# Reservoir geophysics exercises

Series Investigations in Geophysics Öz Yilmaz http://dx.doi.org/10.1190/1.9781560801580 ISBN 978-1-56080-094-1 SEG Online Store

Exercise 11-1. Derive equation (2a) for the Fresnel zone using the geometry of Figure 11.1-3.

Exercise 11-2. Refer to Figure 11.4-1a. Consider a surface multiple from the first reflecting interface. Trace the traveltime on the VSP diagram in Figure 11.4-1b. Multiples do not reach the downgoing wave path; thus, they can be eliminated by corridor stacking.

Exercise 11-3. Refer to Figure 11.4-1b. Should the slopes of the downgoing and upcoming waves associated with a layer be the same in magnitude?

Exercise 11-4. What procedure does CMP stacking correspond to in the f − k domain?

Exercise 11-5. Sketch the traveltime response for a point scatterer on a zero-offset VSP record.

Exercise 11-6. Consider a CMP gather with a single reflection event. Suppose you have applied hyperbolic moveout correction using equation (90) and discovered that the event is not flat for all offsets. Instead, the moveout-corrected event may have one of the three shapes shown in Figure 11.E-1. Match each of the curves A, B, and C with the following three possibilities:

1. You have applied hyperbolic moveout correction using an erroneously low velocity in equation (90).
2. You have applied a second-order moveout correction (equation 3-4b) to an event that has a fourth-order moveout behavior described by equation (3-5a).
3. You have ignored anisotropy in moveout correction described by equation (92).

## Figures and equations

 ${\displaystyle r={\sqrt {\frac {z_{0}\lambda }{2}}}.}$ (2a)

 ${\displaystyle t^{2}=t_{0}^{2}+{\frac {x^{2}}{v_{NMO}^{2}}}.}$ (90)

 ${\displaystyle t^{2}=t_{0}^{2}+{\frac {x^{2}}{v_{NMO}^{2}}}-{\frac {2\eta x^{4}}{v_{NMO}^{2}\left[t_{0}^{2}v_{NMO}^{2}+(1+2\eta )x^{2}\right]}},}$ (92)