Spatiotemporal pore pressure evolution due to fluid-mass point sources in dynamic poroelasticity

SUMMARY

The spatiotemporal behaviours of pore pressure induced by a fluid mass point source in quasi-static and dynamic poroelasticity are compared and contrasted. Explicit results for the pore pressure in time domain are derived using the known fundamental solution of dynamic poroelasticity in frequency domain. Depending on the frequency content of the source function, different regimes can be identified. First, the diffusive regime where only the diffusive slow wave exists; the latter is equivalent to the process of pore pressure diffusion. Second, there is the propagation–diffusion regime where slow and fast wave modes coexist. It is shown that the amount of induced pore pressure due to the diffusive slow wave is different for quasi-static loadings (e.g. fluid injection experiments) and transient loads (e.g. propagating low-frequency seismic waves). The results are discussed in the context of fluid injection experiments where short-term fluctuations of the injection rate can create both, the fast compressional wave and the slow diffusive wave. The results can be used in order to generate synthetic seismograms and validate numerical schemes for pressure disturbances in dynamic poroelasticity.