Morphologic Dating of Fluvial Terrace Scarps and Fault Scarps

8/12/2019 Morphologic Dating of Fluvial Terrace Scarps and Fault Scarps

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Geological Society of America Bulletin

doi: 10.1130/0016-7606(1984)952.0.CO;2

1984;95, no. 12;1413-1424Geological Society of America BulletinDAVID B. NASHYellowstone, MontanaMorphologic dating of fluvial terrace scarps and fault scarps near West

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1414 D. B. NASHR.4E. R.5E.

T.12S.T.13S~

BOZE MAN , MT. 83 Ml. f

SCALE R.4E. R.5E WEST YELLOW STONE, MT. 0 .5 Ml .^0.5 1 .0 1 .5 2 .0

MILES2.5

0 1 2 3KILOMETERSFigure 1. Map of the West Yellowstone Basin south of Hebgen Lake. Study site 1 is located south of the Madison River, and study site 2 is

located east of the South Fork Madison River.West Yellowstone Basin. This broad, remarka-bly flat, outwash-inantled, structural depressionis bound ed to the south by the Madison Plateau,to the southwest by the Henry M ountains, to theeast and no rtheast by the Gallatin Range, and tothe west by the Madison Range. The elevatedcentral portion of the basin south of HebgenLake is nearly featureless and is tilted a fewdegrees to the north (Myers and Hamilton,1964, suggested that the tilting is a result of on-going regional tectonic warping). Th e only largetopographic features within this area ofthebasinare north-facing, eiist-west-trending fault scarpsranging in height from


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DATING OF SCARPS, WEST YELLOWSTONE, MONTANA 1415

Figure 2. M ap of fluvial terraces south oftheMadison River and north of West Yellow stone,Montan a. There are five well-developed sets of terraces, from the oldest and highest (T l) to theyoungest and lowest (T5). Radiocarbon dating of wood collected from a conical depression onterrace T4 provides a minimum age for that terrace of 7,100 50 yr. The short, numbered linesindicate locations at which the profiles of the scarps above each terrace (show n in Fig. 9) weremeasured.

(Fig. 3), several kilometres west of site 1 andimmediately east of the South Fork MadisonRiver, contains an intersecting fault scarp andfluvial terrace scarp.O B S E R V A T I O N SInitial Morphology of Terrace Scarps andFault Scarps

The initial morphology of degraded terracescarps and fault scarps may be inferred fromactive cut-banks and recent fault scarps withinthe same area and underlain by the samematerial. The fault scarps formed during the1959 earthquake south of Hebgen Lake and thehigh, active cut-banks along the Madison andSouth Fork Madison R ivers are assumed to haveformed in the sam e way as the older fault scarpsand terrace scarps and are underlain by the sameobsidian sand and gravel deposit.

The profiles of the modern cut-banks consistof a straight midsection separating a straight,nearly horizontal base and crest (defined inFig. 11a below). The profile midsection is keptat the angle of repose of the underlying sand andgravel, 33.5, by fluvial undercutting (Fig. 4).The in situ angle of internal friction,, mea-sured with an Iowa Bore Hole Shear, 1 wasfound to be identical to this angle of repose. Theangle of repose for most cohesionless materialwill be equal to the angle of internal friction ofthat material (Carson, 1977). The crest and thebase of the profile intersect the midsection toform a sharp basal concavity and a crestal con-vexity (Fig. 9a).

The initial morphology of the fault scarps ismore complex than that of the cut-banks. Nor-mal faulting in the West Yellowstone Basin re-flects ongoing, north-south crustal extension(Smith and others, 1977). The n ear-surface faultplanes in the cohesionless, frictional sands andgravels therefore form in a state of active Ran-kine stress and dip at an angle of 45 + 0 /2 . Formost com mon cohesionless sands and gravels,will be between 30 and 40, resulting in aninitial scarp slope angle between 60 and 65which exceeds the angle of repose of the under-lying material. The initial scarp midsection,termed the free face by Wallace (1977), re-treats at a high angle (by raveling), progres-sively burying its base with an apron of debrissloping at the angle of repose of the underlyingmaterial (Fig. 5). The same pattern of free-faceretreat and build-up of a basal debris apron isobserved along the base of the walls of borrow

'Handy Geotechnical Instruments, Inc., Ames,Iowa.

pits in the W est Yellowstone obsidian sand andgravel deposit (Fig. 6). Variable time is requiredfor complete burial of the retreating free face bythe basal debris apron (Wallace, 1977, 1980).After 20 yr, only a small remnan t ofthe freefaceremains on fault scarps formed during the 1959earthquake (Fig. 7). After the free face has beencompletely buried, a scarp profile identical tothat of a fluvial cut-bank form s: a straight, nearly

horizontal base and crest separated by a straightmidsection (the debris apron) inclined at theangle of repose (33.5) of the underlying obsid-ian sand and gravel. The basal concavity andcrestal convexity formed by the intersections ofthe crest and base with the midsection of thefault scarp profile will be quite sharp.

Immediately after faulting, the fault scarp pro-file will seldom be as simple as shown in Figure


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1416 D. B. NASH

a l luv ia l * - v s /fan

T e r r a c e T 62 / alluvial/ fan

Faul t Scarp F1 211110? B ? 6 5

Fa u l t S c a rp F11

T e r r a c e T 6

t -

NA

0 5 0 1 0 0

Sca le (Meters )

Study S i te 2By South Fork Madison River

Scarp cont inuesbut was not mapped

Figure 3. Map of a faulted fluvial terrace of the South Fork Madison River west of WestYellowstone, Montana. The short, numbered lines indicate locations at which profiles of theterrace scarp arid the fault scarp (shown in Fig. 10) were measured. Faulting both predatesterrace formation (the segm ent of the terrace scarp T6 , upstream from the fault, is higher thanthe segment T6, downstream from the fault) and postdates terrace formation (the terracesurface is faulted). Field eviden ce indicates that, since being rem oved during terracing, the F1segment of the Ifault scarp has moved only once prior to 1959 and is therefore amenable tomorphologic dating.

5. Frequently, deep fissures or broad, shallowgrabens form at the scarp base (Wallace, 1980).The progressive outward growth of the debrisapron will, however, bury these features, pro-ducing a simpler profile morphology. Another,more serious complication frequently resultsfrom splaying of the fault surface near theground surface, yielding not one scarp but anassemblage of two or more smaller scarps(termed multiple scarps by Mayer, 1982). Ifthe individual scarps are closely spaced alongthe p rofile, the re treat of the free faces will causethem to run together, forming a single, continu-

ous debris apron. If the individual scarps arewidely spaced, they will not run together. Evenafter the free face of each scarp has been elimi-nated, the scarp profile will consist of two ormore separate debris aprons. South of the DuckCreek Highway Maintenance Station, one mayobserve such a fault scarp several metres high,formed during the 1959 earthquake. Approxi-mately 50% of the total length of this fault scarpconsists of a single debris apron (Fig. 8a), and50% consists of two or more separate debrisaprons (Figs. 8b and 8c). All but one of the fa ultscarps that formed in the West Yellowstone ob-

sidian sand plain during the 1959 earthquakewere superimposed on pre-existing fault scarps.The present fault scarp thus is the result of atleast two separate faulting events. Mayer (1982)terms scarps formed by more than one faultingepisode composite scarps. Both multiple (seeabove) and composite fault scarps pose liifiicul-ties for morphologic dating. Offset due to faultcreep would pose a further complication, but itis doubtful whether creep contributed signifi-cantly to the total offset of the faults, as there isno indication of any disturbance to roads or tothe runway of the West Yellowstone Airportwhere they cross faults active during the 1959earthquake.Degraded Terrace Scarps inStudy Site 1

By studying the series of terrace scarps of in-creasing age in study site 1, the pattern of hill-slope degradation with time can be determined.The five terraces are numbered from th; oldestand highest, Tl, to the youngest and lowest, T5(Fig. 2). The terrace scarp separating a giventerrace from the next higher terrace is given thelabel of the lower (younger) terrace surf ice (forexample, terrace scarp T4 separates temces T4and T3). The scarps were formed by the sameprocess and are underlain by the same obsidiansand and gravel deposit as are the modern cut-banks along the Madison and the South ForkMadison rivers and therefore are assumed tohave had the same simple initial morphology: anearly horizontal base and crest separate by astraight midsection sloping at the angle of repose(33.5) of the underlying sand and gravel. Cer-tain data were not collected. The oldest terracescarp, Tl, was not analyzed because its mor-phology was substantially altered during clear-cutting of the lodgepole pine cover, whichinvolved extensive bulldozing and removal ofsoil. Scarps for med b y the intersectionol two ormore terrace scarps were not analyzed becausetheir initial morphologies may have bei:n quitecomplex: undercutting during the formation ofthe younger terrace scarp may not have com-pletely rem oved the older terrace surface, result-ing in an initial profile consisting of two or moresubsidiary terrace scarps. This poses a problemfor morphologic dating similar to that posed byboth multiple and com posite fault scarps.

Terrace scarps T2, T3, and T4 were profiledat 20-m intervals along their bases, using theprofiling technique described by Nash (1980b).The profiles of these scarps (Figs. 9b-?d) aremarkedly different than those of modern cut-banks (Fig. 9a). They are no longer the sim-ple straight-line intersection of base with midsec-tion and of midsection with crest. Now the basal


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Figure 4. Cut-bank of the South Fork Madison River (SE1/4 sec. 14, T. 13 S. , R. 4 E.).Active fluvial undercutting keeps bank face at 33.5, the angle of repose and the angle ofinternal friction of the underlying obsidian san d and gravel deposit .

concavity and crestal convexity have becomemore rounded by growing outward at theexpense of the base, midsection, and crest. Theslope angle of the midsection has decreasedsignificantly from its initial angle of 33.5. Thestraight, nearly horizontal crest and base of theprofile may still be seen beyond the limits of thecurvature of the crestal convexity and basalconcavity. It is interesting to note that theyoungest profiled terrace scarp, T4 (Fig. 9b), hasa significantly lower midsection slope angle thanthe two older terrace scarps, T3 a nd T 2 (Figs. 9cand 9d), demonstrating the danger of assumingthat the midsection gradient alone may be usedto determine the relative ages of hillslopes.

The ages of the terraces are unknown, al-though all must be younger than 28,00 0-40 ,000yr, the age of the underlying obsidian sand andgravel reported in Porter and others (1983). Anunsuccessful search w as made for organic mate-rial that had been buried in the river channelwhen basal undercutting of the cut-bank ceased.The only datab le organic material was found ina deep con ical depression located on the surfaceof terrace T4 (Fig. 2). Currently 20 m wide and3 m deep, the depression is of unknow n origin,but it is probably related to seismic activity(Myers and Hamilton, 1964; Nash, 1981b).Digging at the bottom of the depression, wefound the top 75 cm to be made up of sand and

gravel containing specks of charcoal. At depthsfrom 75 to 175 cm, we found peat with occa-sional logs, underlain, in turn, by logs mixedwith abu ndant volcanic ash (identified by R. E.Wilcox, U .S. Geol. Survey, Denver, as MazamaAsh). K. L. Pierce (U.S. Geol. Survey, Den ver)suggested an age of 6,600 to 6 ,700 yr for the ash.At a depth of 190 cm, a large, well-preserved logwas encountered. A sample of the log, sent tothe U.S. Geological Survey Branch of IsotopeGeology (Lab Sample Number W-4795),yielded a radiocarbon age of 7,100 50 yr.More sand and gravel were encountered beneaththe log, presumably indicating the original bot-tom of the depression. The dated log provides aminimum age for the conical depression andthus also for terrace and terrace scarp T4, butthe terrace may well be considerably older than7,100 yr.In tersec t ing Degraded Terrace Scarpand Fault Scarp in Study Site 2

The second study site is the intersection of afault with a fluvial terrace and a terrace scarpcarved during a still-stand of the north-flowingSouth Fork Madison River. The portions of theterrace on the downthrown and on the up-thrown sides of the fault are labeled T6 and

T 6 \ respectively, in Figure 3. Where the faultscarp crosses the terrace surface, it is labeled

F l, and where it extends up and across thearea above the terrace scarp, it is labeled F l' .

The history of the terrace and fault scarp iscomplex, involving several separate faultingevents. Fault scarp Fl - F l ' consists of a fresh,small scarp (or set of small scarps), ranging from5 to 40 cm in offset, that was superimposedduring the 1959 earthquake on a pre-existingscarp 1.5 to 3 m in height. The surface of theterrace is offset by Fl, and so the most recentpre-1959 movement of the fault must postdatethe formation of the terrace. The height of theterrace scarp, however, averages 7.7 m on theupthrown block of the fault (section T6') butonly 4.6 m on the downthrown block (section

Figure 5. Raveling of the init ial loosening-limited fau lt scarp in cohe-sionless, frictional material causes scarp face (or free face) to retreat,forming a basal apron of debris. Because the material fails in an activeRankine stress state, the init ial scarp face should be at a slope angle of45 =/2 4>is the angle of internal friction of the material) . The slopangle of the de bris ap ron will be equal to , or very ne arly equal t o, (assum ed to be 35 here). The diffusion model for hil lslope deg radatio nis not appropriate for the raveling process. Rapid raveling buries thesteep scarp face with a continuous debris apron relatively quickly, usu-ally less than 50 yr, resulting in a hillslope with a simple initial profileamenable to morphologic dating.


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1418 D. B. NASH

Figure 6. Borrow pit a t the north e nd of runway of the West Yellow-stone A irport ( NE 1/4 sec. IS, T. 13 S., R. 5 E.) . Raveling of the s teep,loosening-limited'. free face is producing a transport-limited debrisapr on sloping un iformly at 33.5, the angle of internal fr ic t ion and theangle of repose for the obsidian sand gravel deposi t overlying theWest Yellowstone Basin south of Hebgen Lake.

Figure 7. Fault scarp, formed during the 1959 Yellowstone earth-qua ke, south of i the Du ck Creek High way M aintenan ce Stat ion(SE1/4 sec. 22, T. 12 S., R. 5 E.) . Raveling of the loosening-l imitedfree face produces a basal debris apron at the angle of repose (33.5)of the underlying obsidian sand and gravel deposi t . After 20 yr , theretreat ing fault scarp has been nearly buried by upward growth of thebasal debris apron.

T6 of the terrace scarp), indicating that an ear-lier faulting event created a scarp prior toterracing.

In 1959, an active cut-bank of the South ForkMadison River provided a clear cross section offault scarp F l- F l' , imm ediately west of profilelocation Fl-11 (Fig. 3). Although the cut-bankis now abandoned and the cross section com-pletely buried, it was studied intensively byMyers and Ham ilton (1964, their Fig. 34). Fromtheir observations ofthisexposure, they inferreda sequence of events similar to that listed above.Photos and diagrams of the exposure indicatethat the fault moved twice after the creation ofterrace T6-T6': once in 1959 and once prior to1959.

Profiles of terrace scarp T6-T6' and of faultscarp Fl - F l ' are shown in Figures 10a -lOd(the location at vrhich each profile was mea-sured is shown in Fig. 3). The same pattern ofdegradation observed on the profiles of terracescarps in study site1 was observed on profiles ofscarps T6 -T 6' and F l- F l ' : the gradient of themidsection decreases and the initially sharpbasal concavity and crestal convexity becomemore rounded. The original, nearly horizontalcrest and base may still be observed beyond thelimits of the crestal convexity and basal concav-ity. The mean midsection slope ang le of the

higher, T6' segment of the terrace scarp is 11.3,significantly greater (see Table 2 below) than themean midsection slope angle of 14.5 deter-mined for the lower T6 segment of the scarp.The difference in angle for two hillslopes of thesame age again demonstrates the danger of usingmidsection slope angle alone to determine rela-tive ages of hillslopes.

After burial of the retreating free face by thebasal debris apron, the morphology of the F1segment of fault scarp F l - F l ' presumablyshowed the same proportion of single to multi-

a

bM

c

I 1 10 10 20Sca le Meters )No Ver t ica l Exaggera t ion)

ple scarp profiles as was observed along the faultscarp that formed in 1959 south of the DuckCreek Highway Maintenance Station (Figs.8a-8 c). Because the initial profile morphclogy ismore variable for fault scarps than for :erracescarps, greater variability in the degraded profilemorphology would also be expected. This ex-pectation is confirmed by comparing the stan-dard deviation of the midsection slope angles ofprofiles from T6 (0.9) and T6' (1.2) with thatof profiles from the F1 (2.8) segment cf faultscarp F l -F l ' (Tab le 2 ) .

Figure 8. Profi les of faul t scarps south ofthe Duck Creek Highway Main tenance S ta -t ion north of West Yellowstone, Montana.All scarps were offset during th e 1959 Yel-lowstone earthquake but are superimposedon a much older , much degraded scaip. (a)Simple, single scarp. After 20 yr, the initialscarp has been nearly buried by the basal de-bris apron, (b) Mult iple scarp consis t ing oftwo smaller scarps, (c) Mult iple scarp consis t-ing of three smaller scarps.

Ap prox ima tely 50% of the lateral ex t ent ofthe recently formed fault scarp is a s ingle ,s imple scarp, and th e other 50% is made up ofmultiple scarps.


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3 0SC AL E METER S)N O VER T IC AL EXAG GER ATION )

F l - 3

0 SO 40SCALE METERS]N O VER TIC AL EXAGGER ATION )

Figure 9. Profiles ofterrace scarps cut by theMadison River north ofWest Yellowstone, Mon-tana (location of each pro-file is shown in Fig. 2).Dots represent the profilepredicted by the hillslopedegradation model, equa-tion 1, and from a simpleinitial profile (Fig. 11)using values for H a , 36 an dt cgiven in Table 1.(a) Modern cut-bank ofthe Madison River, (b)Terrace scarp T4. (c) Ter-race scarp T3. (d) Terracescarp T2.

T 6 ' - 5

F l ' - B

F l ' - 5

Figure 10. Profiles of terrace scarp and fault scarp west of West Yellowstone, Montana(location o f each profile is show n in Fig. 3). D ots represent the profile predicted by the hillslopedegradation model, equa tion 1, and from a simple initial profile (Fig. 11) u sing values forH a,P 0 an dt cgiven in Table 2. (a) T6 segment of terrace scarp, (b) T6' segment of terrace scarp,(c) F1 segment of fault scarp, (d) Fl' segment of fault scarp.

M O R P H O L O G IC D A T IN GO F H IL L SL O P E S

The general characteristics of the degradedfault and terrace scarps in West Yellowstone,including the decrease in curv ature of the crestalconvexity and the basal concavity and the de-crease in gradient of the midsection, are all con-sistent with the predictions of a simple mo del ofhillslope degradation (Nash, 1980a, 1980b,1981a, 1981b). Furthermore, as shown else-where (Nash, 1980a), under some conditions themorphology of a degraded scarp may be used todate the scarp. By using the radiocarbon dateavailable for terrace scarp T4, the model can b ecalibrated and then used to morphologicallydate the other scarps.M O D E L O FH IL L SL O P E D E G R A D A T IO N

Morphologic dating is based on a simplemodel of hillslope degradation that yields theequation

dt dx2 (1)At any point on the hillslope, the rate at whichthe elevation (j>) changes with time (/) is thuslinked by a constant of proportionality (c) withthe second derivative, in which x symbolizes thehorizontal coordinate of the point. Given a sim-ple initial profile (Fig. 11a), the model predictsthat as time elapses, the curvatures of the crestalconvexity and th e basal concavity must decreasewhile their lateral extents increase, thereby low-ering the gradient of the midsection (Fig. lib).Not only are these predictions consistent withthe shapes of the terrace scarps and the faultscarps south of Hebgen L ake (the observed pro-file and the profile predicted by the model aredisplayed in Figs. 9 and 10), but they are alsoconsistent with the pattern of degradation ob-served on aband oned wave-cut bluffs along theshores of Lake Michigan (Nash, 1980b). Thismodel further explains the observation made byBucknam and Anderson (1979) that the midsec-tion gradient of a degraded fault scarp and alacustrine wave-cut bluff near Drum Mountain,Utah, increased with increasing height of thescarp (Nash, 1980a).

The model is applicable only to transport-limited hillslopes (slopes on which more loos-ened debris is available for transport than thetransportational processes are capable of remov-ing) (Gilbert, 1877; Nash, 19 81a). Although themodel is inapplicable to loosening-limited hill-slopes (slopes on which debris is removed asrapidly as it is loosened from the surface), it isnevertheless ideal for describing the degradationofslopesunderlain by u nconsolidated, cohesion-less sands and gravels on which the primary


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1 4 2 0 D. B. NASH

Midsection

Base

Figure 11. (a) Profile ofa scarp having a simple initialmorphology, consisting of astraight base and crest ata uniform slo|ie angle, 0 anda straight midsection at aslope angle if a 6 (a istermed the ''initial excessmidsection slopeangle ). Thescarp offset, H is the per-pendicular distance betweenthe crest and base.

(b) With time, the curva-ture of the crestal convexityand the basal concavity ofa transport-limited slope isr e d u c e d ( b e c o m e s m o r erounded). The slope angle ofthe midsection, /? 0 (/3 istermed the degraded exc essmidsection slope angle ), isdefined as the average slopeangle over the central 10% of the scarp offset. Note that although the sections of the crest andthe base immediately adjacent to the midsection are progressively consumed by outwardgrowth of the crestal convexity and the basal concavity, their initial slope angle, 0, and theinitial scarp offset,H may still be measured from the remaining undisturbed, straight sections(c = 1.5 x 10 3m2 / y r ,H =1.2 m,t =1,000 yr, a = 15, /3 = 11.8, 0 = 20).

Meters )No Ver t ica l Exaggera t ion )

debris-transporting mechanism is soil creep. Themodel thus opens the way to morphologic dat-ing of mostfluvial terrace scarps cut in alluviumand of some sciirps produced by norm al faultingof alluvial fans.

P R E D I C T E D R E L A T I O N S H I PB E T W E E N H I L L S L O P E A G EA N D M O R P H O L O G Y

Analysis of the hillslope degradation modelindicates that the rate at which the gradient ofthe profile midsection decreases is related to c(assumed to be independent of x an d t) and tothe height and midsection gradient of the initialprofile. The following discussion ofthis relation-ship will be limited to hillslopes underlain bycohesionless materials and having a simple in-itial profile, such as fluvial cut-banks, marineand lacustrine wave-cut bluffs, and some scarpsproduced by normal faulting.

The offset (H) of the initial hillslope profile isdefined as the perpendicular distance separatingthe crest and base (Fig.1la). Even on a substan-tially degraded hillslope, the initial offset maystill be determined by extending the profilebeyond the limits of the basal concavity andcrestal convexity to points at which the originalstraight crest and base have not been altered(Fig. lib). The initial excess midsection slopeangle (a) is defined as the angle by which theinitial slope angle of the scarp midsection ex-

ceeds the slope angle (0) of the crest and base(Fig. 11a). The original slope angle (a + 0) ofthe midsection of a degraded scarp may be de-termined either by measurem ent of the angle ofinternal friction oftheunderlying material or byobservation of modern, actively forming, loosen-ing-limited hillslopes underlain by the samematerial. Assumed to be the same for crest andbase, the angle 0 may still be measured on adegraded scarp by observing the profile upslopefrom the crestal convexity or downslope fromthe basal concavity. The degraded excess slopeangle of the hillslope midsection (/3) is deter-mined by measuring the angle by which the ob-served profile midsection exceeds 0. Simplycalculating /3 from the slope angle of the centralor steepest line segment of the profile midsectionis ill advised, because this angle will be a func-tion of the segment length (the shorter the seg-men t, the steeper j3 becom es). To avoid thisproblem and other problems associated withdifferent-sized hillslopes,/}+ 0 is here defined asthe average slope angle of the central 10% of theprofile midsection (Fig. lib).

In an analysis of the hillslope degradationmodel, Nash (1980a) found that the time (t) inwhich the excess midsection slope angle de-creases from a toj8is proportional to the squareof the profile offset (f f) . Further analysis of themodel shows that to any given value of tan(/J)/tan(a), there corresponds a unique value ofthe dimensionless quantity ( t c / H 2 ) tan 2a).

Thus any combination of values for c, H, t,aa that yields the same value for{tc/H2) ta n2 (necessarily results in identical values of ta(/3)/tan(a) (Nash, 1981b). The morphologdating technique used in the present: study based on the plot of tc/H1) ta n2 (a) versus t(/3)/ tan(a ), displayed in Figure 12, foi values 0 < 10. From Figure 12, it is observed that tdecrease in the grad ient of the m idsec tion is itially rapid until tan(/?)/tan(a)


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o . sV8

0.5

< 0 .

Figure 12. Relationship amon g initial excess mid-section slope angle, a; degraded excess midsectionslope angle, /?; scarp offse t,H ; hillslope diffusivity,c; and the age of the hillslope, t. This plot may beused for dating hillslopes if c is known or may beused for determining cif tis known. It is applicableto hillslopes having a simple initial morphology ifthe slope angle of the crest and base, 0, does notexceed 10.

( t c / H ) t a n ( t t )

0 2 4Sca le (Meters )(No Vert ica l Exaggeration)

Figure 13. (a) Degraded fault scarp having a simple initial profil(c = 1.5 x lO 3m2 / y r H = 4.2 m, t= 2,000 yr, a= 35, 0 = 28.6, 60).

(b) Degraded multiple fault scarp. Although the age, total scaroffset, and the slope angle of each small scarp are the same as for thsimple scarp in Figure 4a, the degraded exc ess midsection slope angleP, is much lower. Multiple slopes are not amenable to morphologidating unless their initial morph ologies are k nown in detail (/? = 22.1)

and testing statistics. The hillslopes profiled inthe present study were analyzed with a BASICprogram, SLOPEAGE. The program util izes alookup table of values for tan(/3)/tan(a) and(tc/H2) tan 2 (a) rather than the curve shown inFigure 12.2

Multiple fault scarps cannot be dated by theabove technique. As they degrade, the smallerscarps are rapidly smoothed o ut and, after a rela-tively short time, a degraded multiple scarp willresemble a degraded single scarp. If both a singleand multiple scarp have identical values of a, c,H, an d t, 3 for the degraded multiple scarp(Fig. 13b) will be considerably lower than itwould be for the degraded single scarp(Fig. 13a). Due to this lower value for /3,morphologic dating will yield too great an agefor a multiple scarp.

Selective sampling provides a possible ap-proach to the multiple scarp problem. In thevicinity of Hebgen Lake, -50% of the lateralextent of scarps produced by the 1959 earth-quake was observed to be multiple scarps. It isnot known whether a similar proportion of mul-

2The program is written for use with the IBM PCand is available from the author at no cost. Send astamped, self-addressed envelope for details.

Figure 14. (a) Degradationof a simple fault scarp. Initialprofile is d ashed line; profileafter 1,000 yr is dotted line;and profile after 2,000 yr issolid line (c = 1.5 x 10 3m 2 / y r , H = 4.2 m, a = 35,final p = 28.6, 6 = 0).

(b) Degraded compositefault scarp offset 1.1 m in-itially (dashed line) and thenagain by 3.1 m 1,000 yr later(dotted line). After 2,000 yr(solid line), the degradedcomposite fault scarp appearsvery similar to the scarpformed by a single faultingevent (Fig. 5a). Althoughboth had the same initial ex-cess midsection slope angleand the same total offset, thedegraded excess slope angle,/3, of the composite faultscarp is steeper than the sin-gle event fault scarp (finalfi =31.0).

0 4 8Scale (Meters)(No Vertical Exaggeration)


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1422

tiple scarps characterized scarps that were pro-duced by pre-1959 faulting, but that seems to bea reasonable assumption. If, then, successiveprofiles were made at fixed horizontal intervalsalong the base of a fault scarp, the 50% of theprofiles with the lowest values oft c would pre-sumably represent degraded m ultiple scarps, andcould be eliminated fro m the final analysis. Thisselective sampling procedure is usable only ifone can make a reasonable estimate of the ratioof single to multiple scarps. It cannot be as-sumed, a priori, that this ratio will be 50% inother areas, because the ratio is likely to be afunction of several parameters, including the na-ture of the surface materials.

Morphologic dating of composite scarps alsoyields erroneous ages. As in the case of multiplescarps, a degraded composite scarp will, after arelatively short time, appear very similar to adegraded simple scarp produced by a singlefaulting event (Figs. 14a and 14b). No modifica-tion of the presen t proc edur e is likely to yieldreliable dates for the individual faulting eventsthat produce a composite scarp. Hanks andothers (1984) proposed a method for calculat-ing average offset rates, but different values of3may result from identical average offset rates(Figs. 14a and 14b). In the present study,evidence found in cross-sectional exposures ofthe fault and from other independent observa-tions permitted identification of compositescarps and their elimination from the finalanalysis.

Dating should not be attempted with a hill-slope on which the angle of the crest and of thebase differ by more than a few degrees. Thetechnique is also inappropriate for use with hill-slopes on which the rounding of the basalconcavity and of the crestal convexity differ sig-nificantly. According to equation 1, hillslopeshaving a simple initial morphology (Fig. 11a)should show a symmetry in the degree of round-ing of the crestal convexity and of the basalconcavity with time. Hillslopes with asym metricrounding cannot be modeled using equation 1(profiles having a more rounded and extensivebasal concavity tfcian crestal convexity probablydeveloped by slojje wash and must be avo ided).A N A L Y S I S O F D A T ACalculation of c

For terrace sca.rp T4, Table 1 givestc = 10.59 1.64 m 2 . D ividing this value by the best avail-able age for that scarp,1=7,100 50 yr, yieldsc= 2.00 0.24 x 10" 3 m 2 /yr. Because 7,100 50 yr is the minimum age for terrace T4, theactual value ofc may be smaller than calculated.The age of a hillslope calculated with this value

D. B. NASHTABLE 1. DATA DE RIVED FRO M PROFILES O F TERRACE SCARPS IN STUDY SITE 1

Profile Offset,H Average slope(m) angle of crest

and base, 0(degrees)

Present (K/H 2 tan 2(a> tcmidsection slope (m 2)

angle,+B(degrees)

T2- 1 3.41 2.1T2- 2 3.76 0.1"T2- 3 2.64 1.4T2- 4 3.06 1.4T2- 5 5.87 -0.9 T2- 6 6.10 -1.2 T2- 7 5.03 -0.4 T2- 8 4.52 0.8T2- 9 5.71 -0.4 T2-10 3.97 1.8Mean 4.41 0.5S.D. 1.23(28% ) 1.2 (240%)T3- 1 4.39 1.0T3- 2 5.40 0.0T3- 3 5.20 -0.4 T3- 4 4.62 0.7T3- 5 4.07 1.1Mean 4.74 0.5S.D. 0.55(12%) 0.6 (130%)T4- 1 2.81 -0.7 T4- 2 3.10 -1.1 T4- 3 2.51 -0.7

Mean 2.81 0.8S.D. 0.30(11%) 0.2 (25%)

13.3 0.714 22.514.0 0.523 16.913.1 0.688 12.311.7 0.906 21.516.1 0.356 26.115.6 0.376 29.111.6 0.753 42.214.5 0.509 25.117.7 0.293 21.016.8 0.380 15.714.4 23.22.1 (14%) 8.4 (36 d)13.8 0.583 27.715.8 0.392 26.219.0 0.246 14.716.8 0.353 18.019.8 0.237 9.717.0 19.32.4 (14 ) 7.6 (39%)11.9 0.693 11.710.6 0.840 16.99.9 1.007 13.9

10.8 14.21.0 (9%) 2.6( 181 )2 2Note:calculation of (tc/H ) tan (a) andtc based ona +B = 33.5.

TABLE 2. DATA DERIVED FROM PROFILES OF TERRACE SCARPS AND FAULT SCARP IN STUDY SITE 2

Profile Offset,H Average slope(m) angle of crest

and base, 6(degrees)

Present (tc/H 2) ta n2 (o ) tcmidsection slope (m 2)

angle,+B(degrees)

T6-1 5.08 0.5T6-2 5.18 -0.4T6-3 3.70 0.9Mean 4.65 0.3Si ). 0.83(18%) 0.7 (233%)T6'-l 8.02 -0.7T6'-l 7.02 -0.2 T6'-3 7.65 -0.9 T6'-4 7.77 -0.6 T6'-5 7.79 -0.5 T6'-6 7.87 -0.7 Mean 7.69 -0.6 S.D. 0.35 (5%) 0.2 (33%)Fl- 1 1.82 -0.4 Fl- 2 1.90 -0.1 Fl- 3 2.55 -0.8Fl- 4 3.49 -1.7Fl- 5 2.69 0.2Fl- 6 3.16 -1.4Fl- 7 3.45 -1.5Fl- 8 2.11 0.1Fl- 9 2.03 -0.3Fl-10 1.82 0.0Fl-1 1 1.40 1.4Mean 2.40 -0.4 S.D. 0.71 (30%) 0.9 (225%)

10.8 0.974 59.410.8 0.874 52.112.3 0.758 25.411.3 45.60.9 (8%) 17.0 (33%)

13.2 0.557 77.313.3 0.572 63.014.6 0.442 55.215.1 0.419 54.714.3 0.476 63.116.3 0.350 47.214.5 60.11.2 (8%) 10.3 (17%)6.0 2.814 20.6*6.2 2.840 23.2*7.5 1.698 23.9*9.6 0.949 23.2*17.4 0.316 5.217.7 0.280 5.89.5 0.990 24.0*13.4 0.577 5.912.0 0.708 6.510.9 0.898 6.713.1 0.688 3.4

11.2 5.64.0 (36%) 1.2 C l%)Note:calculation of (tc/H 2) ta n2(a) andtc based ona*6* 33.5.'Profile assumed to be that of a degraded multiple scarp and thus is deleted from the calculation of the mean tc for fault scarp Fl.

of c will thus be a minimum age. The abovevalue forclies betwe en c=1.2 x 10~2m 2 /y r foraband oned wave-cut bluffs in the northern p r-tion of the lower peninsula of Michigan (Nash,1980b), and c = 4.4 x 10"4 m 2 /yr for a scarp

produced by normal faulting near Drum Moun-tain, Utah (Nash, 1980a). This intermediatevalue forc is not surprising, because the obsidiansand and gravel deposit of the West YellowstoneBasin is coarser grained than the sandy m orainic


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DAT I NG O F S CARP S , W E S T YE L L O W S T O NE , M O N T ANA 1 4 2 3

1 * Terrace Scarp T6_ Terrace Scarp T6

2 5A1

3 . 4A2

_ 6

I I

* 3I I I

TABLE 3. MORPHOLOGICALLY DETERMINED AGES OFTERRACE AND FAULT SCARPS

Scarp Age of scarp(yr)

T2 11,600 6,400(55%)T3 9,600 5,600 (58%)T6 22,800 13,000 (57%)T6' 30,000 10,800 (36%)F1 2,800 1,100(40%)

Note:ages calculated usingcvalue determined from analysis of terrace scarpT4 (c = tc/c = 14.2 2.6 m2/7,100 50 yr = 2.00 0.38 * I0" 3 m2/yr) .

material underlying the hillslopes of Michigan,but it is finer grained than the alluvium underly-ing the Drum Mountain scarp. The climate ofthe West Yellowstone area is similarly interme-diate between the humid temperature climate ofMichigan and the semi-arid climate of north-central Utah.

The coefficientc is likely to be a function ofclimate, underlying material, and aspect. Be-cause the climate and underlying material areuniform throughout the study area, and (exceptfor the west-facing terrace scarp T6-T6') be-cause the aspect of all of the studied scarps is tothe north, the value of c calculated for terrace T4is probably appropriate for all of the scarps ex-cept T6-T6'. It is difficult to determine howsignificantly Holocene changes in climate af-fected c; a difference of two orders of m agnitudebetween thec values derived from Michigan a ndUtah suggests that c may b e strongly affected byclimate. Pleistocene climate differed enoughfrom Holocene climate to make suspect mor-phologically determined ages of > 10,000 yr forhillslopes.Morphologic Dating of Scarps in theWest Yellowstone Basin

For terrace scarps T2 and T3, the meanvalues of tc are 23.2 m 2 and 19.3 m 2 , respec-tively (Ta ble 1). If c is assumed to be equal forall of the scarps, then tc reflects their relativeages. The values fortc calculated for the terracescarps accord well with their relative ages, asinferred from their relative positions (Fig. 2). Itis encouraging that mo rphologic dating duly in-dicates that T2 is older than T3, and that T3 isolder than T4, despite the fact that the meanmidsection slope angles of T2 and T 3 (16.3 an d17.5, respectively) are both steeper than T4(10.8). Using c = 2.00 x 10"3 m 2 /yr, terracescarps T2 and T3 are dated at 11,600 and 9 ,600yr B.P., respectively (T able 1). As the da te forT2 is pre-Holocene, its accuracy is questionable.

The mean values of tc for terrace scarps T6and T6' are 45.6 m 2 and 60.1 m 2 , respectively(Table 2). These two scarps are segments of the

8

Figure 15. Hillslope aspectan d tccalculated for the T6 and 7 0T6' segments of terrace scarpT6-T6'. There appears to be a 6 0poorly d efined tendency for hill-slopes with southern aspects pto have higher values of tc . 5 50The age of the scarp, t isthe same for all profiles; thus,changes in c with hillslope 4 0aspect may account for some ofthe observed trend of decreasing 3 Qtc as scarp aspect changes fromsoutherly to westerly.

same terrace scarp (Fig. 3) and so they must beof the same age and have similar values for tc.The observed large difference int c values resultsprimarily from the anomalously low value forprofile T6-3. Taking c = 2.00 x 10~3 m 2 /yryields an age of 22,800 yr fo r T6 and 30,000 yrfor T6' (Table 3). These dates are Pleistoceneand also are questionable.

K. L. Pierce (1983 , personal com mun.) founda strong correlation between hillslope aspect andc for terrace scarps on incised alluvial fans.Some local confirmation arises from the mean-der of terrace scarp T6-T6', which varies theaspect of the scarp along its lateral extent. Forthe profiles collected from the T6 and T6' seg-ments of the terrace scarp, a plot of scarp aspectagainst tc suggests tha t tc decreases from a m ax-imum for profiles with a southerly aspect to pro-files with a westerly aspect (Fig. 15). With theage of the scarp (t) necessarily the same for allprofiles, the observeddifferenceintc may be duein part to differences in c. Presumably,c reachesa minimum on scarp with a northerly aspect.The value of c appropriate for the west-facingterrace scarp T 6- T6 ' is likely to be significantlygreater than that calculated for the north-facingterrace scarp T4. Such a trend wo uld be consist-ent with several studies of valley asymmetrysummarized by Young (1972). These studies in-dicate that for east-west-trending valleys in thenorthern hemisphere, the valley wall with anortherly aspect is generally steeper than thewall with a southerly aspect.

The pre-1959 profile of a fault scarp may berestored by removing from the profile the still-fresh small scarps formed in 1959. If this re-stored scarp profile is not composite (if it wasform ed by a single pre-1959 faulting event), it issuitable for morphologic dating. It is assumedthat app roximately one-half of the lateral extent

180 210 24 0 270 300 3 30Azimuth of hillslope aspect ()

of a scarp, when p roduced by no rmal faulting ofcohesionless material, will consist of multiplescarps. In that case, if calculated from profilestaken at evenly spaced intervals along the scarpface, about one-half of the dates will overesti-mate the actual age of the fault scarp. Of theeleven profiles collected from the F1 segment offault scarp Fl - F l ' , the six yielding the highestvalues of tc are presumably degraded multiplescarps. With elimination of these six profiles, amean tc = 5.6 m 2is calculated from the rem ain-ing five profiles. Use of c = 2.00 x 10~3 m 2 /yrthen gives a date of 280 0 1100 yr B.P. for thepre-1959 faulting that produced the F1 segmentof fault scarp Fl-Fl ' .C O N C L U SIO N S

Morphologic dating of fault scarps presentssome special difficulties that were not fully ap-preciated prior to this study. Morphologic datingwill result in an erroneously old age if the initialscarp is multiple: consisting of two or moresmaller scarps. Moreover, the selective samplingprocedure suggested here for dealing with mul-tiple scarps must not be used indiscriminately inother areas. Composite scarps, formed by recur-rent move ment along the same fault, also are notamenable to morphologic dating and should beavoided. Given the problems presented by mul-tiple and com posite fault scarps, an indirect ap-proach may, in the long run, offer simpler andmore accurate morphologic dating. When dat-ing scarps produced by normal faulting of allu-vial fans, it may be preferable to date theupstream terrace scarps formed by fan-head en-trenchment rather than to attempt to date thefault sca rp itself.

With only one independently dated hillslope,terrace scarp T4, a quantitative assessment of the


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1424 D. B. NASHaccuracy of morphologic dating cannot bemade. Th e present study does, however, prov idequalitative evidence for its accuracy. Despite thefact that the slope angle of the youngest scarp issignificantly less than tha t of the older scarps, themorpholog ic dating procedure yields, for the ter-race scarps in study site 1, ages consistent withthe known relative ages of the terraces. Since itsformation, terrace scarp T6-T6' has been offsetby the faulting that produced the F1 segment offault scarp Fl-Fl ' . The terrace scarp thus pre-dates the F 1 segment of the fault and, as before,the morphologic dates for the terrace scarp andfault scarp are in accord with their knownrelative ages.

The morphologic dating technique used heregoes beyond Niish (1980a) by developing aprocedu re that is simpler to use, is more widelyapplicable, is more accurate, and is operablewith a smaller number of scarp profiles. Themodified technique provides a rapid and inex-pensive method far dating hillslopes that are notamenable to dating by other means. Although itmust be used with much caution and is not ap-propriate for use on all hillslopes, morphologicdating offers a valuable tool for determining pa-leoseismic chronology and for assessing regionalseismic risks.A C K N O W L E D G M E N T S

This work was sponsored by the U.S. Geolog-ical Survey, Earthquake Hazards ReductionProgram, under Contract 14-03-0001-19109. Ithank Ralph O. Meyer, District Ranger, and his

staff at the Hebgen Lake Ranger District of theGallatin National Forest for their co-operationand help. Robert E . Wallace (U.S. Geol. Survey,Menlo Park) made many helpful suggestionsduring two productive visits to the field area.Kenneth L. Pierce (U.S. Geol. Survey, Denver)is thanked for his help with the field work; forfinding m aterial for radiocarbon dating; for hav-ing that material analyzed by the RadiocarbonLaboratory of the U.S. Geological Survey; andfor his interest, encouragement, help, and enthu-siasm. I am particularly grateful to my two fieldassistants: Michael J. Bolton, who provided am-iable and capable assistance for three gruelingmonths of field work during the summer of1980; and my father, Leonard K . Nash, who didyeoman's service as an unpaid field assistant dur-ing the financially strained but productivesumm er of 1981. M. A. Carson, Arvid M. Jo hn-son, and Leonard K. Nash are thanked for theirhelpful criticisms of this manuscript.REFEREN CES CITEDBucknam, R. G , and Anderson, R. E., 1979, Estimation of fault-scarp agesfrom a scarp-height-slope-angle relationship: Geology, v. 7, p. 11-14.Carson, M . A., 1977, Angles of repose, angles of shearing resistance and a iglesoftalusslopes: Earth Surface Processes, v. 2,p. 363-380.Eardley, A. J., 1960, Phases of orogeny in the deformed belt of southwesternMontana and adjacent areas of Idaho and Wyoming,inCampau, I).K.and A nisgard, H. W ., cds., Billings Geological Society 11th annua l fieldconference, West Yellowstone-earthquake area: p. 92-105.Gilbert, G. K., 1877, Geology of theHenry Mountains: U.S. Geographical and

Geological Survey, 160 p.Hamilton, W., 1960, Late Cenozoic tectonism and volcanism of the Yellow-stone region, Wyoming, Montana, and Idaho, inCampau, D. E., andAnisgard, H. W., eds.. Billings Geological Society 11th annual fieldconference, West Yellowstone-earthquake area: p. 86-91.Hanks, T. C Bucknam, R. C., Lajoie, K. R and Wallace, R. E 1984,Modification of wave-cut and faulting-controlled landforms: Journal ofGeophysical Research, v. 89, no. B7, p. 5771-5790.Mayer, L., 1982, Quantitative tectonic geomorphology with application tonorthwest Arizona [Ph.D. dissert.]: Tucson, Arizona, Arizona Univer-sity, Department of Geosciences, 512 p.

Myers, W. B., and Hamilton, W., 1964, Deformation accompanying the Hebgen Lake earthquake of August 17, 1959: U.S. Geologica Survey Professional Paper 435-1, p. 353-360.Nash, D. B., 1980a, Morphologic dating of degraded normal fault scarpsJournal of Geology, v. 88, p. 353-360.1980b, Forms ofbluffsdegraded fordifferentlengths oftimein EmmCounty, Michigan, USA: Earth Surface Processes, v. 5, p. 331-345.1981a, FAULT: A FORTRA N program for modeling tht degradatioof active normal fault scarps: Computers and Geostience, v. 7p. 249-266.1981b, Fault scarp morphology: Indicator of paleoseismit chronologyU.S. Geological Survey Final Technical Report, Contiact Numbe14-08-0001-19109,132 p.Pierce, K.L. ,1979,H istorya nd dynamics of glaciation in the nort lern Yellowstone National Park area: U.S. Geological Survey Professional Pape729-F, 90 p.Pierce, K. L., Obradovich, J. D., and Friedman, I., 1976, Obsiditn hydrationdating and correlation of Bull Lake and Pinedale glaciatio is near WesYellowstone, Montana: Geological Society of America Bulletin, v. 87p. 703-710.Porter, S. C., Pierce, K. L., and Hamilton, T. D., 1983, Late Wiscansin mountain glaciation in the western United States,inPorter,S.C., ed., The laPleistocene: Minneapolis, Minnesota, University of Minnesota Pressp. 71-111.Sieh, K. E., 1978, Pre-historic large earthquakes produced by slip on the SanAndreas fault at Pallett Creek, California: Journal of Geophysical Research, v. 83, p. 3907-3939.Smith, R. B., Shuey, R. T Pelton, J. R and Bailey, J. P., 1977, Yellowstonhot spot: Contemporary tectonics and crustal properties from earthquake and aeromagnetic data: Journal of Geophysical Research, v. 82p. 3665-3676.Waldrop, H. A., 1975, Surftcial geologic map of the West Yellowstone quadrangle, Yellowstone National Park and adjoining areas MontanaWyoming, and Idaho: U.S. Geological Survey Miscellaneous GeologiInvestigations Map1-648,scale 1:62,500.Wallace, R. E., 1977, Profiles and ages of young fault scarps, north-centraNevada: Geological Society of America Bulletin, v. 88, p. 1267-1281.1980, Degradation of the Hebgen Lake fault scarps of19i 9:Geologyv. 8, p. 225-2 29.Witkind, I. J., 1964, Events on the night of August 17, 1959The humanstory: U.S. Geological Survey Professional Paper 435-A, p. 1-4.1974, Some details of the Hebgen Lake, Montana, earthq lake of August 17, 1959, in Voight, B., ed., Rock mechanics: Th: Americanorthwest, 3rd Congress Expedition Guide: University Pa*k, Pennsylvania, Experiment College of Earth and Mineral Sciences,1lie Pennsyvania State University Special Publication, p. 126-133.Young, A., 1972, Slopes: Edinburgh, Scotland, Oliver and Boyd, p. 288.

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Morphologic Dating of Fluvial Terrace Scarps and Fault Scarps