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Formation of sequences in the cratonic interior of North America by interaction between mantle, eustatic, and stratigraphic processes

Peter M. Burgess* Michael Gurnis Louis Moresi

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Seismological Laboratory, California Institute of Technology, Pasadena, California 91125

ABSTRACT Models integrating geodynamic and stratigraphic processes show that some gross features of Phanerozoic North American cratonic strata can be explained with dynamic topographies generated by subduction and cycles of supercontinent aggregation and dispersal. A three-dimensional finite-element model is used to calculate mantle flow beneath North America during Phanerozoic time in response to episodes of subduction at cratonic margins and two cycles of supercontinent formation and breakup. Dynamic topographies calculated by the flow models are used as input to a stratigraphic model that also includes background subsidence, eustasy, denudation, clastic and carbonate deposition, compaction, and isostasy. These models successfully reproduce aspects of the Sloss sequences; the best matches were obtained by combining two wavelengths of dynamic topography with second-order eustasy. Long-wavelength dynamic topography generates first-order stratal cyclicity. Periods of erosion were shorter when North America was over a dynamic topography low than when it was over a high. Long-wavelength dynamic topography also explains the absence of Mesozoic strata on the eastern portion of the craton. Characteristic stratal patterns are shown to result from subduction-related dynamic topography, although sensitive to sediment supply and other subsidence mechanisms. Aspects of Upper Cretaceous stratal patterns may be explained by the effects of Farallon plate subduction. Generally, strata deposited in a dynamic topography depression

*Present address: Department of Earth Sciences, University of Liverpool, Brownlow Street, Liverpool, L69 3BX, United Kingdom; e-mail: [email protected] Present address: Research School of Earth Sciences, Australian National University, Canberra, ACT 0200, Australia

have low preservation potential because the topography is reversible. Thus, ancient subduction-related dynamic topography is most likely to be represented by unconformities. INTRODUCTION Six Phanerozoic depositional sequences of North America are well known from the synthesis of Sloss (1963) (Fig. 1). Individual sequences last approximately 50 to 120 m.y. and are thinner and represent shorter intervals of deposition at the center of the craton than at the craton margins. The sequences are separated by regionally extensive unconformities varying laterally in duration from approximately 150 m.y. at the craton center to 10 m.y. toward the edges. Relative sea-level change with amplitudes greater than 100 m and periods of approximately 100 m.y. seem essential to generate the bounding unconformities. Eustasy is perhaps the simplest possibility. Changes in global sea-floor spreading rates and/or the age distribution of oceanic lithosphere can generate such second-order eustatic cycles (Pitman, 1978; Kominz, 1984; Heller and Angevine, 1985; Miall, 1995). The responsible mechanism has to be more complex, however, because eustasy alone cannot explain other observed features of cratonic strata such as postdepositional tilting and syndepositional faulting (Bunker et al., 1988; Sloss, 1988a; Marshak and Paulsen, 1996). Such features require tectonic mechanisms, but finding tectonic mechanisms with the correct wavelength, amplitude, and period has proved difficult (Sloss, 1988b). A fundamental concept used here is that of dynamic topography, first described by Pekeris (1935). Dynamic topography is the vertical displacement of the Earth's surface generated in response to flow within the mantle (e.g., Richards and Hager, 1984). It is called "dynamic" because the buoyancy cells within the mantle driving the surface deflections are actively moving and de-

forming. Dynamic topography is contrasted with isostatic topography generated by density contrasts nearer the Earth's surface and close to being in equilibrium. Unfortunately, this definition is vague because crustal thickness variations also induce flow, although with an amplitude significantly smaller than those generated by internal buoyancy. However, dynamic topography gives rise to strong geoid anomalies, whereas isostatic topography generates only small geoid anomalies. Dynamic topography can be generated by the presence of a relatively cold and dense slab of subducting lithosphere (Fig. 2), or on a longer wavelength (>5 × 103 km), by mantle heating beneath insulating supercontinents. To better understand dynamic topography, consider a viscous fluid in which there is initially no surface topography. If a parcel of positive buoyancy appears instantaneously within the fluid, viscous stresses are immediately generated in the fluid and on the top free surface. These stresses cause the free-surface to move upward. For the mantle, the time scale for this motion is essentially equal to the postglacial rebound time scale, but is also strongly dependent on wavelength (e.g., Zhong et al. 1996). For dynamic topography generated by mantle insulation beneath large supercontinents, the time scale will be 104 yr, whereas for tilting associated with subducting slabs, the time scale will be 105 yr (Gurnis et al., 1996). Now consider what would occur if the parcel of buoyancy slowly moves vertically, with velocities of centimeters per year, as it would in the mantle. In 104 to 105 yr the parcel will not change its depth within the mantle significantly (generally by <10 km), and hence the stresses causing dynamic topography will change only slightly. In other words, dynamic topography will slowly change in response to the distribution of buoyancy in the mantle and for all practical purposes remain essentially in equilibrium with buoyancy forces. A long-wavelength (1 to 3 × 103 km) influence

GSA Bulletin; December 1997; v. 108; no. 12; p. 1515­1535; 16 figures; 2 tables.

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West

0 Tertiary Tejas

East

100

Cretaceous

Zuni

Jurassic 200 Triassic Permian 300 Carboniferous Kaskaskia Devonian 400 Silurian Ordovician 500 Cambrian Precambrian Sauk Tippecanoe Absaroka

600

Erosional or non-depositional hiatus

Depositional sequence

Figure 1. Chronostratigraphic diagram modified from Sloss (1963) showing the six North American Phanerozoic depositional sequences and their bounding unconformities.

of subduction on development of stratigraphic sequences was proposed originally by Cross and Pilger (1978), who recognized the anomalous spatial distribution of Campanian to Maastrichtian deposition in the western United States. Dynamic topography was first proposed as a mechanism for this by Mitrovica et al. (1989), and since then further studies have confirmed it as an important phenomenon (Gurnis, 1992b, 1993; Coakley and Gurnis, 1995; Mitrovica et al., 1996) capable of causing hundreds of meters of relative sea-level change and tilting of strata on wavelengths on the order of 103 km. Burgess and Gurnis (1995) proceeded a step further and investigated the stratigraphic influence of longwavelength tilting with a numerical stratigraphic model. Although using only a kinematic approximation to dynamic topography their results show that dynamic topography, generated by cycles of subduction around the margins of a craton

could be significant in generating sequences and their bounding unconformities, as well as features such as postdepositional tilting of strata. Longer wavelength dynamic topography is generated by mantle thermal anomalies formed in response to cycles of supercontinent formation and destruction (e.g., Anderson, 1982; Gurnis, 1988). Beneath insulating supercontinents mantle heating occurs by radioactive decay. Conduction and continental volcanic activity are insufficient to dissipate this heat. At the margins of supercontinents mantle is cooled by subduction of cold, dense slabs. Movement of continents over the resulting dynamic topography, for example from highs to lows during supercontinent dispersal, probably has important effects on continental flooding histories (Worsley et al., 1984; Gurnis, 1990, 1991). Resulting relative sea-level changes will act synchronously over entire continents, or possibly multiple continents, on a time

scale of tens of megayears, and probably affect development of cratonic stratigraphic sequences (e.g., Kominz and Bond, 1991). The geoid is generated by dynamic processes in the mantle and provides another mechanism for relative sea-level fluctuations. However, geoid amplitudes are one to two orders of magnitude smaller than dynamic topography, and are unlikely to contribute significantly to sequence formation (e.g., Gurnis, 1990; Lithgow-Bertelloni and Gurnis, 1997). The purpose of this paper is to determine how relative sea-level changes due to dynamic topography were significant to the formation of North American Phanerozoic strata. We use an integrated approach, combining three-dimensional models of instantaneous mantle flow with a threedimensional model of stratigraphic processes to produce a range of predictions that is tested against the observed stratigraphic record.

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FORMATION OF SEQUENCES IN THE CRATONIC INTERIOR

Dynamic topography

+

-

Flooded continental margin

Subaerially exposed continental interior

Eustatic sea-level change Continental crust

Mantle flow generated by the cold subducting slab Subducting oceanic crust Anomalously hot mantle due to thermal insulation beneath supercontinent

Figure 2. Mechanisms for generating different wavelengths of dynamic topography, 1 to 3 × 103 km over subducting slabs and >5 × 103 km from insulated mantle heating beneath supercontinents.

670 km discontinuity

PHANEROZOIC PLATE TECTONIC HISTORY OF NORTH AMERICA In order to calculate dynamic topographies over the North American craton at times during the Phanerozoic it is necessary to reconstruct aspects of the tectonic history of the craton, specifically its position with respect to assembling and disassembling supercontinents and the geometry and timing of subduction along its margins. The purpose of this work is not to dissent on paleogeography, but rather to illustrate the potential influence of dynamic topography on the development of cratonic sequences. It thus seems justifiable to use the simplified tectonic model described in the following, and accept the consequent limitations in interpretation of the results. A Phanerozoic history of the craton in terms of supercontinent cycles is reasonably straightforward. Necessary information for our models includes the timing of supercontinent formation and breakup, and the approximate position of the craton within the supercontinent. In Late Proterozoic time the craton was part of the Rodinia supercontinent (Dalziel, 1991; Hoffman, 1991; Rogers, 1996). Rifting and disassembly of Rodinia is thought to have started in the Late Proterozoic Era, as evidenced by the development of rift-margin sequences at that time (Bond et al., 1985). If models relating supercontinent formation to mantle convection (e.g., Gurnis, 1988) are accurate, after the breakup of Rodinia at around 700 Ma (Rogers, 1996) North America

should have moved off a long-wavelength dynamic topography high, formed over hot mantle, toward a long-wavelength low over relatively cool mantle. Gurnis and Torsvik (1994) presented evidence and a mechanism for rapid drift of North America at this time, and Kominz and Bond (1991) showed evidence for anomalous subsidence during Paleozoic time, possibly related to long-wavelength dynamic topography. With the assembly of Pangea from around 300 Ma (e.g., Rogers, 1996), the cycle was repeated. Heating of the mantle beneath Pangea led to formation of a dynamic topography high. Pangea rifted apart during the Mesozoic and the continents began to move off this putative dynamic topography high. This motion from dynamic topographic highs to lows through the Phanerozoic may have influenced flooding of the North American craton (Gurnis, 1990) and hence development of cratonic sequences. Phanerozoic subduction around the margins of the North American craton can be broadly subdivided into two episodes: an early Paleozoic episode related to closure of the Iapetus ocean, and a more prolonged late Paleozoic to Cenozoic episode involving subduction of the eastern Pacific and Farallon plates. Aspects of the tectonic histories in both cases are still contended. The subduction histories and cratonic geometry used here represent an obvious simplification, neglecting possible episodes of subduction and changing continental geometry due to terrane accretion, but suffice to illustrate the gross effects

on development of cratonic strata. Subduction of Iapetus oceanic lithosphere is assumed to have started at 480 Ma and continued until 420 Ma (van der Pluijm et al., 1990; McKerrow et al., 1991). The polarity of this subduction is crucial in the model. Coakley and Gurnis (1995) reviewed the evidence for and against a slab dipping west beneath North America and provided further evidence for this geometry from tilting of Ordovician strata in the Michigan basin. We have chosen to follow this model and assume that a slab of oceanic lithosphere with a thermal age of 80 Ma penetrated beneath North America from 480 Ma with a dip of 20°, the front of the slab steepening to a dip of 70° after penetrating about 800 km (Fig. 3). Subduction then ceased between 430 and 420 Ma. There are undoubtedly other possibilities regarding the closure history of Iapetus. For example, Dalziel et al. (1994) suggested that the Appalachian orogen formed by collision between Laurentia and the proto-Andean margin of South America. However, the data constraining geometry and timing of subduction are identical and accounted for within our study. The subduction history of the Farallon slab beneath western North America is better constrained, at least for Cenozoic time, because of its younger age. Various studies have attempted to reconstruct the subduction history and relate it to tectonic events. Coney and Reynolds (1977) first used spatial and temporal distributions of magmatic arc rocks to infer subduction geome-

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10 Ma. 10 Myr slab

20 Ma. 20 Myr slab

30 Ma. 30 Myr slab

70

70

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50 Ma. 55 Myr slab

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70 Flat

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70 Flat

70 75 Ma. 80 Myr slab

70 240 Ma. 80 Myr slab

70 70 Flat 70 430 Ma. 80 Myr slab

70 70 70 450 Ma. 80 Myr slab

70 70 70 470 Ma. 80 Myr slab

the basis of evidence from Lower Triassic volcaniclastic rocks, replacing a subduction complex that had existed in a seaward position since Paleozoic time. The age of initiation of this earlier subduction is contended; estimates vary from late Paleozoic (Burchfiel and Davis, 1972; Miller et al., 1992) to Precambrian (Scotese and Golonka, 1992), but there is consensus that any subduction zone present was situated some distance west of the continental margin. To calculate Farallon plate dynamic topographies for our models, we have chosen to use two different histories, allowing a degree of comparison between end-member possibilities. The first history assumes that subduction started at the continental margin at 250 Ma with slabs dipping at 70° in an east-northeasterly direction (Fig. 3). The second assumes that subduction started farther west at 500 Ma and persisted, with one slab dipping at 70° (Fig. 4), until a new subduction zone was initiated at 250 Ma, as in the first history. In both cases subduction continued from 250 to 75 Ma, when a flat slab began to penetrate eastward at 60 km depth, reaching a maximum length of 1000 km at 65 Ma and then retreating westward from 50 to 30 Ma, leaving a steeply dipping slab at 20 Ma (Fig. 3). Thermal ages of the slabs from 70 Ma to present are taken from Severinghaus and Atwater (1990) and prior to 70 Ma are assumed to be 80 Ma. Observed Stratigraphic Data The composite chronostratigraphic diagram of Sloss (1963) (Fig. 1) provides the fundamental comparison for model-generated stratigraphic patterns. Because it represents only a generalized approximation, albeit one based on compilation of many stratigraphic data, it is also important to consider other forms of such data. Bunker et al. (1988) provided a series of cross sections through Phanerozoic cratonic strata of the central midcontinent region of the United States as well as isopach and paleogeographic maps of the same area. The sections show a number of the Phanerozoic sequences and their bounding unconformities, all clearly influenced by postdepositional tilting and erosion, and syndepositional to postdepositional faulting. Useful summary maps of lithofacies and accumulation rates for the North American Phanerozoic sequences were also given by Bally (1989). More detailed stratigraphic data were taken from Cross and Pilger (1978) and Cross (1986), who gave subsidence and isopach maps for Upper Cretaceous strata in the western United States. These data will be used to interpret the significance of model results by comparison between model chronostratigraphic diagrams, cross sections, isopach maps, accumulation rate maps, and

70 20

20

20

Figure 3. The history of Phanerozoic subducting slab geometries used in the model runs. For each instant, slab corners are shown projected vertically onto a horizontal plane along with their dips and age of lithosphere at subduction. An outline of North America and the North American craton indicates relative positions of slabs.

tries beneath the Cordillera, concluding that there was a decrease in slab dip between 120 and 40 Ma, during which time a near-horizontal slab penetrated approximately 1000 km beneath North America. Subsequently, further evidence for this model has been discussed, both tectonic features related to the Laramide orogeny (Dickinson and Snyder, 1978; Bird, 1984, 1988) and stratigraphic trends based on thickness and dis-

tribution of Upper Cretaceous strata (Cross and Pilger, 1978; Cross, 1986). The age of the subducting lithosphere has been deduced from studies of isochron patterns (Severinghaus and Atwater, 1990). Determining the subduction history further back into the Mesozoic is more difficult. Lawton (1994) suggested initiation of subduction at the western continental margin at around 240 Ma, on

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FORMATION OF SEQUENCES IN THE CRATONIC INTERIOR

250 Ma. 80 Myr slab

70

430 Ma. 80 Myr slab

450 Ma. 80 Myr slab

70

70 20

70

20

470 Ma. 80 Myr slab

490 Ma. 80 Myr slab

70

20

70

Figure 4. An alternative subduction history to that shown in Figure 3, with subduction initiating at 500 Ma off the western cratonic margin. paleogeographic maps. Comparisons must take into account known omissions and simplifications in the model, e.g., no compressional tectonics, and no climatic control on denudation and deposition. A complete and unique match with observation is not expected. However, sensitivity tests where important parameters are varied should elucidate the degree to which dynamic topography may have controlled formation of North American cratonic strata. QUANTITATIVE MODELS We integrate results from two quantitative models. A three-dimensional finite element model of mantle convection was used to calculate dynamic topography on the basis of the tectonic history described above. These dynamic topography fields were then used as input, along with various other parameters, to a stratigraphic model. Output from the stratigraphic model was compared with data from North American Phanerozoic cratonic strata. Instantaneous Flow Model The equation of motion for a viscously dominated fluid with no inertial force like the Earth's mantle is ­(f) + p = (x,y,z)g¸ subject to the incompressibility constraint u = 0, (2) (1)

where is the dynamic viscosity, f = (ui/xj +uj/xi)/2 is the strain rate tensor in which u is the velocity, p is the pressure, is the density anomaly distribution, g is the gravitational acceleration, and ¸ is a unit vector in the vertical direction. We solved these equations using the threedimensional Cartesian finite element code CITCOM (for California Institute of Technology, Convection in the Mantle). A finite element method is suited to this problem because the ac-

curacy of the solution is not significantly influenced by lateral variations in viscosity. This has been verified for the two-dimensional version of this code by extensive comparison with analytic solutions with strong viscosity steps in both vertical and horizontal directions (Moresi et al., 1996). Iterative multigrid methods (Brandt, 1982) are required in three dimensions because their consumption of computer resources scales much more slowly with the number of grid points compared to direct solution schemes (e.g., Cahouet and Chabard, 1988). Moresi and Solamatov (1995) described in detail the multigrid method used and presented further benchmarks of the method. Flow was solved in a box with 65 by 65 nodes in map view, and 33 nodes in depth. The domain had reflecting boundary conditions on all vertical edges, but a free slip top and bottom. The box was assigned nondimensional lengths 5 by 5 by 1, respectively, allowing easy scaling to dimensional values of 5000 by 5000 by 1000 km. The size of the box must be sufficiently large relative to the dimensions of the buoyancy anomaly so that return flow is not influenced by the presence of vertical boundaries. In three dimensions, the length scale of flow induced by sinking slabs is smaller than it would be in a two-dimensional calculation, so a box 5 by 5 by 1 was found to be sufficient in all cases. Subducted lithosphere was modeled as a perturbation in the thermal field. Problems with poor definition of the slab resulted from relatively low grid resolution, but were resolved by increasing the volume of the slab and scaling its internal temperature accordingly. This method ensures that the overall buoyancy anomaly was independent of grid resolution. The temperature anomaly was defined as constant through each slab, and found by integrating the semi-infinite half-space geotherm (appropriate to the age of the lithosphere at subduction) down to a fixed temperature of 1330 K. At the relatively long wavelengths dealt with here this approximation had little or no influence on dynamic topography. Moresi and Gurnis (1996) used a similar slab parameterization to model the geoid associated with subducted lithosphere in the western Pacific Ocean. They concluded that the lithosphere appears to be weakened during subduction, and therefore the most suitable viscosity model for the mantle is that originally derived under the assumption of uniform viscosity layers by Hager (1984). The viscosity structure used in the model is shown in Figure 5. Dynamic topography was determined accurately using a consistent boundary flux method (Zhong et al., 1993) to calculate the surface normal stress. The topography is assumed to balance this stress locally. Once the topography has been

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North American craton

Dimensionless viscosity,

0.1 80 1.0 10.0

Cold subducting slabs

Depth (km)

670

1000

Free slip top and bottom Reflecting sidewalls

Figure 5. Length scales, node distributions, and viscosity structure for the finite element calculation of instantaneous mantle flow solutions. The position of the North American craton on the grid is shown along with an example of subducting slabs at 50 Ma.

calculated for a given temperature field it can be directly transformed via linear interpolation from the 65 by 65 node area used in CITCOM to the 100 by 100 nodes used in the stratigraphic model grid, because the length scales of 5000 km by 5000 km are the same in both cases. Time evolution is simulated using an imposed buoyancy method wherein the buoyancy field is changed in a reasonable manner as a function of time (e.g., Gurnis, 1992b). Topography is always in equilibrium with this buoyancy because the time scale for changing buoyancy by the present scenario is ~107 yr, much longer than the time for topography to readjust to this force (~104 yr) (Richards and Hager, 1984; Gurnis et al. 1996; Zhong et al., 1996). Effects of supercontinent formation and dispersal are modeled here by using CITCOM to calculate patterns of dynamic topography over thermal anomalies of 20 K extending throughout the mantle. This temperature is chosen as reasonable for the temporal evolution described with heat generated by radioactive decay within the mantle, as well as a contribution from plume heating and secular cooling of the Earth (Gurnis and Torsvik, 1994). Horizontal anom-

aly distributions are shown in Figure 6. An early Paleozoic cool mantle anomaly is centered in the model grid, thus ignoring any detail in the pattern of mantle cooling. A younger hot anomaly is offset to one side of the grid to account for the position of North America on the western edge of Pangea. Implications of this will be discussed below when considering results from model runs. Simple harmonic functions vary the magnitude of applied dynamic topography through the duration of a model run (Fig. 6), simulating movement of the craton over evolving temperature anomalies. The component of vertical motion of a single point in the center of the craton due to dynamic topography is shown in Figure 6C. For the subduction history shown in Figure 3 dynamic topography is calculated by CITCOM at the times and with the slab geometries shown (Fig. 7), and then linear interpolation is used for times between snapshots. In all cases it takes 10 m.y. to progress from a time of no dynamic topography at the start of the sequences (480 and 250 Ma) to the first snapshot in the sequence (470 and 240 Ma). Similarly it takes 10 m.y. for dynamic topography to disappear.

Stratigraphic Model The stratigraphic process model is modified from Burgess and Gurnis (1995), and comprises a three-dimensional grid using chronostratigraphic surfaces (chrons) to simulate deposition, erosion, and preservation of strata. Processes represented in the model are subsidence and uplift driven by dynamic topography, spatially variable background subsidence, eustasy, regional denudation, external clastic sediment supply, deposition of clastic and carbonate strata, isostasy, and mechanical compaction. The elevation of each point on each chron surface, h, can be represented as h(x,y,t) = h(x,y,t ­ t) + S(x,y,t) ­ D(x,y,t) +T(x,y,t) + I(x,y,t) ­ C(x,y,t)

(3)

where S is subsidence (or uplift), D is magnitude of denudation, T is thickness of accumulated strata, I is isostatic response to denudation and accumulation, and C is subsidence due to compaction of previously deposited strata. Subsidence and uplift are calculated from a combination of relatively slow background continental subsidence and dynamic topography.

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FORMATION OF SEQUENCES IN THE CRATONIC INTERIOR

A

1.0

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0.5 Scaling factor Scaling factor

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Figure 6. Long-wavelength dynamic topographies and time-variable scaling factors to model movement of North America over cold and hot mantle thermal anomalies. (A) For the period 600 to 300 Ma, a dynamic topography low centered beneath the craton is scaled from a factor of ­1 at 700 Ma to simulate a high at the time of breakup of Rodinia, to a factor of 1 at 300 Ma to simulate a postsupercontinent breakup low. (B) From 300 to 0 Ma a dynamic topography high is positioned beneath the eastern cratonic margin, reaching maximum amplitude at 100 Ma prior to the breakup of Pangea. (C) Dynamic topography resulting from these two anomalies through time at point P.

Denudation is calculated according to simple diffusion and advection relationships so that denudation rate is dependent solely on topographic slope. The thickness of accumulated strata at any point during each time step depends on clastic sediment supply, which is distributed as equal thickness across the craton, and an in situ carbonate production rate, dependent on water depth and clastic supply. Isostatic response to loading and unloading is calculated with a one-dimensional Airy response, and compaction is calculated assuming purely mechanical processes using a porosity-depth curve from Sclater and Christie (1980). These model components were described in more detail in Burgess and Gurnis (1995). Four important modifications have been made to the original model: (1) background subsidence rates are now spatially variable, (2) input of clastic sediment additional to that supplied by calculated denudation has been included, (3) clastic deposition has been restricted to the platform according to sediment supply and accommodation, and (4) values calculated by the mantle flow model are used for dynamic topography. Background subsidence was found to be essential to the preservation of any significant thickness of cratonic strata (Burgess and Gurnis, 1995), but in that study background subsidence was constant in both space and time. A more realistic scenario is used in this study, whereby rates of subsidence vary across the craton according to tectonic age of underlying cratonic crust (Fig. 8B). Thus there is no subsidence on the area of the craton composed of Archean age basement rocks, slow subsidence on areas underlain by Proterozoic age basement (1.0 m · m.y.­1 based on observed thickness of strata on Proterozoic basement), and relatively high subsidence on the margins of the craton (3.0 m · m.y.­1), intended to loosely simulate the long-term time-averaged subsidence histories of various active and passive margin basins. Clastic sediment supply from subaerial denudation was calculated from a slope-dependent advective-diffusive scheme and was found to be too low to account for observed volumes of clastic strata despite careful constraint of advection and diffusion coefficients with observational data (Burgess and Gurnis, 1995). There are two main reasons to account for this low clastic supply. First, because the model contains no elements of compressional tectonics, model slopes are generally too low compared with those observed on modern and assumed on ancient continents. Second, denudation is probably not simply slope dependent, but varies according to factors such as climate, vegetation cover, and bedrock type (e.g., Bull, 1991; Hovius, in press). A facility for additional clastic supply was added to the model to

Dynamic topography (m)

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Alternative slab model for early Farallon subduction

Figure 7. Dynamic topography generated by slab subduction for the snapshots from Figure 3. Significant downward tilting of the craton over subducting slabs is apparent; wavelengths at times exceed 2000 km.

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Iapetus subduction

Farallon subduction

FORMATION OF SEQUENCES IN THE CRATONIC INTERIOR

A

Archean craton

Proterozoic craton

100 0 N 5000 4000 Dis 3000 2000 tan ce N 1000 -S ( km ) -500 Elevation (m) -1000 4000 3000 ) (km 2000 E-W 1000 ce tan Dis

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Figure 8. (A) Initial model topography, with the Archean cratonic area at 100 m elevation and the surrounding Proterozoic craton at 0 m, surrounded by a marine shelf dropping off to an oceanic trough. (B) Background subsidence rates on the craton and surrounding shelf and trough. (C) Location of cross sections (A­A and B­B from Fig. 11 and S from Fig. 16) and points for which subsidence curves were generated in Figure 10.

4

A'

0

0 0 2000 4000 Distance E-W (km)

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1.0 2.0 Subsidence rate (m Myr-1)

3.0

circumvent the first problem and allow higher clastic supply during times of orogenic activity. Quantification of additional factors that may influence denudation is not possible on a suitable temporal and spatial scale. Spatial restriction of clastic deposition was added to the model to improve the simple layercake depositional model used in Burgess and Gurnis (1995) by accounting for variations in accommodation on the cratonic platform and margins. The cratonic platform and margins in the initial model topography are surrounded by deep-water sinks, representing abyssal plain areas. If accommodation is sufficient, clastic deposition is limited to points with initial elevations greater than ­200 m, i.e., on the cratonic platform and margins. If there is insufficient volume on these grid points, any additional clastic sediment is deposited as an equal thickness layer in deeper water.

Stratigraphic Model Parameters and Initial Conditions Model runs with various eustatic curves and dynamic topographies are presented in the following. The initial topography represents the craton surrounded by a 1000-m-deep oceanic trough; cratonic topography is subdivided between the Archean shield at 100 m elevation, and the Proterozoic and marginal areas at 0 m (Fig. 8A). These subdivisions are also used to define spatial distribution of background subsidence rates, which are as much as 3 m · m.y.­1 on cratonic margins and in the deep ocean trough, 1 m m.y.­1 on Proterozoic craton, and 0 on Archean age craton (Fig. 8B). First-order eustatic curves and external sediment supply curves are shown in Figure 9. The nonzero eustatic curves have amplitudes based on estimates of Phanerozoic eustatic change from

Harrison (1990). Curve periods represent firstorder cycles in the form of either an arbitrary sinusoid or the first-order element of the Vail curve (Vail et al., 1977). A second-order curve with a 100 m.y. period and a 100 m amplitude is also used in some model cases; parameters are based loosely on estimates of eustatic change due to variable rates of sea-floor spreading (Harrison, 1990; Dewey and Pitman, 1995). External sediment supply is nonzero during times of orogenic activity on the margins of the craton (Rast, 1989; Oldow et al., 1989; Miller et al., 1992), when it is likely that significant topography existed and was denuded, supplying clastic material for cratonic and cratonic margin deposition. The volumetric magnitude of external supply is 105 km3 · m.y.­1. According to Milliman and Meade (1983) the modern Mississippi delivers 210 × 109 kg · yr­1; assuming a sediment density of 2650 kg · m­3, this gives 7.9 × 104 km3 · m.y.­1. In order to be

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Background subsidence

0 100

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Supercontinent dynamic topography 2

Subduction related dynamic topography 3

Combined dynamic topography 4

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Age (Ma)

200 300 400 500 600 0 2000 4000 0 2000 4000 0 2000 4000 0 2000 4000

-100 0 100 200 0 50000 100000 Eustatic sea-level (ma) Sediment supply (km3)

Distance (km) Non-depositional hiatus

0

Distance (km)

Distance (km)

Distance (km) Erosional hiatus

2

13

20

>20

Rate of Deposition (m/Myr)

Figure 9. Chronostratigraphic diagrams showing rates of deposition along section A­A for model cases 1 to 12 (see Table 2) with accompanying eustatic and clastic sediment supply curves.

TABLE 1. PARAMETER VALUES HELD CONSTANT FOR ALL MODEL CASES Parameter Chron interval Time step Advection coefficient Diffusion coefficient Carbonate production rate Maximum carbonate depth Clastic threshold Mantle density Sea water density Uncompacted sediment density Value 6 m.y. 0.1 m.y. 0.01 m yr­1 100 m2 yr­1 50 m m.y.­1 100 m 10 m 3330 kg m­3 1030 kg m­3 1760 kg m­3 Source

Burgess and Gurnis (1995) Burgess and Gurnis (1995) Enos (1991) Wilson (1975) Burgess and Gurnis (1995)

Sclater and Christie (1980)

representative of a Phanerozoic river of similar size, this value probably needs to be reduced to account for the influence of glacial material on sediment load in the modern Mississippi, but then increased to yield a suitable value for sediment supply for the craton from multiple rivers, making the chosen value a reasonable, if very poorly constrained, estimate. All other model parameters are held constant (Table 1) at values described in Burgess and Gurnis (1995), with the exception of the carbonate deposition rate, which has been increased to 50 m · m.y.­1 to maintain carbonate deposition during eustatic sea-level rise.

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FORMATION OF SEQUENCES IN THE CRATONIC INTERIOR

MODEL RESULTS Various modeling studies demonstrate that dynamic topography is important to the development of cratonic sequences (e.g., Mitrovica et al., 1996). Because an understanding of the mechanisms responsible for formation of the North American cratonic sequences remains incomplete, we have conducted a series of model runs (Table 2) to investigate the potential contribution of dynamic topography and how dynamic topography might interact with eustasy in determining cratonic stratal patterns (Fig. 9). Chronostratigraphic diagrams are taken from section A­A in Figure 8C. Although variations in stratal patterns occur in three dimensions across the craton, this line of section is chosen as representative of the overall patterns. When combined with cross sections and isopach maps for a more detailed view, the model results help provide insight into formative mechanisms of cratonic sequences. Constant Eustatic Sea Level In order to understand contributions of dynamic topography to stratal patterns, we present four model runs with eustatic sea level held constant. The simplest model (Fig. 9) includes no dynamic topography (case 1), and accommodation is created only by spatially variable background subsidence (Fig. 8B). Strata accumulate slowly on the craton throughout the Phanerozoic (<5m · m.y.­1), controlled primarily by subsidence rate, and cratonic margin basins fill during the early Paleozoic at low accumulation rates that increase during times of external input (see ac-

companying sediment supply curve, Fig. 9). When the marginal basins have filled, at around 300 Ma, sediment overflows into surrounding deep-water areas and deposition remains constant across the grid until the model run ends. Long-wavelength dynamic topography driven by long-wavelength mantle thermal anomalies related to aggregation and dispersal of supercontinents (Fig. 6) is added to produce more complex stratal patterns (case 2, Fig. 9). Three visible effects result from this ~200 m amplitude dynamic topography. A craton-wide nondepositional hiatus can be seen from 380 to 350 Ma, caused by the combined influence of a growing dynamic topography low centered beneath the craton causing subsidence rates of ~1.7 m m.y.­1 (Fig. 6) and sudden cessation of external clastic supply, leaving accommodation unfilled and water depths too great for carbonate deposition to catch up. Increased rates of cratonic margin deposition are prolonged because of the additional accommodation created by the dynamic topographic low. An erosional unconformity starts to form at 300 Ma and lasts until around 120 Ma, eroding older strata of ages between 300 and 340 Ma. This unconformity develops in response to cratonic tilting up to the east over a hot thermal anomaly at ~1.2 · m m.y.­1. The anomaly is centered beneath eastern North America and represents hot insulated mantle developing beneath Pangea (Fig. 6). On the basis of the features of the unconformity, long-wavelength dynamic topography can be seen to be an important control on development of cratonic accommodation, and hence it is very significant to development of cratonic stratal patterns.

TABLE 2. VARIABLE PARAMETERS FOR MODEL CASES 1 TO 19 Eustasy* Long-wavelength Slab-related dynamic topography dynamic topography 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 · · S1 S1 S1 S1 V V V V · · · · · · · · · 1 1 1 1 2 2 2 1 1 1 1

S2 S2 S2 S2

*Three different curves are used; S1 indicates a first-order sinusoidal curve; V indicates a first-order Vail curve; S2 indicates a secondorder sinusoidal curve. Two different subduction histories are used; 1 indicates initiation of subduction on the western cratonic margin at 250 Ma; 2 indicates initiation at 500 Ma.

Dynamic topography generated by subducting slabs is also an important influence (case 3). In this case (all other parameters are identical to case 1) two erosional unconformities related to episodes of subduction on opposing cratonic margins are apparent (Fig. 9). Development of the older unconformity follows a pattern apparent from its timing and geometry and may be understood in terms of an interaction between reversible dynamic topography, deposition, and erosion. At the time of maximum slab penetration (430 Ma) the amplitude of the dynamic topography reached approximately 3000 m and a wavelength of 2000 km, causing tilting and subsidence over almost half the craton (Fig. 7). Maximum cratonward extent of the unconformity occurs at 420 Ma, and is produced by erosion of strata deposited and then uplifted in slab-related dynamic topography. Amplitude of the dynamic topography is greater toward the craton margins, so stratal thicknesses are greater, elevation of the uplifted wedge is greater, and the unconformity extends further backward in time from 420 Ma to around 440 Ma. Denudation continues on the wedge until, combined with background subsidence, it entirely removes the positive topography, and onlap completely buries the unconformity surface at 230 Ma. Note that the two spikes of erosion extending back in time from the main unconformity are artifacts of model resolution. This pattern of unconformity development illustrates the stratigraphic significance of dynamic topography and results from the reversible nature of subsidence due to dynamic topography. In the absence of other subsidence mechanisms and given enough time after subduction ceases, all or most strata deposited in dynamic topography lows but subsequently uplifted by the cessation of dynamic topography will be eroded, leaving only an unconformity as evidence of their existence. A younger unconformity related to Farallon slab subduction is shown in ongoing development on the western cratonic margin (Fig. 9). This unconformity will probably repeat the pattern described previously and consume strata deposited in the dynamic topography low back in age to about 250 Ma. At the end of the model run, however, much strata of this age remains, and demonstrates the influence of slab-related dynamic topography. A wedge of increased accumulation rates extends around 1000 km onto the craton at 250­230 Ma. This represents tilting and subsidence of the craton by dynamic topography in response to initiation of subduction at 250 Ma. Higher accumulation rates cease when the plate has penetrated to the 670 km discontinuity, dynamic topography is established, and the extra accommodation created has been filled. Penetration of a flat slab from 75 to 30 Ma created much additional accommodation on the craton, and

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higher accumulation rates can be seen extending almost 3000 km at 60 Ma. The youngest strata filling this space have been eroded, and those remaining have low preservation potential. We now combine both slab-related dynamic topography and longer-wavelength dynamic topography due to mantle insulation thermal anomalies. Different signatures of vertical motion are generated by the two scales of dynamic topography (case 4). Iapetus subduction is clearly evident in dynamic topography and basement elevation on the eastern cratonic margin (point 4, Figs. 8C and 10), while influence of Farallon subduction is most evident in the west (point 1, Figs. 8C and 10). Cyclical basement subsidence and uplift at a point near the craton center (point 3, Figs. 8C and 10) are due to long-wavelength dynamic topography. From the patterns of strata (Fig. 9) it is apparent that the unconformity generated by Iapetus subduction merges with the younger unconformity generated by sub-Pangea heating, showing how the two different scales of dynamic topography may interact. Strata formed

in subduction-related dynamic topography was uplifted to elevations higher than the surrounding craton when subduction ceased, and hence was more susceptible to subsequent erosion, particularly when enhanced by further longer-wavelength uplift. Erosion of these strata increases clastic sediment supply from 420 to 360 Ma, preventing development of the 380 to 340 Ma hiatus seen in case 2. Cross sections and isopach maps illustrate overall patterns of cratonic and marginal basin strata, as well as complex stratal geometries produced by dynamic topography (Figs. 11 and 12). Wedges of increased stratal thickness result from filling of slab-related dynamic topography over significant areas of the craton. Clearly evident are ~3000 m of Upper Cretaceous to Eocene strata (75­40 Ma) deposited in dynamic topography over the Farallon slab and subsequently uplifted and tilted (Fig. 11, section A-A). Isopachs also show this wedge of strata and a wedge developed from 250 to 220 Ma related to subduction initiation (Fig. 12). Similar wedges

related to Iapetus subduction are not well developed (total thickness <400 m), mainly due to low clastic supply prior to 450 Ma and abundant accommodation. However, there is a trend of eastward-increasing thickness from 480 to 430 Ma (Fig. 12), developed in response to tilting over the Iapetus slab. This trend is reversed from 430 to 420 Ma, when subduction ceased and dynamic topography reversed. Phanerozoic platform strata, approximately 1200 m in thickness, are divided into four sequences by unconformities that developed in response to complex interacting dynamic topographies (Fig. 11, section A-A). The influence of longer-wavelength dynamic topography is evident in unconformity surface A (Fig. 11), developed over the eastern two-thirds of the craton from 300 to 0 Ma (Fig. 12). The converse of this phenomenon is represented by an outlier of Lower Paleozoic strata on the Archean craton (Fig. 11, section B-B' and Fig. 12) that was deposited during cratonic flooding due to a dynamic topography low (Fig. 6). Preservation of

2

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Basement elevation Dynamic topography

-3000

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Time (Ma)

Figure 10. Basement elevation and dynamic topography through time at five locations on and adjacent to the craton (Fig. 8C). Long-wavelength dynamic topography is best illustrated in 3, while slab-related effects are best developed in 1 and 4. Basement elevation is uncorrected for compaction or isostasy.

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FORMATION OF SEQUENCES IN THE CRATONIC INTERIOR

4000

B

Overflow into oceanic trough, 270 - 0 Ma, with hiatuses

2000

Platform strata developed adjacent to the Archean craton, 530 - 100 Ma

Remnant outlier, 480 - 540 Ma

Exposed Archean cratonic basement

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Increased thickness related to initiation of subduction at 250 - 220 Ma

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70 - 45 Ma wedge from penetration of flat Farallon slab

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Exploded view of box in section A­A

20 Ma to present

Elevation (m)

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Unconformity surface A

-1000 400 - 330 Ma -2000 2000 540 - 430 Ma

140 - 60 Ma

2500

Distance (km)

3000

Figure 11. Two cross sections from case 4 (Fig. 9) taken along lines A­A and B­B. An exploded view from section A­A shows detail of platform strata. this outlier is an artifact of low topographic slopes in the area, but illustrates the extent of early Paleozoic cratonic flooding and deposition in the model due to the long-wavelength dynamic topography low. First-Order Sinusoidal Eustasy We now investigate the combined influence of eustasy and dynamic topography on cratonic stratal patterns. A sinusoidal eustatic curve with a 300 m.y. period and 100 m amplitude is added to four cases (cases 5­8) that are identical in all other respects to cases 1­4 (Fig. 9). The influence of eustasy on stratal patterns is most apparent comparing the two cases without dynamic topography, i.e., case 5 with Case 1. Not surprisingly, three unconformities develop during falling eustatic sea level, from 600 to 520, 370 to 200, and 70 to 0 Ma. Erosion rates are highest toward the cratonic margins because of the higher slopes, and some older strata are removed. Rates are lowest in the center of the craton, where slopes are so low that no significant thickness of older strata is removed. Interaction with long-wavelength dynamic topography both retards and accentuates stratal response to eustatic sea level (case 6, Fig. 9). For example, the dynamic topography low at 300 Ma reduces erosion due to falling sea level from 370 to 220 Ma, preventing removal of older strata beneath the unconformity. The asymmetric high developing from 300 to 100 Ma, however, accentuates erosion, extending the unconformity time span in the east. Results of slab-related dynamic topography are similarly mixed (Fig. 9). Unconformity development is reduced in the case of Iapetus subduction, which occurred in case 7 during a time of rising eustatic sea level, but is only slightly accentuated in the case of Farallon subduction. In case 8, the combined influence of rising eustatic sea level and a long-wavelength dynamic topography low significantly reduces development of the unconformity related to Iapetus subduction (Fig. 9). First-Order Vail Eustasy Consequences of varying the pattern of eustatic change are examined using the first-order Vail curve (Vail et al., 1977) in cases 9 to 12 (Fig. 9). All other parameters are as in cases 1 to 4. Stratal

Geological Society of America Bulletin, December 1997

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A Farallon subduction

250-220 Ma 220-75 Ma

75-40 Ma

Figure 12. Isopach maps from case 4 showing thickness and distribution of strata deposited in and/or eroded over dynamic topography. Zero rates of deposition, shown in white, on the craton and shelf generally represent development of erosional unconformities but represent nondepositional hiatus in the oceanic trough.

Hiatus 0

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B Iapetus subduction

430-480 Ma 420-430 Ma

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FORMATION OF SEQUENCES IN THE CRATONIC INTERIOR

patterns in case 9 are very similar to those in case 5 except for reduced duration of the late Paleozoic unconformity due to reduced magnitude of eustatic fall, and a period of deposition from 350 to 320 Ma. This deposition is due to a slightly reduced rate of eustatic fall and subsequent creation of accommodation space through subsidence. The addition of long-wavelength dynamic topography has much the same effect as in case 6, but higher eustatic sea level on the Vail curve leads to enhanced development of nondepositional hiatuses from 520 to 350 Ma, restricting carbonate deposition to a smaller area on the craton (Fig. 9). Differences in unconformity development in case 11 are more pronounced. Erosion due to reversal of dynamic topography over the Iapetus slab is enhanced with respect to case 7, removing all strata in the east above the previous

unconformity at 560 Ma (Fig. 9). Erosion is enhanced because uplift from 430 to 420 Ma occurs during slowly falling eustatic sea level, as opposed to rising eustatic sea level in case 7. The same unconformity is reduced in magnitude in case 12 compared to case 11, due to a combined dynamic topography low and a eustatic high. Alternative Western Margin Subduction History Initiating subduction on the western cratonic margin at 500 Ma instead of 250 Ma, with an 80 m.y. slab dipping at 70° (Fig. 4), and keeping all other parameters as in case 4, has minimal impact on stratal patterns (case 13, Fig. 13). There is no apparent stratigraphic signature from the dynamic topography for two reasons. First, the slab

is situated more than 500 km west of the cratonic margin, and hence amplitudes of dynamic topography on the craton are small. The cratonic margin is tilted down to the west, but water depths are already high, so impact on deposition is minimal. Second, and most important, clastic sediment supply is low. No clastic supply is available to fill the extra accommodation generated by dynamic topography, and water depths are too great for significant carbonate growth, illustrating again the importance of sediment supply in developing stratal signatures from dynamic topography. Clastic Sediment Supply From the prior cases it is apparent that clastic sediment supply plays a major role in the development of model stratal patterns, particularly

0 100

13

Age (Ma) Age (Ma)

200 300 400 500 600 0 100 200 300 400 500 600 0 100

14

Figure 13. Chronostratigraphic diagrams showing rates of deposition along section A­A for model cases 13 to 15 (Table 2) with accompanying clastic sediment supply curves.

15

Age (Ma)

200 300 400 500 600 0 2000 4000 0 50000 Sediment supply (km3)

Distance (km) Nondepositional hiatus

Erosional hiatus

0 2 13 20 >20

Rate of Deposition (m/Myr)

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Case 14 High sediment supply

500 Ma

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Figure 14. Cross sections along line A­A for model cases 14 and 15 illustrating the importance in the model of clastic sediment supply to the development of stratal patterns associated with subduction-related dynamic topography.

when dynamic topography creates increased accommodation and water depth. In case 14, maintaining clastic supply at 105 km3 · m.y.­1 throughout the model run and using the slab model with Farallon subduction initiated at 500 Ma demonstrates that increased sediment supply significantly alters the stratal signature of dynamic topography. High clastic supply fills available accommodation in the marginal basins by 560 Ma (Fig. 13), and overflow into the deep ocean trough occurs from 560 to 470 Ma. Trough deposition is interrupted at 470 Ma by creation of significant amounts of dynamic topography accommodation on both western and eastern cratonic margins. Wedges with increased accumulation rates are developed at 490 Ma in the west, and from 470 to 420 Ma in the east (Fig. 14), though many of the latter strata are subsequently eroded after uplift, so that development of unconformities on the eastern side of the craton is also en-

hanced by increased clastic supply prior to onset of erosion. Reducing clastic supply to 5 × 104 km3 m.y.­1 in case 15 significantly reduces stratigraphic traces of dynamic topography. Cratonic margin accommodation space remains partly unfilled at 500 Ma, and thus no stratal wedges are formed in dynamic topography (Fig. 14). Consequently, development of unconformities is curtailed, with only minor erosion in the east after cessation of subduction (Fig. 13). Second-Order Sinusoidal Eustasy Second-order eustatic sea-level change has been postulated as the most likely mechanism to account for the six North American sequences. To avoid circular reasoning we used a sinusoidal curve with an arbitrary starting point rather than a curve with highstand and lowstand timing based on sequence ages. Deriving a curve from known

stratal patterns with lowstands at times of unconformities would produce patterns similar to those observed, but only via circular logic. Using an arbitrary curve allows examination of second-order eustatic influence without making assumptions a priori about mechanisms of sequence formation. Development of six sequences bounded by cratonwide unconformities due to second-order eustasy and background subsidence is illustrated in case 16 (Fig. 15). The first unconformity is of shorter duration than latter examples because accommodation due to the initial eustatic rise is not filled, so subaerial erosion does not commence immediately after sea level starts to fall as it does in younger cycles. A different pattern of unconformity development occurs in case 17 (Fig. 15), with long-wavelength dynamic topography accentuating unconformity development from 600 to 520 Ma and from 300 to 100 Ma, and mitigating development from 500 to 300 Ma. When slab-related

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Background subsidence

0 100

16

Supercontinent dynamic topography 17

Subduction related dynamic topography 18

Combined dynamic topography 19

Age (Ma)

200 300 400 500 600 0 2000 4000 0 2000 4000 0 2000 4000 0 2000 4000

-100 0 100 200 0 50000 100000 Eustatic sea-level (ma) Sediment supply (km3)

Distance (km)

Distance (km)

Distance (km)

Distance (km)

Non-depositional hiatus

0 2 13 20 >20

Erosional hiatus

Rate of Deposition (m/Myr)

Figure 15. Chronostratigraphic diagrams showing rates of deposition along section A­A for model cases 16 to 19 (Table 2) with accompanying eustatic and clastic sediment supply curves. dynamic topography is added in case 18 (Fig. 15), the six sequences and bounding unconformities due to eustasy are still present, but the unconformities are extended spatially and temporally due to uplift after periods of subduction. Complex stratal patterns result in case 19 (Fig. 15) when second-order eustasy, supercontinent dynamic topography, and slab-related dynamic topography are combined. Six depositional sequences are formed, generally of shorter duration on the craton than at the margins, and of variable cratonward extent. For example, the 250 to 180 Ma sequence is absent in the east, whereas from 500 to 450 Ma a sequence extends across the whole craton, bounded by unconformities on the craton that are absent at the cratonic margins. Interesting interactions between dynamic topography and eustasy are apparent. An unconformity from 470 to 420 Ma in case 16, developed in response to a eustatic fall, is reduced in spatial and temporal extent in case 19 by additional accommodation generated by dynamic topography. Conversely, part of the overlying 420 to 370 Ma sequence present in case 16 is eroded in the east in case 19 after being uplifted upon cessation of subduction. Longer-wavelength dynamic topography tilting the craton up to the east limits the 220 to 180 Ma sequence to the western side of the craton. DISCUSSION Expectations regarding the degree of match between model results and observed stratigraphic patterns should be tempered with awareness of model formulation. Numerous assumptions and exclusions weaken its predictive power, and derivation of the subduction history in part by reference to observed stratigraphy lends a degree of circular reasoning. Despite these weaknesses, however, useful and significant comparisons with observation can be made. Because eustatic sea level is held constant in case 4 it is the best example to use to illustrate the importance of dynamic topography. Comparison of the case 4 chronostratigraphic plot with that from Sloss (1963) (Fig. 1) highlights some interesting points. The four unconformities in case 4 can be approximately matched with those separating four of the Sloss sequences, but show different geometries and are generally of greater duration. The model unconformity spanning 600 to 540 Ma reproduces the general geometry and duration of the base-Sauk unconformity. The unconformity separating the Tippecanoe and Kaskaskia sequences is perhaps comparable with the unconformity developed due to Iapetus subduction in case 4. Zuni and Absaroka strata are separated by an unconformity lasting from around 270 to 120 Ma, broadly comparable with the unconformity due to sub-Pangea heating. Particularly notable in this comparison is the shared asymmetry of modeled and observed unconformities; both unconformities are of greater duration in the east, showing onlap of Jurassic and Cretaceous strata from the west (Fig. 9 and Fig. 12) and an absence of preserved Jurassic to Cretaceous strata on the eastern side of the continent (e.g., Bally, 1989). Such a stratal distribution is unlikely to occur through eustasy alone, unless there was a significant long-wavelength topographic high on the eastern side of the craton. Tilting of the craton up to the east over a dynamic topography high seems more likely. The unconformity currently developing above the Tejas sequence can be matched with the model unconformity from approximately 70 to 0 Ma, due to reversal of Farallon slab dynamic topography. Comparison is also possible between model cross sections and a section from Bunker et al. (1988) (Fig. 16). Overall thicknesses are in broad agreement, and both show features due to tilting and erosion, particularly long-wavelength tilting up to the east resulting in an eastward increase in age of strata outcrops. Geometries of unconformities developed in the sections differ. Those in Figure 16A are laterally more uniform than those in Figures 11 and 16B, suggesting a longer wavelength mechanism than slab-related dynamic topography. Observation and model both show a wedge of Cretaceous strata thickening to the west (discussed below). Shorter-wavelength processes such as faulting and folding were not included in the model formulation, and so real geologic features such as faults, basins and arches, all showing a history of multiple reactivation throughout the Phanerozoic (Fig. 16A), are not reproduced. These broad comparisons are by no means high-resolution model reproductions of observed stratigraphic patterns. However, within model constraints they serve to suggest potential mechanisms for formation of specific sequences and their bounding unconformities. Overall patterns

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1000

W

Cenozoic & Quaternary K

Nebraska K

Iowa K

Up. P Mid. P

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A

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-2000 0 200 400 Distance (km) 600

Figure 16. (A) A geologic cross section through the United States central midcontinent region from Bunker et al. (1988). (B) A magnified view of a section from case 4 (see Fig. 8C for location). In section A, six Phanerozoic sequences are visible having variable lateral extents and capped or truncated by unconformities. Ages of strata outcrops generally increase to the east, providing evidence for up-to-the-east tilting of the craton over a long-wavelength dynamic topography high. Evidence for slab-related dynamic topography is shown by the angular discordance of Cretaceous strata, and periodic reactivation of fault zones and basin and arch structures is indicated by syndepositional and postdepositional offset, onlap, and truncation of strata. Angular discordance of Cretaceous and younger strata, development of sequences, and long-wavelength up-to-the-east tilting are also visible in section B. C--Cambrian, O--Ordovician, S--Silurian, D--Devonian, M--Mississippian, P--Pennsylvanian, Perm-- Permian, J--Jurassic, K--Cretaceous.

of North American Phanerozoic sequence development can be viewed in relation to formation and breakup of supercontinents. The base-Sauk and Zuni-Absaroka bounding unconformities are the two longest duration sequence-bounding unconformities; they formed when North America was probably part of a supercontinent and thus on a dynamic topography high. Increased elevation extended the duration of the unconformities. Conversely, the shortest duration unconformities bounding the Tippecanoe and Kaskaskia sequences formed when the continent probably occupied a dynamic topography low. Eustasy is commonly assumed to be of singu-

lar importance in generation of these sequences (e.g., Vail et al., 1977; Haq et al., 1987). The Paleozoic portion from the eustatic curve of Vail et al. (1977) is based primarily on evidence from North American sequences. Considering case 4, it is apparent that sequence-controlling mechanisms were probably more complex. An apparent early Paleozoic eustatic highstand and late Paleozoic to early Mesozoic eustatic lowstand can be explained in terms of supercontinent motion and dynamic topography, as suggested by Gurnis (1991), rather than just first-order eustasy. This dynamic topography is capable of producing synchronous vertical motions of similar magnitudes

on several continents, hence creating an impression of eustatic sea-level change. Although eustasy is important in formation of cratonic sequences, these results suggest that it is not acting alone and probably not at amplitudes commonly assumed from stratigraphic studies, because these do not account for vertical cratonic motion due to dynamic topography. Although case 4 demonstrates that dynamic topography was probably significant in formation of cratonic sequences, it does not show the requisite six sequences. Case 19 is more successful in this respect, suggesting that second-order eustasy (10 to 100 m.y. periods), possibly due to

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changes in spreading rates, subduction rates, and age distribution of oceanic lithosphere, was also important in forming the North American sequences. Timing of individual sequences and bounding unconformities does not match particularly well with ages of observed cratonic sequences. This is not surprising, because the eustatic curve consists only of simplified 100-m.y.-period, 100-m-amplitude cycles. The curve could be adjusted to produce patterns of sequence and unconformity more akin to those observed, but adjustment of the curve based on observed stratal patterns, even accounting for possible influence of dynamic topography, is a circular methodology. No independent methods exist to derive a second-order eustatic curve, although a truly global study looking at stratal patterns on all continents would be helpful. Further work on explaining the link between spreading and subduction rate, oceanic lithosphere age distributions and eustasy (e.g., Gurnis, 1990), and the implications for cratonic stratal patterns is also needed. However, despite a lack of detailed fit between model result and observation, case 19 illustrates that second-order eustasy combined with dynamic topography can account for the basic patterns in the six North American cratonic sequences and bounding unconformities. Cratonic accumulation rates in cases 1­4 are generally comparable to those shown by Bally (1989) i.e., about 1000 m final thickness of Phanerozoic cratonic strata preserved. This is not surprising, because accumulation rates are controlled primarily by background subsidence rate, which was chosen on the basis of observed thicknesses. Locally, cratonic basins show higher rates leading to greater preserved thickness (Bally, 1989). On the cratonic margin, ignoring the influence of dynamic topography, final preserved model thickness was about 4000 m. This is significantly less than thicknesses developed in actual marginal basins, because responsible subsidence mechanisms are not included in the model. Another significant weakness in the model is the lack of deposition above sea level, which will tend to increase areal and temporal extent of unconformities in the model. For example, the onset of erosion at the base of the 330 to 120 Ma unconformity in case 2 (Fig. 9) would probably have been delayed by terrestrial deposition, thus correlation with the base-Zuni unconformity of Sloss is improved. Extensive early Paleozoic cratonic flooding due to a long-wavelength dynamic topography low is indicated in case 4 by an outlier of lower Paleozoic strata atop Archean basement (Fig. 11, section B-B', and Fig. 12). Evidence of such flooding is preserved on the Canadian shield as rare diatreme xenoliths of lower Paleozoic strata in intrusive igneous rocks (Cook and Bally, 1975;

Sloss, 1988b). Model results from case 4 demonstrate that it is unnecessary to invoke eustasy to explain such flooding, emphasizing the problems in compiling a eustatic curve for the Paleozoic using stratal patterns without accounting for vertical cratonic motions. Dynamic topography related to Iapetus subduction generated the 420 Ma unconformity in case 4 (Fig. 9). If such dynamic topography existed, a stratal signature should show evidence of its development. Ordovician and Silurian strata on the eastern cratonic margin have been interpreted solely as foreland basin deposits (Read, 1980; Quinlan and Beaumont, 1984; Mussman and Read, 1986), but Coakley and Gurnis (1995) suggested that eastward tilting of the intracratonic Michigan basin in Middle Ordovician time is best explained by dynamic topography. Because the subducting slab responsible for this tilting must have passed beneath the cratonic margin, this raises the possibility that accommodation space presumed to have formed in a foreland basin may actually have been due in part to dynamic topography. Evidence for a foreland basin subsidence mechanism comes from the general basin geometry (greatest stratal thickness in the east) and a presumed link between Appalachian tectonic events and same-age strata (Quinlan and Beaumont, 1984; Howell and van der Pluijm, 1990). Thus contribution to subsidence from dynamic topography across the eastern cratonic margin, producing the same areal distribution and thicker-in-the-east geometry, is not ruled out. More problematic is the case 4 unconformity related to cessation of subduction, and postdepositional removal of strata deposited in the dynamic topography trough. Preservation of significant thicknesses of strata as observed can be explained if there were other subsidence mechanisms, such as thrust-wedge loading. This may also explain how the Tippecanoe-Kaskaskia sequence-bounding unconformity could have formed due to removal of a subducting slab and consequent uplift, but still be of shorter duration away from the cratonic margin (Sloss, 1963). Further work is required to help constrain possible contributions of dynamic topography in this area during Ordovician-Silurian time. Cross and Pilger (1978) and Cross (1986) described anomalously high Late Cretaceous subsidence rates in the southwestern United States, resulting in a postcompaction Campanian to Maastrichtian stratal thickness of almost 3000 m. They ascribed this event to low-angle penetration of the Farallon slab beneath this area; this is supported by modeling studies of Bird (1984, 1988) and Mitrovica et al. (1989). In case 4 dynamic topography related to flat penetration of the Farallon slab beneath the craton (Figs. 3 and 7) has been filled by strata producing a wedge more

than 2500 m thick, ranging in age from 76 to 45 Ma and topped by a developing erosive unconformity surface (Figs. 9, 11, and 12). The greatest preserved postcompaction stratal thickness occurs between 72 and 48 Ma, as opposed to 83 to 74 Ma according to Cross and Pilger (1978). This discrepancy suggests that penetration of the flat Farallon slab may have occurred earlier than suggested in the model. Rapid filling of accommodation in the Campanian and an absence of deep-water environments is demonstrated by multiplicity of evidence for shallow-water shelf deposition (Klug, 1993; Elder et al., 1994). High sediment supply in the model leads to the same pattern of shallow-water deposition, and highlights the importance of sediment supply to the stratigraphic signature of dynamic topography. Stratal patterns would be very different both in the model and in reality had abundant clastic sediment not been available to fill accommodation as it formed. In general, the good match between observed and modeled thicknesses is a powerful argument for operation of dynamic topography and its importance to cratonic stratal patterns. Comparing observed and modeled lateral extents of Upper Cretaceous strata across the craton is also of interest. Cross and Pilger (1978) showed a zero-thickness contour for Campanian and Maastrichtian strata that reached a maximum eastward extent at approximately long 95° W, 1500 km west of the cratonic margin. This does not appear to take full account of postCretaceous erosion, however, because outliers of Cretaceous strata were shown by Bunker et al. (1988) as far east as long 90° W in western Wisconsin, suggesting that deposition extended farther east. In case 4, Upper Cretaceous strata extend across the entire craton (Fig. 9), with breaks due only to erosion on high slopes at the front of the tilted wedge (Fig. 11). Craton-wide extent of this deposition is due to combined influence of subduction-related tilting and longer-wavelength subsidence related to the Pangea breakup. Observed stratal patterns do not refute this, but rather suggest that increased efficiency of postCretaceous erosion combined with possible Tertiary relative sea-level fall have removed much Cretaceous strata preserved in case 4. The age of initiation of subduction off the southwestern margin of Paleozoic North America is poorly constrained. The presence of an offshore arc is inferred from distribution of Paleozoic units in California and the western Great Basin, but subduction may have started from Ordovician (Oldow et al., 1989) to Late Permian time (Lawton, 1994). Strata commonly interpreted as having deposited in a passive margin setting accumulated throughout early Paleozoic time, and presumably these strata may contain a record of any dynamic topography generated by

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early Paleozoic subduction. Two alternative initiation times for subduction have been investigated and, dependent on sediment supply, it seems possible that penetration of a slab beneath the western margin of the craton would leave a stratal signature. However, parameters such as trench position, slab dip, and age of lithosphere at subduction are unknown, and combined with various poorly constrained stratigraphic parameters (e.g., clastic sediment supply, water depths, climatic influences) make more detailed predictions of dubious worth. More work is required to examine lower Paleozoic units for evidence of anomalous subsidence and deposition events that may indicate influence by dynamic topography. Sediment supply is an important variable in the stratigraphic model, but is also difficult to quantify in studies of ancient strata. In general terms, from Ordovician to Mississippian time, carbonate deposition was dominant on the craton (Cook and Bally, 1975); this suggests low clastic supply, perhaps a result of limited topographic relief and trapping of clastic material in marginal basins. Clastic deposition increased from Pennsylvanian time onward, presumably as a result of the creation of more significant relief on cratonic margins by collisional tectonic processes and bypass of clastic sediment from the margins. This pattern is reproduced successfully in the model using an external sediment supply curve to account for higher clastic supply during times of orogenic activity. Model stratal signatures developed in response to dynamic topography have been shown to be sensitive to clastic sediment supply. Development of the Upper Cretaceous stratal wedge, possibly deposited in dynamic topography, occurred with abundant clastic sediment from nearby orogenic topography (Cross, 1986). Presumably this stratal signature would have been less well developed without such clastic supply, lending a degree of observational support to the dependence on clastic supply demonstrated in the model. Abundant clastic supply was apparently also available for most of the history of the Appalachian basin (Quinlan and Beaumont, 1984), but the potential influence of dynamic topography is more difficult to interpret in this case. Further work with a refined model including compressional tectonic processes and more realistic spatially variable depositional processes is necessary to progress further. CONCLUSIONS This work demonstrates that it is possible, using integrated geodynamic and stratigraphic models, to generate six cratonic sequences with general properties similar to those observed in North American cratonic strata. 1. The most successful reproduction of ob-

served cratonic stratal patterns is achieved by combining a sinusoidal second-order eustatic curve with long-wavelength and subductionrelated dynamic topography. 2. Long-wavelength dynamic topography associated with supercontinent formation and breakup can explain first-order features of North American cratonic sequences. The relatively extended sub-Sauk and sub-Zuni unconformities developed when North America was atop a dynamic topography high, and the four other shorter unconformities formed during times of dynamic topography low. Furthermore, the asymmetric nature of the sub-Zuni unconformity can be explained by up-to-the-east tilting of North America over a dynamic topography high centered beneath Pangea. 3. First-order eustatic change is not necessary to reproduce this basic pattern of sequences and unconformities. Vertical motions induced by long-wavelength dynamic topography over several continents simultaneously may easily be mistaken for a eustatic signal. First- and secondorder eustasy can no longer be considered in isolation as responsible for stratal patterns, because its origins are essentially tectonic (e.g., ridge spreading rates, age distribution of oceanic lithosphere, subduction rates) and therefore have other effects (e.g., dynamic topography) equally capable of influencing sequence development. 4. Preservation potential of strata deposited in dynamic topography over subducting slabs is low, because such dynamic topography is reversible. Consequently, the most likely record of ancient dynamic topography is an unconformity increasing in duration toward a cratonic margin, though this pattern is sensitive to sediment supply and the presence of other subsidence mechanisms. 5. Stratigraphic signatures of subductionrelated dynamic topography are illustrated in the model, and are shown to be sensitive to clastic sediment supply. Model results match reasonably well, given this constraint, with the observation of the Late Cretaceous tilted wedge presumed to have formed over the subhorizontal Farallon slab. Determining the degree of influence of subduction-related dynamic topography from closure of Iapetus and earlier subduction on the western margin of the craton is more problematic, and requires further study. ACKNOWLEDGMENTS The work was funded by the David and Lucile Packard Foundation and National Science Foundation grants EAR-9496185 and EAR-9417645. We thank D. Kemp, S. Zhong, P. Allen, J. Verlander, and G. S. Robertson for helpful discussions, D. Anderson and J. Grotzinger for their comments on the manuscript, and S. Dorobek,

B. Coakley, and an anonymous reviewer for thorough, thoughtful reviews. This represents contribution number 5673 of the Division of Geological and Planetary Science, California Institute of Technology.

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GSA Bulletin: Formation of sequences in the cratonic interior of North America by interaction between mantle, eustatic, and stratigraphic processes