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2D examples of a two-layer model

To test the performance of the proposed methods with a rough velocity model, we use a two-layer model with high velocity and density contrasts. The model is defined on a $ 501 \times 501$ grid, with $ \Delta x=\Delta z=10 m$ and $ \Delta t=1.5ms$ . Velocities of the upper and lower layers are $ 1.3 km/s$ and $ 3.2 km/s$ . The densities of upper and lower layers are $ 1.7 g/cm^3$ and $ 2.7 g/cm^3$ respectively. A point source of a Ricker-wavelet with dominant frequency of 20 Hz is located in the center of the model at a depth of $ 0.2 km$ .The maximum frequency ($ f_{max}$ ) is around $ 60Hz$ . Following Song et al. (2013), we still use the CFL number $ \alpha$ to specify the stability and define dispersion factor as $ \beta=v_{min}/(f_{max}\Delta x)$ to indicate the sample points per wavelength, where $ v_{min}$ is the minimum velocity of the model. For modeling with above parameters, $ \alpha=0.32$ and $ \beta=2.2$ .

Figure 12 shows a wavefield snapshot generated by lowrank FD with a time interval equal to $ 2 ms$ . At this time interval, the SGFD method becomes unstable.

lfd4snap2 lfd8snap2
lfd4snap2,lfd8snap2
Figure 12.
Wavefield snapshot in a two-layer model with variable density and velocity using (a) 4th order SGLFD method and (b) 8th order SGLFD method.
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2014-06-02