Figure 5
From: The surge of earthquakes in Central Oklahoma has features of reservoir-induced seismicity
Analytic pressure and stress solutions for a time-dependent boundary condition. To study the influence of the time that the fluid needs to accumulate at the TOB, a time-dependent boundary condition for p0 is defined, based on the injection rate in our study area between 01/2009 and 12/2015 (blue line, panel (A)). We extrapolated the data until 12/2018, using information of the Volume Reduction Plan, to allow for predictions of the seismicity rate after 12/2015. Calculating \({\int }_{0}^{t}\,Q(\tau )\,{\rm{d}}\tau \), yields p0(t). Solving analytically for equations (2)–(5) and subtracting the gravity effect yields changes of the pore-fluid pressure (B), the vertical (C) as well as the horizontal (D) stress. Colour-coding shows the corresponding profile along the depth for times 01/2010, 01/2013, 01/2015 and 12/2018 (light to dark colours). In spite of the fact that the pressure perturbation is generally higher than stress changes, at some depths and times they can have the same order of magnitude. This results in various signatures of URIS under different stress regimes and is a direct result of the poroelastic coupling.
