A consistent implementation of point-sources on finite-difference grids

Abstract

In finite-difference (FD) simulations of the wave equation, point-sources are typically implemented by sampling a sinc function onto the FD grid. However, the sinc point-source is a suboptimal way to introduce a point-source, as (1) it can introduce ringing into the model and (2) computed synthetic traces with constant source-receiver distances (but varying offset with respect to the grid) do not yield identical results. We propose a new implementation of point-sources to use in FD modeling of the wave equation. This new point-source implementation is a function of the FD coefficients used to propagate the wavefield, and boosts or suppresses wavemodes such that the created wavefield corresponds to the spectrum that a true point-source would generate. Through homogeneous examples we show that this new point-source gives a good fit to analytical solutions, reduces ringing artifacts, and can compute synthetic traces for constant source-receiver distances (for a varying offset to the grid) that are identical to within machine precision.