Using spectral decomposition to investigate detailed thickness variations is a problematic solution. The low spectral decomposition components represent thick beds, while the high

Figure 1. Spectral decomposition takes the seismic volume on the left and expands it into a multitude of volumes as shown on the right. In this example, only every fifth output volume is shown. The color scale on the bottom right illustrates increasing spectral amplitude from left to right. Once the decomposition has been generated, the problem becomes extracting useful information from 20 to 100 volumes instead of just one. (All images courtesy of Stark Reality)
spectral decomposition components represent thin beds. This is good and useful. However, spectral decomposition takes a single volume and turns it into many volumes. Depending upon the input data volume and the spectral decomposition method utilized, users start with one volume and can wind up with 100 or more volumes. The problem then becomes how to view or extract useful thickness variations given a 20- to 100-fold increase in the volume of data points to study. Conventional hardware and software can easily handle a single data volume, but what about 20 or more equally sized volumes?

One solution to this problem is to utilize software that takes advantage of the multi-volume and sequential volume rendering capabilities of the TeraRecon VolumePro 1000 volume rendering accelerator board. This is combined with an Age Volume generated from the seismic data volume and a ColorStack. The volume generated from the spectral decomposition results in several different techniques to interactively view spectral decomposition data as a function of relative geologic time. These techniques utilize either an Age Volume generated from the seismic data volume, or a ColorStack volume generated from the spectral decomposition results, or both.

Figure 1, which contains data provided by Santos and the South West Queensland Unit Joint Venture (Santos, Delhi and Origin), is an example of this problematic solution. On the left is approximately 800 milliseconds (ms) over 38.6 sq miles (100 sq km) taken from a much larger
Figure 2. A Relative Geologic Time Volume, when combined with the proper hardware and software, can be used to better visualize the spectral decomposition results. It can be used for interactive volume sculpting, either of the individual cubes (Figure 3), or of a color stacked cube (Figure 4). This volume can also be used to covert the vertical axis of the data volume to relative geologic time, thus producing the Wheeler Volumes shown in Figure 5.
land 3-D survey. Wulf Massell of Fusion Petroleum Technologies Inc. ran his company’s EPD spectral decomposition routine, ExSpect, on this seismic data to produce 100 spectral decomposition volumes. According to Massell, these volumes contain the high resolution spatial and temporal distribution of the instantaneous spectral amplitudes associated with wavelets from 1 Hz to 100 Hz. The 20 images to the right represent every fifth spectral decomposition volume. Each spectral decomposition volume is the same size as the original seismic volume, but for display purposes they appear smaller.

In order to generate a ColorStack volume, these 100 volumes need to be reduced to just three. There are a variety of ways in which this can be accomplished. For this particular study 1 Hz to 27 Hz volumes were summed to generate a “red” or low-frequency volume. The “green” or mid-frequency volume is the sum of the 28 Hz to 42 Hz volumes, while the “blue” or high-frequency volume is the sum of the 43 Hz to 100 Hz volumes. Summing the volumes in this way destroys most of the frequency resolution obtained from the spectral decomposition, but it still maintains the spatial and temporal resolution. These frequency bands were selected so that the resultant volumes each contained approximately the same maximum spectral amplitude. The red, green, and blue “boxes” in Figure 1 denote the volumes used for the ColorStack component volumes. ColorStack results will be shown in Figures 4 and 5.

Figure 3. The Age Volume is used to interactively sculpt the spectral decomposition cubes to a desired horizon. By utilizing a VolumePro 1000 board, these 25 volumes are sequentially volume-rendered in a little more than 1 second. As the frequency volumes change, the interpreter can also interactively modify the view orientation, color scale, and/or sculpted horizon to search for interesting frequency anomalies. Frequency increases from left to right and top to bottom, similar to reading a line of text.
An Age Volume is required in order to interactively view the spectral decomposition results as a function of relative geologic time. Figure 2 contains the Age Volume for this data set. This Age Volume was generated using an interactive three-dimensional instantaneous phase unwrapping technique. In an Age Volume every seismic sample in the region of interest contains a representation of relative geologic time. The color bar at the bottom illustrates geologic time increasing from left to right. A vertical cut through the Age Volume is a geologic cross section, while a horizontal cut represents a geologic map.

A series of screen captures (Figure 3) illustrates how the spectral decomposition volumes, Age Volume and Volume Pro 1000 board combine to interactively view changes in spectral content for a particular horizon. In Figure 3, starting in the upper left and going from left to right and top to bottom, each of the 25 sub images is a 4-Hz step through the spectral decomposition volumes. The Age Volume has been used to sculpt the data volumes to the same geologic horizon by making all samples younger than a specified age transparent. The purple line on the backside of each cube is used to gauge the frequency of the current volume. By utilizing the VolumePro board, it takes less than 2 seconds to cycle through these 25 volumes. The user can also interactively change the orientation, color table or desired sculpting age as the program cycles through the frequency volumes. Often the frequency changes occur too fast and have to be slowed down so that the user can fully appreciate the spatial variations in frequency.

The ColorStack Volume is another method of showing the thickness variations implied by the spectral decomposition results. With this method (Figures 4 and 5) three frequency components are stacked using color: red for low frequencies, green for mid frequencies and blue for high frequencies. As a result, red and yellow colors indicate thick beds, while blue and cyan indicate thin beds, with green being something in between. Again the Volume Pro 1000 board allows for this type of volume to be generated and interactively displayed with the proper volume rendering of the ColorStack colors.

Figure 4. The ColorStacked spectral decomposition (right hand column) provides significantly more geologic information in a single display than the standard seismic amplitude display (left hand column). The top row corresponds to the data displayed in Figure 1, while the bottom row corresponds to the data displayed in Figure 3. The middle row is a comparison of a single time slice shown in standard amplitude on the left and ColorStack amplitude on the right. To generated the ColorStack, the spectral decomposition volumes have been reconstituted into three spectral bands as per the red, green and blue boxes in Figure 1. These three volumes are then combined using gradational red, green and blue color scales for the low, mid and high frequencies, respectively.
In Figure 4 three different red-white-blue amplitude displays are compared with the ColorStack display method. At the top of this figure is a comparison of the data volumes. Note that with the ColorStack on the right, each event has a unique color and that this color should be useful in helping to correlate events across the faults. In the middle portion of the figure is a comparison of a single time slice. Note that there are two small channels in the ColorStack display. The color of these channels (one is green; the other is cyan) indicates that they have different internal bedding. These two channels are practically invisible on the standard time slice display. Finally, at the bottom the two volumes have been sculpted to the same horizon used for the data shown in Figure 3. This horizon corresponds to the time of the cyan channel in the middle display. The ColorStack figure contains a synthesis of the information presented in Figure 3. The red-yellow areas indicate large low- and mid-frequency contributions (i.e. thick beds), while the cyan areas represent large mid- and high-frequency contributions (i.e., thin beds).

Sculpting the data utilizing the Age Volume allows us to see the data samples that are older than a particular desired age, but it does not allow for the easy identification of the hiatus locations. The Age Volume has sufficient resolution to identify hiatus locations if it is used in a slightly different manner. When the Age Volume is used to convert the input data from two-way travel time to relative geologic time, the hiatus locations can be preserved as demonstrated by the gray colors in Figure 5. Figure 5 contains pairs of Wheeler Volumes utilizing a standard red-white-blue color scale on the left with the spectral decomposition ColorStack on the right. Gray in both displays represents the hiatus locations. The vertical axis of these volumes is relative geologic age.

The relative age of the top slice of the volumes increases down the page and then from left to right. These 6 images cover about 1.5 local wavelengths and are not at the age resolution available from either the Age Volume or spectral decomposition volumes. Note in particular how both the shape of the hiatus and the color in the ColorStack displays change with these small steps of relative geologic time.

Figure 5. Comparison of seismic amplitude and ColorStack Wheeler Volumes. The vertical axis in each sub-display is relative geologic time. The top slice of each of these cubes is progressively older in relative geologic time as you go further down each column pair. Geologic time increases first down the page in each column pair. These 6 relative geologic time slices cover about 1.5 seismic cycles. The gray represents hiatus locations. Note the temporal and spatial changes in color in the ColorStack displays — these represent local changes in bed thickness. See cover for additional Wheeler Volume displays.
These few images begin to illustrate the vast amount of geologic detailed information that can be seen when utilizing spectral decomposition. The ColorStack method is particularly powerful in displaying the thickness variations in a single image, although it lacks the frequency resolution available from the volume animation techniques. It is expected that similar results would be obtained utilizing other spectral decomposition methods. As yet it has not been possible to duplicate the ColorStack volume rendering or the Age Volume based interactive sculpting capabilities without utilizing the VolumePro 1000 board.

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