Zeng Etal 1998 Part1

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GEOPHYSICS, VOL. 63, NO.2 (MARCH-APRIL 1998); P. 502-513,11 FIGS., 2 TABLES.

Stratal slicing, Part I: Realistic 3-D seism ic mod el

Hongliu Zeng*, M ilo M. B ackus, Kenneth T. Barrow * * ,and Noel Tyler§

ABSTRACT

Two-dimen sional, fenced 2-D, and 3-D isosurface dis-

plays of some real is tic 3-D seismic m odels bui l t in thel ower Miocene Pow derhorn F ie ld , Ca lhoun County ,Texas , dem onstra te that a se ismic event does not nec-essarily follow an im pedance bounda ry defined by a ge-ological time su rface. Instead, the position of a filteredimpedance boundary relative to the geological t ime sur-face may vary w ith seismic frequency becaus e of inade-quate resolut ion of seismic data and to the en echelonor ramp arrangem ent of impedan ce anom alies of sand-s tone. Except for som e re la t ively t ime-paral le l se ismicevents, the corre la tion error of even t picking is la rgeenough to d is tor t or even miss the m ajor ity of the tar -get zone o n stratal slices. In som e cases, reflections from

sandstone bod ies in different deposit ional units interfereto form a single even t and, in one instance, an event ty-ing as man y as six deposit ional units (interbedded sandyand shaly layers) over 50 m w as observed. Frequency in-dependence is a necessary condit ion for se lecting t ime-parallel reference events. Instead of event picking, phan-tom m apping between such reference events is a bet tertechnique for p icking s t ra ta l s l ices , making i t poss ib leto m ap deta i led deposi t ional fac ies with in reservoir se-quences routinely and reliably from 3-D seismic data.

INTRODUCTION

Currently there are two approaches to m aking a stratal slice:hand picking and computer auto-tracking. When hand picking,an interpreter tracks a seismic event from line to line, mappinga surface around c losed loops . When auto-t racking , the com-puter picks a seismic event based o n cri teria such as semblance,

crosscorrelation, or amplitude extremes (peak or trough). Bothevent picking approaches tend to generate stratal slices withoutpolarity reversals, with all amplitudes being pos it ive (peak) ornegative (trough), except where picking cannot be conducted.

Flattening the data volume a gains t a reference reflect ion andthen s l ic ing horizonta l ly through the f la t tened vo lume at thelevel of in terest is considered to be s im ilar to auto- tracking(Brown, 1992a), a l though i t may cause the am plitude imagesto have polari ty reversals . Som e of the m ost s t r iking image sof deposit ional facies on stratal slices have been m ade by thisapproach (Brow n et al. , 1981; Brow n, 1992a,b; Hardage et al. ,1994).

W hatever method is used, the underlying assum ption is sim-ple: se ismic reflect ions from w ith in a deposi t ional sequenceshould be gene rated along stratal sur faces that are lateral lycontinuous and have significant acoustic impedance co ntrasts.Because stratal surfaces are assumed to be relict depositional

surfaces or bedding planes that are formed alm ost instanta-neously (in geologic terms), those reflections are then assum edto be chronostratigraphically m eaningful. This assum ption hasdominated the ge ological interpretation of seismic data for thelast three decad es. Vail et al . (1977) suggested "no physical sur-face that could ge nerate a reflec tion parallel with the top of at ime-transgressive fo rmation (lithostratigraphic unit) exists innature."

There a re two a spec ts o f the a ssumpt ion tha t need to beexplored. Firs t, a re the s t ra ta l surfaces gene ral ly cont inuouslaterally and do they have significant acoustic impedance con -trast? Tipper (1993) ra ised this issue and de signed an "u n-s teady sed imenta t ion" m ode l i n w hich s t r a ta l su r faces a reacoustically invisible except in a transit ion zone where the lat-

eral changes of l i thofacies are s ignif icant . We tend to agreewi th Vai l e t a l . (1977) becau se the ev id en ce f ro m o u tc ro psstrongly suggests that the lithologically and acoustically layeredmo del is a correct characterization for mos t, if not all , deposi-t ional sequence s. Second, do the stratal surfaces thus defined

Manuscript received by the Editor May 22, 1996; revised manuscript received May 2, 1997.* F o r m e r l y Texaco Inc., 4800 Fournace Place, Bellaire, TX 774 0 1 -2 32 4 ; presently Bureau of Economic G eology, The University of Texas at A ustin,10100 Burnet Rd., Bldg. 130, Austin, TX 7875 8-4 4 9 7 . E-mail: zengh@ begv.beg.utexas.edu.$Milo M. Backus, Department of G eological Sciences, The University of Texas at A ustin, Austin, TX 78712. E-mail: backus@ maestro.geo.utexas.edu.* * * K e n n e t h T . B a r r o w , F o r m e r l y B u r e a u o f E c o n o m i c G e o l o g y , T h e U n i v e r si ty o f T e x a s a t A u s t in , U n i v e r s it y S t a ti o n , B o x X , A u s t i n , TX 78713-7508;presently Simtech Consulting Services, 35 0 Indiana Street, Ste. 500, Golden, CO 70401.

§N oel Tyler, Bureau of Economic G eology, The University of Texas at A ustin, U niversity Station, Box X, Austin, TX 78713-7508.© 1998 Society of Exploration Geophysicists. All rights reserved.

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Stratal Slicing: 3-D Model 503

necessarily produce t ime-parallel seismic events? If not, whatis the appropria te way to m ap a s t ra ta l surface from seism icdata? This is the major concern of our paper.

C O N S T R U C T I N G A R E A L I ST I C M O D E L

3-D seismic m odeling is an inexpensive and effective way tos tudy the problem at hand. Yet from o ur experience, a s tan-da rd concep tua l mode l in wh ich one o r m ore m ode l p rop e r-

t ies (thickness, porosity, velocity, etc.) are assum ed to be con-s tant cannot suff ic ient ly describe a ge ological ly com plicatedsystem, causing the results to be inconclusive. Therefore, w efirst need a realist ic 3-D stratal model that is geologically rea-sonable and ha s similar stratal complexity to real deposit ionalsequences. W ith all stratal surfaces and impedance bou ndariesbeing known, we can then generate an idealized 3-D syntheticseismic m odel and analyze the relationship between strata! sur-faces and seismic events.

Such a real is t ic 3-D s t ra ta! model has been crea ted by de-scribing depositional facies with reservoir and aco ustic prop-erties from more than 110 w ells covering a 250-m section overan area of 13 x 9 km in Pow derhorn Fie ld, Calhoun Coun ty ,

Texas. A ll rock properties are spatially variable, matched withthe interpretation of deposit ional facies. The m ultilayered m e-dia were conden sed from a real stack of 14 sandy deposit ionalunits and 15 interbedded shale uni ts . The con volut ion of th ismo d el w i th a wave le t p ro d u ced a 3 -D m igra ted se i smic r e -sponse (Figure 1) . A detai led descr ipt ion of the mode l con-struction can be found in Zeng (1994) and Zeng et al. (1996).W hat follows are som e basic characteristics of these models.

(1 ) The m odels are based on a genet ic s t ra tigraphic fram e-work consisted of deposit ional units and deposit ional sur-faces or bedd ing p lanes . Facies m apping f i ts to currentknowledge of deposi t ional sys tem s and facies arch itec-ture , incorporat ing a l l s ignif icant sandstone t rends and

facies patterns as mapped by a geo logist .(2 ) The m odels were c onstructed with a s t ra ta l complexity

similar to real geology at reservoir (between-w ell) scale,and al l the rock proper t ies descr ibed for ea ch layer inthe mo d els w ere co n s t r a in ed by wir e l in e lo gs an d a r edistributions rather than constants.

FIG. 1. 3 -D synthetic seismic volume of the Powderhorn m odel,constructed with a 40-Hz Ricker wavelet.

(3) The modeled sandstone thickness (1-37 m, average 8 m)and reflection coefficient on the top of sand stones (-0.25to +0.25, average +0.035) are typical in Tert iary sand-stone-sha le sequences in the G ulf Coast a rea .

A lthough these models are real is t ic only to a macroscopic ,or we ll-to-well, scale, they are suitable for the study of m od-ern 3-D seismic methods . In h igh-frequency cases (dominant

frequency 60 H z or higher in G ulf Coast), omitt ing lamination-scale or smaller bedding surfaces will lead to a layered mediain which the thickness of mo st layers is larger than the tuningth ickness . As a resul t , the top and bot tom of m ost layers canapparently be resolved by seismic reflection, creating a less re-al is tic s i tuat ion. How ever, most mo dern se ismic data have adominant f requency much lower than this (usua l ly 15-40 Hz) .A finer layered model is not necessary.

O B S E R V A T IO N S O N T H E T IM E T R A N S G R E S S IO N O FSEISMIC EVEN T S

In the following discussions, a seismic event is recogn ized asa peak or t rough, or a c ol lection of la tera lly cont inuous se is -mic reflection s ignals characterized by s imilar waveform andpolarity. For seismic interpreters, the seismic event is actually asynonym of the seismic reflection because it is very difficult, ifnot impossible, to recognize a polarity reversal on the sam e re-flection surface without a very special reason (e.g., a gas/watercontact). Connected amplitude anomalies with obvious stair-l ike am plitude shapes, how ever, are m ore l ikely generated fromdifferent reflection surfac es, and therefore w ill not be treatedas a seismic event .

Single 2-D section

The section in Figure 2 is sliced in the dip direction o f themo del (A A ' in Figure 1) . The im pedance d is tr ibution of the

sect ion (Figure 2a) show s that al l o f the s tratal sur faces areimpedan ce boundaries . There are no faul ts , uncon form it ies ,onlaps , or off laps . Two seismic sect ions (Figures 2b ,c) weregenerated f rom this impedanc e sect ion . A seismic event in-terpreted visually is a function of wavelet frequency. W hen thewavele t f requency is high (80-Hz R icker, Figures 2b) , a lmostall seismic events follow the bound aries of the layers. Seismicevents become th icker, reorganized, and reduc ed in numbe rwhen the frequency is lower (25-Hz R icker, Figures 2c). Someof the low-freque ncy events can stil l be t ime parallel , roughlyfo llowing som e imped ance bou ndar ies (e.g . , events aa ' , ee ',and gg'). However, unless known geologic constraints (in thiscase, depositional surfaces) exist, there may be a tenden cy topick some time -transgressive events that pass through stratalsurfaces (e vents cc ' , dd ' , and f f ' ) . The t ime transg ression inevent cc ' has a m agni tude of 35 m s of two-way t ravel t ime (or50 m) and straddles six deposit ional units. Compared with theimpedance sect ion (Figure 2a) , event cc ' (Figure 2c) fol lowsa series of three en echelon lent icular channel sandstone s ofhigher impedance an d cuts across the boundar ies of severaldeposit ional units . Other deviat ions of seism ic events f romgeologic bou ndar ies , such as eve nts dd ' and f f ', can also beobserved.

The ramp pattern observed on a strike section (BB in

Figure 1) also exhibits time transgression (Figure 3). Similarto the section in Figure 2, seism ic events follow the boundaries




504 Zeng et al.

FIG. 2 . A d ip sec t io n A A ' sho win g the t ime t r an sgress io n o f se i smic even ts r espo n d in g to en ec he lo n l i tho fac ies pa t te rn . ( a )Impedance sect ion, with sands general ly h igher in impedan ce over surrou nding shales ; (b) 80-Hz R icker synthet ic sect ion, withalmost all the seismic events following the deposit ional surfaces; (c) 25-Hz Ricker synthetic section showing t ime-parallel eventsaa' , ee ', and gg ' , and t ime-transgressive even ts cc ' , dd', and ff ' . See Figure 1 for location.





F I G . 3. A strike section BB' showing the t ime transgression of seismic events responding to a ram p lithofacies pattern. (a) Impedancesect ion, with sands general ly h igher in impedanc e over surroun ding shales ; (b) 80-Hz R icker synthet ic section, with the se ismicevents following the deposit ional surfaces; (c) 25-Hz Ricker synthetic section showing t ime-transgressive event dd' . See Figure 1for location.




50 6 Zeng et al .

of the layers when the wa velet frequency is high (80-Hz R icker,Figure 3b), but some of them appear to have the characteris -t ics of a t ime-t ransgress ive pat tern when the frequen cy is re-duced (25-Hz Ricker, Figure 3c). Without necessary geologicconstra ints , event dd ' fol lows the top o f three s tep l ike sand -stone bodies (wave-dom inated delta and barrier bar sands) thatform a ram p and are characterized by similar high impedances(Figure 3a). The shale beds among these sandstones yield no

s ignif icant ref lect ion s ignal because they are se ismical ly toothin relative to a 25-Hz w avelet. Again, the seismic event cutsacross deposi t ional surfaces . The t ime t ransgress ion in eventdd ' has a magni tude of about 30 ms of two-way t rave l time (or45 m) .

Other examples of frequency-dependent t ime transgressionare present on other 2-D sections sliced from the seismic mod-els created with different wavelet bandw idths . In each case ,se ismic events tend to fol low fi l tered imped ance boun dariesother than the physically defined stratal surfaces. The stratalsurfaces are the correct impedance boundaries only w hen thewavelet has an inf in ite bandwidth. However , the model f i l -ter (wavelet) change s with f requency an d so do the f i lteredimpedance boundaries. The filter effect may easily mask actual

geologic changes (as i l lustrated in Figures 2 and 3) to make aninterpretation nonunique without known geologic constraints.G eologically, seismic t ime transgressions are possible wherever

shales are interbedded w ith sandstones to create significant lat-eral variat ions of l i thology and im pedance corresponding to thechanges in depositional environment (e.g., from fluvial chan-nel to floodplain, from barrier bar to lagoon , or from turbiditechannel to overbank deposits).

Fenced 2 -D sections

Four sect ions are taken f rom the s ides of the 3-D seismicmo de l to mimic a co r re l a t ion gr id o f 2 -D se i smic sec t ions(Figure 4). The impedance sections (Figure 4a) shows that allmodeled s t ra ta l boundaries are c losed and rou ghly paralle l toeach other. On the se ismic sect ions , the negat ive am plitudeshave been rem oved to s imulate se ismic events corre la ted onreal seismic sections (Figures 4b,c). Seismic frequencies (30-and 40-H z R icker) are selected so that a typical f requency-dependent t ime transgression is apparent. Three different t imetransgressive behaviors are identified by tracking these seismicevents.

Closed event that follows a geologic time surface. —For someevents in Figures 4b and 4 c (indicated by the arrows), if you start

corre la t ing from one point , you w il l re turn to that point aftertracking the loop. These events satisfy the "rules of closure"that have governed seismic data interpretation for m any years.

FIG. 4 . Fenced sec t ions show ing looped co r re l a ti ons o f se i smic even ts , bo th t ime pa ra l l e l and t ime t r ansgre ss ive . (a ) Im -pedance se ct ions ; (b) pos it ive ampli tude f i ltered from 30-H z R icker synthetic data ; (c) pos i tive ampli tude f i l tered from 4 0-HzRicker synthetic data.





A lso, these events are essentially parallel to stratal surfacesand therefore follow geologic time surfaces.

Closed event that d oes not follow a geologic time surface.—

One event in Figure 4b (indicated by the open triangles) alsosatisfies the "rules of closure" but is not parallel to stratal sur-faces and does no t follow geologic timelines. R eferring to theimpedanc e sections (Figure 4a), this event follows the top of

several sandstones from three different sandy units that areseparated by two thin shale units, instead of following the topof one single sandstone as is comm only supposed. Later we w illshow that such an event m ay lead to an erroneous interpreta-tion of depositional environments.

Unclosed event that does not follow a geologic time sur-

face.—A m ore difficult situation occurs in the case of the eventidentified by the shade d triangles in Figure 4c . This feature is

neither closed n or time para llel . If the event is started at theintersection of sections I and IV, the picks do not close at thestarting point. Referring to the impedance sections (Figure 4a),this event first follows the top of a sheetlike sandstone (sectionsI and II), then crosses the tops of tw o en echelon san dstones(sections III and IV). Even w ithout the knowledge of the truestratal structure, such an unclosed loop must be time transgres-sive. This observation, made from a realistic geological model,

helps explain why the "rules of closure" are often not satisfiedfor many real seismic events.

3 -D isosurface display

A comm on hypothesis amo ng interpreters is that the correla-tion on a single 2-D section or on fenced 2-D sections is subjectto subjective interpretation of seism ic events, and that a 3-Disosurface display is superior for correlation. A 3-D isosurfacedisplay (Figure 5) was filtered from the 30-Hz Ricker synthetic

FIG. 5. Three-dimensional isosurface display filtered from 30-Hz R icker synthetic data volume. Events aa' , bb', and ee' are judgedtime parallel; events cc ' , dd', ff , and gg ' are time transgressive.




508 Zeng et al.

seismic data volume, and a l l of the negat ive am plitudes wereremoved so that one can see into the model and view the corre-lat ion framew ork of seismic events. A mon g seven selected seis-mic even ts, three are approxim ately time pa rallel (events aa',bb', and ee'). Event dd' (same event as dd' in Figures 2c and 3c)is t ime transgressive, crossing three sandy units and two shaleunits , and has a m aximum total thickness of approximately50 m (35 m s). Events ff and gg ' appear to be t ime paral le l in

three direct ions (sides II ,1I1, and IV) but are t ime transgressivewhen viewed from the fourth direction (side I). The t ime trans-gess ion in the fourth direct ion is characterized by the m ergeof the two even ts. The t ime-transgressive nature of event cc ' isnot straightforward in this display, but becomes clear if viewedf rom a d if ferent angle (not show n) . I t is evident that in themod el a seismic event tends to follow an impedance bo undarycom prised of many sm all , discontinuous surfaces that are strati-graphically close, but different, deposit ional surfaces with sig-nificant impedance contrasts. The result ing seismic event doesnot necessarily coincide with any single de posit ional surface.

It should be pointed o ut that the correlat ion of ref lect ionevents using 3-D seismic data produces a stratigraphic frame-work that has m inimum of t ime-transgressively interpreted sur-

faces. In a regional 3-D correlation, an interpreter does not paygreat a t tention to patchy events between two main reflect ionsurfaces or local fade out of an event, which are often m islead-ing when tracking an event on a 2-D section.

CONDITIONS AND MAGNITUDES OF TIME

TRANSGRESSION

From the observat ions above, the fol lowing condit ions areresponsible for t ime transgression of a seismic event:

Condition 1: Inadequate seismic resolution for a given de-

positional seq uence.—Whe n a layer is too thin, the reflectionsfrom the top and base of the layer will not be resolved in termsof peak-to-trough separation (R ayleigh's criterion, Jenkins andWhite, 1957; Kallweit and W ood, 1982). Instead, the two reflec-t ions interfere with each other to form a single reflection. Thisbehavior is true also in the case of the interbedded thin sand -stones and shales, where on ly the total net sandstones in a thin-bed interval can be measured as an am plitude varia tion, eventhough bedding planes between sandstone and shale canno t bedetected (Meckel and N ath , 1977; Neidel l and Poggiagl iolmi,1977; Schram m et al . , 1977). Multiple de posit ional surfaces areimaged in low er frequency data by fewer se ismic events thatusually follow the layers having the strongest reflect ion energy.In other words , a model of interbedded h igh-impedance an d

low-impeda nce layers is enough to produce t ime-transgressiveseismic ev ents. Special deposit ional history like the "unsteadysedim entation" in which the stratal surfaces are visible acous-tically only in a transit ion zone (T ipper, 1993) is not necessaryto produce t ime transgression of seism ic reflections.

Condition 2: Indented stack of thickness or impedanceanomalies.—For a group o f laterally continuous and internallyhomogeneous sandstones and shales, seismic events should bet ime paral le l , even when co ndit ion 1 exis ts. How ever, an in-dented s tack of th ickness or impedan ce anom alies can createa ref lect ion event that is comprised of d if ferent segme nts of

reflections from different deposit ional surfaces. We have rec-ognized two geological ly mean ingful indented pat terns fromour Powderhorn model : en eche lon and ramp. The en eche lonpat tern can be observed in ma ny deposi t ional environm entsbecause the on ly condit ion necessary for i t s existence is thesingle-directional migration of similar-size lithofacies causedby channel evulsion, accretion, progradation, or transgression.The ramp pattern differs in that in addition to the single-

directional m igration of lithofacies, the size of the lithofaciesalso increases or decreases w ith geologic t ime. A lthough beingable to develop in m any depo si t ional se t t ings , the ram p pat-tern may be found m ore f requently in environmen ts relatedto progradat ional or t ransgress ive processes , such as f luvia l-dominated deltas, progradational barrier/lagoon systems, andtransgressive beach ridges and barrier bars.

Figure 6 plo ts the magnitude of t ime transgression for al ltraceable seismic events in all west-east and north-south sec-t ions of the 30-Hz R icker synthetic seismic volum e. Displayedas the maximu m e rror of a hand-picked event re la t ive to thenearest time line, the distribution of time tran sgression of thismode l h as a m in imum va lue o f ze ro , an ob se rved max imumvalue of 37 ms (55.5 m), a peak value of 3 ms (4.5 m), and an av-

erage value of 8.4 m s (12.5 m). R egardless of the risk of trackingseverely t ime-transgressive events (right tai l) , for 30-Hz data inour limited study area Vail et al.'s (1977) assumption about thechronostratigraphic meaning of seismic events is correct whenthe seismic sequences are much thicker than the mean plus ones tandard deviation (STD) of the dis t r ibut ion, 14 .6 m s (22 m ).Considering that the average width of a seismic event (peak ortrough) in this mode l is 13 ms, a seismic sequence should be atleast five events (three peaks plus two troughs, or three troughsplus two peaks) thick to keep the correlation error below 25% .For th inner se ismic sequen ces , especia l ly a s ing le sandstoneless than 22 m thick, however, the risk of severely distorting oreven missing m ost of the target sandstone will greatly increase,

and V ail et al.'s (1977) assumption w ould not be applicable.

Thickness (m)

0 6 12 18 24 30 36 42 48 54 60

0 4 8 12 16.20 24 28 32 36 40

Two-way traveltime (ms)

FIG. 6. Magnitude of t ime t ransgress ion of 30-Hz R icker syn-thet ic seismic model, co llected f rom all correlat ive seismiceven ts fo r a l l sandy un i t s i n a l l nor th-sou th and we s t -ea s tsections.

350

300

250

C 200

a

Q 150u _

100

50





This result , however, seems to have u nderestimated the t imet ransgression of seismic events . The de posit ional facies de-sc r ibed by the Po wd erho rn m o d el , a m icro tid a l sho re zo n esystem, is less dramatic in facies variations com pared to man ydeposit ional environments, for example fluvial and submarinefan sys tems. The l imited s tudy area is not com parable to thes ize of m ost deposi t ional bas ins . The smo othed nature of thegeologic m odel, restricted by w ell spacing, prevented Figure 6

from including the effect of the t ime t ransgress ion caused bysmall-scale ( laminat ion or sm aller) fac ies changes . As shownin the companion paper, m ore serious t ime-transgression is ex-pected in real seismic data.

WR ONG FACIES PATTERN FROM A

TIME - TRANSGRESSIVE EVENT

A se ismic even t can have d i f f e r en t mea n in gs , d epen d in gon i ts synchronous or asynchronous nature. The geologicalin terpretation of a s trata] s l ice c annot be correct i f the s l icedoes not fol low a s t ra ta l surface . As an example , sandy units3, 3A 1, and 3A 2 (Figures 7a ,c ,e) are separated by two shaleunits . The sandstones in the sandy units are th ick (10-25 m )

co mpared w i th the sha le u n i ts (0 -19 m) an d a r e am o n g thecleaner sandstones in the sequence. U nit 3 is part of a w ave-dom inated delta (Figure 7a) . A large, d ip-elongate d is tr ibu-tary channel occurs in a broad upper del ta p la in; i ts dow ndippart cuts into the strike-elongate strandplain sandstones . Un its3A 1 and 3A 2 (Figures 7c,e) both contain deposits of a bar-r ier bar/lagoon sys tem. The sys tem w as framed by the mas-s ive , s trongly s t r ike-oriented barr ier core san dstones , whichwere transected by t idal- in let sands and w ere f lanked land-ward by back barrier deposits comprising flood-tidal deltas andwashover fans (Figures 7c ,e ) and somet imes seaward by ebb-t idal deltas (Figure 7e). The back barrier/lagoon transition inunit 3A1 introduces a major shaly sandstone/shale lithofacies

change that creates a d is t inct indented pat tern together w ithth e unde r lying more con t inuous s ands tones o f un i t 3A 2 andoverly ing s t randplain and dis t r ibutary channel sandstones o funit 3, which favors the t ime transgression of seismic event.

The idealized strata] slices, or the slices following the ex acttops of each of the three units, were generated from a 30-HzRicker data cube (Figures 7b,d,f). These slices can also be inter-preted, at least in part, in terms of depo sitional facies . The posi-t ive high amplitude zones in Figure 7b almost duplicate the dis-tributions of distributary channel and strandplain sandstones inunit 3. Part of the flood-tidal delta and inlet sandstones at un it3A 1 are highlighted by strong, posit ive amplitudes (Figure 7d);but the clean barrier-core sandstone produces negative ampli-tudes similar to lagoonal shale. U nit 3A2 is characterized by the

widespread clean barrier-core sandstones having moderate- tolow-am pli tudes t ransected by h igh-ampli tude zo nes of shalyflood-t idal delta sand stones (Figure 7f). The t idal inlet and ebb-t idal delta are hard to delineate because their thicknesses andimpedances are similar to those of the surrounding lithofacies.Compared to unit 3, the images of units 3A1 an d 3A 2 have beenconsiderably altered by uneven interference from im mediatelyoverlying and underlying heterogeneous sandstones. For thesetwo stratal levels, the interpretation is not straightforward onseismic data.

Event dd' (Figure 5) connects the strong reflections from allthree sandy units and apparently is not parallel with any single

bedding surface . A peak-picked s l ice (Figure 7g) was ge ner-ated by searching a travelt ime window centered at the peak ofthe event. Where a polarity reversal was encountered, pickingwas completed by interpolating surrounding grid nodes. Com-pared w ith the idealized stratal slices (Figures 7b,d,f), one ca nident i fy the s t rand p la in and dis t ributary channel sands fromunit 3, a f lood-t idal delta from un it 3A1, and another flood-t idaldel ta and barr ie r-core sands f rom uni t 3A 2. Various fac ies in-

terpretations are possible for this slice, but as expected, non eof them reflects the true relat ionship of facies. A possible inter-pretation con s iders those sandstones a s a basal t ransgress iveunit deposited on a coastal erosional surface bec ause of theangular occurrence of the seismic event and the "onlap" eventobserved on it (Figure 5, dd'). This type of misinterpretationcould plague any t ime-transgressive event.

STRATAL SLICING

Selecting time - parallel reference events

Based on the observation of our seismic models, mo st seismicevents are a function of w avelet frequency. If a series of fi lters(designed w ithin the bandw idth of the data) is applied, the oc-

currences or slopes of some seism ic events will keep changingwith frequency (frequency dependent) and others will not (fre-quency independ ent). Apparently for a given data set , a seismicevent is t ime transgressive if i ts occurrenc e is frequency d epen-dent . I f one cou ld e l iminate non stra t igraphic factors ( faul ts ,fluid contacts, etc.) and time- transgressive stratigraphic phe-nomena (e.g. , a ravinement surface), then the corollary wouldalso be true: a seism ic event is t ime parallel only if its occur-rence is frequency independent.

From the limited experience on our seism ic models, seismicdata need to cover a t leas t one octave of frequen cy range fora successful selection of time-parallel reference events. For in-stance, i f a data set has a f requency range of 10-50 H z with

a dom inant frequency of 30 Hz, one disp lay f i l tered to 40-H zdominan t f req uency and ano th e r f i lt e red to 20-H z dom inan tfrequency would be necessary. A panel-filtering covering moredom inant frequencies (e.g., 15, 20, 25, 30, 35, 40, 45 H z) wouldbe better.

G eological ly , a t ime-paral le l reference event represents ageological sur face or a de posit ional unit that dominates thereflection en ergy of the even t because it is isolated, thick, oracoustically abnormal, and can be correlated over a large area.Condensed sect ions a long ma ximum flooding surfaces , shelfstorm san dsheets, and distal basin floor turbidite in relativelysand-poor sequences are probably among the best candidates.Comm on geologic t ime markers (for example l igni tes or coa l ,and thin l ime stone beds) may also generate good reference

events . For smaller f ie ld s tudies , however, a good referenceevent may also be created by less ideal sediments, for examplefluvial deposits encased in thick shales, as shown by event bb'(Figure 5 ).

Phantom mapping between reference surfaces

Once referen ce seismic events are selected, an interpolationalgor ithm serves to build a s tratal t ime m odel t (x, y , s) be-tween the reference events, where s is geologic t ime. This mo delapproximates t rue s t ra ta l t ime s t ructure T(x , y, s), or

t(x, y, s) — T(x, y, s),1)Downloaded 21 Feb 2012 to 202.173.95.254. Redistribution subject to SEG license or copyright; see Terms of Use at http://segdl.org/



51 0 Zeng et al .

FIG. 7. Mis interpreta tion of fac ies from a t ime-t ransgress ive se ismic event . (a) Facies map of un i t 3: DC = dis t r ibutary channel ;LV = levee; A C = abandoned chann el ; DP = del ta p la in; LK = lake; SPL = s trandplain; SW = sw ale; (b) 30-Hz R icker idealizedstratal slice at top of un it 3; (c) facies m ap of unit 3A 1: BC = barrier core ; IF = inlet fi l l ; IN = inlet; FTD = flood-tidal delta; LG =lagoon; (d) 30-Hz R icker idealized s t ra ta l s l ice a t top of u ni t 3A 1; (e) fac ies map o f uni t 3A 2: ETD = ebb-tidal del ta ; others sameas (c); (f) 30-Hz R icker idealized stratal slice at top of unit 3A 2; (g) 30-Hz R icker peak-picked slice following a t ime-transgressiveevent (dd' in Figure 5) that conne cts the strong am plitudes from all three units.




Stratal Slicing: 3-D Model 51 1

an d sho u ld be u n iqu e o r be in d epen d en t o f d a ta f r equ en cy .One experiment is based o n the s im ples t interpolation, a l in-ear funct ion between reference events , assuming that deposi-t ion is la tera l ly proport ional in th ickness for a l l d eposi t ionalunits. With this method, well information is not needed. Moresophisticated slicing needs careful calibration of travelt ime in-terpolation functions based on nonlinear velocity and geo logict ime funct ions at d if ferent well locat ions and is beyond the

scope of this paper.The experiment shows that the error of stratal slicing, mea-sured as the traveltime difference between an actual pick andnearest deposit ional surface, is related to the numbe r of refer-ence events used in the interpolat ion (Figure 8 an d Table 1) .For comparison, the peak-picked errors for all seven events areshown (Figure 8, column 1: 0 reference case) (event gg' is ar-t ificially made m ore t ime parallel by increasing the reflectioncoeff icient to 0 .1 at top and to -0 .1 at base o f the sandstoneso that i t can be treated as a reference event) . First , one canuse a s ing le reference event and m ake paral le l t ime s l ices oneither side of i t . This is the approach of Brow n et al . (1981) andBrown (1992a) for flattening a reference event and then takinghorizontal t ime slices (horizon slice). We chose event aa ' from

the top of the sequence as the reference. From Figure 8 andTable 1 (colum n 2: 1 referenc e case), it is apparent that map-ping quality generally deteriorates with distance away from thereference. A lthough resul ts can be improved for even ts withlarge time-transgressive character (e.g., event dd'), this hori-zon s l ice approach is gen eral ly poorer than event p icking interms of p icking error . A ccum ulat ion of depth and t ime per-turbat ions f rom the reference surface c aused by d if ferent ialsubsidence, deposition, and compaction is responsible for thepoor performance. A pparently, this method can be applied onlyto uniformly deposited, or sheetlike, sedimentary successions.For the more comm on s i tuat ion w here th ickness changes la t-erally, more reference events are needed for mapping. Slicing

between two reference events ( top and base of the sequence)significantly reduces the m apping error and is better than eventpicking for time-transgressive events (events cc' , dd' , and ff,Figure 8, column 3: 2 references case). A dding a third referenceevent improves the result further (Figure 8, column 4: 3 refer-ences case). Phantom mapping, however, behaves more poorlythan event picking for time-parallel seismic events other thanthe references (e.g. , event bb').

A nothe r cause o f e r ro r i s the e r ro r i n p i cking the r e fe r -ence e vents . Omit t ing the s i tuat ion of t reat ing an event froma t ime-t ransgress ive geological surface as a reference event ,this error is mostly a function of the data frequency (Figure 9).In the experiment, the error in picking the three reference

events a l l decreases with increas ing data frequencies from 30Hz to 90 Hz (events aa ' , ee ', and gg ' , Figure 9, Table 2) . A p-parently, higher frequen cy referenc e events better reflect ge-ographic re l ief on deposi t ional surfaces and so have sm allerpicking error. How ever, a series of stratal slicing to the 30-Hzmodel d ata amon g these three reference events (Figure 9 andTable 2) dem onstrate that using lowe r f requency referencesyield slightly smaller m apping errors, although these reference

FIG . 8. Error of phantom m apping of stratal slices as a functionof the number of reference events from 30-Hz R icker syntheticdata. R eference events are shaded. Event gg' is art ificially mademore t ime parallel by increasing the reflect ion coefficient to 0.1at the top and to -0.1 at the base of unit 5 so that it can be treatedas a referenc e event . See Figure 5 for the locat ion of the events.

Table 1. Standard deviation (STD ), left-bound (LB ) and right-bound (RB) error (ms) of phantom mapping of stratal slices as afunction of the number of reference events from 30-Hz data.

Event ST D0 reference event

LBB ST D1 reference event

LBB

2 reference eventsST DBB

3 reference eventsSTDBB

aa ' 1.42 -4 . 41 6.06 0.14 -0 .32 0.36 1.43 -4 . 37 5.94 1.43 -4 . 37 5.94bb ' 1.46 -4 . 50 6.82 2.64 -7 .31 7.72 2.11 -5.51 8.15 2.04 -5.61 8.16cc ' 3.61 -7.50 10.06 3.85 -10.8 14 .05 2.73 -9.53 11.25 2.61 -9.11 9.50dd ' 8.47 -18.3 20.64 4.48 -11.1 17.51 2.34 -9 . 42 8.58 2.35 -8 .74 10.21ee ' 1.47 -5 . 46 6.51 4.39 -11.8 19.57 2.71 -8.12 10.95 1.49 -5 . 62 6.58if ' 3.25 -10.6 9.57 4.12 -11.4 19.81 2.78 -9.61 9.27 2.05 -8.91 6.67gg ' 1.32 -7.69 8.23 5.80 -15.5 26.02 1.39 -8.11 8.18 1.39 -8.11 8.18




512 Zeng et al.

events bear larger event picking er rors themselves. De spitemore detailed surficial variations expected from the higher fre-quency re fe rence events , a smoother m apping of se ismic t imeto stratal level could better, or at least equ ally, recover stratalinformation.

In com par i son wi th the peak-picked re su l t (Figure 7g) ,phan tom-m apped s t r a ta l s li c e s (F igure 10) a re taken f rom30-Hz R icker data cube between two reference events from the

same frequency data volum e (events aa ' and ee ' in Figure 5) .A cross t ime-t ransgress ive event cc ' and fol lowing smo othedtop of units 3, 3A1, and 3A2, these slices clearly pass throughvariable phases in the data and are frequency independent. Themajor characterist ics are impress ively s imilar to those of theidealized stratal slices (Figures 7b,d,f). Most of the impor tantfacies patterns [distributary channel (unit 3), flood -tidal deltas(units 3A1 an d 3A 2) and barrier core/back barrier/lagoon tran-sit ion (unit 3A 1)] that were missed by event picking have beenimaged. Of course , the phantom-m apped s t ra ta l s l ices are notidentical to idealized ones because of various mapping errors,especial ly the one ca used by the use o f l inear in terpolat ionfunction.

Other geological situations

When more complicated s i tuat ions are encountered, s imi-lar linear interpolation scheme s can be applied, in most cases

without great difficulty. In cases whe re a fault or offiap is in-volved (Figures 11a,b) , phantoms may a lways be draw n afterthe first-order stratigraphic framework is established by select-ing and correlating t ime-parallel seismic events. Incorporatingava i lable wel l d a ta m ay be n ec essary to co r r e la te the samegeological boundary across faul ts. Phantoms can never crossan angular unconformity separating di fferent deposi t ional

FIG. 9. Er ro r o f phan tom m apping amo ng three r e fe renceevents from different frequency data cubes . R eference eventsare shaded. See Figure 5 fo r the location of the events.

F I G . 10. Correct recovery of stratal slices by the phantom m ap-ping of units 3, 3A1, and 3A 2 from 30-H z Ricker synthetic datacube. Notice the similarity of (a), (b), and (c) with, respectively,(b), (d), and (f) in Figure 7.





Table 2. STD, L B and RB error (ms) of phantom mapping among three reference events from different frequency data cubes.

30 Hz 50 Hz 70 Hz 90 Hzreference events reference events re fe rence events re fe rence events

Event ST D LB R B ST D LB R B STD LB R B STD LB R B

aa ' 1.43 -4.37 5.94 0.99 -2.85 5.27 0.79 -3.54 4.76 1.26 -6.19 2.88bb' 2,04 -5.61 8.16 2.73 -6.61 9.04 2.71 -7.03 8.29 2.76 -6.98 8.54c c 2.61 -9.11 9.50 2.25 -6.47 8.74 2.32 -8.74 9.63 2.88 -9.60 10.98

dd ' 2.35 -8.74 10.21 3.40 -9.88 8.09 3.27 -11.2 7.73 3.35 -10.3 7.59ce ' 1.49 -5.62 6.58 1.46 -7.34 6.14 0.98 -5.37 5.67 0.92 -5.16 5.50f f ' 2.05 -8.91 6.67 2.56 -9.63 7.82 2.52 -9.26 8.42 2.54 -9.25 8.01g g ' 1.39 -8.11 8.18 1.22 -6.06 8.90 1.02 -6.56 7.43 1.02 -6 .47 7.60

possib le to res tore the deta i led de posi t ional h is tory of a g ivenstratigraphic section.

ACKNOWLEDGMENTS

FIG. 11. Phantom mapping in some complicated geologicalsi tuations.

sequences (Figure lie). Instead, they should be drawn inde-

penden t ly on e i ther s ide of the uncon form ity. The inf luenceof l ight hydroc arbons ca n be cal ibrated by correct ing for thet ime-de lay caused by abnorma l ly low ve loc i ty in the reservoi rinterval (Figure 11d).

CONCLUSIONS

In our Powderhorn model , we have documented m any t ime-transgressive seismic reflections that clearly cross geologict ime-equiva lent impedance bo undar ies . The f requency depen-dence of se i smic events i s the most obvious evidence of t imet ransgress ion. The exis tence of t ime- t ransgress ive sei smic re-flections obscures reservoir-scale facies description from stratalsl ices and high-frequency sequence st ra t igraphy where onlyone o r t wo r e f l ec ti ons a r e i nvo l ved . M any s t ud i e s h ave b eenpotent ia lly defec t ive because they s imply u sed hand -picked orcom puter auto-p icked hor izon s l ices as geologic- t ime equiva-lent stratal s l ices. Time-paral lel ism ca nnot be assum ed; i t needsto be proven , for exam ple, by panel f i l ter ing , which tes t s thechronos tra t igraphic mean ing of a se i smic event .

Picking of geological ly time-equivalent stratal s l ices should

be unique, frequency independent, and not constrained by seis-

mic pha se (pe a k o r t ro u gh) . Th i s c a n be a c c o m pl ishe d m o s ts imply by phantom ma pping , or by apply ing l inear interpolat-ing functions between two time-paral lel seismic events. Stratals l ices c rea ted by phan tom m apping not only prov ide be t te r f a -cies informa tion for individual reservoir units , but also make i t

This research was suppor ted by funds provided and adm in-istered by the Office of the Governor of Texas through the

State Lands Energy Resource Optimization project. Addi-

t ional funding wa s provided by the Depar tment of G eological

Sc i ences , U n i ve r si ty o f T exas a t A us t in ; A R C O E xp l ora t ionand Product ion Technology; and the G ul f Coas t Assoc ia t ion of

G eologica l Socie ti es . The authors g ra te fu lly thank Joseph Yehfor the computer suppor t . The authors a l so apprec ia te the com -ment s and r ecom menda t i ons f r om Bob A . H ar dag e , a s soc i a teed i t o r W i ll iam L . A b r i e l, and r ev i ewer s Joh n A . War d , W al -t e r E . J o hn so n , a n d a n a n o n ym o u s r e v ie w e r . Pu b l ishe d w i thpermiss ion of the D i rec tor , Bureau of Econom ic G eology, TheU niversi ty of Texas a t Aus t in .

REFERENCES

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1992b, Seismic interpretation today and tomorrow . The Lead-ing Edge, 11, No. 11, 10-15.

Brown, A . R., Dahm, C. G., and G raebner, R. T., 1981, A stratigraphiccase history using three-dimensional seismic data in the Gulf of Thai-land: Geophysical Prospecting, 29 , 327-349.

Hardage, B. A ., Levey, R. A ., Pendleton, V., Simmons, J., and Edson, R .,1994, A 3-D seismic c ase history evaluating fluvially deposited thin-bed reservoirs in a gas-producing property: Geophysics, 59, 1650-1665.

Jenkins, F. A ., and White, H. E., 1957, Fundamentals of o ptics: McG rawHill Pub. Co.

Kallweit, R. S., and Wood, L. C., 1982, The limits of resolution of zero-phase wavelets: G eophysics, 47, 1035-1046.

Meckel, L. D., Jr . , and N ath, A. K ., 1977, Geologic con siderat ionsfor stratigraphic modeling and interpretation, in Payton C. E., Ed.,Seismic stratigraphy: Am. A ssn. Petr. Geol. Memoir 26,417-4 38.

N eidell, N. S. and Poggiagliolmi, E., 1977, Stratigraphic mod eling andinterpretation-geophysical principles and techniques, in Payton,C. E., Ed., Seismic stratigraphy: Am . Assn. Petr. Geol. Memoir 26 ,

389-416.Schramm , M. W., Jr., Dedm an, E. V., and Lindsey, J. P, 1977, Prac-t ical stratigraphic m odeling and interpretation, in Payton, C. E.,Ed., Seismic stratigraphy: Am. Assn. Petr. Geol. Memoir 26, 477-502.

Tipper, J. C., 1993, Do seismic reflections nece ssarily have chronos-tratigraphic significance? Geological Magazine, 130, 47-55.

Vail, E R., Todd, R . G. and Sangree, J. B.,1977, Seismic stratigraphy andglobal changes of sea level, Part 5: Chronostratigraphic significanceof seismic reflections, in Payton, C. E., Ed., Seismic stratigraphy:Am . Assn. Petr. G eol . Memoir 26 , 99-116.

Zeng, H., 1994, Facies-guided 3-dimensional seismic modeling andreservoir characterization: Ph. D diss., Univ. of Texas at Austin.

Zeng, H., Backus, M. M., Barrow, K . T., and Tyler, N ., 1996, Facies map-ping from three-dimensional seismic data: potential and guidelinesfrom a Tertiary sandstone-shale sequence model, Powderhorn field,Calhoun County, Texas: AA PG B ull., 80,16-46.

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