  We present a mechanism to explicitly couple the finite-difference
discretizations of 2D acoustic and isotropic elastic wave systems that are
separated by straight interfaces. Such coupled simulations allow the
application of the elastic model to geological regions that are of special
interest for seismic exploration studies (e.g., the areas surrounding salt
bodies), while with the computationally more tractable acoustic model still
being applied in the background regions. Specifically, the acoustic wave system
is expressed in terms of velocity and pressure while the elastic wave system is
expressed in terms of velocity and stress. Both systems are posed in
first-order forms and discretized on staggered grids. Special variants of the
standard finite-difference operators, namely, operators that possess the
summation-by-parts property, are used for the approximation of spatial
derivatives. Penalty terms, which are also referred to as the simultaneous
approximation terms, are designed to weakly impose the elastic-acoustic
interface conditions in the finite-difference discretizations and couple the
elastic and acoustic wave simulations together. With the presented mechanism,
we are able to perform the coupled elastic-acoustic wave simulations stably and
accurately. Moreover, it is shown that the energy-conserving property in the
continuous systems can be preserved in the discretization with carefully
designed penalty terms.
