A fast algorithm for 3D azimuthally anisotropic velocity scan

Example 3

Finally we consider a field-data example. A subset of the McElroy dataset from West Texas was formed in a supergather (Figure 7). This dataset was studied by Burnett and Fomel (2009), in which they proposed a velocity-independent moveout correction to avoid costly velocity scan. With the fast algorithm, we are now able to compute the semblance efficiently: only 45 s for a single Radon transform when $N_t=N_{\tau}=400$ , $N_x=N_y=297$ , and $N_{W_{\cos}}=N_{W_{\sin}}=200$ ; direct computation at this sampling would take approximately 30 hours.

Although the original data have been isotropically NMO corrected, the time slice still shows a subtle directional trend to flatness (Figure 7). From the semblance plot (Figure 8), we observe some nonzero values of anisotropic parameters.

super
Figure 7. An isotropically NMO-corrected supergather from the McElroy dataset, West Texas. $N_t=400$ , $N_x=N_y=297$ . $\Delta t=0.002$ s, $\Delta x=\Delta y=25$ m.

semb
Figure 8. Semblance plot computed by the fast algorithm. $N_{\tau }=400$ , $N_{W_{\cos}}=N_{W_{\sin}}=200$ .

A fast algorithm for 3D azimuthally anisotropic velocity scan