Check Shot Correction

Check Shot Correction TheoryThis theory is used in the Log Check Shot Correction function. Why Use Check Shots Sonic (velocity) well log tools measure discrete transit times of the rock adjacent to the well bore. The measurements start at the subsurface, usually just below the bottom of the well casing so there is no steel casing separating the logging tool from the rock. Note that the loose upper surface and the water-bearing rock near the surface must be cased before any logging tools can be run, so there will never be sonic data for the very top of a well. The depth of a sonic log is measured as the depth of the tool below the kelly bushings on the drilling floor (kelly bushings are the metal parts that grab and rotate the kelly, and as the kelly holds the drill pipe with the drill bit at its end, the "K.B.'s" therefore rotate the drill bit). The transit times are made over a set tool distance for each depth sample, and the interval velocity is derived over that distance (see Velocity Definitions). From these velocities, a time-depth curve can be calculated. The time refers to the time a vertically traveling signal takes to reach that depth. The resulting integrated time-depth curve will usually require correction to a seismic datum, which could well be the surface itself, but is usually the horizon just below the loose overburden.  Then this log is used to create a depth-time table, through:     As the time to a layer depends on all the velocities above that layer, it includes the unmeasured "first" velocity (V1) of the first layer to the surface (i.e. the section that was cased and never logged). That velocity is usually assumed equal to the first measured velocity. If the well is deviated (not drilled straight down), then measured depths must also be corrected to the true vertical depth. Fortunately, this information is always available for deviated wells. The sonic log will not perfectly match the seismic data because:   a.  The seismic and log datums are usually different.   b.  The first layer velocity is unknown.   c.  Errors in calculating time-depths form logs accumulate.   d.  The interpreted seismic data may be mis-positioned if migrated improperly.   e.  The seismic data may have time stretch caused by frequency-dependent absorption and short-period mu   f.  Surface seismic data are subject to greater dispersion and absorption than the sonic data recorded in the Therefore, check shots are used to improve the depth-time conversion. They are also needed to correct sonic logs for the Roy White Wavelet Extraction method. See Roy White Theory. Note that vertical seismic profiles (VSP's) are treated as seismic data, not checkpoint data, in HR software. The Correction The check shot 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 Vz, since V = z/t, we can derive a time-depth curve tz as:    (1) 1 ¼ M) along the whole time-depth curve t(z) which has as many samples as the sonic log itself. {za.   As time always increases. We calibrate the time-depth curve tz. we can input tz directly. May not reflect geolog Polynomial(n) (z. (t2.  We could then obtain a corrected sonic as the derivative of the corrected time-depth curve. 2. The time-depth curve (and optionally the sonic log) are "check shot corrected" using the drift curve. z1). da}) 2 . Drift Curve We can only measure the discrepancies da (a = 1. 2. da}) in equation (3): Drift Description Honors Piecewise linear interpolation between data Data points Linear (z. For this discussion. ¼ A bent line of straight segments. We only change the time-depth curve where there is sonic log data. but we want to compute interpolated drifts di (i = 1. da+1)  a = 1. ¼ (tN. 2. 2. can have both signs and can increase or decrease as well. If there is a gap in the sonic log curve. 2. zN). {za. da} obtained from check shot data. time must increase). representing an error. da}) points (za. z2).   Check shot times can be input as either 1-way or 2-way times. z2). ¼ N              where M>>N The function Drift is a function of depth z and should honor all calibration points {za. 2. ¼ N       (2)   Wanted:   interpolated drift samples di at all depths zi of the time-depth curve di = d(zi) = Drift(zi. but we will apply a more direct correction. (t2. 2. za) = check shot times ta measured at depth za for check shot number a da = measured time of check shot #a – (time of time-depth curve at depth za) da = ta –t(za)   for each check shot a = 1. ¼N) between check shot data (t1. 2. da) and (za+1. Our problem is as follows: Given:             (ta.  Alternatively.   Note: 1. with the N-1 data points being the segment ends. slicing it into pieces and forcing it to go through the check shot points. we usually see discrepancies with tz. HR provides 3 ways to calculate the function Drift(z. The check shot correction is done in 2 steps: 1. {za. ¼ M   (3) a = 1. Matching the time-depth curve tz with independently acquired check shot data (t1. which we have to compensate with the check shot correction.   Least squares fit of an n-th degree None. but the drift curve. any check shot data in that gap will not be used. z1). da})      i = 1. the check shot data and the time-depth curves are monotonically increasing functions (as depth increases. {za. A drift curve is interpolated to measure the discrepancy between the time-depth curve and the check shot data. ¼ (tN. 3. zN) and the time-depth curve tz at a "few" isolated check shot depths. they are assumed to be 2-way times. da}) Resembles a sharply curving and weaving line through every point. the velocity change which makes the seismic wave travel dti slower or faster through the depth interval dzi between the depths zi-1 and zi. from the first depth sample (which may be well below the surface) to the last one. May not reflect geolog polynomial through all data points (za. Check Shot Correction The time-depth curve tz and the sonic log must be corrected using the drift curve dz obtained from equation (3). i. The resulting log will integrate to the desired times but will need a bulk time shift. a = 1. Spline (z.e.e.   We can then extract :     (5)   and apply it to the i-th sample of the sonic log. ¼ N   The output of each of these 3 functions can be smoothed.   Cubic spline through all data points (za. overall curvature a = 1. we have: 3 . Time-depth curve:   Each sample is corrected with the corresponding sample of the drift curve:    (4) Sonic Log: For the sonic log.. Under this option from the Check Shot Parameters window.  This is described in the next section. as you can enter the length of the smoothing operator. {za.  The correction is applied differently to a velocity curve Vz or a transit-time curve tz. 2. Higher degrees can induce large amplitude oscillations. Velocity curve: We have to convert the time correction dti into a corresponding velocity correction dVi. 2. a sample of the drift curve d(zi) expresses the cumulative effect of all the time corrections dtj applied to all previous sonic samples. because the curves will not be corrected for the first drift value of z1 which bears the log errors accumulated from the surface to the first depth sample. first derivatives. The resulting curves Vzcorr and tzcorr will be only relatively correct. An additional correction will be necessary to have an absolutely correct log. including the current one. ¼ N  Low degrees (n = 2 or 3) are recommended. Sonic Log Change: Apply Relative Changes This option changes only the velocities for layers between the first and last check shot depth. i. If the time-depth curve is expressed in 2-way time.Least squares fit of an n-th degree Resembles a gentle curve None. the check shot correction is applied only along the log range. da)  as well. da)  Data points. we have:     (7)     Sonic Log Change: Apply all changes This options changes all the velocities in the log so the new log integrates to the exact desired times. 2.           (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 dti over the depth interval dzi. A safe solution is to append a linear velocity ramp uniformly sampled from the surface to the velocity curve .  In other words we have:             4 . this correction occurs in 2 steps: 1.  The only information we have is  from (5).  We now extend the check shot correction from the first logged depth z1 up to the surface. Sonic Log: For the sonic log. The corrected velocity curve  needs a further adjustment.  The option "Apply relative change" is executed using (6) or (7).  We can achieve that by providing extra velocity samples back to the surface. If we express transit time as 1way time in microseconds. Under this option from the Check Shot Parameters window.  We have accumulated dt1 milliseconds of successive errors.  We have now to distribute this total error into partial errors occurred during successive simulated logging steps from surface to z1 meters. the check shot correction is applied from the surface to the last logged depth. when logging from the surface to a depth of z1 meters. The velocity above the first log measurement is "ramped" to handle the bulk time shift and minimize the effect of spurious reflections on the synthetic. the depth sampling interval Dz being the smallest depth interval of the velocity curve. we get:  by the ramp function Ramp an equation of degree (Madd -1) for C.      Setting k = Madd + 1. Velocity curve: That way we get a complete corrected velocity curve:   [From (8)]   [From (6)]   which.   We extrapolate linearly from velocity to V1 to V0. will yield an absolutely correct time-depth curve   . we have to find C such that:   Each depth increment Dzk being constant = Dz and replacing (k×Dz). we can verify that the ramp ties with the first sample V1 the velocity curve.  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 . which we can solve via a least squares fit algorithm. Transit-time curve: The corrected transit time curve is the inverse of the corrected velocity curve obtained from (10): = 1000000 / Ramp (z) if  0 < z < z1 (11) if  zi > z1 = 1000 000 /     5 . if integrated. Setting V0 = CV1. the corrected time-depth curve is obtained by integrating the corrected velocity curve (10)   z0 = 0 being the surface.76         3500 4000 4400 2363.  The following figures illustrate the check shot correction applied with different options.00   1500.           Sonic Log Change Apply relative changes Apply all changes Apply all changes Apply all changes Type of interpretation Linear Linear Spline Polynomial order ta TWT ms 1000.  Time-depth curve: According to (1).30     The depths are measured from the surface.86   3000 4100 1908.00     2300.36         2100 2500 3200 1664.74 1500 2000 2600 1352.00   6 . Sample Problem Let us use a model inspired by the Ostrander (1984) gas sand model: Log Data                                             Check Shot Data zi V(zi) ti za m m/s TWT ms m 1500 3100 967. 000 2600.383 tcorr ms 1000.000 1500.357 1664. In order to increase the sonic times to match the check shot times.000 2100.000 4100.000 2500.740 4143. The drift curve has been piecewise linearly interpolated between the check shots and extrapolated beyond the last check shot depth.760 2363.000 2332.000 3500.686 1772.000 1428.00 Vcorr m/s 3100.710 2908.857 1908.000 3200. the sonic velocities must be decreased.000    ms 967.000   ta ms 1000. The values for this example are shown here:   zi m 1500.000 4000.742 1352.  Apply relative changes with linear interpolation.521 2044.305 7 .368 3675.000 3000.273      m/s 3100.000 4400.000 2300.575 2527.Figure 1. Here the check shot correction applies only on the depth range over which the log was measured.000 2000. The check shot correction is applied from the surface to the total log depth.  Apply all changes with linear interpolation.  A linear velocity ramp (see equation (8)) is appended to the velocity function already corrected under the option "Apply relative change". Figure 3.Figure 2.  This enables us to have a corrected time-depth curve extending to zero time at the surface. 8 .  Apply all changes with spline interpolation.   Apply all changes with polynomial interpolation of order 1. but using a drift curve interpolated by a spline function.  This results in a smoother correction. Figure 4. The present version allows only three out of the four possible cases:     Check Shot depths from:   Sonic log depths from:     surface: KB: surface Yes Yes KB No Yes Geoview database surface KB  Inside Geoview surface surface All 3 options give identical corrected time-depth curves and velocity curves. within our software. 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 Logs function. and the database stores and exports the depths as they were input. but still represents a best compromise when the drift data have erratic behavior. The assumption we use is as follows:   Input Depth from surface Depth from KB   In other words.  The resulting correction is less accurate. the check shot correction uses and plots depths from surfaces.Figure 3 also shows the check shot correction applied up to the surface. Kelly Bushing (KB) Considerations The depth values can be measured either from surface or from the Kelly Bushing table on the drill rig floor. but represents a best fit through them. This last figure shows that the polynomial fit does not honor the check shot data.   9 . Documents Similar To Check Shot CorrectionSkip carouselcarousel previouscarousel nextcheckshot.pdfSeismic Reference DatumCalibration of Seismic and Well DataSeismic InversionSynthetic SeismogramsSeismic Inversion by Mrinal K. 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