Sensitivity of migration to velocity error

Figure 13 shows how the migration impulse response depends on velocity.

 

sensitive
Figure 13 Velocity error sensitivity increases with angle up to $90^\circ$. Migration of a data impulse as a function of velocity. Three possible choices of constant velocity are shown superposed on one plane.

Recall that migrated data is ordinarily displayed as a time section. Arbitrary velocity error makes no difference for horizontal bedding.

Different people have different accuracy criteria. A reasonable criterion is that the positioning error of the energy in the semicircles should be less than a half-wavelength. For the energy moving horizontally, the positioning error is simply related to the dominant period $\Delta T$ and the travel time T. The ratio $T/ \Delta T$ is rarely observed to exceed 100. This 100 seems to be a fundamental observational parameter of reflection seismology in sedimentary rock. (Theoretically, it might be related to the ``Q'' of sedimentary rock or it may relate to generation of chaotic internal multiple reflections. Larger values than 100 occur when (1) much of the path is in water or (2) at time depths greater than about 4 seconds). Figure 14 compares two nearby migration velocities.

 

senser Figure 14 Timing error of the wrong velocity increases with angle.

The separation of the curves increases with angle. For the separation to be less than a wavelength, for $90^\circ$ dip the velocity error must be less than one part in 100. For $45^\circ$ migration velocity error could be larger by $\sqrt{2}$.

Velocities are rarely known this accurately. So we may question the value of migration at wide angles.