(3) |
angles
Figure 1 Definition of angles for the converted-mode reflection experiment. The angles , , , represent the full-aperture, the incident, the reflection, and the geological dip angles, respectively. |
The main goal of this paper is to obtain a relationship between the known quantities from our image, and the full-aperture angle (). Appendix A presents the full derivation of this relationship. Here, we present only the final result, its explanation and its implications. The final relationship we use to obtain converted-mode angle-domain common-image gathers is the following (Appendix A):
(4) |
this equation consists of three main components: is the
P-to-S velocity ratio, is the pseudo-opening angle,
and
is the field of local step-outs of the image.
Equation 4 describes the transformation from
the subsurface-offset domain
into the angle domain for converted-wave data.
This equation is valid under the assumption of constant velocity. However, it
remains valid in a differential sense in an arbitrary-velocity medium, by
considering that is the subsurface half-offset. Therefore, the limitation of
constant velocity applies in the neighborhood of the image. For ,
it is important to consider that every point of the image
is related to a point on the velocity model with the same image coordinates.