Seismic Problem 1

The test problem is a periodic square of size $(256,256)$ with a square central region of size $(123,123)$. The wave speed in the central region is $4$, the density is $1/4$. In the exterior region, the wave speed and density are $1$. The source term is a second derivative Ricker wavelet with $5$ grid points per median wavelength at $N=256$ and $10$ grid points per median wavelength at $N=512$.

We compare the Acousmod2d and wavelet-Galerkin solutions. The optimized $D16$, $D30$ and $D38$ wavelet solutions are calculated at $N=256$.The Acousmod2d solutions are calculated at $N=512$ and $N=1024$. The solutions are sampled at the grid points $y=32,67,128$ for $N=256$ and $y=64,134,256$ for $N=512$, etc., corresponding to the exterior,interface and central regions.

The model is identical to that considered previously. The difference is we consider data with fewer grid point per median wavelength, and sample data along lines of receivers. This allows the development of test data sets that are related to the geophysical problem.

Figure 83: Model for symmetric source problem. Data recorded at Exterior line: $y=32$, Interface line, $y=67$, and Center line, $y=128$.

Figure 84: Acousmod2d solution with $N=512$ measured at the interface. $10$ grid points per wavelength.

Figure 85: Acousmod2d solution with $N=512$ measured at the center. $10$ grid point per wave length.

Figure 86: Acousmod2d solution with $N=1024$ measured at the center. $20$ grid point per wave length.

Figure 87: Acousmod2d solution with $N=512$ measured at the exterior. $10$ grid point per wave length.

Figure 88: Optimized D16 wavelet solution with $N=256$ measured at the interface. $5$ grid points per wavelength.

Figure 89: Optimized D16 wavelet solution with $N=256$ measured at the center. $5$ grid point per wave length.

Figure 90: Optimized D16 wavelet solution with $N=256$ measured at the exterior. $5$ grid point per wave length.

Figure 91: Optimized D30 wavelet solution with $N=256$ measured at the interface. $5$ grid points per wavelength.

Figure 92: Optimized D30 wavelet solution with $N=256$ measured at the center. $5$ grid point per wave length.

Figure 93: Optimized D30 wavelet solution with $N=256$ measured at the exterior. $5$ grid point per wave length.

Figure 94: Optimized D38 wavelet solution with $N=256$ measured at the interface. $5$ grid points per wavelength.

Figure 95: Optimized D38 wavelet solution with $N=256$ measured at the center. $5$ grid point per wave length.

Figure 96: Optimized D38 wavelet solution with $N=256$ measured at the exterior. $5$ grid point per wave length.