Poroelastic modeling of seismic boundary conditions across a fracture.
Permeability of a fracture can affect how the fracture interacts with seismic waves. To examine this effect, a simple mathematical model that describes the poroelastic nature of wave-fracture interaction is useful. In this paper, a set of boundary conditions is presented which relate wave-induced particle velocity (or displacement) and stress including fluid pressure across a compliant, fluid-bearing fracture. These conditions are derived by modeling a fracture as a thin porous layer with increased compliance and finite permeability. Assuming a small layer thickness, the boundary conditions can be derived by integrating the governing equations of poroelastic wave propagation. A finite jump in the stress and velocity across a fracture is expressed as a function of the stress and velocity at the boundaries. Further simplification for a thin fracture yields a set of characteristic parameters that control the seismic response of single fractures with a wide range of mechanical and hydraulic properties. These boundary conditions have potential applications in simplifying numerical models such as finite-difference and finite-element methods to compute seismic wave scattering off nonplanar (e.g., curved and intersecting) fractures.
Nakagawa
Seiji
S
Earth Sciences Division, Lawrence Berkeley National Laboratory, Berkeley, California 94720, USA. snakagawa@lbl.gov
Schoenberg
Michael A
MA
D002140:California; D004190:Disasters; D004548:Elasticity; D055593:Geological Phenomena; D005844:Geology; D007700:Kinetics; D008962:Models, Theoretical; D011312:Pressure; D015203:Reproducibility of Results; D013016:Sound