Synthetic examples

Data was also synthesized through a model containing two synclines. Figure a shows summed wavefields with the same direct arrival time. Panel (b) is the sum of the same wavefields after applying random phase delays to each. Panel (b) has all sources firing within the 4 seconds plotted, which results in some wrap-around. Bandlimited impulses were used as sources without any addition of randomness.

 

dat.syn
Figure 5 (a) Perfectly stacked shots from a double syncline model. (b) Stack of wavefields after applying a random time delay in the Fourier domain.

Figure  shows zero offset images produced by direct migration of the data shown in Figure . Panel (b) is not as high quality as panel (a). A faint reflection mimicking the first event can be seen at z=350m. This could be in part from events wrapping around the time axis when applying their respective phase delays. This is probably a worst-case result, that can be avoided by processing a time-window several times longer than the minimum, t. Given the dramatic departure of the data Figure b) from a horizontal planewave source, significant energy may also be at ${\bf h}\not=0$. The most obvious difference is the diminution of the multiple from the first reflector at z=485. The second reflector is much clearer in panel (b) without its interference.

 

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Figure 6 (a) ${\bf h}=0$ image produced by direct migration of Figure  panel (a). (b) ${\bf h}=0$ image produced by direct migration of Figure  panel (b).