VSP survey design using Finite Difference Modeling

We present a novel way to predict the outcome of a Vertical Seismic Profile (VSP).  Using synthetic data generated by Finite Difference Modeling (FDM), we were able to study the effects on the final image quality due to variations in shot spacing, maximum offset, and receiver positions.  This method resulted in a design survey with a shot spacing of 150 m, a maximum offset of 6 km and with the receivers located at 4,550 m to 5,425 m.  The conclusions of this project had a major influence on the final survey design.  A similar exercise would prove to be highly valuable in comparable large-scale VSP programs.

A large multi level 3D VSP was being planned.  The objective was to optimize survey parameters to obtain a quality survey at a manageable cost.  Critical parameters are the shot positions on the surface and the receiver positions in the well bore.  These parameters are commonly determined from two methods.  The first method determines the parameters from a simple equation based on ray tracing in a uniform velocity earth (Van der Pal et al., 1996; Jones, 1998).  The second method is based on complex 3D ray trace modeling programs that determine the shot density and the maximum imaged area from the various surveys (Van der Pal et al., 1996).  Based on these methods, our initial chosen parameters were 160 m shot spacing and 6.25 km maximum offset, with the receivers located at 4,000 to 5,000 m depth, or about 3,000 m to 2,000 m above the main target.

We were in a unique position to use a third method.  This method consisted of a series of imaging experiments involving different source and receiver combinations of the previously generated synthetic data set.  Decisions on survey parameters were based on analysis of the quality of the images.

The synthetic data set was generated by Full Wavefield Elastic Finite Difference Modeling of a 2D line that crossed the well for the proposed VSP.  The model was highly populated with both sources and receivers, which allowed us to study the effects of eliminating certain shot and receiver positions from this data set.  The velocity model was a smoothly varying function with depth.  The contrast in the image was generated by density changes in the model.  An image of a small part of the density of this model is given in Figure 1.  Our main focus was on the separate sand bodies around the reservoirs.  These sand bodies were put into the model to give us an idea about the vertical resolution of the images.

Figure 1:  Density profile of the model that was used to generate the synthetic data.

The model spacing is 12.5 m by 12.5 m.  The well is located in the middle of the model and contains 221 receivers located at positions ranging from 3 km to 8.5 km in depth, with 25 m receiver spacing.  The sources used in this study are located at the surface ranging from the well to a maximum offset of 9 km on both sides of this well, with a shot spacing of 50 m.  The center frequency of this synthetic data set is about 13 Hz, as it was designed to mimic the streamer seismic data.  We have observed in previously collected VSP’s that the center frequency of VSP data is around double the center frequency of the synthetic data set.  Therefore, we also need to double the density of the shots to get similar un-aliased values in the field.  In the proposed survey, we were limited to 12 receivers or any multiplication of this number with a 50 ft receiver-offset.  Because of time and money constraints we had limitations on number of receiver settings, shot spacing and maximum source offset, especially as for the 3D survey the number of shots will increase geometrically.

Processing Flow

All the different runs are processed using the same basic processing sequence.  For simplicity we have only used the z-component of the data.  First, the down going wavefield is removed using a median filter.  Then, the down going shear wavefield is removed using a tau-p filter.  We also mute out the reflection coming from the base of the model.  As this is synthetic data, a deconvolution was not deemed necessary.  Most of the interfering events, which are the sea floor converted wave energy, the reflection coming from the base of the model and the first water bottom multiple, do not interfere with the upcoming wave fields from the target.  The noise in the data consists of remaining down going P- and S-wavefields and upcoming converted wavefields.

After these pre-processing steps, we arrive at the most important step, the imaging algorithm.  We have used a shot record migration (Ristow and Rühl, 1994), which is very accurate, but expensive.  However, as we are working with a small 2D VSP data set, this is not a problem.  The velocity model used for the migration was the same as the model that produced the synthetic.

In the first series of runs, we studied the effects of the amount and the location of the shot positions.  We changed two parameters, which are the shot spacing and the maximum shot offset.  The goal was to find the maximum possible shot spacing that results in an un-aliased image.  Also we wanted to look at the trade-off in image quality with the maximum offset.  Both of these factors influence the total number of necessary shots and thereby the time and cost of the survey.  A risk with having a large shot spacing is aliasing.  It may be that data that are theoretically aliased on a single receiver basis will, with an array of receivers, combine into an unaliased image.  The second parameter, the maximum shot spacing, affects the areal coverage of the image.  However, beyond a certain offset there is little gain in image coverage with additional increases in offset; it is important to find that limit.

Figure 2 shows the resulting images from the varying the amount of shots.  Along the horizontal axis, we limit the maximum offset, which is respectively 3 km, 4.5 km, 6.75 km, and 9 km offset on each side of the well.  Along the vertical axis we vary shot spacing of 100 m, 200 m, 300 m, and 400 m.  For all these images we have taken 36 receiver positions, located from 5,150 m to 6,025 m depth, with a receiver spacing of 25 m.

Figure 2:  Matrix with images resulting from varying the shot spacing (vertical axis) and the maximum shot offset (horizontal axis).  The upper right image includes the highest number of shots and the largest maximum offset and should be the best.  A diagonal from upper left to lower right represents an equal number of shots, and consequently is similar to an equal cost line.

From these images we eliminated the 3 km maximum offset because of poor image quality, the 9 km maximum offset because of cost and only limited improvement in the final image, and continued to investigate the 4.5 km and 6.75 km of maximum offsets.  We also eliminated the shot spacing of 100 m because of cost and 400 m because of reduced image quality, and continued investigation of the 200 m and 300 m shot spacings.

Another way to look at the shot spacing problem is by the means of aliasing.  If the shot spacing is too large the recorded wavelets will be aliased and the final image will contain noise and migration artifacts.  To study this problem we examined the shot record at the receiver located at the main target, which was at 6,925 m depth.  To prevent aliasing the first incoming arrival should not be more than half a wavelet off, from one shot point to the next shot point.  As shown in Figure 3, the wavelet is repeated after about 5 shot points.  This means aliasing occurs at 2.5 shot points which is equal to 125 m spacing in the synthetic data, corresponding to about 62.5 m in the field, again due to the planned difference in frequency content.

Figure 3:  The down going wavefield recorded at receiver depth 6,925 m.  Shot spacing is 50 m.

After this first selection, we tried another set of runs with respectively 4.5 km, 5.25 km, 6 km, and 6.75 km maximum offset, and decided to use the 6 km maximum offset in the field.  In the field we will be able to study some of these effects by limiting the amount of shots and maximum shot offset in a 2D walkaway VSP line that was collected prior to the acquisition of the 3D VSP.

Varying the receiver depth

In the next series of runs, we changed the location of the receivers.  We kept the set of 36 receivers intact, but moved them up in the well bore.  Therefore, we optimized the offset of the final image versus the resolution of that image.  When the receivers are closer to the target, the image resolution increases.  However, when the receivers are further away from the target, the maximum offset in the image is larger.

We studied the location of receivers at the range of 4,250-5,125 m, 4,550-5,425 m, 4,850-5,725 m, and 5,150-6,025 m.  For all these images, which are shown in Figure 4, we have taken 36 receiver positions, with a receiver spacing of 25 m.  We repeated this exercise twice, once for a shot spacing of 200 m and a maximum offset of 4.5 km, and once for a shot spacing of 300 m and a maximum offset of 6.75 km.

Figure 4:  Matrix with images resulting from varying the receiver location.  The images on the left have a shot spacing of 200 m and a maximum offset of 4.5 km, the images of the right have a shot spacing of 300 m and a maximum offset of 6.75 km.

From these runs we conclude that the shot spacing of 300 m with a maximum offset of 6.75 km is preferred.  Furthermore, we prefer receiver positions from 4,550 m to 5,425 m, or about 2,500 m to 1,500 m above the main target.  When we lower the receivers, the extent of the image reduces too much.  In the highest receiver position, we do not see much improvement in image quality and know that the frequency content of the final image will reduce, as we are moving farther away from the target horizon.  In the field, this positioning will also be dependent on cement quality.

Using FDM generated synthetic data we created a methodology to design the survey parameters for a 3D VSP survey.  The procedure involved creating test images while changing shot spacing, maximum offset and receiver location.  This was very important in our final decision on the 3D VSP survey design.  A similar method could be applied to other large-scale VSP programs to make them more cost efficient and evaluate image improvement versus cost.

In the first step we changed the amount of shot points and decided on using a maximum offset of 6 km and a shot spacing of 300 m, which is comparable to a shot spacing of 150 m in the field.  This should give us enough coverage and we should be able to collect this data at reasonable cost.  In the second step we decided to collect the data using receiver combinations at a depth of 4,550 m to 5,425 m above the main target.

Our final recommended VSP survey specifications were: 3 combinations of 12 receivers, each at 25 m spacing, ranging from 4,550 m to 5,425 m above the target, with a shot spacing of 150 m and a maximum offset of 6 km.

 Acknowledgements

We would like to thank BP and in particular, the Deepwater Development BU for permission to publish and present these results.  Don Herron provided the depth model.  We want to thank Carl Regone for generating the synthetic data set.  We want to thank Bertram Nolte for his help with implementation of the shot record migration.  Finally we want to thank John Etgen, Randol Read, Leon Thomsen, and other members of the Reservoir Management and Geophysical Imaging and Operations Teams for advice and discussions.

 References

Jones, M., 1998, Cost effective VSP survey parameters, VSP Update, Schlumberger, no. 1

Ristow D. and T. Rühl, 1994, Fourier finite-difference migration, Geophysics, vol. 59, no. 12, p. 1882-1893.

Van der Pal, R., M. Bacon, and D. Pronk, 1996, 3D walkaway VSP, enhancing seismic resolution for development optimization of the Brent field, First Break, vol. 14, no. 12, p. 463-469.

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