The work is devoted to the theoretical substantiation of a new geophysical technology for studying a unique geological object with unconventional hard-to-recover hydrocarbon reserves. The technology is based on transient electromagnetic sounding from a spatially distributed system of highly deviated wells drilled in target objects near the Bazhenov Formation. The results of computer modeling predetermine a new direction for geological exploration of unconventional hydrocarbon deposits. We consider a numerical solution to the 3D direct problem of pulsed electromagnetic sounding and, on its basis, develop a computational scheme and computer program. A mathematical model is built that describes the sensing process through a pulsed source for electromagnetic field excitation. The Fourier transform is used for time discretization, and the vector finite element method for spatial discretization. This approach makes it possible to obtain many independent 3D problems and effectively solve them in parallel by applying the modern multiprocessor technology. Using the KNL and Broadwell computing nodes of the Siberian Supercomputer Center SB RAS, we performed calculations of electromagnetic signals, which showed a high efficiency of the devised computing scheme and a high performance of the implemented algorithm. Despite the fact that the total peak performance of the KNL nodes is 2.5 times higher than that of the Broadwell nodes, their practical application for performing large-scale 3D modeling on the cluster shows a high efficiency of the latter. When choosing the most suitable computing architecture for the implementation of mass calculations, one should not rely on their formal characteristics only; significant performance is achieved taking into account the peculiarities of the computational methods employed for solving a specific problem. The implemented more efficient ways of performing parallel matrix-vector operations did not significantly increase the performance for this computational scheme. The created computational tools form the basis for further design of the configuration of a pulsed electromagnetic sounding system, and for identifying the capabilities of the new geophysical technology for examining complex geological media.