Vertical seismic profiling book

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Problem 13.4a

A source is offset 1000 m from a vertical well in which a geophone is suspended, and a horizontal reflector is present at a depth of 2000 m. Calculate the traveltimes for the reflection when the geophone is 800, 1200, and 1600 m deep if the velocity =3000 m/s


Using a coordinate system with origin at the source and the -axis positive downward, the image point (see problem 4.1) in Figure 13.4a is at (0, 4000) and the geophone coordinates are (1000, ); hence,

Figure 13.4a.  Raypaths for vertical profiling and a horizontal bed.

For 800 m depth ; for 1200 m, ; for 1600 m, .

Figure 13.4b.  Raypaths for vertical profiling and a dipping bed.

Problem 13.4b

Repeat for reflectors dipping , where the reflector intersects the well at the same point as in part (a) (see Figure 13.4b).


i) Dip down toward the well

ii) Dip down toward source

Coordinates of image are (, 4170),

Table 13.4a shows calculated traveltimes for , 1200, and 1600 m.

Table 13.4a. Traveltimes for dipping reflectors.
Depth(m) 800 1200 1600
time (s) 1.09 0.97 0.86
time (s) 1.14 1.00 0.87
Table 13.4b. Effect of well deviation on .
800 958 799 1.114
1200 937 1198 0.985
1600 916 1598 0.857

Problem 13.4c

By how much do the values in part (a) change if the well deviates by towards the source (see Figure 13.4c)?


Well inclination changes the geophone coordiantes from (1000, ) where the in-hole depth , 1200, 1600, to where

Figure 13.4c.  Vertical profiling in a deviated well.

where subscript denotes values for the deviated well. The image point remains at (0, 4000), so the traveltime is


Substituting the values of , we get the results in Table 13.4b. is the difference in traveltime from that calculated in part (a).

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Guided (channel) waves and normal-mode propagation Effect of velocity change on VSP traveltime
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