3D example

The 2D example shown above demonstrated the efficiency of the hybrid strategy. To further examine the performance of the hybrid scheme, I test it on a 3D TTI salt dome model.

The models shown in Figure 4.6 consist of five major layers: a water layer, three sedimentary layers with a salt dome embedded in the middle center, and the salt base. The water layer ($v_v$ =$1500~m/s$ ) and the salt ($v_v$ =$4500~m/s$ ) are set to be isotropic ($\delta$ = $\varepsilon$ =0, $\theta$ =$0^{\circ}$ ). And the three sedimentary layers are TTI media with (Figure 4.6a); (Figure 4.6c) and $\varepsilon=0.12,0.05,0.2$ (Figure 4.6d) from shallow to deep. A simple 2.5D tilt angle model (ranges from to $50^{\circ}$ ) was adopted with a tilt axis normal to the salt flank (Figure 4.6b). A constant $\phi=15^{\circ}$ is used in the test.

The 3D model has $201$ grid points along $Z$ , and $651$ grid points along $X$ and $Y$ with a uniform grid point spacing of $20~m$ in all three directions. For each CSG, the 3D RTM used a local computation grid of $301$ x$401$ x$401$ (100 grid points padding in each direction) with a total of 4802 time steps in both the forward and backward propagation operations. Table 4.4 lists the runtimes of the 3D TTI RTM using one CSG on the 12-core computing node. The isotropic and VTI RTM runtime results are also presented for comparison. These computational costs with different RTM algorithms are then graphically illustrated in Figure 4.7.

Table 4.4: 3D 1-shot RTM runtime comparison with different shemes.

method	3D Runtime ($mins$ )
media	FD	PS	Hybrid
Isotropic	23.7	35.4	$-$
VTI	39.2	50.1	$-$
TTI	98.2	138.5	94.3

Figure 4.6: 3D salt dome models: a) $v_v$ and b) $\theta$ , c) and d) are Thomsen's parameters $\delta$ and $\varepsilon$ . The front frame and side frame correspond to 2D slices at $Y$ =$6.5$ $km$ and $X$ =$6.5$ $km$ , respectively.

Figure 4.7: 3D 1-shot runtime comparison with different RTM shemes.

For the 3D model, the hybrid method is still faster than the pseudospectral method by around $29\%$ because more than half the number of 3D FFTs are replaced by less expensive finite-difference calculations. Besides, just like we saw in 2D, the new hybrid scheme in 3D achieves an even better computational efficiency in comparison with the standard finite-difference solution of the TTI coupled equations. Figure 4.8 displays the 3D TTI RTM image.

Figure 4.8: TTI RTM image of the 3D salt dome model.