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 - $ D_{gm} $, geophone depth with respect to well datum
4 - $ D_{s} $, depth of source
5 - $ t_{uh} $, uphole time
6 -$ t_{c} $, arrival time at reference geophone
7 - $ {T} $, arrival time at well geophone plus polarity and quality grades
8 - $ D_{gs} $, geophone depth with respect to source elevation; $ D_{gs}=D_{gm}-D_{s}-\Delta e=D_{gm}-D_{s}-29 $
9 - $ {H} $, horizontal distance of source from wellhead
10,11 - tangent, cosine of angle between straight raypath and vertical; $ \tan i={\rm {H}}/{\rm {D}}_{gs} $
12 - $ T_{g} $, vertical traveltime from source to geophone $ =T\cos i $
13 - $ \Delta sd $, source to datum elevation difference: Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://en.wikipedia.org/api/rest_v1/":): \Delta {\rm sd}=D_{s} -D_{e} =D_{s} -78 ; a minus sign means that the shot was above datum
14 - time correction for Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://en.wikipedia.org/api/rest_v1/":): \Delta {\rm sd}
15 - Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://en.wikipedia.org/api/rest_v1/":): T_{gd} , vertical traveltime from datum to geophone
17 - Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://en.wikipedia.org/api/rest_v1/":): D_{gd} , depth of geophone below datum
18 - Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://en.wikipedia.org/api/rest_v1/":): \Delta D_{gd} , depth difference between successive geophone depths
19 - Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://en.wikipedia.org/api/rest_v1/":): \Delta T_{gd} , time difference between successive geophone arrivals
20 - Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://en.wikipedia.org/api/rest_v1/":): V_{i} , interval velocity Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://en.wikipedia.org/api/rest_v1/":): \Delta D_{gd} /\Delta T_{gd}
21 - Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://en.wikipedia.org/api/rest_v1/":): T_{gs} , vertical traveltime from source to geophone Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://en.wikipedia.org/api/rest_v1/":): =T\cos i
Depths below the datum are positive. The velocity used to correct Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://en.wikipedia.org/api/rest_v1/":): \Delta sd is Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://en.wikipedia.org/api/rest_v1/":): V=D_{gs} /T_{gs} \approx 0.163/0.102\approx 1.60\ {\rm km/s} (also obtainable from Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://en.wikipedia.org/api/rest_v1/":): D_{gd} /T_{gd} ). Note that the column headed Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://en.wikipedia.org/api/rest_v1/":): \Delta {\rm sd/V} is in milliseconds whereas all other times are in seconds. Column #16 headed Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://en.wikipedia.org/api/rest_v1/":): T_{gs}/ 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%.
| Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://en.wikipedia.org/api/rest_v1/":): z \ (\rm m) | Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://en.wikipedia.org/api/rest_v1/":): V_{i} \ (\rm {m/s}) | Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://en.wikipedia.org/api/rest_v1/":): \Delta z \ (\rm m) | Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://en.wikipedia.org/api/rest_v1/":): z \ (\rm m) | Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://en.wikipedia.org/api/rest_v1/":): V_{i} \ (\rm m/s) | Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://en.wikipedia.org/api/rest_v1/":): \Delta \ z(\rm m) |
|---|---|---|---|---|---|
| 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 Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://en.wikipedia.org/api/rest_v1/":): V_{o} and $ a $ for a velocity-function fit to the data in (a) assuming the functional form Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://en.wikipedia.org/api/rest_v1/":): V=V_{o} +az , where Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://en.wikipedia.org/api/rest_v1/":): V is the interval velocity and Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://en.wikipedia.org/api/rest_v1/":): z the depth.
Solution
We can find Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://en.wikipedia.org/api/rest_v1/":): V_{o} and Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://en.wikipedia.org/api/rest_v1/":): a by (i) plotting the data and measuring the slope Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://en.wikipedia.org/api/rest_v1/":): a and intercept $ V_{o} $ 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 Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://en.wikipedia.org/api/rest_v1/":): z as the depth in meters below datum to the center of each interval Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://en.wikipedia.org/api/rest_v1/":): \Delta z and give each data pair Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://en.wikipedia.org/api/rest_v1/":): (V_{i} ,\; z) the weight (see problem 9.33b) Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://en.wikipedia.org/api/rest_v1/":): \Delta z . Using the data in Table 5.14a, we get Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://en.wikipedia.org/api/rest_v1/":): V = 2400+0.98z , 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
External links
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