A simplified model for hydraulic fracturing and its role in seismicity

In this study we propose a simple mathematical model to evaluate the seismic energy (magnitude) generated by the injection of a pressurized liquid in a geothermal area. The aim is to distinguish between induced and triggered seismicity. We compute the induced seismicity by a simple equation that allows to evaluate the energy contribution of the human activity. By using the classical linear elastic fracture theory, we obtain a formula that correlates the strain energy to the injection pressure, to the material parameters of the rock under consideration and to the characteristic seismic length. We compare the results of the model with a series of recorded data available in the literature, showing that our model is capable of defining the maximum magnitude of seismic events caused by human activity. Consequently, the model puts in evidence the "triggered" events with larger magnitude that are produced by the elastic energy accumulated in the rocks at depth by other natural means (e.g. tectonic).