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Based on mathematical modeling, the paper presents the estimation of the length of dilatancy zones developed near a free surface during the preparation of earthquakes. An algorithm for the calculation of dilatancy zones has been developed and applied for numerical modeling. Estimated examples of the development of near-surface dilatancy zones before the Kamchatka earthquakes with a magnitude M = 6.7-7.8 are given. The results of the numerical experiments under the accepted assumptions solve the problem of the long-range influence of a future earthquake source on a limited remote zone of microseismic information gathering: the model admits the development of near-surface dilatancy zones in the vicinity of a station recording seismic noise that can trigger forerunner anomalies. [ABSTRACT FROM AUTHOR]