth.

Data can also be inverted to generate revised sections with vertical scales in depth rather than electrode separation that provide greatly enhanced pictures of actual resistivity variations. Due to the broad use of these methods in recent times, inadequacies of simple depth sounding have become much more extensively identified. Extra time and effort involved in obtaining more complete data are almost always justified by results.

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