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Operations including borehole fluid injections are typical for exploration and development of hydrocarbon or geothermic reservoirs. Microseismicity occurring during such operations has a large potential for understanding physics of the seismogenic process as well as in obtaining detailed information about reservoirs at locations as far as several kilometers from boreholes. We propose that the phenomenon of microseismicity triggering by borehole fluid injections is related to the process of the Frenkel-Biot slow wave propagation. In the low-frequency range (hours or days of fluid injection durations) this process reduces to the pore-pressure diffusion. We search for diffusion-related features of induced micro seismicity....