Barry’s delay-time refraction interpretation method

ADVERTISEMENT
From SEG Wiki
Revision as of 14:22, 30 July 2019 by Ageary (talk | contribs) (added page)
(diff) ← Older revision | Latest revision (diff) | Newer revision → (diff)
Jump to: navigation, search

Problem 11.9

Source is 2 km east of source . The data in Table 11.9a were obtained with cables extending eastward from ( is the distance measured from ) with geophones at 200 m intervals. Interpret the data using Barry’s method (Barry, 1967); km/s. Assume that the delay-time curve for the reverse profile is sufficiently parallel to yours that step (d) below can be omitted.

Background

Barry’s method requires that the total delay time be separated into source and geophone delay times. Two sources on the same side of the geophone are used to achieve this. In Figure 11.9a. and are sources, and are geophones, being the critical distance (problem 4.18) for source . We write and for the source delay times, and for the geophone delay times, , , etc., for the total delay times. We get the source delay times from the intercept times if we assume zero dip [see equation (11.9a)]. The delay time at source , , is due to travel along , so


(11.9a)


(11.9b)
Figure 11.9a.  Determining delay times.

Note that equations (11.9a,b) apply at any point on the profile where the dip is very small, not merely at souce points.

To find the geophone delay times we have from equation (11.8c)

For zero dip, , so we can write


(11.9c)


(11.9d)
Table 11.9a. Time-distance data.
(km) (s) (s) (km) (s) (s)
2.6 1.02 0.25 5.4 1.62 1.28
2.8 1.05 0.34 5.6 1.66 1.31
3.0 1.10 0.43 5.8 1.72 1.36
3.2 1.24 0.52 6.0 1.75 1.42
3.4 1.18 0.61 6.2 1.80 1.47
3.6 1.20 0.70 6.4 1.85 1.53
3.8 1.26 0.78 6.6 1.91 1.56
4.0 1.32 0.87 6.8 1.97 1.59
4.2 1.35 0.96 7.0 2.00 1.63
4.4 1.39 1.05 7.2 2.02 1.67
4.6 1.45 1.10 7.4 2.05 1.70
4.8 1.50 1.14 7.6 2.10 1.73
5.0 1.56 1.20 7.8 2.13 1.78
5.2 1.59 1.22 8.0 2.16 1.81

To use these equations we must find the point , preferably by expressing in terms of delay times. From Figure 11.9a and equation (11.9b) we get


(11.9e)

Interpretation involves the following steps:

  1. The traveltimes are corrected for weathering and elevation (problem 8.18)
  2. Total delay times are calculated and plotted at the geophone positions
  3. The distance in Figure 11.9a is calculated for each geophone using equation (11.8a), and the total delay times shifted the distances toward
  4. The curves in (b) and (c) should be parallel; if not, is adjusted until the curves are sufficiently close to being parallel
  5. The total delay times in (b) are separated into source and geophone delay times and then plotted above points , , and . Delays times can be converted into depths using equation (11.9b)

Solution

The data are plotted in Figure 11.9b. Measurements give an average value of 4.60 km/s for and intercept times s, s, s. The critical angle is , , . Using equation (11.9e), we have

Figure 11.9b.  Plot of data.

Thus, is located at km. Also, we need :

Figure 11.9b shows that we observe refraction data from both sources only for km. We show the calculations in Table 11.9b. Column 1 is the offset measured from , columns 2 and 6 are traveltime for sources and , columns 3 and 7 are the source-to-geophone distances divided by , columns 4 and 8 are the total delay times [the differences between columns 2 and 3, 6 and 7, respectively—see equation (11.8b)], column 5 is the differential delay time between geophones at and , column 9 is [see equation (11.9c)], column 10 is , column 11 is column 1 minus column 10 = location of in Figure 11.9a. Depth values can be obtained by mutliplying in column 9 by [see equation (11.9a)].

We used a new value of . Comparing the new and old values of for and , we see that rounding errors are not responsible for the anomalies. The anomaly at km is 0.01 s whereas the original data are also given to the nearest 0.01 s, so this anomaly could be the result of rounding off of the original time values; however, the anomaly at is too large to be due to this.

Table 11.9b. Delay-time calculations.
1 2 3 4 5 6 7 7 8 10 11
4.6 1.45 1.00 0.45 0.00 1.10 0.57 0.53 0.27 0.52 4.08
4.8 1.50 1.04 0.46 –0.01 1.14 0.61 0.53 0.27 0.52 4.28
5.0 1.56 1.09 0.47 –0.02 1.20 0.65 0.55 0.29 0.56 4.44
5.2 1.59 1.13 0.46 –0.01 1.22 0.70 0.52 0.27 0.52 4.68
5.4 1.62 1.17 0.45 0.00 1.28 0.74 0.54 0.27 0.52 4.88
5.6 1.66 1.22 0.44 0.01 1.31 0.78 0.53 0.26 0.50 5.10
5.8 1.72 1.26 0.46 –0.01 1.36 0.83 0.53 0.27 0.52 5.28
6.0 1.73 1.30 0.43 0.02 1.42 0.87 0.55 0.27 0.52 5.48
6.2 1.80 1.35 0.45 0.00 1.47 0.91 0.56 0.28 0.54 5.66
6.4 1.85 1.39 0.46 –0.01 1.53 0.96 0.57 0.29 0.56 5.84
6.6 1.91 1.43 0.48 –0.03 1.56 1.00 0.56 0.30 0.58 6.02
6.8 1.97 1.48 0.49 –0.04 1.59 1.04 0.55 0.30 0.58 6.22
7.0 2.00 1.52 0.48 –0.03 1.63 1.09 0.54 0.29 0.56 6.44
7.2 2.02 1.57 0.45 0.00 1.67 1.13 0.54 0.27 0.52 6.68
7.4 2.05 1.61 0.44 0.01 1.70 1.17 0.53 0.26 0.50 6.90
7.6 2.10 1.65 0.45 0.00 1.73 1.22 0.51 0.26 0.50 7.10
7.8 2.13 1.70 0.43 0.02 1.78 1.26 0.52 0.25 0.48 7.32
8.0 2.16 1.74 0.42 0.03 1.81 1.30 0.51 0.24 0.46 7.54

Note. .

Table 11.9c. Part of Table 11.9b with increased precision.
1 2 3 4 5 6 7 8 9
4.8 1.50 1.043 0.457 –0.008 1.14 0.609 0.531 0.270
5.0 1.56 1.087 0.473 –0.024 1.20 0.652 0.548 0.286
5.2 1.59 1.130 0.460 –0.011 1.22 0.696 0.524 0.268
5.4 1.62 1.174 0.446 0.003 1.28 0.739 0.541 0.269
5.6 1.66 1.217 0.443 0.006 1.31 0.783 0.527 0.261
5.8 1.72 1.261 0.459 –0.010 1.36 0.826 0.534 0.272

Continue reading

Previous section Next section
Delay time Parallelism of half-intercept and delay-time curves
Previous chapter Next chapter
Geologic interpretation of reflection data 3D methods

Table of Contents (book)

Also in this chapter

External links

find literature about
Barry’s delay-time refraction interpretation method
SEG button search.png Datapages button.png GeoScienceWorld button.png OnePetro button.png Schlumberger button.png Google button.png AGI button.png