Depth Conversion with ISMap

Transcription

1 Depth Conversion with ISMap Brian Russell July 5, 2012

2 Introduction This article will compare two different approaches to depth conversion between measured well depths and a map of seismic two-way travel-time (TWT) picks. The first approach is the standard kriging with external drift (KED) approach. The second approach is the method described by Dubrulle (2003), which uses depth residuals. Both methods are implemented using the Hampson- Russell ISMap program. Note that the first method is standard in ISMap, but that the second method required some tweaking of the program. 2

3 The dataset The dataset that was used to test the two methods was the depth versus time dataset supplied with the ISMap software for testing purposes. It consists of a set of 25 measured well depths and a picked seismic two-way time map over a Devonian pinnacle reef. These data were read into the program as columnar ASCII files. Since two of the wells fall outside the limits of the seismic survey, they were deleted from the original ASCII file. 3

4 Input well depths dpth_str.txt : dpth_str_2.txt : Here are screen captures of the two ASCII files, where the left one is the original and right one is the edited file. These two wells were deleted. 4

5 Reading the depths in ISMap Displaying the file shows there are two header lines to skip: 5

6 Displaying the wells Here is a display of the depths at each of the wells, where the values are labeled as well as coloured. 6

7 Input seismic times (TWT) X, Y and TWT are in the first three columns and there are two header lines: 7

8 Input TWT dataset This display shows the picked two-way travel-times (TWT), where the black squares represent the well locations. 8

9 Crossplot A crossplot of TWT versus depth, where TWT is the dependent variable. 9

10 Well-to-well variogram Here is the computed well-to-well variogram on the left, with its computed parameters (range, sill and nugget) shown on the right. A spherical variogram model has been used. 10

11 Seismic-to-seismic variogram Here is the computed seismic-to-seismic variogram on the left, with its computed parameters (range, sill and nugget) shown on the right. A spherical variogram model has been used. 11

12 KED with well variogram We next compute the External Drift result using the well-to-well variogram, which is the default. 12

13 KED with well variogram Here is the KED result. Notice that the well values tie, since they have the same colour scheme as the computed depth map. 13

14 KED with seismic variogram We then used the Markov- Bayes approach to apply KED with the seismic variogram. 14

15 KED with seismic variogram Here is the result of applying KED using the seismic-to-seismic variogram. The comparison between the two KED results is shown on the next slide. 15

16 KED comparison KED with well variogram. KED with seismic variogram. 16

17 The Dubrulle approach Dubrulle s (2003) method of performing depth conversion is as follows: Read in the well depths and seismic TWTs, as before. Compute the regression between the well depths and seismic TWTs, where depth is the dependent varible. Apply this regression to the TWTs at the well locations and also to the full map of TWTs. Compute the residuals between the measured and computed depths at the wells. Krige these depth residuals. Add the kriged depth residuals to the TWT map regression. This approach will now be shown. 17

18 Computing depth residuals First, we export the X, Y, Depth and TWT values from the crossplot in ASCII format (Columns 1, 2, 3 and 4.) We then read this file into Excel, compute the regression coefficients, apply them (column 5), and subtract to find the residual (column 6). 18

19 Depth residuals session We next create a second ISMap session by reading the previous ASCII file. Note that column 6 contains the depth residuals. 19

20 Depth residuals session ISMap keeps track of the number of sessions and allows you to display them independently. Although the TWT seismic data does not match the residuals, it is used to define the grid for the kriging operation, since if we add maps they must be gridded the same. 20

21 Depth residuals map Here is a map showing the depth residual values, both annotated and in colour. 21

22 Residual variogram Here is the variogram computed from the depth residual. Notice the small range value. 22

23 Kriging the residuals We now apply Ordinary Kriging to the depth residuals. 23

24 Kriged residuals Here is the kriged result using the well-to-well variogram from the depth residuals. 24

25 Apply regression The next step is to apply the regression in the depth session window. Here is the result of applying the regression. 25

26 Map math Next, we use map math, selecting the regression from session 0 and the kriged residuals from session 1. 26

27 Map math Above, we call the output the Final Depth Map, and to the right we give the variables simpler names. 27

28 Map math Finally, we add the regression to the kriged residuals to get the final depth map. 28

29 Final map Here is the result. Note that the lower left corner is a bit ragged, probably due to the very small range on the kriged map. 29

30 Kriging with seismic variogram We then redid the kriging of the depth residual with the seismic variogram. 30

31 New map Here is the new map, where the kriged residuals have used the seismic variogram. The result is much smoother, as expected. A comparison to the KED map with the seismic variogram is shown next. 31

32 Comparison KED with seismic variogram Residual depth approach 32

33 Conclusions This PowerPoint compared two different approaches to depth conversion between measured well depths and a map of seismic two-way travel-time (TWT) picks. The first approach was the standard kriging with external drift (KED) approach. The second approach was the method described by Dubrulle (2003), which uses depth residuals. Both methods were implemented using the Hampson- Russell ISMap program. However, the first method is standard in the program, and the second method required some tweaking of the program. These tweaks may be implemented in a future release. 33

34 References Dubrulle, O., 2003, Geostatistics for Seismic Data Integration in Earth Models: 2003 Distinguished Instructor Short Course, Distinguished Instructor Series. No. 6, SEG and EAGE. 34