  This paper presents two approaches to mathematical modelling of a synthetic
seismic pulse, and a comparison between them. First, a new analytical model is
developed in two-dimensional Cartesian coordinates. Combined with an initial
condition of sufficient symmetry, this provides a valuable check for the
validity of the numerical method that follows. A particular initial condition
is found which allows for a new closed-form solution. A numerical scheme is
then presented which combines a spectral (Fourier) representation for
displacement components and wave-speed parameters, a fourth order Runge-Kutta
integration method, and an absorbing boundary layer. The resulting large system
of differential equations is solved in parallel on suitable enhanced
performance desktop hardware in a new software implementation. This provides an
alternative approach to forward modelling of waves within isotropic media which
is efficient, and tailored to rapid and flexible developments in modelling
seismic structure, for example, shallow depth environmental applications.
Visual comparisons of the analytic solution and the numerical scheme are
presented.
