2D example

The grid size of the computational 2D domain is $1001$ grid points in $Z$ and $1061$ grid points in $X$ , and a total number of 12267 time steps is computed for both forward propagation and back propagation in the RTM calculation. The computational costs for different RTM strategies running on a 12-core Intel Xeon computing node are listed in Table 4.3, and the corresponding histogram is displayed in Figure 4.3.

Table 4.3: 2D 1-shot RTM runtime comparison with different shemes.

method	2D Runtime ($mins$ )
media	FD	PS	Hybrid
Isotropic	1.9	16.4	$-$
VTI	9.2	28.0	$-$
TTI	68.7	94.4	65.5

Figure 4.3: 2D 1-shot runtime comparison with different RTM shemes.

From the runtime comparison, we see that a transfer from isotropy to anisotropy complicates the RTM algorithm by taking into account two or more anisotropic parameters, which results in gradually increasing computational cost with increasing anisotropic complexity. I also notice that the standard pseudospectral method costs much more than the conventional finite-difference approach due to the introduced FFTs for better accuracy. However, by solving the TTI pure P-wave equation in a hybrid method, the RTM cost per shot (24534 time steps in total) is reduced from $94.4~mins$ to $65.5~mins$ with the pseudospectral method, where an almost $31\%$ saving is achieved. And it is even less expensive than the finite-difference solution for the TTI coupled equations ($68.7~mins$ per shot), which usually suffers from shear-wave artifacts.

A stacked TTI RTM image of all 1641 CSGs using the hybrid solution for the pure P-wave equation is shown in Figure 4.4. It is almost a perfect replication of the actual reflectivity model shown in Figure 4.5 except for some white shadows due to imperfect illuminations.

Figure 4.4: TTI RTM image of the BP 2D TTI model.

Figure 4.5: Actual reflectivity of the BP 2D TTI model.