Statistics of fracture strength and fluid‐induced microseismicity

In this paper we develop an approach for estimating the strength of rocks by analyzing fluid‐induced microseismicity. The strength corresponds to the value of critical pressure in the pore space that must be exceeded in order to activate preexisting fractures, i.e., to trigger earthquakes. We assume that during hydraulic injection experiments in boreholes, microseismicity is mainly triggered by a diffusive process of pore pressure perturbation. An analytical solution can be applied to find time‐dependent pore pressure perturbations in rocks caused by fluid injections. Characteristics of the spatiotemporal evolution of microseismic clouds can be then used to estimate minimum and maximum pressures necessary to trigger earthquakes. Moreover, we present a method for reconstruction of the full spectrum of rock strength; that is, we show how to estimate the probability density function of the critical pressure. We verify the approach using numerical data and apply it to real data of injection‐induced microseismicity from two Hot Dry Rock tests in crystalline rocks and one hydraulic fracturing experiment in a sedimentary rock. The results show that such an analysis of microseismicity is able to provide us with a completely new feature of natural fractured rocks in situ, namely, the statistics of their strength. We find that very low critical pressures, in the range 0.001–1 MPa, characterize the strength of preexisting cracks for all data sets analyzed. The range of critical pressures is broadly distributed within 3 to 4 orders of magnitude. However, the probability density functions of critical pressure change very quickly from the zero level to significant values and from significant values to the zero level at the lower and upper limits of their nonvanishing value ranges, respectively. The lower bound of critical pressure is possibly defined by the magnitude of tidal‐induced stresses, permanently occurring and relaxing in the Earth.