Martin Almquist
TDB, IT, UU
Marine seismic exploration uses pressure waves generated by an array of airguns, dragged behind a boat, to determine material properties of the subsurface. Mathematically, the problem may be formulated as the inverse problem of estimating parameters of the coupled acoustic-elastic wave equation. Given seismograms at point locations, we set up a misfit functional (MF) that measures the difference between simulated and recorded data. The gradient of the MF can be computed efficiently by solving the adjoint equations. We discuss the adjoint of the discrete equations and how seismogram data in the MF give rise to singular source terms.
Earthquake sequence simulations, which simulate faults over multiple seismic events, are now widely used in the earthquake modeling community. Unlike a dynamic rupture simulation of a single event, earthquake sequence simulations can be used to estimate recurrence intervals and study how fault-slip history influences subsequent events. We discuss stable discretizations of the governing equations for a viscoelastic solid with a nonlinear rate-and-state friction law on the fault.