Theory of differential offset continuation

Example 2: point diffractor

The second example is the case of a point diffractor (the left side of Figure 4). Without loss of generality, the origin of the midpoint axis can be put above the diffraction point. In this case the zero-offset reflection traveltime curve has the well-known hyperbolic form

$$t_0\left(y_0\right)={\sqrt{z^2+y_0^2} \over u}\;,$$ (38)

where $z$ is the depth of the diffractor and $u=v/2$ is half of the wave velocity. Time rays are defined according to equations (28-29), as follows:

$$y_1\left(t_1\right)={{u^2\,t_1^2-z^2} \over y_0}\;;\; u^2\,t... ...left(t_1\right)= u^2\,t_1^2\,{{u^2\,t_1^2-z^2} \over y_0^2}\;.$$ (39)

ococrv
Figure 4. Transformation of the reflection traveltime curves in the OC process. Left: the case of a diffraction point. Right: the case of an elliptic reflector. Solid lines indicate traveltime curves at different common-offset sections, dashed lines indicate time rays.

Theory of differential offset continuation