3-D seismic discontinuity for faults and stratigraphic features: The coherence cube MIKE BAHORICH Amoco Corporation Denver, CO STEVE FARMER Amoco Corporation Tulsa, OK Seismic data are usually acquired and processed for imaging reflections. This paper describes a method of processing seismic data for imaging discontinuities (e.g., faults and stratigraphic features). One application of this nontraditional process is a 3-D volume, or cube, of coherence coefficients within which faults are revealed as numerically separated surfaces. Figure 1 compares a traditional 3-D reflection amplitude time slice with the results of the new method. To our knowledge, this is the first published method of revealing fault surfaces within a 3-D volume for which no fault reflections have been recorded. Traditional 3-D seismic interpretation. A major advantage of 3-D technology is that, unlike 2-D which is essentially limited to vertical cross-sections, it allows seismic data to be displayed in horizontal or map form. Geoscientists have traditionally used two kinds of seismic map displays: amplitude time and seismic horizon slices. The former is a horizontal plane through the 3-D data volume (Figure 1 a) without reference to a stratigraphic horizon. It permits an interpreter to view geologic features in map form without having to first pick seismic events. In spite of this advantage, leading voices in the industry (such as Alistair Brown) maintain the time slice is quite underutilized. A probable reason is that amplitude time slices are often difficult to interpret. When using traditional methods, it is often difficult to get a clear and unbiased view of faults and stratigraphic features hidden in the 3-D data. Faults are (often) readily seen on individual vertical cross-sections, but many of these must be examined to determine the lateral extent of faulting. Stratigraphic changes are difficult to detect on vertical seismic lines because of the limited profile they present in this view. Time slices are more suitable for detecting and following faults and stratigraphy laterally. However, interpretation is often complicated by the fact that time slices can cut through different stratigraphic horizons. This problem can be avoided through the use of the horizon slice - the set of seismic amplitudes associated with an interpreted horizon surface, generally at some consistent stratigraphic level. Although horizon slices are more useful than amplitude time slices for following faults and stratigraphic features, they too have disadvantages. The geoscientist must pick a stratigraphic horizon. This can be difficult and time consuming, and it also imposes an interpretive bias on the data set. 3-D coherence. Coherence calculations can help with the problems mentioned above. 3-D seismic data are generally binned into a regular grid. By calculating localized waveform similarity in both in-line and cross-line directions, estimates of 3-D dimensional seismic coherence are obtained (Figure 2). Small regions of seismic traces cut by a fault surface generally have a different seismic character than the corresponding regions of neighboring traces (Figure 3). This results in a sharp discontinuity in local trace-to-trace coherence. Calculating coherence for each grid point along a time slice results in lineaments of low coherence along faults. When this process is repeated for a series of time slices, these lineaments become fault surfaces, even though fault plane reflections have not been recorded. Stratigraphic boundaries generate similar discontinuities. The technique may be employed to produce coherence horizon slice maps, or to transform a reflection amplitude 3-D data volume into an entirely new volume or cube of coherence coefficients. Map views of coherence data afford the opportunity to see stratigraphic changes more clearly. For example, the channel features that are readily apparent to laymen in the coherence time slice of Figure 4a are very difficult to see in a traditional amplitude time slice... even for an experienced geoscientist. Coherence information provides a different perspective when used in conjunction with amplitude data. In areas where high seismic amplitudes are often associated with hydrocarbon accumulations (such as the Gulf of Mexico), the stratigraphic and structural context may be identified more clearly from coherence data. As an example, the bright spot in Figure 4b is located within the channel seen on the coherence display (Figure 4a). Faults parallel to strike. Conventional amplitude time slices are often useful for viewing faults that run perpendicular to strike. However, when faults run parallel to strike, they become more difficult to see because the fault lineaments become superimposed on bedding lineaments. The coherence calculation suppresses laterally consistent features, in effect removing the bedding. Because of this, the 3-D coherence algorithm reveals faults in any orientation equally well. Figures from a 3-D survey in Trinidad illustrate this point. A fault trace is highlighted with dots on the amplitude slice in Figure 5a. The fault is clear until it cuts parallel to the strike of bedding, where it becomes quite difficult to see on the time slice. The fault is clear in every orientation on the coherence time slice of Figure 5b. Regional geologic interpretation. Until recent years, most 3-D surveys covered relatively small areas. But the success of the technique and falling costs have caused surveys to become larger. Now some vast spec 3-D surveys cover hundreds of square kilometers and run to tens of millions of traces. Sorting through that amount of information is a daunting task. However, since calculating coherence is an noninterpretive process, it can quickly provide the geoscientist with a view of regional faulting. Compare Figure 6a (time slice) and OCTOBER 1995 THE LEADING EDGE 1053
Figure 1. (a) Traditional 3-D seismic time slice. Faults parallel to strike are difficult to see. (b) Coherency time slice. Faults are clearly visible. Figure 6b (coherence time slice). A flip frame animation of coherence time slices can provide a quick view of how faults are changing with depth. S tructure, stratigraphy, and hydrocarbons. Several interesting relationships between structure and stratigraphy are apparent in Figure 6b. Two major channels run from north-tosouth toward a salt dome. As they approach the intrusive salt, which has caused upward distortion of the bedding adjacent to the intrusion, the channels deflect away from the structural high. On the southeast portion of the display, a channel system crosses a fault and makes an abrupt turn to the east, paralleling the fault on the downthrown side. Note the point bar that is clearly seen within the channel. In the northeast portion of the survey, bright spots are represented by areas of 1054 THE LEADING EDGE OCTOBER 1995 high coherence trapped against fault lineaments. Also note the bright spot within the channel system in the south central portion of the survey. H orizon dip/azimuth/edge pitfalls. Several map analysis techniques exist for highlighting faults on an interpreted surface. The dip magnitude or dip azimuth of the surface may be estimated and edge detection (or enhancement) techniques may be applied. These methods have proven very useful for the detection of subtle faults. However, these techniques may only be employed after the horizon has been interpreted by a geoscientist. In addition, successive horizons must be interpreted in order to get a 3-D perspective of faulting. One potential pitfall in using these methods is that they are dependent upon the skill of the interpreter and upon the
Figure 2.3-D coherence may be measured by calculating seismic trace similarity in the inline and crossline directions. A three-trace operator is depicted. This is the minimum size required for a 3-D calculation although more traces can be used. Coherence may be measured from trace A to trace C and from trace A to trace B. A combination of these 2-D measurements provides a measure of 3-D coherence. For a nine-trace operator, coherence might be measured from the center trace to each of its neighbors. Even larger operators can be applied in a second-stage process that is particularly useful when dealing with noisy data. Figure 4. (a) Coherence slice across a channel system. Coherence images the stratigraphic context better while amplitude data in the next panel image hydrocarbons more clearly. (b) Average amplitude over a series of time slices. Note that the bright spot is located within the channel seen on the coherence display. Figure 3. Faults are highlighted by the 3-D coherence technique because traces are not identical on opposite sides of a fault. In this example, missing stratigraphic section from one side of a fault to another generates slightly different reflectivity on one side of the fault. The coherence is lower when the traces are less similar. Figure 5. (a) Time slice from Trinidad over typical complex faulting. Note that the fault is difficult to see when parallel to strike (look between the middle two dots). (b) Coherence slice of same region. Note that parallel or perpendicular faulting is highlighted equally well. OCTOBER 1995 THE LEADING EDGE 1055
Figure 6. (a) Time slice at 1250 ms exhibits two major channels, a minor channel including evidence of a cut bank and point bar, en-echelon growth faults, radial faults, a salt dome and bright spots. (Data courtesy of Geco-Prakla). (b) Coherence slice at 1250 ms shows clear relationship between faults and stratigraphic features. The two channels avoid the high generated by the salt dome. The channel in the lower center of the figure crosses a major fault and abruptly turns to the east, paralleling the fault and leading to a cut bank and point bar. Note the radial and en-echelon faulting. 1056 THE LEADING EDGE OCTOBER 1995
Figure 8. (a) Edge detection performed on the interpreted water-bottom horizon. The channel is partially visible hut the fan is not. (b) Coherence calculated on the seismic data about the water-bottom horizon. The channel is more continuous on the coherence data and the fan is visible. Figure 7. (a) Dip map generated over a carefully picked and autotracked horizon in an area of fair-to-poor data quality. Poor data have caused the generation of spurious linear and circular features. Note the fault marked with an arrow has a bend. (b) Coherence slice generated about a constant time window approximately equivalent to the horizon of interest in Figure 7a. This coherence slice appears somewhat out of focus due to the fair-to-poor data quality. Note that the fault marked with an arrow does not have a bend. (c) Dip map generated over the same horizon as Figure 7a after reinterpretation of the horizon using information from the coherence slice. Note that the fault marked with an arrow no longer has a bend. accuracy of the horizon autotracking software. In certain situations, the horizon autotracker may mispick the desired horizon. Subsequent analysis with horizon-based fault detection techniques sets up a scenario where the autotracker creates a discontinuity that the dip, azimuth, or edge map confirms. A dip map was generated from a carefully picked and autotracked horizon interpreted over a land data set with poor signal-to-noise ratio (Figure 7a). Note that the fault marked with an arrow has a bend in it. A coherence time slice (Figure 7b) was run about a time slice as close as possible to the time of the horizon of interest. Note that it appears somewhat out of focus due to the poor seismic data quality and that it reveals OCTOBER 1995 THE LEADING EDGE 1057
Figure 9. (a) Coherence time slice at 1700 ms in light blue; coherence time slice at 1750 ms dark blue. Top view. (b) Shallow times (1500 ms) are red, medium times (1750 ms) are green, and deeper times (2000 ms) are dark blue. (c) 3-D visualization in which high coherence values are transparent and low values remain, revealing fault surfaces. Note that the fault orientation is seen in three dimensions though no fault reflections have been recorded. No interpretation has been performed to reveal the faults; this is a display of raw seismic after application of the 3-D coherence algorithm. a continuous fault without a bend. Because of the discrepancies between the faults seen on the coherence time slice and the dip map, the horizon and fault were reinterpreted and the dip map regenerated (Figure 7c). Note that the bend in the fault is now removed and the fault s overall appearance is more similar to the one seen on the coherence time slice. In areas of fair to poor data quality, coherence maps may appear more out of focus than those obtained with traditional map-analysis techniques (dip, azimuth, edge detection, and residual) although the latter exhibit spurious linear and circular features. If the data are of good quality and the interpreter and horizon autotracker have performed well, coherence along a horizon may highlight faults in a fashion similar to the results obtained with conventional map analysis techniques. Stratigraphic features are often better imaged with the coherence method. An example involves a waterbottom horizon interpreted on a 3-D seismic survey in the Gulf of Mexico. 3-D coherence, calculated over a fixedlength window tracking below the water bottom, revealed a submarine channel system leading to a recent deep-water fan. Figure 8 compares edge detection and coherence displays of this feature. Note that portions of the channel are more continuous on the coherence data and the image of the submarine fan is better. F ault surfaces. In the process of calculating coherence for a 3-D data volume, faults become numerically separated from the data which surrounds them. In other words, faults generate surfaces of low coherence. By employing visualization software, these fault surfaces may be observed in three dimensions from any perspective even though no fault planes have been recorded (Figure 9). Not only are these surfaces distinctly separated from neighboring data, they are also numerically separated, enabling them to be picked using horizon autotracing software. This fault autopicking technique enables the interpreter to have a fault pick on every trace, adding significant detail to the fault interpretation. 3-D seismic discontinuity/coherence has important applications for the analysis of 3-D structure and stratigraphy, and is a valuable adjunct to conventional amplitude data. This method reveals fault surfaces within a 3-D seismic volume where no fault plane reflections have been recorded. Conclusions. This new method of detecting, imaging, and autotracking faults and stratigraphic features has had immediate and significant financial impact evidenced by reserves highlighted in Amoco s 1994 annual report to shareholders. 1058 THE LEADING EDGE OCTOBER 1995