# Well-velocity survey

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

Title | Problems in Exploration Seismology and their Solutions |

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

Chapter | 5 |

Pages | 141 - 180 |

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

ISBN | ISBN 9781560801153 |

Store | SEG Online Store |

## Problem 5.14a

Figure 5.14a shows data from a well-velocity survey tabulated on a standard calculation form. Calculate the average velocity and interval velocity, and plot graphs of time, average velocity, and interval velocity versus depth using a sea-level datum.

### Solution

Figure 5.14a shows only the measured data on a standard form whereas Figure 5.14b shows also calculated values. The successive columns in this form list

1 - Record number

2 - Source (shothole) location

3 - , geophone depth with respect to well datum

4 - , depth of source

5 - , uphole time

6 -, arrival time at reference geophone

7 - , arrival time at well geophone plus polarity and quality grades

8 - , geophone depth with respect to source elevation;

9 - , horizontal distance of source from wellhead

10,11 - tangent, cosine of angle between straight raypath and vertical;

12 - , vertical traveltime from source to geophone

13 - , source to datum elevation difference: ; a minus sign means that the shot was above datum

14 - time correction for

15 - , vertical traveltime from datum to geophone

17 - , depth of geophone below datum

18 - , depth difference between successive geophone depths

19 - , time difference between successive geophone arrivals

20 - , interval velocity

21 - , vertical traveltime from source to geophone

Depths below the datum are positive. The velocity used to correct is (also obtainable from ). Note that the column headed is in milliseconds whereas all other times are in seconds. Column #16 headed average is not used.

Figure 5.14c shows average velocity, interval velocity, and time plotted against depth.

## Problem 5.14b

How much error in average velocity and interval velocity values would result from (i) time-measurement errors of 1 ms, and (ii) depth-measurement errors of 1 m?

### Solution

- A 1-ms time error produces an error in the average velocity of 0.1% to 1.5% and an error in the interval velocity of 1.5% to 8.3%.
- A depth error of 1
*m*produces an error in the average velocity of 0.03% to 0.9% and an error in the interval velocity of 0.5% to 1.5%.

236 | 2200 | 255 | 1970 | 5400 | 65 |

441 | 2400 | 155 | 2038 | 3700 | 70 |

551 | 2600 | 65 | 2118 | 3900 | 90 |

661 | 2500 | 155 | 2228 | 6500 | 130 |

820 | 3100 | 165 | 2360 | 4000 | 135 |

973 | 2700 | 140 | 2506 | 4400 | 155 |

1101 | 3600 | 115 | 2643 | 4300 | 120 |

1203 | 2400 | 90 | 2783 | 4100 | 160 |

1350 | 4800 | 205 | 2928 | 4500 | 130 |

1508 | 4200 | 110 | 3043 | 4800 | 100 |

1603 | 2200 | 80 | 3145 | 5200 | 105 |

1730 | 7600 | 175 | 3243 | 6000 | 90 |

1878 | 5000 | 120 |

## Problem 5.14c

Determine and for a velocity-function fit to the data in (a) assuming the functional form , where is the interval velocity and the depth.

### Solution

We can find and by (i) plotting the data and measuring the slope and intercept of the best-fit straight line, or (ii) using the least-squares method (see problem 9.33). The former method is difficult because of the large, irregularly spaced jumps in the curve, and therefore we shall use the latter method. We take as the depth in meters below datum to the center of each interval and give each data pair the weight (see problem 9.33b) . Using the data in Table 5.14a, we get , as shown in Figure 5.14c.

## Continue reading

Previous section | Next section |
---|---|

Quick-look velocity analysis and effects of errors | Interval velocities |

Previous chapter | Next chapter |

Geometry of seismic waves | Characteristics of seismic events |

## Also in this chapter

- Maximum porosity versus depth
- Relation between lithology and seismic velocities
- Porosities, velocities, and densities of rocks
- Velocities in limestone and sandstone
- Dependence of velocity-depth curves on geology
- Effect of burial history on velocity
- Determining lithology from well-velocity surveys
- Reflectivity versus water saturation
- Effect of overpressure
- Effects of weathered layer (LVL) and permafrost
- Horizontal component of head waves
- Stacking velocity versus rms and average velocities
- Quick-look velocity analysis and effects of errors
- Well-velocity survey
- Interval velocities
- Finding velocity
- Effect of timing errors on stacking velocity, depth, and dip
- Estimating lithology from stacking velocity
- Velocity versus depth from sonobuoy data
- Influence of direction on velocity analyses
- Effect of time picks, NMO stretch, and datum choice on stacking velocity