Numerical noise suppression for wave propagation with finite elements in first-order form by an extended source term

Finite elements can, in some cases, outperform finite-difference methods for modelling wave propagation in complex geological models with topography. In the weak form of the finiteelement method, the delta function is a natural way to represent a point source. If, instead of the usual second-order form, the first-order form of the wave equation is considered, this is no longer true. Fourier analysis for a simple case shows that the spatial operator corresponding tothe first-order form has short-wavelength null-vectors. Once excited, these modes are not seen by the spatial operator but only by the time- stepping scheme and show up as noise. A sourcewith a larger spatial extent, for instance a Gaussian or a tapered sinc, can avoid the excitation of problematic short wavelengths. A series of numerical experiments on a 2-D problem with an exact solution provides a suggestion for the best choice of parameters for these sourceterm distributions. The tapered sinc provided the best results and the resulting accuracy can be better than that of the second-order form. The higher operation count of the former, however, does not make it more efficient in terms of accuracy for a given computational effort, at least not for the 2-D examples considered hereApplied Geophysics and Petrophysic