Moveout, velocity, and stacking

Stabilizing RMS velocity

With velocity analysis, we estimate the RMS velocity. Later we will need both the RMS velocity and the interval velocity. (The word ``interval'' designates an interval between two reflectors.) Recall from chapter  equation ()

$$t^2 \eq \tau^2 + \frac{4h^2}{V^2(\tau)} \nonumber$$

The forward conversion follows in straightforward steps: square, integrate, square root. The inverse conversion, like an adjoint, retraces the steps of the forward transform but it does the inverse at every stage. There is however, a messy problem with nearly all field data that must be handled along the inverse route. The problem is that the observed RMS velocity function is generally a rough function, and it is generally unreliable over a significant portion of its range. To make matters worse, deriving an interval velocity begins as does a derivative, roughening the function further. We soon find ourselves taking square roots of negative numbers, which requires judgement to proceed.

wgvel1
Figure 10. Left is a superposition of RMS velocities, the raw one, and one constrained to have realistic interval velocities. Right is the nterval velocity.

Moveout, velocity, and stacking