Testing of low-contrast resistivity objects is a difficult problem for electromagnetic methods. If we identify electrical exploration with electrical exploration of TE-polarization, i.e. electromagnetic methods that uses classical sources of the electromagnetic field - a loop or a horizontal line, the problem really looks insoluble. We can suggest the solution of the problem on the other hand - use a circular electric dipole as the source of the electromagnetic field, and excite only the electromagnetic field of the TM polarization in the medium. When electromagnetic field in the medium is only the TM polarization then on the surface will be magnetic field from various three-dimensional objects only. Three-dimensional objects have differences by some electrodynamic parameters with a horizontally layered medium. Anomalous field, as our experience shows, significantly exceeds the field calculated by classical models, using only anomalies of specific isotropic resistance. Such an anomalous field can be interpreted by complicating the generally accepted model, and introducing additional electrodynamic parameters into the calculations. The large anomalous field, which is created not only by a change in the specific isotropic resistance, allows us to confidently solve the problem of identifying three-dimensional objects that are not solvable for the classic TE-polarization.