Structural uncertainty of time-migrated seismic images

Uncertainty in velocity picking

scan,scan2
Figure 6. Velocity scan at 10 km image gather. The curve in (a) corresponds to the automatically picked velocity trend. The curves in (b) identify an approximate range of velocity uncertainty around the picked trend.

Figure 6a shows a semblance scan produced in the process of velocity continuation. A common procedure in migration velocity analysis is picking a velocity trend from the semblance, either manually or automatically. In this example, we use automatic picking with the algorithm described by Fomel (2009).

While picking may select the most probable velocity function, its probability is less than 100%. If we view normalized semblance as a probability distribution and determine a confidence interval corresponding roughly to one standard deviation, it provides an approximate range of uncertainty in velocity determination. This range is shown in Figure 6b and computed according to

$$\delta v(t,x) = \sqrt{\displaystyle \frac{\int\limits_{v_{mi... ...(t,x,v)\,dv}{\int\limits_{v_{min}}^{v_{max}} S(t,x,v)\,dv}}\;,$$ (6)

where $S(t,x,v)$ is the semblance volume that corresponds to $C(t,x,v)$, and $[v_{min},v_{max}]$ is the full range of velociies. The interpretation of semblance picks as probability distributions is heuristic but helps in quantifying uncertainties in velocity picking.

Structural uncertainty of time-migrated seismic images