A PRACTICAL METHOD OF CALCULATING GEOELECTRICAL MODEL GRAPHS FOR HORIZONTALLY STRATIFIED MEDIA*

For the quantitative interpretation of field resistivity curves it is necessary to possess theoretically calculated standard graphs. The problem of calculating such graphs for certain parallel stratified media has been solved long ago. The methods developed so far, however, require facilities, which are not normally available to the geophysicist in the field. It has been shown by experience, that the catalogues of graphs, which have been made available for practical use, are inadequate, when the number of layers exceeds three. For this reason endeavours are made to find a method, to allow the geophysicist to calculate model graphs suited to any given special geological situation, with ordinary field facilities and without too great an expenditure of time. The principle of equivalence implies that such a model graph be known with a high accuracy.

To this end, a method for the calculation of model graphs for a series of parallel beds is described. This method is sufficiently simple – no series need to be summed up – to be applied by the geophysicist in practice, even during field work. The study of the kernel function in Stefanescu's integral representation of the “apparent” resistivity leads to a basis for the set of graphs. The prime elements of this basis form a one‐parametric curve‐system, by means of which the graph for any multi‐layer sequence of strata can be obtained to any degree of approximation by linear combination.

The importance of this method in practice is demonstrated with the help of examples.