The age volume described in this paper can significantlyincrease the amount of useful geologic information extractedfrom a seismic data volume.

This paper has three goals. The first is to introduce anddescribe the relative geologic time volume, referred to herein aseither an RGT volume or an age volume. Every seismic sam-ple in an age volume contains an estimate of the relative geo-logic time for that sample, which automatically relates everysample to a geologic horizon. The second goal is to discusssome of the applications and advantages of using a RGT vol-ume to store and access seismic interpretation. For example,it can be used to sculpt a seismic volume along a desired hori-zon, or view depositional changes as a function of geologictime. The third goal is to describe two methods for generat-ing such a volume, the first employing standard interpreta-tion techniques, and the second relying on unwrappinginstantaneous phase. Unwrapping the instantaneous phase isa new, holistic approach to interpreting seismic data that canproduce a very detailed seismic interpretation.

Background. The goal of building and using an RGT volumeis to extract significantly more geologic information from theseismic data than is available from conventional methods.The RGT volume is both a way of storing and retrieving seis-mic horizons. To generate such a volume each seismic sam-ple needs to be assigned an estimate of relative geologic time,which in essence connects it to a geologically reasonable hori-zon. In “normal sections” these relative geologic time valueswill increase with depth (or traveltime). High gradients in theRGT volume could be indicative of faults, unconformities, fluidcontacts, or interpretation errors, while a constant value sur-face in a RGT volume is a seismic horizon.

Figure 1 contains a portion of the seismic data used to illus-trate the age volume and some applications. This particularvolume comprises 501 inlines by 501 crosslines with 200 4-mstime samples and covers about 100 km2. In the seismic cube,the data sample values oscillate around zero and are dis-played using a standard red-white-blue color scale. The dataare of fairly good quality with several apparently laterally con-tinuous reflections.

Figure 2 contains an age volume corresponding to theseismic data in Figure 1. The age volume has the same dimen-sions and coordinates as the seismic data volume, but insteadof seismic amplitude, each sample contains an estimate of rel-ative geologic time, determined using methods describedbelow. The volume is displayed using a rainbow color scalein which each hue becomes progressively darker with increas-ing relative geologic time. Just like the seismic amplitude vol-ume, the age volume contains significantly more resolutionthan can be represented by a color scale.

The phrase relative geologic time should be interpretedas: “If relative geologic time Ais greater than relative geologictime B, then the rocks of relative geologic time A weredeposited before rocks of relative geologic time B.” Thus,using this volume, we can tell if a data sample A is youngeror older or the same age as data sample B, but we cannot sayhow much older or younger A is than B until a calibrationstep is performed.

Any time slice taken from the age volume in Figure 2 willcontain a geologic map corresponding to that time. Similarly,

any inline or crossline display (faces on the cube) representsa geologic cross-section. Aconstant color represents essentiallya constant age. Therefore, areas on the time slice in Figure 2that have the same color will belong to the same horizon; thiscan be exploited using visual correlation between Figure 1 andFigure 2, or the applications discussed next.

Applications. In this section I will discuss three methods thatuse an RGT volume to help better understand the seismic vol-ume and identify stratigraphic features. All three methodsmake use of the fact that in an RGT volume a constant valuesurface is a constant relative geologic time and therefore a seis-mic horizon. Seismic amplitude along a surface of constantrelative geologic time is analogous to Henry Posamentier’s“proportional slice” or Hongliu Zeng’s “stratal slice” (Zenget al., 2001). I will use the term stratal slice. They have docu-mented the usefulness of these slices for identifying strati-graphic features.

In the first method the stratal slice and its associated struc-ture map are selected and updated using a spatial reference.This user-defined spatial reference point (i.e. inline, crossline,traveltime location) can be interactively changed several timesper second to obtain a stratal slice and structure map which

928 THE LEADING EDGE SEPTEMBER 2004

Relative geologic time (age) volumes—Relating every seismicsample to a geologically reasonable horizonTRACY J. STARK, Stark Reality, Plano, Texas, U.S.

Figure 1. 100 km2 seismic cube used to demonstrate RGT volume applica-tions. (Viewed from NE corner towards SW corner.)

Figure 2. A detailed RGT volume or age volume that corresponds to theseismic data in Figure 1. The colors denote geologic ages. Areas of thesame color are the same geologic age and therefore are part of the sameseismic horizon. This volume was generated by unwrapping the instanta-neous phase. (Viewed from NE corner towards SW corner.)

contains this point. The second method uses the RGT volumeto sculpt the seismic volume, such that all seismic samples thatare younger than a user-defined relative geologic time aremade transparent. The third method utilizes the RGT volumeto sculpt a formation out of the volume, in which all seismicsamples that are either younger than, or older than, a user-defined relative geologic time range are made transparent. Twoways of generating and displaying the sculpted volumes willbe discussed. One uses movie loops generated using con-ventional volume-rendering software, and the other uses a spe-cial volume-rendering graphics board.

Spatial referenced horizons. Figures 3 and 4 illustrate stratalsurfaces generated from the seismic and RGT volumes (shownin Figures 1 and 2) and passing through user-selected refer-ence positions. Each figure contains the following five displaywindows: inline, crossline, time slice, horizon structure and

horizon attribute (amplitude). The black X in these figures rep-resents the user-defined reference point that determines thecurrently displayed horizon. The relative age at the referencepoint is used to extract a surface from the age volume that isconnected to the reference point and is everywhere at sub-stantially the same relative geologic time. The structure of thisextracted surface is shown in the horizon structure display(each color band darkens downdip) and the seismic ampli-tude along this surface is shown in the horizon attribute(amplitude) display. As the interpreter repositions this pointon a seismic section, the displays are immediately updated tocorrespond to the relative geologic time surface that passesthrough the new reference position. The yellow box markedon both the inline and crossline displays indicates the region(i.e. subvolume) in which the high-resolution age volume isavailable, and thus, these stratal slices.

SEPTEMBER 2004 THE LEADING EDGE 929

Figure 3. The program shownin this screen capture uses thereference position X within theyellow box on an inline,crossline, or time slice to extracta constant age surface (i.e.horizon) from the RGT volume.The color-coded structure map(darker colors per hue aredowndip) and horizon attributedisplay are updated immediately(fraction of a second) after anew reference point is selected.Note that this particular horizon contains four-wayclosures. Furthermore, itsamplitude map is not a singlepolarity (contains both reds andblues) and contains severalstratigraphic features.

Figure 4. Similar display toFigure 3. The structure mapand horizon attribute map areapproximately 1/2 cycle belowthe event shown in Figure 3.Note this horizon is also dualpolarity. The meanderingstream channels have a slightlydifferent geometry compared tothe previous figure.

There are many advantages to this method. For instance,the interpreter does not need to remember a name to displaya horizon (although a name can be associated with a partic-ular relative geologic time). The relative geologic time of anexisting map can be either incremented or decremented toobtain a new surface in either a single frame or movie loopfashion. The relative geologic time increment between mapscan be very small, allowing several maps to be generated perseismic wavelet. These methods allow the interpreter to rapidlyscan through the volume perpendicular to the bedding planesto look for stratigraphic features of interest. Some features arevery hard to see if the data are not viewed at least approxi-mately parallel to the bedding.

The horizon in Figure 4 is approximately 1/2 cycle belowthat of Figure 3. By moving the reference point down one halfcycle, parts of the channel system are more visible, while otherportions disappear. Note that the stratal amplitudes are notall the same polarity—both horizons have some positive andsome negative values. Figure 3 has several strong red mean-dering stream channels and possibly a blue incised valley.

The structure maps indicate that the two structural highson the inline section are part of local four-way closures. Dueto the way the age volume is generated, an isopach betweenthe two horizons would show spatial variations in the bedthickness, since Figure 4 is not a simple static or proportionalshift of the horizon in Figure 3.

Volume sculpting. Figure 5 depicts a second way in whichthe age volume can be used to better understand the geologiccomplexities of the seismic cube. This figure contains fourframes of a movie clip. In each frame only the data samplesthat are older than a relative geologic time of interest havebeen displayed; all those younger than the time of interest havebeen rendered transparent. The small cube in the upper leftis the age volume; the larger cube is the seismic volume. Bothcubes have been stripped down to the same stratigraphiclevel. The relative geologic time of interest becomes progres-sively older with each frame of the movie.

This type of display allows the interpreter to see the stratalslices in their current structural position. Note that channelfeatures are visible in two of the four frames, and also that the

data along the fault plane are clearly visible.The last frame in this sequence (lower right) is at approx-

imately the same level (relative age) as the stratal slice inFigure 3, and the potential blue incised valley appears to runalong a present-day high. The relationship of this “blue event”and the structural high would be more apparent if the imageswere in stereo or could be animated. If a movie were gener-ated in stereo or such that the cube rotated slightly with eachframe, then viewing such a movie would better convey boththe stratal amplitude variations as well as the local structuralvariations.

Once generated, the movie can be viewed at several framesa second or it can be interactively scanned up and down ingeologic time to select a particular frame of interest. This issignificantly faster than the several minutes it takes to sculptand render the two volumes for each frame.

Instead of just generating the movie, the sculpted vol-umes can be studied using the regular volume-rendering tools,such as rotation, translation, zoom, clipping, opacity filtering,etc. It takes several seconds per volume to rerender a volumeof this size using standard rendering software on a standarddesk side workstation.

Figure 6 is similar to the last frame of Figure 5 (lower rightimage) but generated using prototype software, a special vol-ume rendering board, and a sculpting technique that is sig-nificantly different and faster than that used to generate theFigure 5 displays. (This sculpting and rendering only takes afraction of a second versus minutes.) This technique com-bines with the age volume and seismic volume to create a two-field voxel. The seismic data are used to control the color ofthe resultant display while the age data are used to controlthe opacity. In this case, all voxels less than age A are trans-parent while all voxels greater than age B are opaque. A lin-ear opacity function is used for the few age values that fallbetween A and B. This transition in the opacity curve allowsfor a range of relative geologic time voxels to be seen at onceon the top of the sculpted volume. Asimple change in the opac-ity curve produces a new sculpted volume in just a fractionof a second. The user interactively manipulates the opacityfunction to achieve the desired cut surface. The view can then

930 THE LEADING EDGE SEPTEMBER 2004

Figure 5. Selectedframes from a volumesculpting movie. The agevolume (upper left ofeach frame) is used tostrip away the youngersediments. The resultingstratal slices are shownin their current struc-tural position. Once themovie is generated it canbe used to study how thestructure and deposi-tional patterns change asa function of relativegeologic time. Eachframe took minutes tosculpt, render, and thencomposite the imagesfrom the two differentvolumes.

be rotated, zoomed, and translated to the desired viewinglocation. This approximately real-time volume sculpting isa significant improvement over the method used to gener-ate the images for the movie loop, but requires a specialgraphics board.

Whichever method is used, being able to see the stratalslices in their current structural position improves the qual-ity of the interpretation. After all, the real interpretationwork is not in creating these images, but in unraveling whatimages such as these tell us about the depositional andstructural environment and how that environment changedwith geologic time.

Formation sculpting. Figure 7 represents a third way ofusing the age volume. Only the seismic data found withina limited relative geologic time range are visible. All othertimes are transparent. The opacity of the visible data couldalso be modified to show a selected range of amplitudes ifdesired, such as the large positive and negative values.

Either the movie loop or interactive program can beused to formation-sculpt the volume to just a narrow rangeof relative geologic time using techniques similar to thosejust described. Once the desired geologic time slab is found,the volume can be rotated, translated, and zoomed to findthe proper viewing location.

The special graphics board can take advantage of the factthat most of the data are not being rendered in order to sig-nificantly increase the frame rate. Alternatively, a larger for-mation sculpted volume can be rendered at about the sameframe rate.

Age volume generation. In this section I will discuss twoways of generating an RGT volume. The first method usesinterpolation and standard horizon interpretation techniquesto store the interpretation in an RGT volume. The secondmethod generates an RGT volume by unwrapping theinstantaneous phase.

Interpolation method. The interpolation method of gen-erating an RGT volume uses standard horizon interpreta-tion techniques. Each interpreted horizon is assigned aconstant age value, or in the case of unconformities, spa-tially varying relative age values. The only constraint is thatthese values follow the law of superposition. (If available,actual geologic time values can be used.) The RGT volumeis then populated by interpolating age values between thepicked horizons. The resultant RGT volume has the samedimensions as the seismic data, but each sample containsan estimate of relative geologic time. This method is faster(given the interpreted horizons) but not as detailed as thephase unwrapping method described next.

Unwrapping instantaneous phase. This is a new, holisticapproach to performing seismic interpretation that is par-ticularly suited for generating an RGT volume. Both RGTvolume generation methods generally make the sameassumptions; however, phase unwrapping creates an RGTvolume with significantly more detail than is obtained fromthe interpolation method.

Phase unwrapping involves adding integer multiples of2π to the phase in order to reduce the number of disconti-nuities in the resultant sum (unwrapped phase). It is not anew concept for the geophysical industry; the syntheticaperture radar (SAR) literature contains many 2D phaseunwrapping techniques. However, to the best of my knowl-edge, I am the first to apply phase unwrapping to instan-taneous phase in order to generate a detailed seismicinterpretation.

The concept of unwrapping instantaneous phase to gen-erate an RGT volume will be illustrated using the syntheticdata shown in Figures 8 and 9. Figure 8 contains the inputand output of unwrapping a single trace while Figure 9 con-tains the section from which this trace was taken.

Referring to Figure 8, the instantaneous phase (yellowline) is generated from the seismic trace (cyan line). Theinstantaneous phase is a cyclic function that wraps, just likeFourier phase and SAR phase, at ±π. But unlike Fourierphase and SAR phase, the instantaneous phase will (or, byflipping its polarity, can be made to) generally increase withtraveltime except for where it wraps.

The cycle number trace (blue step-function line) repre-sents the number of times the instantaneous phase haswrapped. It will normally always increase with traveltime.Notice that every time the instantaneous phase wraps from+π to -π, the cycle number increments by at least one (2π) unit.In general, every time the instantaneous phase decreases, thecycle number is incremented by at least one. There is one loca-tion where there is a local decrease in instantaneous phase,

SEPTEMBER 2004 THE LEADING EDGE 931

Figure 6. Volume-sculpted image generated with a program that takesadvantage of special features of the VolumePro 1000 board. The sculptingis accomplished by modifying the opacity table. As a result, the sculpt agecan be changed interactively with the mouse and the image updated several times per second.

Figure 7. Formation-sculpting of data shown in Figure 6. Only thoseseismic samples that fall within a narrow age range are displayed. Sinceonly a small fraction of the entire data volume are visible, special featuresof the VolumePro 1000 board allow this display to be updated signifi-cantly more times per second than the Figure 6 display.

but not a full +π to -π change in phase. The cycle number stillincrements, and this is said to be a local unconformity. In thecenter of the figure an unconformity is denoted and the cyclenumber experiences a large step. The entire 2D section isrequired to determine the size of this step. If a shorter line seg-ment had been used, the step might have been smaller, andif a longer line segment had been used, the step might havebeen larger—hence it is relative geologic time.

The relative geologic time (red line) equals the unwrappedinstantaneous phase, which equals the instantaneous phaseplus 2π times the cycle number. The relative geologic time isa locally smooth function, with discontinuities that corre-spond to unconformities and faults. It should always (in nor-mal sections) increase with traveltime. Negative verticalgradients are normally indicative of errors in the phaseunwrapping or interpretation. If the spatial derivative anom-alies do not make geologic sense, they are indicating unwrap-ping or interpretation errors.

I should note that not all cycle boundary locations areaccompanied by a negative vertical instantaneous phase gra-dient. Finding and properly connecting these locations in 3Dis the key to proper phase unwrapping, but detailed discus-

sion of this topic is outside the scope of this paper. (Note: Ihave submitted a paper to GEOPHYSICS which contains addi-tional details on instantaneous phase unwrapping.)

Figure 9 summarizes the unwrapping for a single seismicsection. The seismic section in the upper left is used to gen-erate the instantaneous phase in the upper right. The instan-taneous phase is used to generate the cycle boundaries andvalues shown in the lower left. Each color in this display rep-resents an integer multiple of 2π. The instantaneous phase andcycle values are combined to create the unwrapped phaseshown in the lower right. The unwrapped phase is propor-tional to relative geologic time, and a constant value ofunwrapped phase is a seismic horizon. High gradient valuesof the unwrapped phase are indicative of faults and uncon-formities.

Conclusions. There are several advantages to generating anRGT volume. For instance, horizons can be retrieved usingspatial referencing. There is no need to look up a name in alist—simply touch a point on a section to display the relativegeologic time surface that contains that point. It facilitatesinteractively slicing through a volume as a function of rela-tive geologic time or animating an isopach as a function ofrelative geologic time. Additional volumes can be generatedfrom the RGT volume; for example, calculating its temporaland spatial derivatives provides a quality measure along withfaults and unconformities. Alternately, since every time sam-ple is connected to a horizon, a closure volume can be gener-ated to provide a detailed evaluation of the survey area’s trappotential. Such a volume could indicate whether or not a sam-ple is part of a closure, and some attributes of the closure. TheRGT volume allows for new, holistic ways of interpreting ourdata, such as unwrapping the instantaneous phase. This newtechnique essentially generates all horizons at once. The endresult is a complete and consistent interpretation that cannoteasily be obtained by working on just one reflection at a time.

Truly, the relative geologic time volume is a starting pointfor obtaining a fully interpreted seismic cube.

Suggested reading. “Unwrapping instantaneous phase to gen-erate a relative geologic time volume” by Stark (SEG 2003 ExpandedAbstracts). “Using a Relative Geologic Time Volume to identifystratigraphic features” by Stark (AAPG 2004 Abstracts). Two-Dimensional Phase Unwrapping: Theory, Algorithms, and Software byGhiglia and Pritt (John Wiley, 1988). “Stratal slicing, Part II: Real3D seismic data” by Zeng et al. (GEOPHYSICS, 1998). “Stratal slic-ing of Miocene-Pliocene sediments in Vermilion Block 50-TigerShoal Area, offshore Louisiana” by Zeng et al. (TLE, 2001). “Systemfor utilizing geologic time volumes” by Stark (2004, U.S Patent 6708 118). “System for multidimensional data analysis” by Stark(U.S. Patent application 20 030 018 436, 2003) and “System forinformation extraction from geologic time volumes” by Stark(U.S. Patent application 20 030 023 383, 2003). TLE

Acknowledgments: I thank those who have supported me in this endeavor.Santos and the South West Queensland Unit Joint Venture (Santos, Delhiand Origin) provided the 3D seismic data. Wulf Massell suggested I use thephrase “relative geologic age” in addition to “relative geologic time” to avoid“traveltime confusion.” Landmark Graphics, Paradigm Geophysical, SiliconGraphics, Sun Microsystems, and TeraRecon each contributed to the eclec-tic mix of hardware and software I used in this paper. I am especially thank-ful to TeraRecon for access to their Volume Pro 1000 graphics board. Thework on this paper was sponsored by STARK Research.

Corresponding author: tstark3@attglobal.net

932 THE LEADING EDGE SEPTEMBER 2004

Figure 8. Phase unwrapping results of a single trace taken from the mid-dle of the 2D section. The instantaneous phase is generated from theseismic trace. The “cycle number” trace steps every time the local instan-taneous phase gradient is negative. The size of the step is determined bythe data of the entire line. The “unwrapped phase” equals “relative geo-logic time” and is the combination of the instantaneous phase and thecycle number.

Figure 9. Input and output sections of instantaneous phase unwrapping.The seismic data are in the upper left, followed by the instantaneous phasein the upper right. The cycle numbers in the lower left are derived fromthe instantaneous phase. Cycle number boundaries occur everywhere thelocal instantaneous phase gradient is negative as well as a few other loca-tions that are required to generate a geologically consistent result. Theunwrapped phase (or relative geologic time) is in the lower right. It is thecombination of the cycle number and instantaneous phase.