Subjective comparison and evaluation of methods

The three basic methods of migration described in this section are compared subjectively in the following table.

 

Table 1: Subjective comparison of three wide-angle migration methods.

	Hyperbola Sum or Semicircle Superpose	1c|Phase Shift	1c| Stolt
v(z)	1c|ray tracing	1c|easily	approximately by stretching
wide angle?	Beware of data alias and operator alias.	Beware of data alias.	Beware of data alias.
correct phase and obliquity?	possible with some effort for const v	easy for any v(z)	1c|for const v
wraparound noise?	1c|no	on x	on x
v(x)	Production programs have serious pitfalls.	approximately by iteration and interpolation	no known program
side boundaries and irregular spaceing	1c|excellent	1c|poor	1c|poor
Speed	1c|slow	1c|average	1c|very fast

The perspective of later chapters makes it possible to remark on the quality of the wide-angle methods as a group, and it is useful to do that now. Their greatest weakness is their difficulties with lateral velocity variation. Their greatest strength, wide-angle capability, is reduced by the weakness of other links in the data collection and processing chain, namely:

• Shot-to-geophone offset angles are often large but ignored. A CDP stack is not a zero-offset section.
• Why process to the very wide angles seen in the survey line when even tiny angles perpendicular to the line are being ignored?
• Data is often not sampled densely enough to represent steeply dipping data without aliasing.
• Accuracy in the knowledge of velocity is seldom enough to justify processing to wide angles.
• Noise eventually overpowers all echoes, say at time $t_{\rm max}$.Given a depth of interest, the maximum angle is $\cos (z/vt)$.For example, imagine oil reservoirs at a time depth of two seconds, where data recording stopped at four seconds. The implied angle cutoff is at $60^\circ$.