Ossian O'Reilly
Department of Geophysics
Stanford University
Stanford, California, USA
Wave propagation offers a unique opportunity for interrogating fluid-filled cracks in in volcanic conduit systems and wellbore-hydraulic fracture systems in oil and gas industry. For simulating wave propagation in these systems, we develop a high order, energy stable method, coupling fluid-filled cracks to the linear elastic wave equation in first order formulation in two space dimensions. The discretization uses summation-by-parts finite differences on multiblock grids, and coupling conditions are enforced weakly using the simultaneous approximation term (SAT) technique. To improve computational efficiency, we derive an approximation to the compressible Navier-Stokes equations, that exploits the high-aspect ratio geometry of the crack. The crack geometry is a source of stiffness, requiring implicit explicit time stepping (IMEX) for computational efficiency. One or more cracks can branch off of a central fluid-filled conduit. Instead of using SBP-SAT for coupling, we simulate wave propagation in the conduit using a quasi-one-dimensional model in frequency domain and couple to cracks using transfer functions. Transfer functions for cracks are constructed through independent, wave propagation simulations and computing the spectrum of the fluid fields. Small explosions within the crack, or nearby micro-earthquakes might provide a way to determine crack geometry and properties of the fluid within the crack. These events are modeled as point sources that are discretized such that they can be applied anywhere in the domain (do not necessarily have to lie on a grid point), without triggering high frequency content, and without requiring artificial dissipation.