A pre-stack 3-D Tau migration was applied to a 3-D seismic data set acquired in offshore Abu Dhabi, United Arab Emirates. The velocity model was built through an initial series of 2-D Tau migration velocity analysis, and supplemented by 3-D subset migration. A 3-D Tau migration velocity analysis was used for the final two updates of the model. The final interval velocity model provided low residuals in the common-image gathers from different offsets and was consistent with velocities from four wells located in the region. This velocity model included the main known features of the region including a low-velocity zone and a major fault. A final 3-D pre-stack Tau migration was applied using the velocity model and a relatively moderate aperture. This migration imaged the region including part of the critical poor data quality region, which includes the reservoir as well as reflections from the fault. Based on the derived velocity model, we concluded that the major cause for the poor image is the presence of a shallow high-velocity anomaly separated by a fault from a low-velocity anomaly.
Reflections from seismic waves that propagate through regions with complex geology, as characterized by laterally inhomogeneous media, cannot be adequately imaged using conventional processing techniques. This is because conventional techniques do not correctly account for the amplitude distribution and moveout curvature associated with wave propagation in complex media. One of the most challenging tasks in processing this type of seismic data is to build a 3-D seismic velocity model. In some cases the velocity model can be based on conventional 3-D depth migration, but this procedure is usually not robust and the result can be unstable. This is because depth migration is extremely sensitive to lateral velocity variations, and easily affected by errors in the velocity model.
When most velocity analysis techniques fail to adequately image the subsurface, pre-stack 3-D Tau migration may be considered as a last resort. Unlike depth migration, 3-D Tau migration uses the vertical-time domain (denoted by Tau) to avoid estimating depth during image processing (Alkhalifah et al., 1997). By using the Tau domain, this technique bypasses the inherent depth-velocity ambiguity that usually plagues conventional depth-migration velocity analysis (Ross, 1994). This special feature can also improve the performance and convergence of pre-stack migration velocity analysis.
In this paper, we describe the application of pre-stack 3-D Tau migration to a 3-D seismic data set acquired over a structure in offshore Abu Dhabi (Figure 1). The reflections in the center of the survey have poor amplitude and continuity as can be seen in Figure 2. We start the paper by briefly discussing the challenges and objectives of the survey.
CHALLENGES AND OBJECTIVES
Prior to 1992, numerous 2-D seismic lines were acquired over the structure in offshore Abu Dhabi. The resulting images, after conventional processing, pre-stack time migration and pre-stack depth migration from the 2-D lines, were of poor quality over the central part of the structure. In August 1992, a 3-D seismic data set was acquired over the structure. Figure 2 shows Line 120 through the central region of the 3-D survey after conventional post-stack processing. The middle part of the section is poorly imaged with the aperture of the poor-quality region increasing with two-way time. The degradation of the image extends from the top of the seismic section and indicates that a shallow geological feature causes the problem. As a result, key reflections cannot be picked through the central part of the survey. Nor can a major fault that cuts through the structure (as is apparent from the good quality part of the image) be located.
In order to resolve the imaging problem we set the following objectives for our processing:
(1) improve reflection continuity at the reservoir levels between 0.5 and 1.2 seconds to obtain a better structural interpretation; and
(2) improve the seismic reflections at all levels in the poor quality central area of the field in order to image the geometry of the major fault.
Achieving these objectives will not only depend on the techniques used, but also on the inherent quality of the data set itself. If the recorded seismic reflection energy in the middle part of the field is very weak, then no processing technique will succeed.
THE 3-D SEISMIC AND WELL DATA SET
The 3-D seismic data set was acquired in August 1992 and consists of 243 lines separated by 25 m with an inline common depth point gather every 12.5 m. The survey was acquired using a dual streamer/dual source method (off-end shooting, flip-flop pop every 25 m interval per array). The airgun source arrays were separated by 50 m and maintained at a depth of 6 m. The source array volume and array pressure were 2,402 cubic inches and 2,000 pounds/square inch. The GDR-1000 recording instrument system was used with the low-cut and high-cut filters set at 6.0 Hz (18.0 dB/octave) and 125.0 Hz (72 dB/octave). The sample interval was 2 milliseconds and the record length was 5.0 seconds.
The two 3,000-m-long streamers were separated by 100 m and kept at an average depth of 6–8 m. The offset to the nearest trace was 125 m. Both the shot and receiver group intervals were 25 m and the fold was 30. The processing operations applied to the data prior to pre-stack migration velocity model-building included preprocessing, Radon demultiple, and an initial velocity analysis on a 500 x 500 m grid.
Figure 1 shows a structural time map for a reflection from a Late Cretaceous formation and the locations of the four wells in the area. Well 1 and well 5 are the closest to the middle part of the field with well 1 located in the most affected poor-quality data region. As discussed later, the check-shot velocities in well 1 are relatively higher in each layer than all the other wells. The higher velocities in this well continue to a depth that is equivalent to about 1.0 second two-way time. The velocity difference between well 1 and the other three wells is large, which suggests the presence of a shallow high-velocity anomaly. The seismic velocities to the east of well 1, and above the critical area, are generally low. The difference can be attributed to a prominant fault separating the two areas (Figure 1). These patterns will be discussed in greater detail later.
WHY VELOCITY ANALYSIS IN TIME?
The main difference between depth- and time-based velocity analysis is in the conversion of the average slowness (i.e. reciprocal of velocity) to update the interval velocity (Alkhalifah, 2003). To illustrate this feature in simple terms, consider a velocity anomaly in the middle of a homogeneous-medium, with two reflectors: one just above and the second just below the anomaly (Figure 3a). Figures 3b and 3c illustrate how the reflector’s vertical position (after migration) is accurate in time but inaccurate in depth. For example, if an initial high velocity (higher than the background medium velocity) is used in the pre-stack depth migration, then the residual moveout and layer stripping will accurately detect this anomaly but at the wrong depth (Figure 3b). In contrast, depth-independent pre-stack time migration will detect this anomaly at a time that corresponds to a depth that will be resolved at the end of the process when the velocity is accurately estimated (Figure 3c).
The deferment of depthing to the end of the processing in the time imaging approach, speeds up the convergence of the velocity-estimation process. At first glance, the advantages of using the Tau domain for pre-stack migration velocity analysis may not be appreciated, especially since all its components are based on well-established techniques that usually do not work well in the depth domain. The approach discussed here is based on a full Kirchoff pre-stack migration velocity analysis done entirely in the Tau domain. Unlike conventional pre-stack time-migration methods, here the lateral inhomogeneity is treated exactly (within the limits of ray theory). The interval velocity is obtained in the Tau domain, and is kept there to be used for the pre-stack Tau migration. Occasionally, in pre-stack depth migration velocity analysis, the time domain is used to estimate velocity. However, these velocities are converted to depth to perform depth migration. This practice introduces the velocity-depth ambiguity problem we are determined to avoid.
The Data Domain versus the Image Domain
As in the case of depth migration, the data and image domains also differ in the case of Tau migration. The Tau image is only a convenient way to scale the depth image, which tends to stabilize depth migration velocity analysis. Tau migration differs from conventional time migration with the difference governed by a time-scaled, image-ray mapping step.
To obtain an image, the entire data set is input to the migration and the image domain will absorb the information on a gridding structure reflecting the migration objectives. If the objective of the migration is residual velocity analysis, the output image is usually and practically given by a number of 2-D lines, about 500 m apart. If the objective of the migration is a full image of the area, the output is a 3-D image given on a regular grid. More unique grids (such as a polygon) are possible, but probably less practical. In all cases the output trace is the result of a 3-D migration and it will not change whether the output is the whole image domain or subsets of it, or even a single trace. The only thing that will change is the definition of the structure and its resolution in the image domain. Thus, the more complete the output image, the more the structure becomes recognizable and the geological puzzle resolved. However, we can get to a level of decimation that no new information is added by including more lines. In other words, the resolution of the data does not include this extra information. In summary, the Kirchoff implementation is flexible and we will take full advantage of its flexibility.
The output image domain and its gridding are independent of the input domain and the distribution of data. Unlike conventional time migration, the mapping between the data domain and the migrated domain is a full transformation in Tau imaging, not a partial one. Even the zero-offset, zero-dip sample, unlike conventional time migration, will move in Tau migration. In Tau imaging (like in the depth case) aliasing in the data domain depends on the sampling of the data traces, and image domain aliasing results from the sampling of the image. Such a distinction in aliasing domains is not present in conventional time migration.
To transform conventional time-migrated images to Tau (or depth) migrated images, image-ray mapping is required (Figure 4); a process that relies on ray-tracing and accounts for the lateral inhomogeneity in the model. It will not improve the focusing of the image, but image-ray mapping will properly position reflections obtained through time migration in the case of lateral inhomogeneity. Thus, for proper comparison of depth (or Tau) and time-migrated sections, we have applied imageray mapping. Otherwise, such a comparison will lack the position criteria that is required to make a valid judgment on quality.
THE PRE-STACK TAU MIGRATION LOOP
The relationship between vertical time and depth is given by a simple integral equation. Since the velocity is allowed to vary laterally, the equation depends on lateral position. This implies that all derivatives of the travel-time with respect to space (x, y, z) will include additional terms resulting from the lateral dependency. These additional terms depend on a parameter ‘sigma’ (Alkhalifah et al., 1997) such that if the velocity is laterally invariant then sigma is zero, and the additional terms will drop out. The parameter sigma is the key to allowing this time migration to handle lateral inhomogeneity.
Figure 5 shows a chart of the pre-stack Tau migration velocity analysis procedure used here in the 2-D and 3-D implementation. Note that the depth conversion step comes at the very end, a key feature of the analysis. The method as pertains to the offshore Abu Dhabi 3-D data set consists of the following steps:
(1) apply 2-D pre-stack Tau migration analysis on eight lines distributed over the region;
(2) obtain from the 8 lines an initial interval velocity model that is interpolated using the layering as a guide;
(3) pre-stack 3-D migrate subsets of the data using this initial model;
(4) measure the residual moveout after pre-stack migration and use it to update the velocity model;
(5) continue iteratively with steps 3 and 4 until an acceptable model is reached; and
(6) migrate the whole data using the final velocity model.
An Initial Velocity Model
Using the stacking velocity information extracted from conventional processing, we built our first velocity model. The stacking velocity was on a 500 x 500 m grid spacing. These velocities were then interpolated and extrapolated to fill the 3-D velocity volume. The final spatial sampling is 25 m in all directions (x, y, z). The velocity model extends 12 km in the inline direction, 6.1 km in the cross-line direction and is 10 km deep. Figure 6 depicts the velocity cube obtained from converting stacking to interval velocities. Note the low-velocity anomaly in the middle of the region.
Velocity values in Figure 6 range between 1,500 m/sec to 8,000 m/sec. The exaggeration at the high-end is expected since stacking velocities tend to be an unstable source for interval velocity information when converted using the Dix Equation. The velocity generally increases with depth with a low-velocity zone embedded in the middle. Also evident is a shallow low-velocity anomaly in the middle region located over the critical attenuated region.
The initial velocity model was updated using a full 2-D pre-stack Tau migration velocity analysis on 8 lines (located about 500 m apart) through four iterations. After each velocity-update iteration, a 3-D velocity model was built by imposing regularization conditions to help stabilize and filter the results. The reflection interface-based regularization condition was constructed to smooth the difference between the separately analyzed lines. The velocity along the 2-D lines was then extracted from the 3-D model and separate updates were made before the next iteration. Four iterations of this process helped obtain the velocity model shown in Figure 7. Another velocity model displayed in Figure 8 again shows the suspected low-velocity zone in the middle region of the survey. This velocity model was used for the first subset pre-stack 3-D Tau migration.
The residual analysis that was done to update the velocity after each iteration, is also a measure of the accuracy of the velocity model used in the migrations. Low residuals indicate more accurate velocity models. Figure 9 shows the residual after the third iteration along Seismic Line 120 through the attenuated region, for four major reflection horizons. The residuals are displayed for points along the horizon from left to right, with the vertical axis describing velocity and the horizontal axis describing slope (in ray-parameter) for each point along the horizon. The horizon information was extracted from the well logs. Though the semblance amplitude in the middle region is low, it is pickable; and thus it can be used to update the velocity.
After three iterations some work is clearly required to fully align the residual velocity value with the rest of the group. Also notable is how much the velocity has changed laterally in the middle critical region; this is equivalent to RMS residuals. Interval residuals will have more severe variations. From close observations of the horizons in Figure 9, it is apparent that the residuals indicate a high-velocity anomaly followed by a low-velocity anomaly from left to right (i.e. increasing CMP numbers along the line). This severe change can be a direct result caused by imaging across the fault. Well 1 has a relatively higher velocity than the other wells and it is located just at the beginning of the ‘dimmed’ area from the left, as consistent with the velocity observations.
Figure 10 shows a comparison between the check-shot velocity survey in well 5 and a vertical profile from the 3-D velocity model at the same location obtained after the four iterations of 2-D updates. The agreement between the two curves suggests that the velocity model is sufficiently close to start the full 3-D analysis. In particular, the estimated time for the start of the low-velocity layer has been obtained.
The Final Velocity Model
Using the interval velocity described in the previous section, the first 3-D pre-stack migration was applied to the whole data set; for cost purposes the output is only a subset of the image. Specifically, twelve 2-D imaged lines (500 m apart) were produced by concentrating the contributing traces from the 3-D data to them.
To update the 3-D velocity model, the 12 lines were examined for residual moveout in a similar way to that of the 2-D case. However, now the velocity update algorithm is a 3-D one in which the regularization is inherently included in the updating scheme. The updated velocity model was once again used for the pre-stack 3-D Tau migration to obtain a subset of the image (12 lines). Figure 11 shows Line 120 after pre-stack 3-D migration. Some of the energy under the middle part is better focused in comparison with Figure 2. Once again the residuals were used to update and improve the velocity. In the last iteration, the residuals are generally low and there are only minor improvements from the previous iteration.
This final velocity model is given on a 25 x 25 m horizontal grid extending beyond the image space, and especially along the inline direction to cover all possible source and receiver locations (the aperture). In fact, it extends more than one kilometer in the inline direction on both sides. The velocity was developed and updated in the Tau domain with a vertical sampling of 8 msec and extends up to 4.0 seconds.
Figure 12 shows a vertical and horizontal slice through the final 3-D interval velocity model. The inline direction is given by the arrow. Evidence of the fault is clearly apparent where, as expected, the velocity decreases across it (the brighter colors correspond to lower velocities). This feature is in agreement with what is observed from well 1 (Figure 1). In well 1 the velocity is higher than at the other wells, especially relative to well 5 (the other side of the fault). The velocities are extrapolated toward the sides, especially along the inline direction.
In Figure 13, the shallow low-velocity feature is at a depth of 700 m in the final velocity model. This anomaly might be part of the cause for the poor image below this middle region. Figure 14 shows the characteristics of the velocity model at depth with the dominant structural feature (the fault) clearly apparent. Also apparent is a plunge in the middle of the structure. Evidence for the fault, given by the anticline, can be seen in the velocity model. Also notable is a low-velocity layer.
The final velocity model provided low residuals in the common image gathers and thus is expected to provide good final images. We also compared the check-shot velocities from the four wells to the Tau migration interval velocities (Figure 15). Well 4 extends to 1.6 seconds and the agreement was good even up to this extended time. The agreement in the time-depth plot at these three wells suggests that good depth placing of reflections will be achieved by using the velocity models at these locations. At all well locations, the seismic velocities accurately predicted the top position of the low-velocity layer at about 0.8 seconds as well as its thickness. We use this final velocity model to apply the full 3-D pre-stack migration.
Final 3-D Pre-Stack Tau Migration
After some analysis of the data, including examination in the frequency-wave number spectrum (F-Kx-Ky) of a stacked image with gridding of 25 x 25 m of a single offset, it was determined that the gridding in the crossline direction of the final image could be reduced to 50 m. This is because energy towards the high wave numbers (50 m) is extremely low. The reduction of the grid size from 25 m to 50 m translates to a cost saving by a factor of two. Considering that the velocity is high and the target is mostly located within a depth of 4.0 km, the migrated Tau range was limited to 2.3 seconds. These measures were used to reduce the cost of the full migration.
The procedure was organized so that a single offset bin was migrated (with a range of 100 m) at a time. Using the 100 m range resulted in 30 offset bins. This approach allowed us to examine images from the separate offset bins and evaluate the performance of the migration at an early stage. Figure 16 shows the image for offset 1,665 m (centered at that number) for a depth slice of 1,700 m. The image, despite representing only one offset, looks adequately imaged and has interesting features some of which will be discussed in detail later.
After imaging all the offset bins, the offsets were stacked to obtain a final 3-D image. Figure 17 shows eight lines from this image, mostly concentrated in the middle critical region. Some of the reflections in the critical zone might not seem structurally accurate showing a syncline; however, these sections are Tau sections. When accurately scaled to the depth domain the shape of the reflections will change. Line 120 passes through the middle of the critical dimmed area. Nevertheless, unlike previous results the migration shows reasonable continuity through the region and also it partly shows the fault location: a major goal of this study. Improvements are also noticeable on all other lines – especially Lines 100 and 140, which also pass through the sides of the middle critical region.
Next, the final interval velocity model shown in Figures 12 to 14, was used to convert the Tau image to depth. This was achieved via velocity-dependent vertical stretching. Thus, the image results displayed in the next few figures are given in depth. Figure 18 displays slices and sections from the final 3-D image in depth. The vertical inline section is from the far side of the image (inline 4). Figure 18a corresponds to a depth of 1,260 m and shows the fault reflection which appears to cut through the middle of the section passing the complicated region. The fault reflection appears to be curved with two major parts tied in the center of the image. One part has a strike in the cross-line direction, and the other part verges right from the main cross-line direction.
Figure 18b shows a slice of the 3-D image at a depth of 1,600 m. At this depth, the fault has better continuity and the rest of the structural features seem better imaged. Deeper depth slices are also well-imaged using the 3-D pre-stack Tau migration. Figure 18c shows a depth slice from 1,980 m. The fault appears to be straight, extending from one side of the image to the other side.
Another way to observe the fault is to extract vertical slices of the image from various directions. Figure 19 shows a vertical slice extending across the entire image in which fault reflections appear. The fault reflections tend to agree with the predicted fault location given by the discontinuities of horizontal reflections. The fault practically extends from depth of 1,200 m all the way to 3,000 m, the location of the depth slice.
We applied 3-D pre-stack Tau migration velocity analysis on a 50 sq km, 3-D data set in offshore Abu Dhabi. All previous attempts to image the middle part of the structure were unsuccessful. Here, we applied a multi-level approach starting with 2-D analysis to a full 3-D pre-stack migration velocity updating. The final velocity model contains a number of layers with the major fault apparent in the velocity structure. The velocity decrease (reversal) apparent in the check-shot data from four wells was clearly present in the final interval velocity model. In fact, the final velocity model not only reduced the residuals in the common image gathers, which is the source of velocity information, but also agreed well with the check-shot velocities from four wells in the area. At least three wells showed similar velocities to the final velocity model at the well locations. Well 1, which includes relatively higher velocities, was an exception. Using this final velocity model, we applied a final pre-stack 3-D Tau migration to the whole input data. The migration showed acceptable results and managed to image the critical fault present in the dimmed area.
We would like to first thank Abu Dhabi National Oil Company (ADNOC) and Abu Dhabi Marine Operating Company (ADMA-OPCO) for the opportunity to show the results of this study. We also thank Spectrum Energy for their pre-processing of the data. Tariq Alkhalifah would like to thank King Abdul Azizi City for Science and Technology (KACST) for their support. We also thank three anonymous reviewers for their useful comments, Abdullatif Al-Shuhail for proof-reading the paper and GeoArabia’s editors and staff for editing and designing the final manuscript.
ABOUT THE AUTHORS
Tariq Alkhalifah received a BSc degree in 1988 in Geophysics from the King Fahd University of Petroleum and Minerals in Saudi Arabia, an MSc in Geophysical Engineering in 1993, and a PhD in 1997 in Geophysics from The Colorado School of Mines. Tariq worked as a post-Doctoral Researcher at the Stanford Exploration Project, Stanford University, until 1998. He currently works at the King AbdulAziz City for Science and Technology in Riyadh, Saudi Arabia. Tariq received the J. Clarence Karcher Award from the SEG in 1998 and the Conrad Schlumberger Award from the EAGE in 2003. His current research interests include ray tracing, velocity inversion and imaging, especially in anisotropic media.
Saif Al Sharif received a BSc in Geophysics in 1995 and an MSc in Engineering and Technology Management in 1997, both from Tulsa University, Oklahoma, USA. He worked as a Geophysicist for Yemen Oil and Mineral Company until joining ADMA-OPCO in 1998. Saif is a Review Geophysicist at ADMA-OPCO.
Kamal Belaid is Team Leader, Undeveloped Structures (sub-surface) at ADMA-OPCO. He received a BSc in Physics in 1974 from Tunis University, Tunisia, an MSc in Geophysics from Paris-VI University (Marie-Curie) France in 1976, and an Engineering Diploma in Geophysics from Institut Français du Pétrole, France, in 1977. Kamal then spent two years as a Trainee with Shell International in Houston (USA), two years with the Tunisian National Oil Company, ETAP, and one year with Amoco Tunisia as a Geophysicist prior to joining ADMA-OPCO in 1982 as a Geophysicist.