Temporal significance of sequence boundaries

Transcription

1 ELSEVIER Sedimentary Geology 121 (1998) Temporal significance of sequence boundaries Octavian Catuneanu a,ł, Andrew J. Willis b, Andrew D. Miall c a Department of Geology, Rhodes University, Grahamstown 6140, South Africa b Rigel Energy Corporation, 1900, 255 5th Ave. S.W., Calgary, Alberta T2P 3G6, Canada c Department of Geology, University of Toronto, Toronto, Ontario M5S 3B1 Canada Received 15 May 1997; accepted 22 June 1998 Abstract This paper analyses the temporal significance of stratigraphic surfaces bounding the marine portions of the depositional sequence, genetic stratigraphic sequence and transgressive regressive sequence. These bounding surfaces, known as the correlative conformity (c.c.), maximum flooding surface (MFS) and conformable transgressive surface (CTS), respectively, may either be defined on the basis of stratal stacking patterns (which we call type A surfaces ), or on the basis of water-depth changes and relative sea-level changes (which we call type B surfaces ). The type A MFS and CTS are time lines in a depositional-dip section, corresponding to the turnaround points from shoreline transgression to regression and vice versa. They separate prograding (coarsening-upward) from retrograding (fining-upward) geometries, with a timing determined by the interplay between the rates of sedimentation and relative sea-level rise in the shoreline area. The timing of type A MFS and CTS is not affected by the offshore variations in sedimentation and subsidence rates, but it is only controlled by the shoreline movements and the associated facies shifts. The type A c.c. separates rapidly prograding and offlapping forced regressive strata from the overlying lower rate prograding and aggrading normal regressive strata. This surface is diachronous, younger basinward, with the rate of offshore sediment transport. The timing of the type A c.c. in the shoreline area corresponds to the end of relative sea-level fall, but it develops under relative sea-level rise conditions offshore. The timing of the type B MFS and CTS depends on the offshore variations in the sedimentation and subsidence rates. These surfaces, defined on the basis of bathymetric changes, become younger and older seaward, respectively, tending to merge together offshore. The type B c.c. marks the end of relative sea-level fall in any point along a depositional-dip section. It is diachronous, older basinward, as its timing depends on the offshore variations in subsidence rates. The diachroneity of type B surfaces reaches a quarter of the period of the highest frequency variable, whichever that is among the eustasy, tectonics or sedimentation controls. Types A and B surfaces merge together in the shoreline area, but they become temporally divergent offshore. Deepening-upward and shallowing-upward facies should not be confused with transgressive and regressive systems tracts. The latter are strictly controlled by the shoreline movements, which determine the direction of facies shifts and the stratal stacking patterns Elsevier Science B.V. All rights reserved. Keywords: sequences; systems tracts; bounding surfaces; diachroneity Ł Corresponding author. oc@rock.ru.ac.za /98/$ see front matter c 1998 Elsevier Science B.V. All rights reserved. PII: S (98)

2 158 O. Catuneanu et al. / Sedimentary Geology 121 (1998) Introduction A controversial topic in modern stratigraphy is the assessment of the relationship between sequence stratigraphy and chronostratigraphy. Are the sequence-bounding surfaces time lines, i.e. generated at the same time everywhere within the area of occurrence? The answer to this question is of paramount importance for stratigraphic correlation, and although this problem has been around for some time (Miall, 1991, 1994), an agreement is yet to be reached. Part of the problem derives from the way concepts are defined and used, often with contradictory meanings, as we present in this introduction. The various types of sequences and bounding surfaces are illustrated in Fig. 1. The depositional sequence (Jervey, 1988; Posamentier et al., 1988; Van Wagoner et al., 1990; Haq, 1991; Vail et al., 1991; Hunt and Tucker, 1992) is defined in relationship to the relative sea-level (base-level) curve, and it is bounded by the subaerial unconformity (SU) and its marine correlative conformity (c.c.). The timing of the SU is generally related to the stage of baselevel fall (Fig. 1; Posamentier et al., 1988; Hunt and Tucker, 1992; Embry, 1995), whereas the c.c. was initially considered to form during early sea-level fall (Posamentier et al., 1988) or at the beginning of the sea-level fall (Posamentier et al., 1992), which was later revised to the end of relative fall (Fig. 1; Hunt and Tucker, 1992; Helland-Hansen and Martinsen, 1996). The depositional sequence comprises four systems tracts with distinct stratal stacking patterns (Figs. 1 and 2): the highstand systems tract (HST) forms during late relative rise, when the sedimentation rate exceeds the rate of relative rise in the shoreline area (normal regression); the falling stage systems tract (FSST) forms during relative fall (forced regression); the lowstand systems tract (LST) forms during early relative rise, when the sedimentation rate exceeds the rate of relative rise in the shoreline area (normal regression); and the transgressive systems tract (TST) which forms when the rate of relative sea-level rise in the shoreline area exceeds the sedimentation rate. The former three systems tracts (HST, FSST and LST) form together a progradational package known as a regressive systems tract (RST; Embry and Johannessen, 1992). A RST followed by a TST form together a genetic stratigraphic sequence (Fig. 1; Galloway, 1989), bounded by maximum flooding surfaces (MFS). The combination of a TST followed by a RST gives the transgressive regressive (T R) sequence (Fig. 1; Embry and Johannessen, 1992; Embry, 1993, 1995), bounded by conformable transgressive surfaces (CTS) in the marine portion of the basin. The nonmarine correlative of the CTS is either unidentifiable within the fluvial succession overlying the SU, or eroded by the ravinement surface. In either case, the SU was conveniently chosen to represent the T R sequence boundary in the nonmarine succession (Embry, 1993, 1995). We focus our analysis on bounding surfaces developed within marine successions, i.e. the c.c., CTS and MFS. The c.c. may be defined in three ways, which allow for different temporal interpretations. (1) It is a surface taken by definition as a time Fig. 1. Types of sequences, bounding surfaces and systems tracts, defined in relationship to the relative sea-level and transgressive regressive curves. The relative sea-level depends on the combined effect of eustasy and tectonics, whereas the generation of transgressive and regressive facies depends on the combined effect of relative sea-level changes and sedimentation. The depositional sequence boundary (i.e., subaerial unconformity and its marine correlative conformity) is generated at the end of relative sea-level (base-level) fall (Hunt and Tucker, 1992; Helland-Hansen and Martinsen, 1996). The genetic stratigraphic sequence boundary (i.e., maximum flooding surface) is taken at the top of marine and nonmarine transgressive facies (Galloway, 1989). The T R sequence boundary is taken at the top of marine regressive facies (i.e., the conformable transgressive surface, Embry, 1995). Within nonmarine facies, the T R sequence is arbitrarily chosen to coincide with the depositional sequence in spite of the fact that the RST extends above the SU, due to the difficulty in field recognition of the CTS-correlative. In special circumstances (i.e., short LST stages and strong erosion associated with the ravinement surface), the most basinward portion of the nonmarine LST may not be preserved and thus the CST could be mapped in the continuation of the SU. Note that normal regressive facies accumulate in the earliest (LST) and latest (HST) stages of relative sea-level rise, due to sedimentation outpacing the low rates of relative rise. We take here the LST to be equivalent to the lowstand prograding-wedge systems tract of Hunt and Tucker (1992). Abbreviations: DS D depositional sequence; GS D genetic stratigraphic sequence; T R D transgressive regressive sequence; LST D lowstand systems tract; TST D transgressive systems tract; HST D highstand systems tract; FSST D falling stage systems tract; RST D regressive systems tract; SU D subaerial unconformity; c.c. D

3 O. Catuneanu et al. / Sedimentary Geology 121 (1998) correlative conformity; CTS D conformable transgressive surface; CTS-c D CTS-correlative (i.e., the nonmarine correlative of the marine CTS); MFS D maximum flooding surface; R D ravinement surface; BSFR D basal surface of forced regression; IV D incised valley; (A) D creation of accommodation space (base-level rise); NR D normal (sediment supply-driven) regression; FR D forced (base-level fall-driven) regression.

4 160 O. Catuneanu et al. / Sedimentary Geology 121 (1998)

5 O. Catuneanu et al. / Sedimentary Geology 121 (1998) line, which begins at the basinward termination of the SU and extends throughout the conformable marine succession (Jervey, 1988; Embry, 1995). The timing of this conformable surface was related to various portions of the sea-level or relative sea-level curves, finally settling at the end of relative fall in the shoreline area, i.e. the depositional surface which existed at the end of the forced regression of the shoreline (Embry, 1995: The subaerial unconformity is developed and migrates seaward during base-level fall and reaches its maximum extent at the end of the fall :::, the depositional surface in the marine realm at this time of change from base-level fall to base-level rise is the correlative conformity, portrayed as a time line in his fig. 1). The time line significance of such surface is of course valid along a depositional dip section, as varying subsidence rates along the depositional strike may offset the transition between base-level fall and base-level rise along the shoreline; (2) It is a surface defined on the basis of stratal stacking patterns, separating the offlapping forced regressive lobes from the overlying aggradational LST (Fig. 2; Haq, 1991: a change from rapidly prograding parasequences to aggradational parasequences ). This definition implies a diachronous c.c., younger basinward, with a diachroneity rate that matches the rate of offshore sediment transport (Fig. 3). The transport rate of terrigenous sediments along the depositional dip within a marine basin varies from m=s in the case of low gradient marine systems, to m=s in the case of turbiditic flows associated with higher gradients (Reading, 1996). For this reason, the c.c. is represented with a higher diachroneity within the terrigenous progradational wedge relative to the deeper marine basin where it tops the submarine fan deposits (Fig. 3). (3) It is the surface that marks the end of relative sea-level fall within the marine basin (Posamentier and Allen, 1993: eustasy and sea-floor subsidence=uplift determine the timing of sequence bounding surfaces ). This definition also implies a diachronous c.c., as the relative sea-level partly de- pends on varying subsidence rates across the basin. We investigate in this paper the diachroneity rate of this type of c.c. The CTS represents the marine T R sequence boundary, and only a systems tract boundary in the view of the depositional sequence model (Fig. 1). It may be defined either: (1) on the basis of stratal stacking patterns, as a conformable surface which separates regressive strata (progradational pattern) below from transgressive strata (retrogradational pattern) above (Embry, 1993, 1995); or (2) on the basis of bathymetric (water-depth) changes, as a conformable surface recording the start of a deepening episode, i.e. formed when the water-depth reaches the shallowest peak (Embry, 1993). Although these two definitions are considered equivalent, they allow different temporal significances for the CTS. The former relates to the shoreline movements and the associated changes in stacking patterns, which brings the CTS to a time line in a depositional dip section, independent of the offshore variations in sedimentation and subsidence rates, as there is only one point in time where the shoreline is at its most basinward position. The sediment supplied from the onshore during the shoreline regression generates a coarsening upward marine succession related to the basinward facies shift, sharply overlain by much finer transgressive strata as the coarse terrigenous sediments are trapped within the shoreline systems during transgression (Fig. 3). This provides a lithological criterion to pinpoint the CTS position in outcrops or subsurface logs (Embry, 1993; fig. 5 in Catuneanu et al., 1997). The second definition implies a diachronous CTS, as the water-depth changes depend on varying sedimentation and subsidence rates across the basin. In this light, it is recognized that the CTS is younger in areas with higher sedimentation rates, where the transition from shallowing to deepening may occur later, although this diachroneity is considered minor (Embry, 1995). We investigate in this paper the diachroneity rate of this type of CTS. TheMFSmayalsobedefinedintwoways:(1) Fig. 2. Systems tracts of the depositional sequence, defined on the basis of stratal stacking patterns. The sinusoidal curves illustrate relative sea-level changes in the shoreline area, which may be different in terms of rates and sign from the coeval relative sea-level changes occurring farther offshore.

6 Fig. 3. Wheeler diagram illustrating bounding surfaces defined on stratal stacking patterns. Zone A D low-rate diachroneity at the top of the condensed section, which equals the rate of offshore sediment transport. Zone B D higher-rate diachroneity at the top of the condensed section, which equals the rate of shoreline regression. 162 O. Catuneanu et al. / Sedimentary Geology 121 (1998)

7 O. Catuneanu et al. / Sedimentary Geology 121 (1998) on the basis of stratal stacking patterns, marking the change from transgressive strata below to regressive strata above (Galloway, 1989); or (2) on the basis of bathymetric (water-depth) changes, being formed when the water reaches the deepest peak (Naish and Kamp, 1997). Again, these two approaches define bounding surfaces which are not necessarily superimposed. In the former approach, the MFS is associated with the condensed section separating retrograding facies, below, from prograding facies above. Ideally, it corresponds to the time line coeval to the moment in time where the shoreline is at its most landward position within a given depositional dip section (Fig. 3). In this case, the MFS separates retrograding from prograding stratal patterns (downlap surface) irrespective of the variations in sedimentation and subsidence rates along the depositional dip. Even so, a certain diachroneity exists along the depositional strike, as variations in sedimentation and subsidence rates determine temporally offset transitions from transgression to regression along the shoreline (Gill and Cobban, 1973; Martinsen and Helland-Hansen, 1995). In practice, it is very difficult to pinpoint the time line surface within the condensed section, and the more readily recognizable base of the overlying terrigenous progradational wedge (limit between the condensed section and the overlying terrigenous prograding facies in Fig. 3) may be approximated as the downlap surface. This MFS is of course diachronous, with the rates of offshore sediment transport (zone A in Fig. 3) or shoreline=sedimentary lobes progradation (zone B in Fig. 3), which can be emphasized using volcanic ash layers as time markers (Ito and O Hara, 1994). The latter definition implies a diachronous MFS along both depositional dip and strike sections, as the basin bathymetry depends on varying sedimentation and subsidence rates. As noted by Naish and Kamp (1997), the maximum water depth (i.e., their MFS) often occurs within the lower part of the HST (normal regressive) progradational wedge. Thus the boundary between prograding and retrograding geometries (downlap surface) will correspond to a physical surface, recognizable on the basis of stratal stacking patterns, whereas the MFS is unknowable lithologically and can only be identified using foram paleobathymetry. We apply end-member boundary conditions to surfaces formed as a result of the complex interplay between eustasy, subsidence and sedimentation (i.e., CTS and MFS defined on the basis of water-depth changes), as well as to surfaces formed as a result of the interaction between eustasy and tectonics (i.e., the c.c. formed at the end of relative fall, and its counterpart, the surface marking the start of relative fall). The temporal significance of these surfaces will be compared with the timing of surfaces defined on the basis of stratal stacking patterns. 2. Controlling factors on relative sea-level changes and water-depth changes The water-depth changes depend on the interplay between eustasy, tectonics (which combined give the relative sea-level changes) and sedimentation (Fig. 4). Sediment compaction may also interfere in this process by creating additional accommodation space (base-level rise effect), but it has exactly the same consequences as the tectonic subsidence and therefore we incorporate compaction within tectonics in our quantitative modelling. The causes, magnitudes and rates of change of these variables have been described at length by Galloway (1989) and need not be reiterated here. It is sufficient to note that all three variables can attain comparable rates of change and thus have equal potential to influence the generation of CTS and MFS. A positive rate of change of the water-depth (i.e., deepening) will result in upward-deepening facies (UDF), and a negative rate (i.e., shallowing) in upward-shallowing facies (USF). The boundary between UDF and overlying USF (and vice versa: MFS and CTS respectively) therefore occurs at the point where the rate of water-depth change is equal to zero. Similarly, the correlative conformity portion of the depositional sequence boundary (c.c.), as well as the surface marking the start of relative fall, form when the rate of relative sea-level changes equals zero. As sequence-bounding surfaces form only where the rate of water-depth or relative sea-level changes is equal to zero, it is implicit that the interacting variables must be of the same order of magnitude to periodically balance one another and meet this condition. If the magnitude of one of the variables

8 164 O. Catuneanu et al. / Sedimentary Geology 121 (1998) Where the rates of change of the variables are in the same range, one will normally vary with a higher frequency than the others. The higher-frequency variable will be the driving force behind the high-frequency changes in the stratigraphic record. It is commonly assumed that eustasy is the higherfrequency variable (Posamentier and James, 1993), but this need not be so. It is quite conceivable that eustasy could maintain a uniform rate of change over the duration of several episodes of subsidence and uplift. In this case tectonic subsidence=uplift would be the driving force behind sequence formation, as it the case for instance with the Late Cretaceous sequences of the western Canada foreland basin (Catuneanu et al., 1997). To facilitate simpler graphical presentation of the results, the rate of water-depth change (W) can be obtained from the three variables rate of eustatic change (E), rate of tectonic subsidence (T) and rate of sedimentation (S), via derived proxy variables in three ways, two of which make geological sense (Fig. 4). Fig. 4. Diagrammatic illustration of two ways in which the rate of water-depth change (W) can be obtained from the three primary variables eustasy (E), tectonics (T) and sedimentation (S) via subsidiary derived variables. Reducing the three primary variables to combinations of two proxies facilitates the construction of simple geometrical models which still retain the effects of all three, rather than the usual approach of eliminating one variable. Case 1 combines the rate of tectonic subsidence=uplift (T) and the rate of sedimentation (S) to define the rate of movement of the depositional surface (D), which when added to the rate of eustatic change (E) gives the rate of water-depth change (W). Case 2 combines the rates of eustatic change (E) and tectonic subsidence=uplift (T) to define the rate of relative sea-level change (R), which when added to the sedimentation rate (S) also gives the rate of water-depth change (W). is always much larger than the others, then the effect of the smaller variables will be effectively suppressed. For example, if the rate of subsidence is always greater than the combination between eustasy and sedimentation, continuous relative sealevel rise and transgression occur and no sequencebounding surfaces will form. An example of such disparity between subsidence and eustatic rates is described from the Banda Arc by Fortuin and de Smet (1991) Case 1 If we combine the rate of tectonic subsidence (T) with the rate of sedimentation (S), we arrive at a derivative variable (D) reflecting the rate of movement of the depositional surface. The sum of the rate of movement of the depositional surface (D) and the rate of eustatic change (E) gives the rate of change of the water-depth (W), which controls the stratigraphic pattern of UDF and USF as described above Case 2 We can also arrive at the rate of change of the water-depth (W) in a second way. The rates of eustatic change (E) and tectonic subsidence (T) can be combined into a variable reflecting the rate of relative sea-level change (R) (Posamentier et al., 1988). By combining this derived variable (R) with the primary variable rate of sedimentation (S), we arrive at the rate of water-depth change (W). If the rate of relative sea-level rise exceeds the rate of sedimentation (S), then (W) will be positive, a continuous UDF succession will be deposited, and no bounding surfaces will form. If the reverse is

9 O. Catuneanu et al. / Sedimentary Geology 121 (1998) true, i.e. the rate of sedimentation (S) is greater than the rate of relative sea-level rise, then (R) will be negative and continuous shallowing ( normal regression in the shoreline area) will occur. 3. Timing of bounding surfaces controlled by water-depth changes 3.1. Two-dimensional model To illustrate the effect that subsidence and sedimentation rates have on the temporal formation of CTS and MFS defined on the basis of bathymetric changes, we have constructed a simple two-dimensional geometrical basin model applied to an open marine shelf setting, which we will refer to as Profile A. We have chosen to model the case where eustasy is the highest-frequency variable and subsidence and sedimentation are grouped together as the variable (D) (Case 1 in Fig. 4), since it facilitates comparison with the depositional sequence model of Posamentier et al. (1988). The input values used for the variable rates of change are obtained from the literature (Pitman, 1978; Pitman and Golovchenko, 1983; Angevine, 1989; Galloway, 1989; Jordan and Flemings, 1991; Macdonald, 1991; Frostick and Steel, 1993). The assumptions of the model are as follows: (1) Eustasy varies sinusoidally with an amplitude of 10 m and period of 2 Ma (Fig. 5). For the sake of brevity, we have illustrated only half of the eustatic cycle, from highstand to lowstand. The rate of eustatic fall increases from zero at highstand (0 Ma) to a maximum of 15.7 m=ma at the inflexion point (0.5 Ma), and then decreases to zero at lowstand (1 Ma). (2) The modelled portion of the basin is 200 km across, and the tectonic subsidence rate (T) is constant at any particular point, but increases basinward from 20 m=ma at the proximal end of the profile to 40 m=ma at the distal end. This is similar to the simple divergent margin models of Pitman (1978), Angevine (1989) and Jordan and Flemings (1991). (3) Rather than assuming an unrealistic constant sedimentation rate (S) across the basin, we assume that (S) decreasesfrom 15 m=ma at the proximal end of the basin profile to 5 m=ma at the distal end. This reflects the tendency of coarser-grained sediments to be trapped close to the shoreline. A consequence of this is that since the sedimentation rate at any point along the basin profile is a function of its distance from the shoreline, it must therefore vary in time as the shoreline progrades and retreats. It is this feedback loop between water-depth changes and sedimentation that causes progradation and retrogradation (Demarest and Kraft, 1987). Incorporation of Fig. 5. The eustatic variation considered in the model. Eustasy is assumed to vary sinusoidally with an amplitude of 10 m and period of 2 Ma. Only half the eustatic cycle (180º phase or 1 Ma) from highstand to lowstand is shown. The rate of eustatic change at each Ma time increment, given by the differential of the sine curve, is shown on the left.

10 166 O. Catuneanu et al. / Sedimentary Geology 121 (1998) Fig. 6. Computation of the rate of facies shift as a function of the rate of water-depth change and gradient of the depositional surface. This phenomenon links facies progradation retrogradation and water-depth changes. this induced facies shift into the model would necessitate recalculating the sedimentation rate at each point along the profile at each model time step. The magnitude of the sedimentation rate shift is a function of the rate of water-depth change and the gradient of the depositional surface (Fig. 6). By assuming an extreme shelf gradient of 1º and using our highest rate of water shallowing (20.7 m=ma), we calculate that the maximum lateral sedimentation rate shift is 148 m per Ma (one time step). At the scale of the modelled basin profile (200 km) this is insignificant, so we have ignored it and assumed the sedimentation rate (S) to be constant at any given point through time. Combining the rates of tectonic subsidence (T) and sedimentation (S) at each point along the basin profile gives the rate of movement of the depositional surface (D). As we have demonstrated above that the lateral migration of the sedimentation rate (S) is essentially negligible at the scale of the model, the rate (D) remains constant at any particular point on the profile through the course of the eustatic half-cycle. The value of (D) does vary spatially, reflecting the reality of differential subsidence and sediment supply. The model was advanced in increments of Ma. For each incremental time step, by adding the rate of eustatic change (E) to the rate of depositional surface movement (D) at each point along the profile, we calculate the rate of the water-depth change (W) across the basin. The result is a graphic output (Fig. 7) showing which portions of Profile A are undergoing water-depth shallowing (W negative), and which water-depth deepening (W positive). The boundary between these two zones marks the point at which water-depth is stationary, which as noted above is the condition for a sequence-bounding surface to form. This will be a CTS where it tops USF, and a MFS where it tops UDF Model results The model is started at eustatic highstand, where the rate of eustatic change (E) is zero. The rate of water-depth change (W) at this time is thus equal to the rate of movement of the depositional surface (D) and is positive along the entire length of the profile (Fig. 7). This water-depth deepening results in UDF throughout Profile A. The successive incremental time steps of the model through a 1 Ma eustatic half-cycle from highstand to lowstand are shown in Fig. 7. At each time step, the distance along the profile at which the rate of water-depth change (W) equals zero is indicated; this is the point at which a sequence-bounding surface is formed, separating areas of coeval deposition of upward-deepening and upward-shallowing facies. The bounding surface generated between time steps 1 and 5 is referred to as a MFS because it separates UDF, below, from the overlying USF. The bounding surface generated starting with time step 5 is a CTS as it separates USF from the overlying UDF.

11 O. Catuneanu et al. / Sedimentary Geology 121 (1998) As the rate of eustatic fall (E) increases from time step 1 to 5 (the eustatic inflexion point), a progressively larger value of net subsidence (D) is required to balance it and maintain the stationary water-depth condition under which the MFS forms. This results in the formation of the MFS moving basinward through time in the direction of increasing (D). The MFS is thus younger offshore than it is towards the basin margin. Time step 5 (0.5 Ma) is the inflexion point on the falling limb of the sinusoidal eustatic curve and represents the maximum rate of eustatic fall. This is balanced by (D) at a distance of 71.3 km along the profile (Fig. 7). Basinward of this point, the rate of subsidence of the depositional surface (D) always exceeds the maximum rate of eustatic fall (E), and a MFS is not formed. During time steps 5 to 9 the rate of eustatic fall decreases to zero. Continued subsidence (D) results in a water-depth deepening and UDF. As the rate of eustatic fall decreases, it is balanced by a progressively lower value of (D) and the boundary (in this case the CTS) thus moves toward the basin margin. The CTS is therefore older offshore than it is toward the basin margin (Fig. 7) Strike variability To further illustrate the diachroneity of the bounding surfaces we have added two other basin profiles (B and C) to the model (Fig. 8). These represent dip-sections across the same basin at 50 and 100 km along strike from Profile A. Profiles B and C are assigned slightly different values of subsidence rate (T) and sedimentation rate (S) to reflect the type of strike-variability found in reality. All three models were run through the same eustatic half-cycle, Fig. 7. Timing of sequence-bounding surface formation along basin Profile A as a function of the interaction between eustasy (E), subsidence (T) and sedimentation (S). The input values of (T) and (S) are given at the top together with the resulting range of values of (D). The value of (E) comes from Fig. 5. The rate of water-depth change (W) is shown across the basin profile at nine incremental time steps through a eustatic half-cycle from highstand to lowstand. A sequence-bounding surface forms where the rate of water-depth change (W) equals zero, and migrates laterally with time as different combinations of the three variables meet this criterion.

12 168 O. Catuneanu et al. / Sedimentary Geology 121 (1998)

13 O. Catuneanu et al. / Sedimentary Geology 121 (1998) The diachroneity (duration) of bounding surface formation along the 200 km of Profile B is 0.5 Ma, which is approaching the resolution of ammonite zonation in the Jurassic and Cretaceous. It is noted that the USF generated during the model run, outlined by a MFS at the base and a CTS at the top, does not extend across the entire basin but it wedges out offshore where the rates of relative subsidence of the depositional surface (Fig. 4) completely outpace the rates of eustatic fall and therefore a continuous deepening of the sea takes place (Figs. 7 9). This situation reinforces the fact that bounding surfaces may only be generated when the three controlling factors vary in the same range. 4. Timing of bounding surfaces controlled by relative sea-level changes 4.1. Two-dimensional model Fig. 9. Isochron maps of the basin containing Profiles A, B and C showing the timing of bounding surface formation: (1) the time of formation of the maximum flooding surface (formed during time steps 0 to 5), and (2) the time of formation of the conformable transgressive surface (formed during time steps 5 to 9). The duration of bounding surface formation (i.e., its diachroneity) during the considered half of the eustatic cycle wavelength is 0.5 Ma, or one quarter of the eustatic cycle period. which allows the formation of bounding surfaces to be depicted in a map view. The graphical incremental time steps for ProfilesBandCareshowninFig.8.Byusingthe output time distance data for bounding surface formation point along each of the three profiles, we have constructed isochron maps of sequence-bounding surface formation through the eustatic half-cycle (Fig. 9). The isochrons join points where bounding surface formation was synchronous on the three profiles and show its diachronous movement. The rate of movement varies with the rate of eustatic change. The data input for the numerical model presented in the preceding section depicts a situation in which the subsidence rates are always greater than the rates of eustatic fall. This is a case of continuous relative sea-level rise in which sedimentation, together with varying rates of eustatic fall, represent key elements in the deposition of UDF and USF, and implicitly in the formation of CTS and MFS. However, no surfaces controlled by relative sea-level changes (i.e., the c.c. and its counterpart surface generated at the start of relative sea-level fall) may form during continuous relative sea-level rise (Fig. 1). For these surfaces to form, a transition from relative rise to relative fall and vice versa is required, which may only happen when eustasy and tectonics vary within at least partially overlapping ranges. To model this situation, we take two additional depositional-dip sections, referred to as Profiles D and E (Figs. 10 and 11), which are parallel to each other and separated by a distance of 100 km measured along the depositional strike. We use the same curve of eustatic variation as for Profiles A C (Fig. 5), this time in Fig. 8. Incremental output of Profiles B and C model runs. These profiles are assigned different rates of subsidence (T) and sedimentation (S) to Profile A, but the same eustatic curve (E) shown in Fig. 5 was used. The different rates of movement of the depositional surface (D) in Profiles A, B and C result in along-strike variation in the timing of boundary formation.

14 170 O. Catuneanu et al. / Sedimentary Geology 121 (1998) Fig. 10. Diachronous formation of surfaces separating deposits accumulated under relative sea-level fall and rise conditions (left column), as well as deposits accumulated under water deepening and shallowing conditions (right column). The rates of tectonic subsidence for Profile D have been selected to partially overlap with the rates of eustatic fall (Fig. 5), to allow both relative sea-level fall and rise to manifest within the modelled area. E D rate of eustatic change.

15 O. Catuneanu et al. / Sedimentary Geology 121 (1998) Fig. 11. Similar computations as in Fig. 10, only with a different set of rates for tectonic subsidence, to illustrate the possible strike variability within the sedimentary basin.

16 172 O. Catuneanu et al. / Sedimentary Geology 121 (1998) interplay with lower rates of subsidence and sedimentation. The difference between the sets of input data selected for Profiles D and E consists in the subsidence rates, being slightly greater for Profile E. The model run, advancing at incremental time steps of Ma, is similar to the one described in Section 3.3. The interplay between partially overlapping eustatic and subsidence rates allows the manifestation of both relative sea-level fall and rise during the considered eustatic half-cycle. At each time step, the distance along the profile at which the rate of relative sea-level change (R) equals zero is indicated; this is the point at which a sequence-bounding surface (c.c. or start of relative fall surface) is formed, separating areas of coeval relative fall and rise. As the point of stationary relative sea-level migrates in time within the basin, the c.c. (end of relative fall) and its counterpart (onset of relative fall) are found to be diachronous, with a net diachroneity approaching 0.5 Ma (a quarter of the eustatic cycle; Figs. 10 and 11, left columns). By adding the effect of sedimentation to the relative sea-level changes, the water-depth changes as well as the timing of the CTS and MFS could be modelled as well (Figs. 10 and 11, right columns). The slightly steeper slopes for the CTS and MFS relative to the c.c. and the start of relative fall surface (Figs. 10 and 11) indicate higher rates of diachroneity for the former, which is explained by the additional control of sedimentation. Fig. 12 illustrates the case of Profile D during one and a half eustatic cycles, with the CTS, MFS, c.c. and SRFS (start of relative fall surface) curves plotted from Fig. 10. The shoreline trends, as well as the various types of systems tracts separated by these bounding surfaces are also represented. The basinward increase in subsidence rates, parallelled by a decrease in sedimentation rates, imposes a limit in the seaward extent of the USF, assuming that the subsidence rate in the basin centre exceeds the maximum rate of eustatic fall. The basinward extent of bounding surfaces controlled by relative sea-level changes (c.c. and SRFS) reaches the point where the subsidence rates start to exceed the maximum rate of eustatic fall. Similarly, bounding surfaces controlled by water-depth changes (CTS and MFS) extend up to the point where the rate of relative subsidence of the depositional surface (D D T S, Fig. 4) starts to exceed the maximum rate of eustatic fall. It can be noted that we did not use the terms TST and RST in Fig. 12, but rather UDF and USF, although the second sets of definitions for CTS and MFS (see Section 1) would make the terms TST and UDF, as well as RST and USF, to be equivalent. According to Embry (1995), the CTS may be diachronous because transgression may begin later in areas of high sediment supply, which is exactly the point made in Fig. 12. In this light, the TST would be equivalent to the UDF, and the RST with the USF. On the other hand, transgressive (retrogradational) and regressive (progradational) stacking patterns are controlled by the shoreline movements (Fig. 3), which does not allow for such equivalence (see also the discussion in Section 1) Three-dimensional model The model results from Profiles D and E have been plotted together in bloc diagrams (Figs. 13 and 14) to illustrate different aspects of sequence stratigraphic diachroneity, such as the diachroneity of bounding surfaces along the depositional strike and depositional dip (Fig. 13, lower diagram), and the simultaneous formation of different systems tracts during discrete time steps (Fig. 14). The distance along the depositional strike between Profiles D and E has been selected arbitrarily (100 km in this case), to support a realistic subsidence variability within the basin. Our results suggest that the bounding surfaces controlled by water-depth changes (CTS and MFS) always extend farther basinward than the surfaces controlled by relative sea-level changes (c.c. and SRFS), due to the effect of sedimentation. As a result, the LST and HST merge together beyond the wedging out point of the FSST. The FSST includes strata accumulated under relative sea-level fall conditions, and bounded by diachronous surfaces (c.c. and SRFS) which merge together offshore (Figs ). This raises a recurrent sore issue of sequence stratigraphy: where is the place within the sequence stratigraphic framework of the deep marine gravity flow deposits? While the position of the basin floor submarine fans relative to the depositional sequence boundary is a controversial issue (above the c.c.: Posamentier et al., 1988; Emery and Myers, 1996; or below the c.c.: Hunt and Tucker, 1992; Helland-

17 O. Catuneanu et al. / Sedimentary Geology 121 (1998) Fig. 12. Time distance depositional-dip section based on the model results from Profile D, constructed for one and a half eustatic cycles. The different rates of shoreline regression illustrate forced (high rate) regressions and normal (low rate) regressions. Abbreviations: DS D depositional sequence; GS D genetic stratigraphic sequence; TR D transgressive regressive sequence; LST D lowstand systems tract; FSST D falling stage systems tract; HST D highstand systems tract; USF D upward shallowing facies; UDF D upward deepening facies; CTS D conformable transgressive surface; MFS D maximum flooding surface; SRFS D start of relative fall surface; c.c. D correlative conformity. Hansen and Martinsen, 1996), they are generally regarded as formed during the forced regression of the shoreline and therefore part of the FSST. However, if we define the FSST boundaries on the basis of the interplay between eustasy and varying subsidence rates throughout the basin (Fig. 12), then the gravity flows could be initiated in the shallow marine area subject to relative sea-level fall, but the sediment would be transported and deposited beyond the edge of the FSST, within an area characterized by relative sea-level rise and accumulation of UDF (Fig. 13). 5. Conclusions The timing of bounding surfaces may be assessed in relationship to the criteria employed to define them. There are two main ways to define stratigraphic surfaces: (1) in relationship to the stratal stacking patterns, which we call type A surfaces, and (2) in relationship to the water-depth changes and relative sea-level changes, which we call type B surfaces. The types A and B surfaces are represented in Fig. 15.

18 Fig. 13. Block-diagrams illustrating strike and dip diachroneity of surfaces modelled in Figs. 10 and 11 (profiles D and E). The lower diagram shows a possible relationship between the source area for gravity flow deposits (S), which may be placed within a region affected by relative sea-level fall, and the associated submarine fan (SF) which may be placed in a region characterized by relative sea-level rise. Abbreviations: DS D depositional sequence; GS D genetic stratigraphic sequence; TR D transgressive regressive sequence; LST D lowstand systems tract; FSST D falling stage systems tract; HST D highstand systems tract; USF D upward shallowing facies; UDF D upward deepening facies; CTS D conformable transgressive surface; MFS D maximum flooding surface; SRFS D start of relative fall surface; c.c. D correlative conformity.

19 O. Catuneanu et al. / Sedimentary Geology 121 (1998) Fig. 14. Block diagrams illustrating coeval deposition of different systems tracts, as derived from the model results for Profiles D and E (Figs. 10 and 11). For abbreviations see Fig. 13.

20 Fig. 15. Temporal significance of types A and B surfaces. Type A surfaces depend on the shoreline movements (interplay between the rates of sedimentation and relative sea-level rise in the shoreline area), relative sea-level changes in the shoreline area, and rates of offshore sediment transport (not represented in this figure, but suggested in Fig. 3). They do not depend on the offshore variations in sedimentation and subsidence rates. Type B surfaces depend on the offshore variation in sedimentation and=or subsidence rates. Abbreviations: D D diachroneity rate; E D eustasy, T D tectonics; S D sedimentation; SU D subaerial unconformity; MRS D maximum regressive surface; MTS D maximum transgressive surface; f.u. D fining-upward; c.u. D coarsening-upward; d.u. D deepening-upward; s.u. D shallowing-upward; HST D highstand systems tract; FSST D falling stage systems tract; LST D lowstand systems tract; RST D regressive systems tract; TST D transgressive systems tract. 176 O. Catuneanu et al. / Sedimentary Geology 121 (1998)

21 O. Catuneanu et al. / Sedimentary Geology 121 (1998) The timing of type A surfaces depends either on the shoreline movements, which determine the direction of facies shift and the prograding or retrograding geometries, or on the rate of offshore sediment transport. Type A CTS and MFS are time lines along depositional dip sections, marking the turnaround points from shoreline regression to transgression and vice versa (Figs. 3 and 15). Their timing depends on the interplay between the rates of sedimentation and relative sea-level rise in the shoreline area, and it is not affected by the offshore variations in the sedimentation and subsidence rates. Both type A CTS and MFS are potentially diachronous along the depositional strike, as variations in sedimentation and subsidence rates determine temporally offset transitions from regression to transgression and vice versa along the shoreline. Type A c.c. (end of forced regression of the shoreline) and its counterpart (basal surface of forced regression: onset of forced regression of the shoreline) are diachronous along the depositional dip, with a rate that matches the rate of offshore sediment transport (Fig. 3). They are also not affected by the offshore variations in the subsidence rates. Type A c.c. and basal surface of forced regression are potentially diachronous along the depositional strike as well, due to variations in subsidence rates along the shoreline. All type A surfaces could be theoretically recognized on the basis of stratal stacking patterns (Figs. 2 and 3); also this may often be very difficult at the outcrop scale. Type B surfaces relate to bathymetric changes (CTS and MFS) or relative sea-level changes (c.c. and SRFS) throughout the basin, and are characterized by much higher diachroneity rates than the type A surfaces (Fig. 15). The timing of type B surfaces depends on the offshore variations in the sedimentation and subsidence rates, as modelled in Figs. 7, 8, 10 and 11. The model results indicate that the degree of diachroneity of bounding surface formation spans up to a quarter of the eustatic cycle period, which is in agreement with the quarter-cycle phase shift noted by Angevine (1989) Christie-Blick (1991) and Jordan and Flemings (1991). The cases described above involve a sinusoidal eustatic curve of higher frequency than the other variables. The higher-frequency variable could equally be sedimentation (S) or subsidence (T), so it can be concluded that the degree of diachroneity of a bounding surface reaches up to a quarter of the period of the highest frequency variable. Types A and B surfaces merge together in the shoreline area (Fig. 15). The differentiation between the two becomes more important offshore, especially in regards to the gravity flow deposits (Fig. 15). For practical reasons, the use of type A surfaces for stratigraphic correlation seems to be a better choice, both from a chronostratigraphic point of view, and from the point of view of the field signatures of systems tracts and bounding surfaces. The terms CTS and MFS are currently used with both architectural and bathymetric implications which, as this paper demonstrates, are not equivalent. Alternative terminology is suggested for the boundaries between prograding and retrograding geometries, i.e. maximum regressive surfaces for the top of prograding facies, and maximum transgressive surfaces for the top of retrograding facies (Fig. 15; Catuneanu, 1996; Helland-Hansen and Martinsen, 1996). Acknowledgements Financial support during completion of this work was provided by Rhodes University, NSERC Canada, University of Toronto, AAPG, Petrel Robertson, Wascana Energy, Petro-Canada, Union Pacific Resources and GSA. We thank Ashton Embry, Christopher Kendall and Nicholas Christie-Blick for comments and suggestions on previous versions of the manuscript. We also wish to thank reviewers William Helland-Hansen, Tim Naish and John Howell for valuable advice and constructive criticism; this paper wasverymuchimprovedasaresultoftheirreviews. References Angevine, C.L., Relationship of eustatic oscillations to regressions and transgressions on passive continental margins. In: Price, R.A. (Ed.), Origin and Evolution of Sedimentary Basins and their Energy and Mineral Resources. Am. Geophys. Union, Geophys. Monogr. 48, Catuneanu, O., Reciprocal Architecture of Bearpaw and post-bearpaw Sequences, Late Cretaceous Early Tertiary, Western Canada Basin. Ph.D. thesis, University of Toronto, Toronto, 301 pp. Catuneanu, O., Sweet, A.R., Miall, A.D., Reciprocal ar-

22 178 O. Catuneanu et al. / Sedimentary Geology 121 (1998) chitecture of Bearpaw T R sequences, uppermost Cretaceous, Western Canada Sedimentary Basin. Bull. Can. Pet. Geol. 45 (1), Christie-Blick, N., Onlap, offlap, and the origin of unconformity-bounded depositional sequences. Mar. Geol. 97, Demarest, J.M., Kraft, J.C., Stratigraphic record of Quaternary sea levels: implications for more ancient strata. In: Nummedal, D., Pilkey, O.H., Howard, J.D. (Eds.), Sea-Level Fluctuations and Coastal Evolution. Soc. Econ. Paleontol. Mineral. Spec. Publ. 41, Embry, A.F., Transgressive regressive (T R) sequence analysis of the Jurassic succession of the Sverdrup Basin, Canadian Arctic Archipelago. Can. J. Earth Sci. 30, Embry, A.F., Sequence boundaries and sequence hierarchies: problems and proposals. In: Steel, R.J., Felt, V.L., Johannessen, E.P., Mathieu, C. (Eds.), Sequence Stratigraphy on the Northwest European Margin. Norwegian Petroleum Society Spec. Publ. 5, Elsevier, Amsterdam, pp Embry, A.F., Johannessen, E.P., T R sequence stratigraphy, facies analysis and reservoir distribution in the uppermost Triassic Lower Jurassic succession, western Sverdrup Basin, Arctic Canada. In: Vørren, T.O., Bergsager, E., Dahl-Stamnes, O.A., Holter, E., Johansen, B., Lie, E., Lund, T.B. (Eds.), Arctic Geology and Petroleum Potential. Norwegian Petroleum Society Spec. Publ. 2, Elsevier, Amsterdam, pp Emery, D., Myers, K.J. (Eds.), Sequence Stratigraphy. Blackwell, Oxford, 297 pp. Fortuin, A.R., de Smet, M.E.M., Rates and magnitudes of late Cenozoic vertical movements in the Indonesian Banda Arc and the distinction of eustatic effects. In: Macdonald, D.I.M. (Ed.), Sedimentation, Tectonics and Eustasy: Sea-Level Changes at Active Margins. Int. Assoc. Sedimentol. Spec. Publ. 12, Frostick, L.E., Steel, R.J., Tectonic control and signatures in sedimentary successions. Int. Assoc. Sedimentol. Spec. Publ. 20, 520 pp. Galloway, W.E., Genetic stratigraphic sequences in basin analysis, I. Architecture and genesis of flooding-surface bounded depositional units. Am. Assoc. Pet. Geol. Bull. 73, Gill, J.R., Cobban, W.A., Stratigraphy and geologic history of the Montana Group and equivalent rocks, Montana, Wyoming, and North and South Dakota. U.S. Geol. Surv. Prof. Pap. 776, 73 pp. Haq, B.U., Sequence stratigraphy, sea-level change, and significance for the deep sea. In: Macdonald, D.I.M. (Ed.), Sedimentation, Tectonics and Eustasy: Sea-Level Changes at Active Margins. Int. Assoc. Sedimentol., Spec. Publ. 12, Helland-Hansen, W., Martinsen, O.J., Shoreline trajectories and sequences: description of variable depositional-dip scenarios. J. Sediment. Res. 66 (4), Hunt, D., Tucker, M.E., Stranded parasequences and the forced regressive wedge systems tract: deposition during baselevel fall. Sediment. Geol. 81, 1 9. Ito, M., O Hara, S., Diachronous evolution of systems tracts in a depositional sequence from the middle Pleistocene palaeo-tokyo Bay. Japan. Sedimentology 41, Jervey, M.T., Quantitative geological modeling of siliciclastic rock sequences and their seismic expression. In: Wilgus, C.K., Hastings, B.S., Kendall, C.G.St.C., Posamentier, H.W., Ross, C.A., Van Wagoner, J.C. (Eds.), Sea-Level Changes: An Integrated Approach. Soc. Econ. Paleontol. Mineral. Spec. Publ. 42, Jordan, T.E., Flemings, P.B., Large-scale stratigraphic architecture, eustatic variation, and unsteady tectonism: a theoretical approach. J. Geophys. Res. 96 (B4), Macdonald, D.I.M. (Ed.), 1991, Sedimentation, Tectonics and Eustasy: Sea-Level Changes at Active Margins. Int. Assoc. Sedimentol. Spec. Publ. 12, 518 pp. Martinsen, O.J., Helland-Hansen, W., Strike variability of clastic depositional systems: does it matter for sequence stratigraphic analysis? Geology 23, Miall, A.D., Stratigraphic sequences and their chronostratigraphic correlation. J. Sediment. Petrol. 61, Miall, A.D., Sequence stratigraphy and chronostratigraphy: problems of definition and precision in correlation, and their implications for global eustasy. Geosci. Can. 21, Naish, T., Kamp, P.J.J., Foraminiferal depth palaeoecology of Late Pliocene shelf sequences and systems tracts, Wanganui Basin, New Zealand. Sediment. Geol. 110, Pitman, W.C., Relationship between sea level change and stratigraphic sequences of passive margins. Geol. Soc. Am. Bull. 89, Pitman, W.C., Golovchenko, X., The effect of sea level change on the shelf edge and slope of passive margins. In: Stanley, D.J., Morre, G.T. (Eds.), The Shelfbreak: Critical Interface on Continental Margins. Soc. Econ. Paleontol. Mineral. Spec. Publ. 33, Posamentier, H.W., Allen, G.P., Siliciclastic sequence stratigraphic patterns in foreland ramp-type basins. Geology 21, Posamentier, H.W., James, D.P., An overview of sequence stratigraphic concepts: uses and abuses. In: Posamentier, H.W., Summerhayes, C.P., Haq, B.U., Allen, G.P. (Eds.), Sequence Stratigraphy and Facies Associations. Int. Assoc. Sedimentol. Spec. Publ. 18, Posamentier, H.W., Jervey, M.T., Vail, P.R., Eustatic controls on clastic deposition I, conceptual framework. In: Wilgus, C.K., Hastings, B.S., Kendall, C.G.St.C., Posamentier, H.W., Ross, C.A., Van Wagoner, J.C. (Eds.), Sea-Level Changes: An Integrated Approach. Soc. Econ. Paleontol. Mineral. Spec. Publ. 42, Posamentier, H.W., Allen, G.P., James, D.P., Tesson, M., Forced regressions in a sequence stratigraphic framework: concepts, examples and exploration significance. Am. Assoc. Pet. Geol. Bull. 76, Reading, H.G. (Ed.), Sedimentary Environments: Processes, Facies and Stratigraphy. Blackwell, Oxford, 688 pp. Vail, P.R., Audemard, F., Bowman, S.A., Eisner, P.N., Perez- Cruz, C., The stratigraphic signatures of tectonism, eustasy and sedimentology an overview. In: Einsele, G., Ricken, W., Seilacher, A. (Eds.), Cycles and Events in Stratigraphy. Springer-Verlag, New York, N.Y., pp Van Wagoner, J.C., Mitchum, R.M., Campion K.M., Rahmanian, V.D., Siliciclastic sequence stratigraphy in well logs, cores, and outcrops: concepts for high-resolution correlation of time and facies. Am. Assoc. Pet. Geol. Methods Explor. Ser. 7, 55 pp.