# Barry’s delay-time refraction interpretation method

Series | Geophysical References Series |
---|---|

Title | Problems in Exploration Seismology and their Solutions |

Author | Lloyd P. Geldart and Robert E. Sheriff |

Chapter | 11 |

Pages | 415 - 468 |

DOI | http://dx.doi.org/10.1190/1.9781560801733 |

ISBN | ISBN 9781560801153 |

Store | SEG Online Store |

## Contents

## 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

**(**)

**(**)

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

**(**)

**(**)

(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

**(**)

Interpretation involves the following steps:

- The traveltimes are corrected for weathering and elevation (problem 8.18)
- Total delay times are calculated and plotted at the geophone positions
- The distance in Figure 11.9a is calculated for each geophone using equation (11.8a), and the total delay times shifted the distances toward
- The curves in (b) and (c) should be parallel; if not, is adjusted until the curves are sufficiently close to being parallel
- 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

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.

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. .

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

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Delay time | Parallelism of half-intercept and delay-time curves |

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Geologic interpretation of reflection data | 3D methods |

## Also in this chapter

- Salt lead time as a function of depth
- Effect of assumptions on refraction interpretation
- Effect of a hidden layer
- Proof of the ABC refraction equation
- Adachi’s method
- Refraction interpretation by stripping
- Proof of a generalized reciprocal method relation
- Delay time
- Barry’s delay-time refraction interpretation method
- Parallelism of half-intercept and delay-time curves
- Wyrobek’s refraction interpretation method
- Properties of a coincident-time curve
- Interpretation by the plus-minus method
- Comparison of refraction interpretation methods
- Feasibility of mapping a horizon using head waves
- Refraction blind spot
- Interpreting marine refraction data