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This paper presents two approaches to mathematical modelling of a syntheticseismic pulse, and a comparison between them. First, a new analytical model isdeveloped in two-dimensional Cartesian coordinates. Combined with an initialcondition of sufficient symmetry, this provides a valuable check for thevalidity of the numerical method that follows. A particular initial conditionis found which allows for a new closed-form solution. A numerical scheme isthen presented which combines a spectral (Fourier) representation fordisplacement components and wave-speed parameters, a fourth order Runge-Kuttaintegration method, and an absorbing boundary layer. The resulting large systemof differential equations is solved in parallel on suitable enhancedperformance desktop hardware in a new software implementation. This provides analternative approach to forward modelling of waves within isotropic media whichis efficient, and tailored to rapid and flexible developments in modellingseismic structure, for example, shallow depth environmental applications.Visual comparisons of the analytic solution and the numerical scheme arepresented.

Analytic and numerical solutions to the seismic wave equation in continuous media