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3D Wave Propagation

The method used for wavefield forward and back propagation was time domain finite differencing of the 3D acoustic wave equation. This method approximates the temporal and spatial derivatives as a sum of Taylor series' about a symmetric sequence of points, such that this sum closely approximates the Taylor series of the desired derivative.

$\displaystyle \frac{\partial^2 u(x,y,z)}{\partial t^2} = c(x,y,z)^2 \nabla^2 u(x,y,z)$ (1)

The velocity model (Figure 3) used to test these propagation and imaging routines features velocities ranging between 1490 m/s to 4480 m/s; using a Ricker wavelet of central frequency 25 Hz then time steps of 0.5 ms and spatial sampling of 10m was used, adhering to the guidelines of Dablain (1986), extrapolated to 3D.