Magnetic resonance sounding (MRS) is a geophysical technique developed for groundwater exploration. This technique can be used for investigating karst aquifers. Generally, the study of a karst requires a 3D field setup and corresponding multichannel data-acquisition instruments. Now only single-channel MRS equipment is available; i.e., the time needed for a 3D MRS field survey is multiplied by a factor of four or five. Where karst caverns are natural hazards, as in the Dead Sea coastal area at Nahal Hever, Israel, even an approximate localization of potentially dangerous zones and a corresponding estimation of the hazard dimensions are useful. We studied numerically the accuracy of MRS estimations of the volume of different 3D targets aroundNahal Hever, shifting a 3D target inside the MRS loop and calculating the volume-estimation errors for each target position. The calculations covered targets of different sizes. The size and position of a target being unknown factors in a field survey, the numerical data were considered as random values to be analyzed statistically. Using a 1D approximation of the MRS solution and assuming a MRS loop, the volume of a 3D target under Nahal Hever conditions is estimated within a error when the target is smaller than the MRS loop, and within a error when the target size is about the same as the MRS loop. The lower threshold of karst-cavity detection with MRS is about . For such estimation, only one sounding is required.