Purpose. The main aim of the research is creation of methods for a calculation of a terrain relief influence on the vertical electric sounding (VES) data using the boundary element technique and also presentation of applying these methods for VES to test examples and real mountain terrains. Methodology. An apparent resistivity is equal to true resistivity of a medium in a homogeneous half-space. In the case of a relief surface of the homogeneous medium the ratio of the apparent resistivity to the real resistivity determines the influence value on the electrical resistivity data. To calculate this value the model of the electrical homogeneous medium with a non-conductive relief surface is used. Electrical potentials for such model are calculated using the boundary element technique, which allows to describe complex curved boundaries. The calculated potentials are used to determine the apparent resistivity for any configuration of an electrical prospecting installation. Results. Features of the relief influence on the VES data are considered for models of ridge and ravine. Calculations testify to a significant relief effect from 10-15% (for a slope angle of about 6°) to 30-50% (for an angle of about 17°). The maximum magnitude of the effects is observed for the ratio of a supply line to a model transverse size about three quarters. The relief effect is decreases with increasing the supply size. If receive line is larger as the model size the effect is reduced to almost zero. The relief effect of "ravine" for VES data is greater as "ridge". One of landslide areas of Transcarpathia (Kopashneve-1) is used to calculate the relief effect of the real mountainous terrains. The detailed VES was done for this area. It is presented that the greatest relief effects are observed in places of maximum "curves" (like "ridge" or "ravine") up to 20% on some segments of profiles. Generally the research results testify that the relief effects must be considered for mountain and rough terrains to avoid errors of VES data interpretation. Originality. Using mathematical modeling by boundary element technique the methods for calculating a terrain relief influence on the electrical resistivity survey data are created. Practical significance. The made calculations for model and real examples of complex surfaces testify to a significant relief effect on the vertical electrical sounding data. The use of such methods for above terrains avoids interpretation errors of the electrical prospecting data.

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