Check Shot Menus
Check Check Shot Display Window
The Check Shot Display window shows the check shot correction applied to the sonic log. The items displayed are: – The check shot times for each depth – The integrated sonic log times for the same depths – The difference (or drift curve). – The original sonic log (in red) – The new corrected sonic log (in black).
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The Edit button on the horizontal menuBar contains these items:
Points may be temporarily deleted from the check shot data. To remove one or more points, select them by using the mouse to highlight a region. Then with the selection rectangle visible, click on Edit/Delete Poin t . The drift curve and sonic log correction will now be calculated without that point. To restore deleted points, select them with the mouse and click on Edit/Resto re Point . To restore all deleted points, click on Restore All Points . The Parameters button brings up the Check Shot Parameters menu, which allows you to set parameters for the interpolation of the drift curve. This menu also comes up automatically whenever the Check Shot Display window is created. The check shot correction is not stored into the database until you click on Ok . At that time a menu will appear, confirming that you wish to save a new (modified) sonic log, and allowing you to specify its name. Note that this does not normally overwrite the original sonic log, unless you give the modified log the same name as the original. Clicking on Cancel will remove this window without saving the modified sonic log. The new sonic log is available to all programs that access the GEOVIEW database.
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Check Shot Menus
Check Shot Parameters
This menu allows you to use Linear , Spline, or Polynomial interpolation between the points on the drift curve. A Linear interpolation may have discontinuities at the points on the drift curve, which will cause artificial discontinuities in the corrected sonic log. Choosing either Spline or Polynomial interpolation should minimize these discontinuities. As an additional method of reducing these effects, you may choose to apply a smoother to the drift curve for any type of interpolation. By default, the smoother will be applied when you select Polynomial interpolation. The length of smoother is defined as a number of sample intervals of the sonic log. As this menu indicates, the check shot correction actually modifies the depth/time curve derived from the sonic log. When the Change depth-ti me table only option is selected, only the depth/time curve will be modified, and the original sonic log will be preserved. Note that this means that the depth/time curve cannot be calculated by integrating the sonic log. If you wish, you may also change the sonic log. If you choose to Ap pl y r elat iv e chan ges , the correction is applied to the sonic log only between the first and last points of the check shot log. By choosing Ap pl y al l c han ges , you cause the correction to be applied from the surface in such a way that integrating the corrected sonic log reproduces the time/depth pairs of the check shot log.
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Check Shot Selection
The Check Shot Selectio n menu appears when you click on the Check Shot button on one of the list menus, if you have multiple sonic logs or check shots. A Check Shot correction may be done only if check shot data has been entered for this well as a series of depth/time pairs. A check shot data curve is entered into the GEOVIEW database in exactly the same way as any other log, usually as a General ASCII file or by typing into a spreadsheet table. This menu appears if there is more than one sonic log in the well or if there is more than one check shot curve in the well. The items are: Correct Sonic Log : This list contains all the p-wave or sonic logs currently entered into this
well. The check shot correction will modify one of them and produce a new sonic log. The new modified log will normally have a different name from the original log, so that it will not overwrite the original sonic log. You will specify the output log name in a subsequent menu. Using Check Shot: This list contains the names of all check shot curves currently entered for
this well. You must select one of them to be applied to the sonic log.
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Check Shot Menus
Check Shot Correction Theory Sonic (velocity) well log tools measure discrete transit times or velocities of the rock adjacent to the well bore starting at some sub-surface point. The resulting integrated time-depth curve will usually require correction to a seismic datum, which could well be the surface itself. Surface seismic data are subject to greater dispersion and absorption than the sonic data recorded in the well. Consequently, the time-depth curves obtained from sonic log data (local information) and from surface seismic data (global information) will have differences. The checkshot correction adapts the sonic log velocities and/or the log time-depth curve to match the time-depth relationship obtained from surface seismic data. From a raw sonic log v(z), we can derive a time-depth curve t(z) as: z
t(z) =
dz
∫ v( z )
z 0
z
=
dt dz dz z0
∫
(1)
Alternatively, we can input t(z) directly. Matching the time-depth curve t(z) with independently acquired check shot data (t1, z1), (t2, z2), … (t N, z N), we usually see discrepancies with t(z), which we have to compensate with the check shot correction. Roughly speaking, we calibrate the time-depth curve t(z), slicing it into pieces, and forcing it to go through the check shot points. We could then obtain a corrected sonic as the derivative of the corrected time-depth curve, but we will apply a more direct correction. The check shot correction is done in 2 steps: 1) a drift curve measuring the discrepancy between the time-depth curve and the check shot data is interpolated. 2) the time-depth curve and optionally the sonic log are “check shot cor rected” using the drift curve.
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1. Drift Curve We can only measure the discrepancies δα (α = 1, 2, … N) between check shot data (t1, z1), (t2, z2), … (t N, z N) and the time-depth curve t(z) at a ‘few’ isolated check shot depths, but we want to compute interpolated drifts d i (i = 1, 2, … M) along the whole time-depth curve t(z) which has as many samples as the sonic log itself. Our problem is as follows: Given:
(tα, zα) = check shot times tα measured at depth zα δα = measured time of check shot #α – time of time-depth curve at depth zα
δα = tα –t(zα) for each check shot α = 1, 2, … N
(2)
Wanted: interpolated drift samples d i at all depths zi of the time-depth curve
d i = d(zi) = Drift(z i; {zα, δα})
i = 1, 2, … M α = 1, 2, … N
(3) M>>N
The function Drift is a function of depth z and should honor all calibration points {z α, δα} obtained from check shot data. Notes:
1. As time always increases, the check shot data and the time-depth curves are monotonically increasing functions, but the drift curve, representing an error, can have both signs and can increase or decrease as well. 2. Check shot times can be input as either 1-way or 2-way times into GEOVIEW. For this discussion, they are assumed to be 2-way times. GEOVIEW provides 3 ways to calculate the function Drift(z; {zα, δα}) in equation (3): Drift
Linear (z; {zα, δα})
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Descripti on
Honors
Piecewise linear interpolation between data points (zα, δα) and (zα+1, δα+1) α = 1, 2, … N-1
Data points
Check Shot Menus
(n)
Polynomial
(z; {zα, δα})
Spline (z; {zα, δα})
Least squares fit of an n-th degree polynomial through all data points (zα, δα) α = 1, 2, … N Low degrees (n = 2 or 3) are recommended. Higher degrees can induce large amplitude oscillations.
None
Cubic spline through all data points (zα, δα) α = 1, 2, … N
Data points, first derivatives, minimum overall curvature
Optionally, the output of each of these 3 functions can be smoothed, with the user entering the length of the smoothing operator.
2. Check Shot Correction The time-depth curve t(z) and the sonic log must be corrected using the drift curve d(z) obtained from equation (3).
2.1 Sonic Lo g Change: Appl y r elative c hanges Under this option, the check shot correction is applied only along the log range, i.e. from the first depth sample (which may be well below the surface) to the last one. corr
corr
The resulting curves v (z) and t (z) will be only relatively correct, because the curves will not be corrected for the first drift value of z 1 which bears the log errors accumulated from the surface to the first depth sample. An additional correction will be necessary to have an absolutely correct log. This is described in the next section. Time-depth curve: Each sample is corrected with the corresponding sample of the drift curve: corr
t
(zi) = t(zi) + d(zi)
i = 1, 2, … M
(4)
Sonic Log: For the sonic log, a sample of the drift curve d(zi) expresses the cumulative effect
of all the time corrections δt j applied to all previous sonic samples, including the current one. d(zi) = δti + δti-1 + δti-2 + … + δt1
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We can then extract δti:
δt1 = d(z1) δti = d(zi) -
i −1
∑ δt
j
i = 2, 3, … M
(5)
j =1
and apply it to the i-th sample of the sonic log. The correction is applied differently to a velocity curve v(z) or a transit-time curve τ(z). Velocity curve: We have to convert the time correction δti into a corresponding velocity
correction δvi, i.e. the velocity change which makes the seismic wave travel δti slower or faster through the depth interval δzi between the depths zi-1 and zi. If the time-depth curve is expressed in 2-way time, we have:
δzi = zi – zi-1 δvi =
2δzi ti + δti
−
2δzi ti
(zi) = v(zi) + δvi
corr
v
(6)
Transit-time curve: A transit time expressing a time span spent through a thin layer simply
needs to be corrected with the time correction δti over the depth interval δzi. If we express transit time as 1-way time in microseconds, we ha ve:
τcorr (zi) = τ(zi) +
1000000δ ti 2δ zi
(7)
2.2 Sonic Log Change: Appl y all c hanges Under this option, the check shot correction is applied from the surface to the last logged depth. Sonic Log: For the sonic log, this correction occurs in 2 steps:
1)
The option 2.1 “Apply relative change” is executed using (6) or (7). The corrected corr velocity curve v (z) needs a further adjustment.
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Check Shot Menus
2)
We now extend the check shot correction from the first logged depth z1 up to the surface. The only information we have is δt1 = d(z1) from (5). We have accumulated δt1 milliseconds of successive errors, when logging from the surface to a depth of z1 meters. We have now to distribute this total error into partial errors occurred during successive simulated logging steps from surface to z1 meters. We can achieve that by providing extra velocity samples back to the surface.
A safe solution is to append a linear velocity r amp uniformly sampled from the surface to the corr velocity curve v (z), the depth sampling interval ∆z being the smallest depth interval of the velocity curve. In other words we have: depth sampling interval
∆z = min (z i − z i-1 )
number of additional samples
M add = max((
linear velocity ramp
Ramp (k ⋅ ∆z ) = V0 +
where
V1 = V
and
V0 = first ramp sample
corr
z1
∆z
i = 2,3,...M
− 1), 100)
(V1 − V0 ) M add
(k - 1)
k = 1,2,...M add
(z1 )
Setting k = Madd + 1, we can verify that the ramp ties with the first sample V1 the velocity curve. We extrapolate linearly from velocity to V1 to V0. But which V0? The velocity of the first added sample V0 must be such that the accumulated errors from surface to the first logged sample z1 equals δt1 = d(z1). Setting V0 = CV1, we have to find C such that: 2⋅
M add
∑ k =1
∆z k = v corr (∆z k )
δ t 1
Each depth increment ∆zk being constant = ∆z and replacing v Ramp (k ⋅∆z), we get:
corr
M add
∑ k =1
C+
1 1- C M add
=
(k - 1)
δ t 1 ⋅ V1
2 ⋅ ∆z
(∆zk ) by the ramp function
(9 )
an equation of degree (Madd – 1) for C, which we can solve via a least squares fit algorithm.
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Velocity curve:
That way we get a complete corrected velocity curve:
v
corr
= Ramp (z) (z)
corr
=v
0 < z < z1
[From (8)] (10)
(zi)
zi > z1
[From (6)] corr
which, if integrated, will yield an absolutely c orrect time-depth curve t
(z).
Transit-time curve:
The corrected transit time curve is the inve rse of the corrected velocity curve obtained from (10): = 1000000 / Ramp (z)
τ
corr
(z)
corr
= 1000 000 / v
0 < z < z1 (11)
(zi)
zi > z1
Time-depth curve:
According to (1), the corrected time-depth c urve is obtained by integrating the corrected velocity curve (10) t corr (z i ) = t corr (z i-1 ) + 2 ⋅ z0 = 0 being the surface.
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(z i − z i-1 ) v corr (z i )
i = 1,2,...M + M add
(12)
Check Shot Menus
3.
Sampl e Problem
Let us use a model inspired by the Ostrander (1984) gas sand model: Log Data
Check Shot Data
zi
V(zi)
ti
zα
tα
m
m/s
TWT ms
m
TWT ms
1500
3100
967.74
1500
1000.00
2000
2600
1352.36 2100
1500.00
3500
2300.00
2500
3200
1664.86
3000
4100
1908.76
4000
4400
2363.30
The depths are measured from the surface. The following figures illustrate the check shot correction applied with different options. Sonic Log Change
Type of interpretation
Apply relative changes Apply all changes Apply all changes Apply all changes
Linear Linear Spline Polynomial order
Ap pl y Sm oo th er
-
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Figure 1. Apply relative changes with linear interpolation.
Here the check shot correction applies only on the depth range over which the log was measured. The drift curve has been piecewise linearly interpolated between the check shots and extrapolated beyond the last check shot depth. In order to increase the sonic times to match the check shot times, the sonic velocities must be decreased. The numerical results can be saved to a file using File/Expor t Well Logs /Export ASCII Well Lo gs from the GEOVIEW window and filling the Multipl e Log ASCII dialog accordingly.
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Check Shot Menus
The values for this example are shown here: corr
corr
zi
v(zi)
t(zi)
tα
v
t
m
m/s
ms
ms
m/s
ms
1500.000
3100.000
967.742
1000.000
3100.000
1000.000
2000.000
2600.000
1352.357
-
2332.710
1428.686
2100.000
-
-
1500.000
-
-
2500.000
3200.000
1664.857
-
2908.368
1772.521
3000.000
4100.000
1908.760
-
3675.740
2044.575
3500.000
-
-
2300.00
-
-
4000.000
4400.000
2363.305
-
4143.383
2527.273
Figure 2. Apply all changes with linear interpolation.
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The check shot correction is applied from the surface to the total log depth. A linear velocity ramp (See (8)) is appended to the velocity function already corrected under the option “Apply relative change”. This enables us to have a corrected time-depth curve extending to zero time at the surface.
Figure 3. Apply all changes with spli ne interpolation.
Figure 3 also shows the check shot correction applied up to the surface, but using a drift curve interpolated by a spline function. This results in a smoother correction.
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Check Shot Menus
Figure 4. Apply all changes with polyn omial interpolation of order 1.
This last figure shows that the polynomial fit does not honor the check shot data, but represents a best fit through them. The resulting correction is less accurate, but still represents a best compromise when the drift data have erratic behavior.
4. Kelly Bushi ng (KB) Consid erations The depth values can be measured either from surface or from the Kelly Bushing table. The assumption of GEOVIEW is as follows:
Depth from Depth from
Input surface KB
GEOVIEW database
surface KB
Inside GEOVIEW surface surface
Export surface KB
In other words, within GEOVIEW, the check shot correction uses and plots depths from surfaces, while the database stores and exports the depths as they were input.
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This is why the check shot plot may have different depths from the one presented by the Show Data button of the Display Log menu or the Export Well Log s function of the GEOVIEW menu.
The present version allows only three out of the four possible cases: Check Shot depths from surface
KB
surface
Yes
No
KB
Yes
Yes
sonic log depths from
All 3 options give identical corrected time-depth curves and velocity curves.
September 2004
