Journal of Sedimentary Research, 2007, v. 77, 2–12

Perspectives

DOI: 10.2110/jsr.2007.005

AUTOSTRATIGRAPHY: A FRAMEWORK NORM FOR GENETIC STRATIGRAPHY

TETSUJI MUTO,1 RON J. STEEL,2 AND JOHN B. SWENSON3

1Faculty of Environmental Studies, Nagasaki University, 1-14 Bunkyomachi, Nagasaki 852-8521, Japan

, 2Department of Geological Sciences, The University of Texas at Austin, 1 University Station, C-1100, Austin, Texas 78712, U.S.A.3Department of Geological Sciences, The University of Minnesota Duluth, 1114 Kirby Drive SE, Duluth, Minnesota 55812, U.S.A.

e-mail: tmuto@nagasaki-u.ac.jp

ABSTRACT: Autostratigraphy is the stratigraphy generated by large-scale autogenic processes, and needs to be heeded becauseof a current overreliance on allogenic controls in sequence stratigraphy. Key principles of autostratigraphy, emerging from thetheory of autoretreat and a new understanding of alluvial grade, derive from the non-equilibrium stratigraphic response, i.e., thegeneral lack of equilibrium configuration of depositional systems. The non-equilibrium behavior of fluvial deltas during times(T ) of steady dynamic forcing leads to variable stratigraphic response that is the inevitable result of length (D) and time (t)scaling particular to the depositional system, rather than necessarily reflecting any sudden or unsteady change in the rate ofallogenic forcing. Some abrupt breaks in the stratigraphic record are not necessarily associated with changes in allogenicconditions but can result from purely autogenic processes of the system. When T is comparable to or longer than t, (1) thedepositional system takes the non-equilibrium, large-scale autogenic response, (2) the superposition of autogenic and allogeniccomponents of the forcing is prominently nonlinear, and thus (3) sequence stratigraphic models that have been built on theassumption of equilibrium response are incorrect. Autostratigraphic analysis makes it possible to detect and identify complexautogenic responses and unsteady allogenic events in the stratigraphic record by quantifying a temporal change in themagnitude of D. Autostratigraphy thus functions as a ‘‘norm’’ for genetic stratigraphy.

INTRODUCTION

A stratigraphic example that captures the essence of our discomfortwith the practice of much of conventional sequence stratigraphy is shownin Figure 1. The deltaic stratigraphy (Fig. 1A) preserves clear evidence ofa transition from regressive to transgressive conditions, via aggradationaland moderately transgressive stages.

Interpretation of this shoreline trajectory within conventional sequencestratigraphy would normally require that the ratio of rate of relative sea-level rise (A) to rate of sediment supply (S) changed with time, from lessthan unity to far exceeding unity (Fig. 1B). With a constant magnitude ofS, the landward turnaround of the shoreline would be attributed to anincrease in A, and further discrete increase in A would account for theaccelerated transgression in the late stage. The aggradational stage at thetransition from regression to transgression would be explained with A/S

being unity or A tentatively balancing with S. These stratigraphicinterpretations are consistent, implicitly or explicitly, with the notion ofthe A/S ratio concept (Shanley and McCabe 1994; Muto and Steel 1997;Kim et al. 2006), that (1) there can exist an equilibrium state between Aand S to allow the shoreline to remain stationary for some time, and(2) transgressive and regressive behavior of the deltaic shoreline reflectsunsteady allogenic forcing of the basin (i.e., changes in A and/or S)whereby the equilibrium is broken.

In actuality, the stratigraphic architecture of Figure 1 was produced ina flume experiment with steady dynamic conditions, i.e., constantsediment supply and constant sea-level rise (Fig. 1C; for detailedexperimental conditions see Muto 2001), suggesting that a set of steadyor linear dynamic conditions (i.e., A 5 constant, S 5 constant) of the

basin can give rise to an autogenic behavior of deltaic shoreline that canbe nonsteady and nonlinear, and even associated with an abrupt break insedimentation and depositional geometry. This diagram thereforeillustrates a common misinterpretation of stratigraphic successions,calling on unsteady allogenic control to explain the stratigraphy offluviodeltaic systems.

As well as the above-mentioned example, a recent body of theoretical,experimental, and field-based work (Muto and Steel 1992, 1997, 2002a,2002b, 2004; Swenson et al. 2000; Muto and Swenson 2005a, 2005b, 2006;Swenson et al. 2005; Swenson and Muto 2005, in press) has shownconvincingly that fluviodeltaic systems lack an equilibrium configurationunder steady dynamic forcing (A 5 constant, S 5 constant) and that ingeneral the stratigraphic response of the depositional system proceeds ina non-equilibrium and nonlinear manner. This fundamental aspect ofstratigraphic response has not been recognized in conventional sequencestratigraphy (e.g., Jervey 1988; Posamentier and Vail 1988; Posamentieret al. 1988) and in its derivatives including the Galloway model (Galloway1989a, 1989b), the regime model (Thorne and Swift 1991a, 1991b), thefour-systems-tract model (Hunt and Tucker 1995), the shorelinetrajectory model (Helland-Hansen and Gjelberg 1994), and the T–RModel (Embry 1995).

Autostratigraphy, here advocated in terms of the intrinsic non-equilibrium response, is the stratigraphy that takes full account ofpotential large-scale autogenic changes in the depositional systems inresponse to steady dynamic forcing of basins. Purely autostratigraphicsuccessions are likely to be rare in the geological record, because (1)natural sedimentary processes are rarely entirely autogenic, and (2) onlonger time scales, autogenic processes cannot continue to operate

Copyright E 2007, SEPM (Society for Sedimentary Geology) 1527-1404/07/077-002/$03.00

without allogenic interruptions. However, autogenic processes andresulting autostratigraphic successions have been demonstrated to beimportant, from theoretical consideration, from numerical modeling, andfrom laboratory experiments under controlled steady forcing. For theanalysis of stratigraphic successions, the methodology of autostratigra-phy provides an economic explanation in terms of potential autogenicmechanisms and steady forcing, and should initially be used to explain asmuch of the stratigraphic response as possible. For the remaining signalsthat cannot then be explained, allogenic processes should be brought intoplay. Autostratigraphy therefore provides a logical basis for theidentification of allogenic effects in the stratigraphic record, i.e., in termsof discrepancy from an autostratigraphic prediction.

We make here a first step in the direction of exploring principles,strategy, and methodology of autostratigraphy. The present study limitsthe ‘‘forcing’’ to changes in relative sea level and focuses on fluviodeltaicsystems. The latter are the basic building blocks of stratigraphicsuccessions, the locus for changes in relative sea level, and thus the keydepositional environment considered in sequence stratigraphic models.

AUTOGENESIS AND NON-EQUILIBRIUM RESPONSE

Autogenic vs. Allogenic

The term autogenic, as used here, refers to the intrinsic stratigraphicresponse to the steady component of external dynamic forcing (Blum andTornqvist 2000; Muto and Steel 2001, 2004; Swenson et al. 2005; Mutoand Swenson 2006). Allogenic refers to the stratigraphic response to thenonsteady component of external dynamic forcing (Muto and Swenson2005a, 2005b). For example, sedimentation responding to acceleratingsea-level rise can be regarded as an allogenic process (with respect to sea-level change), whereas sedimentation responding to constant rate of sea-level rise is regarded as an autogenic process (with respect to sea-levelchange). It is important to note that ‘‘steady sea-level forcing’’ meansforcing by sea level that is changing at a constant rate.

In standard sedimentologic usage, an autogenic response arises frominternal feedback between transport processes, independent of temporalchanges in external forcing. Common examples include river avulsion anddelta-lobe switching (Beerbower 1965; Miall 1996), which can be regardedas local or stochastic processes and can occur multiple times undera constant regime of the depositional system. Though the usage of‘‘autogenic’’ here is essentially unchanged from classic sedimentological

usage, the autogenic processes that we treat here are mostly those thatoperate over the entire system, are deterministic, and occur only a singletime during the entire period of a given steady forcing. Our use of‘‘autogenic’’ does not imply a particular, absolute spatiotemporal scale,and it is possible that the time scale for the intrinsic non-equilibriumresponse of the fluviodeltaic system overlaps with the time scales of otherautogenic responses. Whenever we refer to ‘‘large-scale autogenicprocesses’’ in this paper, it is only in the relative sense in terms of thelength and time scales intrinsic to a given depositional system (see below).A fundamental geological problem is that stratigraphic products of large-scale autogenic processes are very likely to be easily misinterpreted asthose of allogenic processes.

The large-scale autogenic processes in fluviodeltaic systems area manifestation of their intrinsic, non-equilibrium response to steadyforcing, which in turn arises from the nature of the moving boundaries ofthe system (Paola et al. 1992; Swenson et al. 2000; Swenson and Muto inpress). Major moving boundaries in the fluviodeltaic system include theshoreline, the delta toe, and the alluvium-basement transition (i.e.,upstream end of the alluvial river) (Fig. 2). Under conditions of constantrate of change in relative sea level, the natural tendency of thefluviodeltaic wedge is to grow through some combination of onlap andofflap at the alluvium-basement transition, and progradation andretrogradation of the delta slope. The reasons for this are tied to howthe basic shape of the fluviodeltaic clinoform (wedge) is maintained and,as a consequence, how the system must partition its sediment budgetbetween the subaerial and subaqueous depositional environments. It isthis dynamic nature of the lateral boundaries on the fluviodeltaic wedgethat, in general, prevents equilibration of the fluviodeltaic system(Swenson et al. 2000; Swenson et al. 2005; Swenson and Muto in press).

Importance of Time Scale

The intrinsic non-equilibrium behavior of a fluviodeltaic systemdepends on how sedimentary bodies accumulate in response to the trinityof sediment supply, subsidence, and eustatic sea level. The question thenbecomes fundamentally one of time scale. The importance of autostrati-graphic concepts hinges on the time scale of fluctuations in externalforcing (T) relative to the time scale (t) of the non-equilibrium response ofthe fluviodeltaic system. Given that sediment transport in our system isslope driven, we might expect this autogenic time scale to be a function of

FIG. 1.— Autostratigraphic versus conventional sequence-stratigraphic models in explanation of a regressive-to-transgressive shoreline turnaround. A) Longitudinalprofile of a delta that was built during experimental run conducted with constant rates of sediment supply (S 5 1.029 6 0.020 cm2/s), upstream water discharge(q 5 4.36 6 0.02 cm2/s), and sea-level rise (A 5 0.0251 cm/s). See Muto (2001) for details of the experimental runs. B) Interpretation from the conventional models ofsequence stratigraphy. C) Interpretation from the viewpoint of autostratigraphy, which is consistent with the actual experimental conditions. Note that, even without anychange in the dynamic parameters, (1) shoreline advance (regression) is halted after a short growth period, turned to a landward retreat (transgression), and (2) sometimeafter the initiation of retreat the delta attains an autobreak event, after which its original clinoform is no longer sustained.

AUTOSTRATIGRAPHY 3J S R

some characteristic length scale D and some effective diffusivity u thatembodies the efficiency of transport processes. Any fluviodeltaic systemwith a steady sediment supply (S 5 constant) and steady rise or fall ofrelative sea level (A 5 constant) has a characteristic length scale (Muto2001; Muto and Steel 2001, 2002a, 2002b, 2004; Muto and Swenson2005a, 2005b, 2006; Swenson and Muto in press)

D ~S

Aj j : ð1Þ

A natural time scale for dispersive systems is

t ~D2

u~

S

Aj j2S

u: ð2Þ

If we assume that fluvial morphodynamics sets the overall time scale forthe fluviodeltaic system, then u represents the fluvial diffusivity (Paola etal. 1992; Paola 2000) and the term S/u is the characteristic slope a of thealluvial surface. In this case, we can write the autogenic time scale as

t ~D2

u~ a

S

Aj j2: ð3Þ

This t scale provides a first-order estimate for the onset of individualautogenic events. For a physically plausible range of sediment and watersupply and rate of sea-level change, this time scale can vary by orders ofmagnitude between fluviodeltaic systems. Equation 3 suggests that gentle-gradient, small alluvial systems are far more sensitive to autogenicresponses than high-gradient, large systems. Although there could bemultiple superimposed scales of autogenic processes, defined bysimultaneously superimposed characteristic lengths and times, we hereconsider only t and D to focus on the ‘‘large-scale’’ autogenic processes.

LARGE-SCALE AUTOGENIC PROCESSES IN FLUVIODELTAIC SYSTEMS

The arguments presented below address idealized river-dominateddeltas that develop on an underlying surface with characteristic landwardand seaward slopes c and w, respectively (Fig. 2). The alluvial river anddelta foreset have characteristic slopes of a and b, respectively. Ourarguments are focused primarily on alluvial responses to steady dynamicforcing, so we assume initially that the shelf surface beyond the delta toeis not affected significantly by marine processes.

Sea-Level Conditions for Attaining Alluvial Grade

Alluvial-river response to changes in relative sea level has beenconventionally assumed to be controlled by the ‘‘equilibrium’’ alluvialprofile. The equilibrium profile is believed to correspond to a hypotheticalalluvial river that neither aggrades nor degrades along its entire lengthand thus bypasses its entire sediment supply to the shoreline (e.g.,Posamentier et al. 1988). In essence, this equilibrium alluvial river is in

a state of large-scale ‘‘grade’’ (sensu Mackin 1948). Conventionalsequence stratigraphy holds that (1) rivers basically aggrade in responseto relative sea-level rise and degrade in response to relative sea-level fall,respectively (Fig. 3A), and (2) grade is the final, stable state of an alluvialriver system and is attained with stationary base level (Gilbert 1877;Davis 1902; Green 1936; Kesseli 1941; Mackin 1948; Leopold and Bull1979; Posamentier and Vail 1988; Thorne and Swift 1991a).

Contrary to this conventional wisdom, however, the non-equilibriumbehavior of alluvial rivers allows grade to be attained with falling sea level(Fig. 3B, C; Muto and Swenson 2005a, 2005b, 2006). The criticalcondition discriminating aggradation and degradational regimes ofalluvial systems is the fall of sea level. Rivers can, in principle, remainaggradational not only with rising and stationary sea level but alsothroughout the duration of sea-level fall, provided the sea-level historydoes not cross the grade curves (Fig. 3B, C). For the graded state to besustained, the fall of sea level has to follow a particular pattern thatdepends in part upon the alluvial and basal slopes (a, w). Fora fluviodeltaic system prograding on a uniform, relatively high-gradient,preexisting surface (a , w 5 c), A (, 0) must be decreasing with time(Fig. 3B; Muto and Swenson 2005a). Steady fall of sea level can allow analluvial river to become graded only where a 5 w, such as where thefluviodeltaic system progrades onto a drowned, antecedent alluvial riverbed (Muto and Swenson 2006). In this latter case, grade can finally beattained and sustained at any magnitude of A (, 0) provided that it iskept constant. This alternative concept of grade provides a new level ofunderstanding as to how base level functions to control aggradation anddegradation in alluvial systems and, as such, provides a basis forinterpreting sea-level history from the stratigraphic records of fluviodel-taic deproits.

Autoretreat and Autobreak: Responses to Steady Sea-Level Rise

With a constant rate of rise (A) in relative sea level, the deltaic shorelinemigrates basinwards during an early stage (precursory advance) butinevitably begins to retreat landwards some time after the beginning ofdelta progradation. This is the phenomenon called autoretreat (Muto andSteel 1992, 1997, 2002a; Milton and Bertram 1995; Swenson et al. 2000).Subsequently there is a break in the geometry and sedimentation of thesystem, referred to as autobreak, after which the existing subaqueousslope is starved of sediment and thereby loses its clear delta-frontconfiguration (Fig. 4A, B; Muto 2001; Muto and Steel 2001; Parker andMuto 2003; Akamatsu et al. 2005).

Shoreline autoretreat arises from a progressive increase of the entiresurface area (the subaerial and subaqueous environments) of thefluviodeltaic clinoform, because of an increase in the storage capacityof the system during relative rise of sea level and from a concomitantdecrease of aggradation rate on the delta. Autobreak occurs when there isa further increase of the surface area of the delta, and the suppliedsediment is entirely consumed by the growth of the subaerial plain. Itshould be noted that abrupt changes in sedimentation have been

FIG. 2.— Geometrical parameters of the flu-viodeltaic system considered in thepresent discussion.

4 T. MUTO ET AL. J S R

documented to occur during linearly varying base-level changes, and thatthe autoretreat and autobreak points do not necessarily coincide withinflection points. If b $ c and T .. t, both autoretreat and autobreakare inevitable, and D simply functions to determine the length and heightof the maximum advance position and autobreak point of the shoreline.However, if b , c, autobreak is not attained because any progressiveincrease in the surface area of the foreset can be fully compensated bya progressive decrease in the surface area of the alluvial system (Fig. 4C;Muto and Steel 1992; Swenson et al. 2000).

If the feeder river system exhibits autocyclic shifting of streamchannels, a stepped topography inevitably forms above the submerged(i.e., abandoned) alluvial plain after the attainment of autobreak(autosteps; Muto and Steel 2001). Each autostep consists of a single, thinregressive delta lobe that forms part of an overall ‘‘backstepping’’ deltaicsystem. Because autostepping requires spatial and temporal localizationof active sedimentation, during aggradation of any active lobe the rest ofthe system is starved of sediment. Autocyclicity also causes eventualreoccupation of earlier abandoned delta-lobe sites. In the transgressivephase, it is unlikely to be common that active delta lobes will progradebeyond and therefore cover older lobes. This unburied surface of olderdelta-front lobes produces the autosteps during transgression.

Autogenic Processes During and After Sea-Level Stillstand

The fluviodeltaic system does not have any particular length (D) andtime (t) scales related to stationary sea level (A 5 0; see Eq. 3). As longas sea level is stationary, the system remains aggradational (Fig. 3B, C)and monotonously progrades basinwards at an ever-decreasing rate.Shelf-platform topography affects this long-lived progradation, i.e.,seaward-increasing bathymetry slows the rate of fluviodeltaic prograda-tion relative to a flat-bottomed bathymetry.

The duration of a stationary sea-level period can exert a significantinfluence on how the shoreline migrates during any subsequent period ofrising sea level, suggesting a sort of ‘‘age dependence’’ in fluviodeltaicbehavior. If a sea-level stillstand persists for a long time, the autobreakevent occurs soon after sea level begins to rise (Fig. 5), and the shorelinejumps landwards for a long distance (Fig. 6A). Physically, this agedependence can be explained in terms of the characteristic alluvialaggradation rate. This aggradation rate is simply the ratio of the steady

sediment supply to the alluvial river length (shoreline to alluvium-basement transition). For constant S, the longer the duration ofprogradation at sea-level stillstand, the longer the alluvial river—andthe smaller the characteristic aggradation rate—at the onset of theensuing sea-level rise or fall. With a smaller initial characteristicaggradation rate, the system quickly experiences autoretreat (autobreak)during the sea-level rise. For the effects of this age dependence to beimportant, the duration of stillstand progradation must be long relativeto a characteristic time scale (ts and tb in Fig. 5). A similar agedependence of an abrupt autogenic event (‘‘autoincision,’’ see below) islikely when a long period of stillstand sea-level stage is followed by steadysea-level fall (Fig. 6B).

Autoincision with Falling Sea Level

Autoretreat principles can be extended to conditions of sea-level fall.When sea level falls, the shoreline does not, of course, retreat. However,the alluvium–basement transition does mimic a shoreline subject to sea-level rise (Muto and Steel 2002a, 2004). There is apparent ‘‘symmetry’’ inautogenic processes for steady rise and fall of relative sea level (Table 1).During steady sea-level fall, the alluvium–basement transition initiallymigrates landward and the entire deltaic system aggrades (Muto and Steel2002a, 2004; Swenson and Muto 2005, in press). This landward migrationand aggradation is arrested after some time, and if a , w the entiresubaerial plain begins to be affected by feeder-channel erosion, orautoincision (Fig. 7A). Autoincision can be physically explained in termsof a characteristic aggradation rate for the alluvial river system. Theprogressive increase in length of the alluvial river continuously reducesthe characteristic alluvial aggradation rate. The rate of foreset prograda-tion on the delta front eventually decreases to a point where the alluvialriver incises at the shoreline, thereby triggering upstream-propagatingknickpoints and signaling the onset of autoincision (Swenson and Muto2005, in press; Muto and Swenson 2005b). After the autoincisionthreshold has been attained, all the supplied sediment bypasses thesubaerial plain and is deposited below sea level on the delta foreset. In thisway, despite widespread alluvial degradation and sediment bypassing, theentire fluviodeltaic system continues to grow seawards via accretion onthe delta foreset. This is conventional forced regression. If a $ w, on the

FIG. 3.—Conventional and new views of alluvial grade in terms of sea-level control. A) Conventional model in which alluvial systems aggrade (degrade) in response tosea-level rise (fall) and eventually attain an equilibrium, bypassing state if sea level remains constant. B, C) New view of alluvial grade, which is incorporated into theframework of autostratigraphy, in which grade is attained only during sea-level fall and never attained with stationary sea level. The sea-level trajectory (Rsl—t curve)required for grade depends on alluvial slope (a) and basin slope (w) onto which the depositional system progrades.

AUTOSTRATIGRAPHY 5J S R

other hand, autoincision does not occur. When a 5 w, in particular,alluvial grade is attained, after which the alluvium–basement transition isstationary and the height and length of deltaic foresets remain constant(Fig. 7B; Muto and Swenson 2006).

In a three-dimensional system, regression after the autoincisionthreshold can be characterized by valley incision and formation of pairedstream terraces on the abandoned delta-plain surface, as autogenicresponse to steady sea-level fall (Muto and Steel 2004; see also Blum andTornqvist 2000). After this first major incision, the subaerial plain of thedelta is no longer able to recover its original valley-free surface. Duringthe subsequent steady fall of sea level, the locus of active sedimentationmigrates progressively seawards. The active locus of sedimentationdownstream of the valley mouth can be analogous in shape to the deltathat was seen before the first major incision. The next major incision

event occurs when the migrating stream returns to an axial position onthe alluvial system where the stream gradient is highest. Multiple streamterraces thus form, one by one, arranged in an offset manner adjacent tothe active feeder stream.

PRIMARY FUNCTIONS OF THE GEOMETRICAL PARAMETERS

The autogenic stratigraphic response of fluviodeltaic systems dependson the geometrical parameters of the receiving basin (e.g., c, w) and theriver delta (e.g., a, b), if D remains constant with time. The geometricalparameters function to determine the subaerial and subaqueouspartitioning of the supplied sediment, and thereby they exert greatinfluence on the autogenic processes in deltas. As already noted above, itis also the geometrical parameters that control whether or not critical

FIG. 4.— Chronostratigraphic charts showingautogenic responses of the fluviodeltaic systemto steady rise of relative sea level. With rising sealevel, shoreline autoretreat is inevitable, andthere are three different patterns in autoretreat-related evolution of the depositional systemdependent on the geometrical conditions.A) Where b . c, the subaqueous surface of thedelta becomes starved of sediment (autobreak)shortly after, or possibly at the same time as, thebeginning of the retreat. In a three-dimensionalsystem where active sedimentation can belocalized and shift its position, delta lobes appearto be backstepping (autostepping) during thistransgression (Muto 2001; Muto and Steel 2001).B) Where b 5 c, autobreak is attained at sometime after the beginning of the retreat. Thesupplied sediment is consumed by covering theentire alluvial plain and barely supplied to thesubaqueous surface of the delta. This criticalstate is sustained during the transgression (Muto2002). C) Where b , c, autobreak is notattained, and thus the subaqueous surface of thedelta remains aggradational and progradationalduring the entire transgression (Swenson et al.2000; Muto 2002).

6 T. MUTO ET AL. J S R

thresholds (e.g., autobreak, autoincision) are attained during steady sea-level rise or fall, and whether or not the alluvial system can attain gradeduring sea-level fall (Figs. 3, 7). Even the intrinsic time scale can bedependent at least partly on the geometrical parameters (Eq. 3). Theimportance of these parameters has commonly been underestimated inconventional sequence stratigraphy.

When A 5 constant . 0, it is w and b that are mostly responsiblefor the manner of shoreline migration (Muto 2001). As w and b de-crease, autoretreat and autobreak tend to occur at earlier stages ofdelta development. When w is very small (say, ,, 1u), (1) theinitial regression of the shoreline can be very brief relative to theperiod of subsequent autoretreat, and (2) the autobreak threshold isreached as soon as autoretreat commences, almost regardless of thevalues of a and b. When A 5 constant , 0, on the other hand, a and cplay a critical role in whether and when autoincision, alluvial grade, orlong-lived aggradation are attained (Fig. 3; Swenson and Muto 2005).When a is much smaller than w, the autoincision threshold is attainedsooner (Muto and Steel 2002a). Alluvial grade, on the other hand, islikely to be attained earlier when a is close to w (Muto and Swenson2005a, 2006).

Response to sea-level fall can vary significantly between fluviodeltaicsystems with different geometrical parameters. For a particular pattern ofrelative sea-level fall, a river system may remain aggradational, whereasa nearby system may maintain grade, and a third one may incise. Hence,stratigraphic correlation on the basis of observed aggradation ordegradation in neighboring alluvial strata should be made with cautionand take full account of the geometrical parameters of the depositionalsystem.

GENERAL STRATIGRAPHIC RESPONSE

The general stratigraphic response is the superposition of componentsdue to steady (autogenic) as well as fluctuating terms of the externalforcing. In principle, reconstructing the history of external forcing thusinvolves a decomposition of the stratigraphic signature into its steady andfluctuating components. We might first attempt to explain as much of thestratigraphic signal as possible in terms of an autogenic response; theremainder of the signal might then be attributed to fluctuations inexternal forcing. However, this decomposition can be a nontrivial exerciseand can lead to erroneous stratigraphic interpretations. To illustrate this,consider the stratigraphic response shown in Figure 8B, where there isa morphodynamic model of fluviodeltaic sedimentation that treats theshoreline as a moving boundary (Swenson et al. 2000). External forcingfor the model system consists of steady sediment supply and subsidencerate and sinusoidal fluctuations in eustatic sea level (Fig. 8A). Steadysediment supply and subsidence rates allow computation of D and tscales. Sediment supply matches the rate at which subsidence createsspace, i.e., S 5 sD. The period of eustatic fluctuations (T) is equal to theautogenic time scale, i.e., T 5 t. In the model, physical time isnormalized with the autogenic time scale. Similarly, eustatic sea level(Zsl) is normalized with an elevation scale (aD) constructed from theproduct of the autogenic length scale and the characteristic fluvial slope.The amplitude of eustatic fluctuations is relatively small, minimizing thecomplexity in the corresponding stratigraphic response and, therefore,better illustrating the potential for erroneous stratigraphic interpretation.Note that the external forcing of the model problem closely resembles theassumed forcing in the conventional sequence-stratigraphic framework.

By inspection, the corresponding shoreline response to external forcingappears to consist of a fluctuating component superimposed on theautogenic response (Fig. 8B). In this example we know the externalforcing and thus we can easily compute the autogenic shoreline response,sauto(t), in the absence of eustatic fluctuations. We can easily decomposethe shoreline trajectory into an autogenic component and a residualcomponent, sres(t), where sres(t) 5 s(t) 2 sauto(t). The residual responseclearly displays a periodicity (Fig. 8B). Hence, one might naturallyassociate the residual shoreline response with the time-varying componentof external forcing to the fluviodeltaic system. Note, however, that theamplitude of the residual response decays strongly with increasing time,or with decreasing age in the stratigraphic record. If we were to applydirectly the equilibrium response, we would likely infer that the amplitudeof external forcing (eustatic sea level, in this case) decreased significantlyover the life of the basin, thereby giving rise to an incorrect sea-levelreconstruction, as the amplitude of eustatic forcing did not change(Fig. 8A).

This simple example illustrates clearly the potential for complexsuperposition of stratigraphic responses to steady and fluctuating externalforcing. The physical reason for the progressive decay in the amplitude ofthe residual shoreline response is tied to the autoretreat phenomenon.During autoretreat, the fluviodeltaic system partitions progressively moreof its sediment budget (S) to the subaqueous realm in order to maintainthe geometry of the delta foreset. This increased subaqueous partitioningresults in the landward migration of the shoreline that is the hallmark ofautoretreat. The increase in sediment delivered onto the delta requires anincrease in the sediment flux reaching the shoreline; in other words,progressively less sediment is sequestered in the ever-shrinking fluvialsystem during autoretreat, thereby leading to an increase in the fractionof the sediment supply that reaches the shoreline. An increase in thesediment supply at the shoreline is accompanied by an increase in theslope of the fluvial surface at and near the shoreline. By simple geometricreasoning, the amplitude of shoreline excursions driven by eustaticfluctuations is inversely proportional to the slope of the fluvial surfacenear the shoreline. Consequently, during autoretreat, the shoreline

FIG. 5.— Effects of a stationary sea-level period (ts) on shoreline migrationduring the subsequent period of constant sea-level rise, under the geometricalcondition that b . c and w 5 c. Height, distance, and time are dimensionless. Assoon as the sea level begins to rise, the shoreline begins to migrate upwards. If thesea-level stillstand stage is shorter than the time interval for the attainment ofautobreak (tb) in case of ts 5 0, the rising shoreline follows a curved trajectory(segment of autoretreat curve) and soon attains autobreak. As ts (, tb) becomeslonger, autobreak is attained at a lower height and in a shorter time (tb 2 ts) afterthe beginning of the sea-level rise. There is a critical value of ts (5 tb) for whichsea-level rise results immediately in autobreak. With a large value of ts (. tb), thedeltaic shoreline advances basinwards for a longer distance, but autobreak can beattained immediately after the beginning of the rise, accompanied by a very rapidlandward retreat of shoreline.

AUTOSTRATIGRAPHY 7J S R

response to superimposed eustatic fluctuations is progressively attenuat-ed, thereby giving rise to the progressive damping of the residual shorelineresponse in Figure 8B (Kim et al. 2006).

AUTOSTRATIGRAPHIC ANALYSIS

An important aim of autostratigraphy is to identify autostratigraphicunits in the geological record, thereby to identify and reconstructunsteady changes in basin forcing (allogenic events) affecting thedepositional system. The autostratigraphic unit can be defined asa succession of strata that accumulated under a discrete set of steady

basin-boundary conditions. For example, if sea level is rising at a constantrate and sediment supply is constant, then all of the resulting strata wouldconstitute a single autostratigraphic unit. If there occurs an allogenicchange in basin forcing (e.g., sea-level rise changed to sea-level fall), thisevent would mark or create a boundary between autostratigraphic units.We do not assume, at least in the early stages, that basin forcing changedcontinuously with time, because (1) allogenic change in basin forcing can bedetected only after testing a primary hypothesis that there was no allogenicchange, and (2) it is reasonable to treat unsteady forcing as a series ofdiscrete changes of steady forcing because of the intrinsic incompletenessand limited chronological resolution of the stratigraphic record.

FIG. 6.—Chronostratigraphic charts showing possible autogenic responses of the fluviodeltaic system to sea-level stillstand and subsequent change. A) Case where sea-level stillstand is followed by constant rise under the geometrical condition b . c. At the onset of sea-level rise, autobreak can be attained immediately and shorelinebegins to migrate landward very rapidly. B) Case where sea-level stillstand is followed by constant fall under the geometrical condition a , w, showing that theautoincision threshold can be attained some time after the beginning of sea-level fall (for this time lag see Swenson and Muto 2005), and then the alluvium–basementtransition abruptly starts to migrate basinward.

TABLE 1.— Apparent ‘‘symmetry’’ in autogenic processes for steady rise and fall of relative sea level.

Sea-level rise Sea-level fall

Horizontal turnabout of moving boundary shoreline (downstream end of alluvial slope) alluvium–basement transition (upstream end of alluvialslope)

- direction of turnabout from landward to basinward from basinward to landward

Break event in geomorphic and sedimentary regime autobreak autoincision- slope condition b . c a , w- when it occurs during transgression during regression

Discrete 3-dimensional topography forming after the breakevent by autocyclic behavior of the feeder system

autosteps autogenic stream terraces

Equilibrium state sustained autobreak threshold sustained alluvial grade- slope condition b 5 c a 5 w- what are in balance rate of subaerial aggradation

and rate of sea-level riserate of subaqueous aggradation and rate of sea-level fall

8 T. MUTO ET AL. J S R

In autostratigraphic analysis of fluviodeltaic deposits, attention needsto be paid to the geometrical patterns of shoreline trajectory (for sea-levelrise) and the trajectory of the alluvium–basement boundary (for sea-levelfall) and to the internal architecture of the deposit. There could be variousmethods of performing this autostratigraphic analysis. A numericalmethod suggested by Muto and Steel (2002b) is to detect a temporalchange in the magnitude of D (possibly t too; see Equations 2 and 3) from

observed shoreline trajectory, by finding autoretreat curves to fitindividual segments of the trajectory. An autoretreat curve passing anarbitrary spatial position x[x: horizontal distance, z; height], measuredfrom a particular shoreline position x0[x0, z0], can be specified witha particular magnitude of D and geometrical parameters (e.g., a, b, c, w).Suppose the shoreline migrated from x0[x0, z0] at time t0, through site 1(x1[x1, z1]) at time t1 and then site 2 (x2[x2, z2]) at time t2 (Fig. 9). If A or S

FIG. 7.— Chronostratigraphic charts showingthe autogenic responses of the fluviodeltaicsystem to steady fall of relative sea level. For theautogenic processes of falling sea level, attentionis paid to the upstream end of alluvial river, orthe alluvium–basement boundary, which, undera particular geometrical condition, can mimicshoreline movement during sea-level rise. A)Where a , w, the upstream end of alluvial riveronlaps landward at early stages but then beginsto migrate basinward. This critical moment ofchange from onlapping to offlapping corre-sponds with the autoincision threshold, whichrepresents change from aggradational to degra-dational regimes of the alluvial system (Mutoand Swenson 2005a; Swenson and Muto 2005,2006). B) Where a 5 w, the upstream end of thealluvial river can become stationary withina finite time after the beginning of sea-level fall.This is the state of sustained grade, during whichsupplied sediment simply bypasses the alluvialsystem and accumulates basinward of theshoreline (mostly, on the subaqueous slope of thedelta) (Muto and Swenson 2006).

FIG. 8.—Theoretical fluviodeltaic response toa combination of steady and fluctuating externalforcing. A) External forcing consists of twoeustatic cycles superimposed on steady sedimentsupply and subsidence rate. B) Decomposition ofthe shoreline trajectory, s(t), into an (autogenic)component, sauto(t), which represents the strati-graphic response to steady sediment supply andsubsidence, and a residual shoreline response,sres(t) 5 s(t) 2 sauto(t). The correspondingshoreline response to external forcing appears toconsist of a fluctuating component superimposedon the autogenic response. The residual responsedisplaying a clear periodicity would imply thatthe residual shoreline response was associatedwith the time-varying component of externalforcing to the fluviodeltaic system. Note, how-ever, that the amplitude of the residual responsedecays strongly with increasing time, or withdecreasing age in the stratigraphic record.

AUTOSTRATIGRAPHY 9J S R

changes during shoreline migration from x1 to x2, the magnitude of D

changes as well, thus causing the trajectory to deviate from the originalautoretreat curve that is assumed for the x0–x1 migration. As noted above(Eq. 1), it is common that any change in A (. 0) cannot be calculatedwithout specifying or assuming S beforehand, and vice versa. On theassumption that S 5 constant, a potential change in A during shorelinemigration from site 1 to site 2 is described by

A12

A01~ z2 { z0ð ÞD02

D01{ z1 { z0ð Þ

� �{1

z2 { z1ð Þ ð4Þ

where A01, A12 are the averaged magnitude of A for time intervalst 5 t02t1, t 5 t12t2, respectively, and D01, D02 are the magnitude of D

for autoretreat curves assumed for the x02x1 and x02x2 intervals,

respectively. If A, instead of S, is assumed to be constant, on the otherhand:

S12

S01~ z2 { z0ð ÞD02

D01{ z1 { z0ð Þ

� �z2 { z1ð Þ{1

~A12

A01

� �{1

ð5Þ

where S01, S12 are the averaged magnitudes of S for time intervalst 5 t02t1, t 5 t02t2, t 5 t02t2, respectively. A temporal change in A

(with constant S) or S (with constant A) can thus be estimated providedthat the numerical values of D01, D02, z0, z1, and z2 are given.

Muto and Steel (2002b) applied the above method to a lower Eoceneregressive shelf-margin succession on Spitsbergen, showing that it wasformed under an overall (i.e., long-term) decelerating rise of relative sealevel. In this local case, there are great uncertainties in the geological data

FIG. 9.— A numerical method of autostrati-graphic analysis for fluviodeltaic deposits thataccumulated with relative rise of sea level.Attention is here paid to if and how themagnitude of D, i.e., ratio of rate of sedimentsupply (S) to rate of sea-level rise (A), changedwith time. If we can specify autoretreat curves(C01, C02) that satisfy the geological dataobtained from each of sites 1 and 2, we canestimate numerically how D (5 S/A) changedwith time (i.e., D12/D01) while shoreline migratesfrom the assumed initial position (x0) to site 2(x2), via site 1 (x1). For detailed explanationsee Muto and Steel (2002b).

TABLE 2.—Comparison bewteen sequence stratigraphy and autostratigraphy.

Sequence stratigraphy Autostratigraphy

Primary view of strata Allogenic (autogenic secondary) Autogenic (allogenic secondary)

Response of depositional system toexternal forcing

Equilibrium Non-equilibrium

Key principles The A/S ratio concept Autoretreat principles

Function of sea level Erosional base level Level to control relative height of subaerial-subaqueousgeometrical contrast

View of alluvial grade A final stable stage of river system attained withstationary sea level, controlling subaerialaccommodation

A non-equilibrium state of river system sustained only with sea-level fall of a particular pattern determined by geometricalparameters of the depositional system

Interest in sedimentology Allogenic control of the formation of sequences Autogenic response of depositional systems to steady dynamicforcing

Interest in stratigraphy Global or regional correlations, primarily in termsof eustatic events

Detection of allogenic events which might be available tocorrelations for different basins

Methology of stratigraphic analysis Identification and recognition of sequences andsequence boundaries

Identification and recognition of autostratigraphic units and unitboundaries

Methodology of exploring principles Primarily inductive from the real stratigraphicrecord (e.g., outcrops, cores, seismic profiles)

Mostly deductive from forward-modeling (e.g., theoreticalmodeling, laboratory experiments)

Preferred sea-level changes tobe considered

Sinusoidal patterns of eustatic or relative sea-levelchanges

Linear-segmented patterns of relative sea-level changes

10 T. MUTO ET AL. J S R

as to the initial shoreline position, the geometrical and topographicalparameters, and the decompacted thickness of the deposit. In combina-tion with a large number (. 106) of runs of numerical simulation,however, the analysis successfully brought about a reconstruction ofchanges in A and S in terms of probabilistic distribution of possiblechanges in D. A change in D represents an interruption of the precedingautogenic stratigraphic response by the occurrence of an allogenic event,and the start of a new autogenic stratigraphic response.

A COMPLEMENTARY RELATIONSHIP WITH SEQUENCE STRATIGRAPHY

Conventional sequence stratigraphy interprets the formation of majorsystems-tract bounding surfaces (e.g., sequence boundaries, floodingsurfaces) as being formed at the inflection points during sinusoidaleustatic changes (superimposed on linear subsidence). Autostratigraphy,in contrast, suggests that abrupt changes in sedimentation occur duringlinearly varying base-level changes, and that the autoretreat andautoincision points do not necessarily coincide with inflection points.The autostratigraphic analysis allows responses resulting from linearchange to be distinguished from those of nonlinear change. The argumenton time scale presented above suggests strongly that many of theconventional sequence-stratigraphic notions do not hold in general (Mutoand Steel 1997) but are valid only when the time scale of externalfluctuations is very short relative to the time scale for the non-equilibriumresponse of the system to steady forcing (i.e., T ,, t). In other words,the conventional sequence-stratigraphic model represents a specific(limiting) case of the more general model developed above.

Time scale (T) can be an issue for consideration when evaluatingwhether the depositional system has taken an equilibrium or non-equilibrium response to external forcing. If the latter is the case, then wecan probably assume the existence of a ‘‘local,’’ quasi-equilibriumstate independent of base level. In this case the A/S ratio concept mightprovide the best insight to interpretation of the stratigraphic record(Muto and Steel 1997; Kim et al. 2006). Sequence stratigraphy andautostratigraphy can thus be complementary (Table 2). Autostratigraphyprimarily assumes hypothetical and simple (or simplistic) conditions.Sequence stratigraphy deals with realistic, natural environments in whichboth autogenic and allogenic processes are in operation. An importantcaution in the application of sequence stratigraphy to the stratigraphicrecord is that there needs to be careful consideration of T and t. If slowfluctuation in an external control is superimposed on the non-equilibriumresponse to the steady (average) component of allogenic forcing (i.e.,T $ t), the conventional sequence-stratigraphic model is likely to beinsufficient.

CONCLUSIONS

Some of the principles of autostratigraphy, the stratigraphy of large-scale autogenic processes of depositional systems and their geologicalproducts, have been explored, particularly as related to fluviodeltaicsystems under sea-level forcing. Key notions of autostratigraphy are asfollows:

1. The large-scale autogenic behavior of fluviodeltaic systems, in-cluding autoretreat, autobreak, autoincision, and attainment ofgrade, arises from their intrinsic non-equilibrium response to steadyforcing. There is unlikely to be an equilibrium configuration in thedepositional system subject to steady forcing.

2. Abrupt breaks and discrete topographic features are not necessarilyassociated with sudden changes in rate of base-level movement butcan result from purely autogenic responses of the system. On theother hand, stratigraphic responses that fall on a break-free curvecan result from an unsteady change in allogenic forcing.

3. Fluviodeltaic systems developing during a change in relative sealevel have particular spatiotemporal scales (length D, time t) thatare characteristic of a particular depositional system and aredefined with parameters of external forcing including rate of thesea-level change (A) and rate of sediment supply (S). Manifestationof the non-equilibrium response is dependent on t relative to theperiodicity (T) of sea-level forcing or the time interval considered. IfT is comparable to or longer than t, the non-equilibrium response isprominent.

4. The superposition of allogenic (or equilibrium) and autogenic (ornon-equilibrium) responses is nonlinear. This nonlinear superposi-tion can be decomposed into the two effects by autostratigraphicanalysis. Possible methods of autostratigraphic analysis to identifynon-autogenic events in the stratigraphic record include numericaldetection of a temporal change in magnitude of D from observedshoreline trajectory.

5. Autostratigraphy is complementary to sequence stratigraphy.Sequence stratigraphy represents a limiting case of a more generalmodel (autostratigraphy), and functions to be valid only whenT ,, t.

ACKNOWLEDGMENTS

This work was financially supported in part by a Japanese Grant-in-Aid forScientific Research (15340171) to TM. RS appreciates the continued supportand encouragement of many individuals in the WOLF-consortium compa-nies. JBS appreciates grants from the Office of Naval Research (GrantN00014-02-01-0233) and the University of Minnesota Graduate School. Weappreciate encouragement and discussion of ‘‘self organization’’ in sedimen-tary systems by Chris Paola, Gary Parker, Janok Bhattacharya, BobDalrymple, Szczepan Porebski, and Piret Plink-Bjorklund. Critical commentsprovided by JSR reviewers (Brian Willis, Rudy Slingerland, JanokBhattacharya, Colin North) were constructive and very helpful in revisionof an early version of the manuscript.

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D length scale LS rate of sediment supply in unit width L2T21

T time TX horizontal distance of shoreline LZ height of shoreline La alluvial slope 1b delta foreset slope 1c basal slope at alluvium–basement transition 1w basal slope at delta toe 1t time scale Tu fluvial diffusivity LT21

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Received 11 December 2005; accepted 30 August 2006.

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