In a recent paper Sampaio presented an analytic solution of the magnetic field problem for a circular magnetized cylinder embedded in a homogeneous magnetized half-space. In his paper, Sampaio also stated that the numerical method for solving magnetostatic problems by Eskola and Tervo (1980) doesn't take into consideration the susceptibility contrast between the half-space and the air. The model treated by Sampaio doesn't actually exist, however. For a magnetized environment, in addition to the upper boundary, there is also a lower boundary, i.e., where the rock loses its magnetization (at least at the Curie point). This boundary holds an additional source of magnetic field that is of the same order of strength as the field caused by the upper boundary, if the horizontal dimensions of the magnetized environment are large. If the horizontal dimensions are not large, the effect of the vertical boundaries of the environment must also be taken into consideration. Eskola and Tervo (1980) find no difficulty in taking into consideration all the boundaries by means of their method.

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