Little is known about controls on river avulsion at geological time scales longer than 104 years, primarily because it is difficult to link observed changes in alluvial architecture to well-defined allogenic mechanisms and to disentangle allogenic from autogenic processes. Recognition of Milankovitch-sale orbital forcing in alluvial stratigraphy would provide unprecedented age control in terrestrial deposits, and also exploit models of allogenic forcing enabling more rigorous testing of allocyclic and autocyclic controls. The Willwood Formation of the Bighorn Basin is a lower Eocene fluvial unit distinctive for its thick sequence of laterally extensive lithological cycles on a scale of 4 to 10 m. Intervals of red palaeosols that formed on overbank mudstones are related to periods of relative channel stability when gradients between channel belts and floodplains were low. The intervening drab, heterolithic intervals with weak palaeosol development are attributed to episodes of channel avulsion that occurred when channels became super-elevated above the floodplain. In the Deer Creek Amphitheater section in the McCullough Peaks area, these overbank and avulsion deposits alternate with a dominant cycle thickness of ca 7·1 m. Using integrated stratigraphic age constraints, this cyclicity has an estimated period of ca 21·6 kyr, which is in the range of the period of precession climate cycles in the early Eocene. Previous analyses of three older and younger sections in the Bighorn Basin showed a similar 7 to 8 m spacing of red palaeosol clusters with an estimated duration close to the precession period. Intervals of floodplain stability alternating with episodes of large-scale reorganization of the fluvial system could be entirely autogenic; however, the remarkable regularity and the match in time scales documented here indicate that these alternations were probably paced by allogenic, astronomically forced climate change.
Understanding autogenic and allogenic controls on fluvial systems is crucial for interpreting the rock record, with the aim of providing realistic analogues of recent surface processes (Blum & Tornqvist, 2000), and for interpreting how the various controls shape alluvial architecture (e.g. Stouthamer & Berendsen, 2007; Karssenberg & Bridge, 2008; Hajek et al., 2012). Disentangling autogenic from allogenic forcing is difficult, because few studies document fluvial responses to allogenic forcing over longer (104 to 106 years) time scales (e.g. Hajek et al., 2012). Long temporal records of river dynamics are hard to link confidently to records of climate or tectonic change, because the temporal resolution is relatively coarse and because coeval climatic or tectonic records at similar time resolutions are typically absent.
Orbital climate change could provide an exception because cyclic allogenic climate forcing is predictable at quasi-periodic time scales (Abdul Aziz et al., 2008). Orbital climate forcing provides a good opportunity to test river dynamics under changing climates and to evaluate how autogenic processes interact with allogenic ones (Stouthamer & Berendsen, 2007). The present study develops an orbital climate forcing hypothesis put forward recently for palaeosol stacking patterns in the fluvial Willwood Formation, Bighorn Basin, Wyoming (Abdul Aziz et al., 2008).
Most sediment in the Willwood Formation was deposited on the floodplains of meandering river systems under warm temperate to subtropical conditions (Bown & Kraus, 1981, 1987; Kraus, 1987). The floodplain deposits are of two kinds. Mudstones with moderately to strongly developed palaeosols alternate vertically with heterolithic deposits of drab mudrocks with weak palaeosol development and small channel and thin sheet sandstones. The heterolithic deposits have been interpreted as avulsion belt deposits that formed on the floodplain as the main channels were abandoned episodically in favour of new channel courses (e.g. Kraus & Gwinn, 1997). The sandstones and mudstones represent crevasse splay channels and floodplain deposits associated with the splay channels. Rapid deposition produced only weakly developed palaeosols on the avulsion deposits. The heterolithic deposits alternate at a scale of 4 to 10 m with the well-developed palaeosols that formed on mud-dominated, true overbank intervals (Kraus, 1987; Kraus & Aslan, 1993; Clyde & Christensen, 2003). Development of the overbank palaeosols depended on sediment accumulation rate (time), parent material, ground water level, vegetation and climate (Bown & Kraus, 1981, 1987; Kraus, 1987, 2002).
The alternation of fine-grained mudrocks having strongly developed palaeosols with heterolithic intervals showing weak pedogenesis was originally termed a ‘simple pedofacies cycle’ or ‘third-order cycle’ by Kraus (1987). These cycles have been related to the autogenic behaviour of the river system (Kraus, 1987; Clyde & Christensen, 2003) and to precession-scale orbital forcing (Kraus & Aslan, 1993; Abdul Aziz et al., 2008; Abels et al., 2012). Abdul Aziz et al. (2008) based their interpretation on field recognition of sedimentary cyclicity and time-series analysis of redness colour records of two Willwood sections; one through the Palaeocene–Eocene transition and the other higher in the lower Eocene. Precession forcing of sedimentary cyclicity would be remarkable in a floodplain setting, which is strongly influenced by the autogenic processes that dominate fluvial systems (Van De Wiel & Coulthard, 2010; Hajek et al., 2012).
To test the role of orbital forcing in floodplain sedimentation and explore the potential mechanism, a fourth section was analysed in the Willwood Formation that is longer but intermediate in age between the sections studied previously by Abdul Aziz et al. (2008) and Abels et al. (2012). The Deer Creek Amphitheater section is long enough to span the ca 100 kyr eccentricity-scale cyclicity. The Deer Creek Amphitheater section was investigated in greater detail sedimentologically than the previously studied sections. Apart from colour records, a Soil Development Index was developed depicting a qualitative estimate of sediment accumulation through time. Time series of both lightness and redness and the newly developed Soil Development Index (SDI) are analysed in relation to average sediment accumulation and the orbital forcing hypothesis of palaeosol stacking patterns.
Geological Setting and Section
The Bighorn Basin is a Laramide intermontane basin that formed in response to high-angle overthrusting of the western margin of the basin. The basin is bounded by the Bighorn, Beartooth and Owl Creek Mountains, which were the main sources of sediment to the basin, and were hydrologically open to the north and west during the early Eocene (Fig. 1; e.g. Bown and Kraus, 1981; Clyde et al., 2007). In the basin, a remarkably continuous and fossil-rich sedimentary record of late Palaeocene to early Eocene age was deposited under warm temperate to tropical conditions (e.g. Bown & Kraus, 1993; Gingerich, 2006). The Palaeogene Bighorn Basin had a summer monsoonal climate in which moist air was pushed north and west from the Mississippi Embayment (Sewall & Sloan, 2006). The strata are dominated by mudrocks that formed on the floodplains of meandering trunk rivers represented by thick, laterally extensive sandstones up to 1·5 km wide and up to 10 m or more thick (Kraus & Gwinn, 1997).
The Deer Creek Amphitheater section (DCA), named after its amphitheater-like outcrop, is located on a small east branch of the main Deer Creek drainage in the McCullough Peaks exposures of the Willwood Formation (Fig. 1). The Wasatchian-age, Wa3 to Wa4 biozone boundary is found in a relatively thin stratigraphic interval ca 100 m below the DCA section. Lateral stratigraphic correlations show that the top of the DCA section is ca 10 to 20 m lower stratigraphically than the lowest known Wa-5 fossil site in the area (Abels et al., 2012). The DCA section was therefore deposited in the upper half of the Wa4 biozone, with an approximate age of 54 Ma (Gingerich, 2010).
The DCA section is a composite section with a thickness of 115 m, measured and logged along four subsections: DCA-A, DCA-B, DCA-C and DCA-D (Fig. 2). The DCA area was chosen for study because of its excellent exposure, and because it enables construction of a one-dimensional vertical composite section that excludes large sandstone bodies.
Stratigraphic sections were measured by digging ca 1 m wide trenches down to fresh rock. Field units were designated on the basis of field estimation of: grain size; matrix colour; abundance, size and colour of mottling; presence, abundance and size of carbonate nodules; and abundance and size of slickensides. Hand sampling and field descriptions are based on methods detailed in the Soil Survey Manual (Soil Survey Division Staff, 1993).
The colour reflectance record was obtained in the field by measuring matrix colour of the strata at 10 cm vertical resolution using a portable photospectrometer (Minolta CM 508i, Minolta Co. Ltd., Japan). Each colour value is based on the automatically calculated average of three measurements at each level. Measurements were performed on freshly broken pieces of rocks to minimize the influence of drying and oxidation. Comparison of field and laboratory measurements from the Willwood Formation shows that high-frequency lithostratigraphic patterns in redness and lightness are well-reproduced, while low frequency patterns are sensitive to measuring circumstances. Redness values are relatively consistent whether measured from wet or dry surfaces, whereas lightness values can be up to 30% lower if surfaces are wet.
Time-series analyses of colour records were performed using the Redfit program of Schulz & Mudelsee (2002) using a rectangular window and standard settings and the Analyseries 1·1 program of Paillard et al. (1996) using the Blackmen Tuckey method with a Barlett window and compromise settings. Bandpass filtering was subsequently performed using the Analyseries program. In the field, matrix and mottle colours were determined using the Revised Standard Soil Colour Charts of Oyama & Takehara (1970). Field colour observations were digitized using the CMC10a computer program (www.wallkillcolor.com) with D65 10° illuminant allowing conversion of Munsell colour codes into the RGB colour space to construct digital images of the lithological logs.
A detailed Deer Creek Amphitheater (DCA) section is presented in Fig. 3. Here, brief sedimentological descriptions and interpretations of the main lithologies are given.
Heterolithic deposits consist of mudrocks, ranging from claystones to sandy siltstones, which surround small channel and sheet sandstones (for example, 37·8 to 38·6 m level; Fig. 3). Mudrocks show local relict bedding and evidence for weak pedogenesis including mottles, many of which are rhizoliths, and slickensides. Mudrocks are commonly grey but can also be yellow-brown or pale brown (Fig. 3; 29 m level and 38 m level). The sheet sandstones are up to 2·5 m thick and, although individual sandstone beds pinch out within metres or tens of metres, the stratigraphic level at which they sit may be dominated by sandstone for distances up to several hundred metres laterally.
Sandstones in the heterolithic intervals of the simple pedofacies cycles are especially continuous, with lateral extents over at least one kilometre. The sandstones show decimetre-scale bedding that is highlighted by very thin (<1 cm) layers of finer-grained sediment. Internally, those beds generally are structureless, although centimetre-scale cross-bedding is preserved locally. Grain size is usually fine and very fine sand, and finer-grained intercalations are common. Mud-filled and sand-filled burrows are common at the tops and bottoms, respectively, of sandstone sheets. Sandstone bases are either sharp, where they overlie well-developed palaeosols (for example, metres 83 to 84; Fig. 4), or gradational, with bedded intervals of siltstone and sandstone becoming gradually coarser upwards.
The weak pedogenesis of the mudrocks indicates relatively rapid sediment accumulation. The combination of fine-grained deposits showing minimal soil development, and sandstones of varying sizes and geometries are characteristic of avulsion deposits (e.g. Kraus & Aslan, 1993; Kraus, 1996). Following those studies, the associated thin sandstones are attributed to higher energy flows during splay events from the main river channel or crevasse channels, although some of the sandstone beds may represent (distal) levée deposits. The 1 km wide outcrop studied here has no major channel sandstone to which the thin sheets can be related, which means that most sandstones probably represent distal splays from flood events or small crevasse channels. The lateral continuity of over 1 km for the sandy intervals suggests time periods that were dominated by crevasse splay deposition. The presence of finer-grained intercalations and burrows within some sandstones also indicates that the sandstones represent multiple depositional events.
The fine sediments between the heterolithic deposits range from claystones to sandy siltstones and show a range of matrix colours including light grey, black, (dark) reddish brown, purple, olive and bright yellowish brown (Fig. 4). Differences appear in terms of colour and size of mottling, presence and abundance of carbonate nodules, presence of organic matter, and abundance and size of slickensides. Detailed chemical and sedimentological analysis has led other workers to identify palaeosol profiles in these deposits (e.g. Bown & Kraus, 1987; Kraus, 1987, 2002). Three kinds of palaeosols are recognized here on the basis of outcrop characteristics resembling palaeosol descriptions from this part of the Willwood Formation.
Purple (Palaeosol 69; Fig. 3) and purple-red (Palaeosol 55; Fig. 4) palaeosols are characterized by purple mudrock with yellow-brown mottles that increase in size and abundance downwards. Slickensides and red mottles are common in the lower part of the purple mudrock. In purple-red palaeosols, the underlying dark red to dark reddish-brown mudrock contains grey mottles, carbonate nodules of various sizes and abundance, and slickensides, especially in the upper part. The purple mudrock is commonly overlain by light-grey mudrock with rare, fine, purple, red-brown and/or orange mottling. In some examples, especially where the palaeosol is overlain by sandstone, a dark (grey) mudrock is preserved above the light-grey unit. Red palaeosol profiles lack the purple layer and less commonly show a (light-) grey top layer; the majority show no or few slickensides (Palaeosol 54).
Carbonate nodules are not observed in purple palaeosols, whereas more than half of the purple-red palaeosols contain carbonate nodules, on average ca 0·8 m below the top of the soil profile, where preserved. Carbonate nodules also occur in the majority of the red palaeosols, especially in the better-developed ones, and range from 0·2 m below the top of the soil profile in thin soils to up to 1·9 m in thick soils.
The mudrocks are interpreted as overbank deposits whose relatively low sedimentation rates allowed moderate to strong palaeosol development (e.g. Bown & Kraus, 1987). Purple, purple-red and red palaeosols were previously recognized as the dominant types of palaeosols in the McCullough Peaks area (Kraus, 2002). The dark-grey top layer and lighter grey zone below are interpreted as A horizons (for example, profiles 55 and 57; Fig. 4). Downwards, the purple and red zones represent Bss horizons, based on the presence of slickensides, or Bssk horizons when carbonate nodules are also present (profile 51; Fig. 4). The prominent, commonly intersecting slickensides indicate that most of the palaeosols are vertic palaeosols (Soil Survey Division Staff, 1993). Cumulative palaeosol formation led to overprinting of older palaeosol profiles by younger profiles, leading to horizons with a complex mix of morphological properties belonging to different stages of pedogenesis. Profiles 49 and 52 provide examples (Fig. 4). The differences in soil colour and carbonate content reflect drainage differences among the different kinds of palaeosols (e.g. Kraus & Hasiotis, 2006).
Pedogenic attributes of the C horizons and some of the A horizons lead to their inclusion with the more strongly developed palaeosols; however, the C horizons are commonly coarser-grained than the overlying B horizons (for example, profiles 51 and 55) suggesting that they are depositionally related to underlying avulsion deposits. Similarly, the A horizons commonly show sparser pedogenic features than the underlying B horizons and are directly overlain by sandstones (for example, the A horizons of profiles 49, 55 and 57) suggesting that they are related to the initiation of avulsion deposition. Thus, it is critical to keep in mind that pedogenic overprinting of the sediment can obscure its depositional origins (Kraus & Wells, 1999).
Soil Development Index (SDI)
Intensity of pedogenesis throughout the DCA stratigraphy can give qualitative estimates of periods of relatively slow and periods of relatively high sedimentation rates (Bown & Kraus, 1993). To estimate relative soil development, the method of Bown & Kraus (1993), in which soil development stages were recognized based on intensity of: horizon development; profile development and thickness; and morphological features including colour, soil nodule development, mottling and nature of contacts within the profile, has been simplified here. This study focused on two key criteria used by Bown and Kraus: palaeosol B-horizon thickness and a simple assessment of the intensity of horizon development. As a third parameter, rubification of the B-horizon was used, which is also viewed as an indicator of soil development (Almond et al., 2007; Harden, 1982). This approach is simple and easy to use in the field, especially if it is necessary to analyse thick stratigraphic successions.
Because these are alluvial palaeosols, thickness reflects upbuilding of the soil through time as a result of continued floodplain aggradation that was accompanied by pedogenesis (e.g. Johnson & Watson-Stegner, 1987; Calero et al., 2008). For equal degrees of pedogenic development, soil thickness is proportional to the length of time that sediment accumulation was relatively low and maintained equilibrium with pedogenic processes. Here, the thickness of the B-horizon was used, because in many cases, the A-horizon disappeared due to erosion or by overprinting of the subsequent soil. Soils were assigned a number between 0 and 1 depending on thickness of the B-horizon (Table S1). Horizon differentiation increases with time (e.g. Johnson & Watson-Stegner, 1987; Turnbaugh & Evans, 1994) and the level of horizon development was rated from 0 for vaguely developed horizons, 0·33 for poorly developed horizons, 0·67 for intermediate development and 1 for well-developed horizons (Table S1). To quantify soil rubification, each soil was assigned a number between 0 and 1 depending on the reddest colour in the B-horizon (Table S1).
Table 1. Calculation of McCullough Peaks sediment accumulation rates and estimated sedimentary cycle durations. The geometric mean of three independent cycle duration estimates is 21.6 kyr, which is consistent with modulation by the climatic precession cycle
Following the approach used in chronosequence studies (e.g. Harden, 1982; Vidic & Lobnik, 1997; Calero et al., 2008), a soil development index (SDI) was determined by, first, standardizing the horizon differentiation, soil thickness and rubification factors of the soils by two standard deviation of the total in the section. Then, the SDI per soil is the average of the three standardized parameters plus 1·0, to make the SDI positive between 0 and 2. Intervals without pedogenic modification were assigned a SDI of 0. Based on this index, and for simplification, palaeosols are assigned to one of three rates of pedogenesis: no or incipient pedogenesis (SDI < 0·5), intermediate pedogenesis (SDI between 0·5 and 1·0) and intense pedogenesis (SDI > 1·0). In the Supplementary Table S1, data are provided for the 78 observed palaeosol profiles.
Stratigraphic relation of sedimentary rocks
Plotting the intensity of pedogenesis for each palaeosol shows regular alternations between intervals with weak or moderately weak pedogenesis (SDI < 0·5 or light grey and 0·5 < SDI > 1·0 or medium grey colour in Figs 3 and 4) and intervals with more intense pedogenesis (SDI > 1·0 or dark grey in Figs 3 and 4). Sixteen cycles, labelled A to P, are recognized and range from 4·3 to 10·4 m thick and average ca 7·1 m in thickness (standard deviation 1·9 m). Cycle transitions were placed at the tops of the intervals showing the most intense pedogenesis. Some cycles are easy to define by their distinct purple-red part and light sandy part (cycles C, E, G, H, I, J, N and O). Some cycles consist mostly of heterolithic deposits (A, M and P). The latter cycles are generally thicker, at least in the one-dimensional view used here, than the cycles with relatively thinner heterolithic deposits.
Distant views of the section show remarkable banding of redder and lighter sediments (Fig. 2) coinciding with cycles A to P in the logged section (Figs 2 and 3). Each major cycle contains multiple, vertically stacked palaeosols (for example, palaeosols 50 to 55 in cycle L; Figs. 3 and 4). In general, these palaeosols are separated by an interval that later became the C-horizon of the overlying palaeosol (Fig. 4). This effect suggests that the lower palaeosol formed as a result of slow sedimentation and that its pedogenic development was halted by rapid burial by the sediment forming the lower portion of the next palaeosol. Eventually, the sedimentation rate slowed again, allowing the subsequent palaeosol to form. Thus, the vertically stacked palaeosols are separated by intervals indicating more rapid sedimentation.
Colour Records, Soil Development Index and Time-Series Analysis
Principal component analysis of the 400 nm to 700 nm reflectance data, both raw and normalized against 440 nm (to correct for lightness), indicated that the reflectance data are dominated by the lightness and redness of the matrix colour. Therefore, the L* and a* records are used as quantitative representations of lithology. Both records follow clearly lithological changes, with light sandy intervals represented in both records, and the red B-horizons of well-developed palaeosols especially well-represented in the redness record (Figs 4 and 5). The colour records can, therefore, be seen as a proxy for lithology. Colour records can partly be seen as a proxy for soil development as well, because sandy intervals are light and palaeosol-rich intervals dominantly red (Figs 4 and 5). If palaeosols have a grey upper horizon, however, the colour record changes stratigraphically below the level at which the SDI changes, because the grey horizons resemble sandstone colours rather than B-horizon colours (for example, profile 55 in Fig. 4).
Both the Blackmen-Tuckey and the Redfit power spectra of the colour records and the soil development index show dominant and significant (α < 0·1) peaks corresponding to a cycle thickness of between 4·5 m and 8·5 m (Fig. 6). Less distinct and less significant peaks occur between 2·1 m and 3·2 m. Bandpass filtering of the colour and SDI records indicates that the 4·5–8·5 m cyclicity corresponds to the lithological cycles recognized in the section (cycles A to P; Figs 3 and 5). Most cycles that consist of alternations of sandy strata with weak palaeosols and muddy strata with strongly developed palaeosols are well-represented in the bandpass filter. The thicknesses of cycles F, K, and L trigger the filters to add an additional cycle. The total number of 16 cycles is present in the section, with an average thickness of 7·1 m.
The filtered records of the 2·1 to 3·2 m cyclicity show that, in the lightness record, most of the power of this periodicity is related to individual sandstone beds that are part of the heterolithic intervals of cycles H, M, N and P (Fig. 5) and to a few grey A horizons or sandstones that cap palaeosols in the dominantly fine-grained intervals of cycles G and H (Fig. 5). Other parts of the section show no consistent pattern at this scale of cyclicity.
Interpretation of overbank–avulsion cyclicity
The heterolithic deposits with only weak soils are interpreted as avulsion deposits, which is consistent with previous interpretations (e.g. Kraus & Wells, 1999). The lateral extent of up to 1 km at the Deer Creek Amphitheater section (DCA) (up to 5 km in the Elk Creek area; Kraus, 1987) and the metre-scale thickness of the heterolithic intervals are characteristic of avulsion deposits rather than simple crevasse splay deposits. For example, along the Brazos River in Texas, Taha & Anderson (2008) found avulsion deposits that cover areas ca 12 km2, which is 25 to 50 times more extensive than non-avulsive splay deposits. Various authors have reported thicknesses of 3 to 4 m for avulsion deposits (Morozova & Smith, 2000; Aslan et al., 2005; Taha & Anderson, 2008).
The fine-grained deposits with more strongly developed palaeosols are interpreted as overbank deposits whose slow accumulation rates allowed the development of one or more (cumulative) palaeosol profiles. The vertical transition from overbank to avulsion deposits is mostly gradual, in line with the progradational style of avulsion in which a sediment wedge extends from the channel and grows in a downflow direction (Slingerland & Smith, 2004).
The metre-thick cycles (equal to simple pedofacies cycles of Kraus, 1987) are distinctive because their heterolithic components (avulsion deposits) are thick and laterally extensive (Figs 2 and 3). In contrast, the stratigraphic intervals that separate the individual palaeosols within the metre-scale cycles are thin and indistinct, and typically show evidence for some pedogenesis (Fig. 4). The present authors speculate that many of the thin intervals are also the result of channel avulsion; however, the difference between the thin intervals and the 3 to 4 m thick, laterally extensive heterolithic intervals is related to the scale of the avulsion. Various authors (e.g. Mackey & Bridge, 1995; Heller & Paola, 1996; Jerolmack & Paola, 2007) have distinguished between local avulsions, in which the new channel rejoins the channel from which it split a short distance downflow, and regional avulsions, which create an entirely new channel in a new floodplain location.
The thinner, less distinct stratigraphic intervals between individual palaeosols probably reflect local avulsion or a simple crevasse splay (Fig. 7; overbank phase). The resulting avulsion belt or splay deposit was small, and the coarser deposits, especially sands, did not extend to the distal floodplain where the more strongly developed soils were forming. Nonetheless, a rapid incursion of sediment onto the floodplain buried and interrupted development of floodplain soils, and that newest sediment became the lower part of the next soil. The local nature of this type of avulsion can explain the relative insignificance of the heterolithic interval it produces and the quick overprinting by pedogenesis. The fact that each pedofacies cycle generally contains several palaeosols is attributed to the shifting locus of avulsion over time. Because avulsion reduces local super-elevation, succeeding local avulsions can move up-channel, although it is observed that the locus of avulsion eventually reverts to a down-channel position and then again moves up-channel (e.g. Mackey & Bridge, 1995; Stouthamer & Berendsen, 2007). In the absence of robust evidence for a connection between local avulsion and climate, and because avulsion is the key autogenic process in avulsion-dominated fluvial systems, the present authors consider the local avulsions in the Bighorn Basin to have been autogenic in nature.
The thick, laterally extensive heterolithic intervals, on the other hand, are attributed to regional avulsion (Fig. 7; avulsion phase). The change from local to regional avulsion may reflect a period in time when, at larger scales in the basin, the channel belts became super-elevated relative to the floodplain, making them susceptible to avulsion. After this phase of channel reorganization, during which gradients between channel belts and floodplains were lowered, a period of relative channel belt stability started, and the floodplain was characterized by a dominance of overbank deposition and development of mature palaeosols (Fig. 7; overbank phase). The data used here were derived from a vertical one-dimensional section supplemented by field tracing of the cyclicity laterally over approximately 1 km. To quantify the regional significance of the overbank–avulsion cyclicity, a three-dimensional stratigraphic analysis is required.
The time-series analysis and bandpass filtering is performed here on depth (thickness) series rather than time series. Therefore, sedimentation rate changes at a scale larger than the overbank–avulsion cyclicity (but shorter than million-year time scale) are hard to detect without additional age constraints. The rate of sedimentation changes within individual overbank–avulsion cycles. Individual palaeosols represent short-term, slow sedimentation and the weak pedogenic modification of the avulsion package indicates a short episode of fairly rapid sedimentation. Spectral power at wavelengths shorter than the overbank–avulsion cyclicity of 4·5 to 8·5 m should, thus, be interpreted with caution because power will be derived from sediment intervals that, while short, may represent various durations in a time domain. This study focuses on the potential allogenic forcing of overbank–avulsion cyclicity, which has to be resolved before smaller time scales can be discussed.
Orbital climate forcing of river avulsion
The magnetochron C24r to C24n.3n boundary was found in the Upper Deer Creek section (Abels et al., 2012) which is located 3·2 km to the south. Stratigraphic correlations in the field place the top of the DCA section at the very base of the Upper Deer Creek section. The DCA section, thus, occurs within the upper part of magnetochron 24r. Chron 24r has an astronomically constrained duration of 3·118 ± 0·158 Myr (Westerhold et al., 2007) and is 1219 m thick in the part of the Bighorn Basin studied here (Clyde et al., 1994), giving a sedimentation rate of 391 ± 21 m/Myr; this rate indicates that a sedimentary cycle thickness of 7·1 m represents approximately 18·2 ± 1·0 kyr, assuming constant sedimentation rates (Table 1).
To reduce the stratigraphic interval over which average accumulation rates are calculated, a second sediment accumulation rate is derived from the estimated 0·8 Myr ± 0·04 duration of mammalian biochron Wa4 (Gingerich, 2010). Uncertainty here is calculated from the 5% uncertainty on the duration of C24r in Westerhold et al., 2007. This zone is approximately 225 to 235 m thick in the DCA study area, yielding an accumulation rate of 288 ± 20 m/Myr. At this rate, a sedimentary cycle thickness of 7·1 m represents 24·7 ± 1·9 kyr (Table 1).
A third sedimentation accumulation rate is derived from the carbon isotope excursions of the ETM2 and H2 hyperthermals, which are recorded in the Upper Deer Creek section (Abels et al., 2012). The peak excursions of both events are separated by ca 30 m stratigraphically and separated by four to five precession cycles, which means ca 84 to 105 kyr as estimated using a marine age model (Stap et al., 2009). The resultant sedimentation rate in the Upper Deer Creek section is 316 ± 41 m/Myr which, when extrapolated to the DCA section, gives a duration of approximately 22·5 kyr ± 3·4 for the 7·1 m cyclicity (Table 1).
The thickness and duration of the overbank–avulsion cycles in the Deer Creek Amphitheater section as recognized in colour records are similar to those found in the Polecat Bench and Red Butte sections (Abdul Aziz et al., 2008), and the Upper Deer Creek section (Abels et al., 2012). In the nearby, but older, Polecat Bench section that encompasses the Palaeocene–Eocene thermal maximum (PETM), cycle thickness is 7·6 m, resulting in a similar period of 19·4 kyr. In the Red Butte section, which is located to the south-east in the basin and is slightly younger, cyclicity was observed to be 8·7 m thick with an estimated period of 22·3 kyr (Abdul Aziz et al., 2008). In the only slightly younger, nearby Upper Deer Creek section, overbank/avulsion cycles are 7·0 m thick with a duration of 23·3 kyr per cycle. These estimates are all within the range of the duration of the orbital and climatic precession cycle with components between ca 18·8 kyr and 22·6 kyr in the early Palaeogene (Berger et al., 1992).
The amplitude of the precession cycle is modulated by the eccentricity of Earth's orbit (Berger et al., 1992) and alternations of differently expressed precession cycles are, thus, expected (Abels et al., 2009). Bundles of three to four clear precession cycles should be interrupted by one or two less developed precession cycles. The combination of lithology and filtered colour records indeed show more distinct cycles occurring in three groups of three or four cycles in the section (C–E, G–J and M–O; Fig. 5) separated by less distinct cycles (A–B, F, K–L and P). If precession is causing the overbank–avulsion cyclicity, this bundling matches the 100 kyr eccentricity cyclicity. The bundles of distinct cycles would relate to eccentricity maxima when precession amplitudes are largest and the climatic differences forcing sedimentation are strongest. The three observed 100 kyr eccentricity bundles (of three or four distinct precession cycles and one or two less distinct precession cycles) in the DCA section then mark a 405 kyr eccentricity maximum. Like the 100 kyr cycles, at the 405 kyr scale, the eccentricity maxima can be linked to well-developed simple pedofacies cycles with clear intervals showing mature palaeosol profiles.
On top of the section, a thick sheet sandstone is present, while, just below and above this sheet sandstone, the simple pedofacies cycles that are present are less developed. Also, just below the DCA section, the stratigraphy is characterized by a longer interval with poorly developed pedofacies cycles and the absence of mature palaeosols (Fig. 2). In line with this, a gradual increase of 0·5 points in the Soil Development Index occurs from the base of the section to the middle part, after which a gradual decrease of 0·5 points occurs towards the top of the section. These observations are consistent with deposition of the studied section during a 405 kyr eccentricity maximum.
Channel avulsion is of considerable interest as a control on stratigraphic patterns in alluvial deposits (e.g. Mackey & Bridge, 1995; Heller & Paola, 1996; Stouthamer & Berendsen, 2007; Hajek et al., 2010). Recent work, for example, has focused on channel sandstone clusters in both laboratory and field settings, and the fact that such clusters can be the result of autogenically controlled avulsion alone (Hajek et al., 2010, 2012). Other workers have ascribed avulsion-generated alluvial stratigraphies to a mix of autogenic and allogenic factors depending on the particular situation (e.g. Stouthamer & Berendsen, 2007; Phillips, 2011). Channel avulsion is principally related to super-elevation of the channel above its floodplain because of differential deposition (e.g. Bryant et al., 1995; Mohrig et al., 2000; Jerolmack & Paola, 2007). Levées directly adjacent to the channel aggrade more rapidly than the more distal floodplain and cause super-elevation, which renders the channel susceptible to avulsion. Eventually, some form of trigger initiates crevassing, and sands and muds are deposited rapidly on the floodplain above the interval with more intense soil development. Triggers include phenomena, such as ice jams or unusual flood discharges, which are spatially or temporally sporadic (Jones & Schumm, 1999).
Although the distinct cyclicity in the Willwood stratigraphy could simply be the result of autogenically controlled regional avulsion, the fact that the cyclicity shows distinct Milankovitch periodicities indicates that avulsion has been influenced by orbital climate change. For example, Nádor et al. (2003) noted that, in dominantly autogenic depositional systems, such as fluvial systems, changes in climate can influence the recurrence time of autocyclicity. Thus, if Milankovitch periodicity is recognized in a dominantly autogenically influenced lithological record, it can be attributed to allogenic modulation of the autocyclicity. In the case of the Willwood Formation, the rate of channel belt build up, and so the time required for the channel to become super-elevated above its floodplain, depended on sediment and water input, but ultimately on the creation of accommodation space by subsidence of the basin. Local accommodation space was generated during the overbank phase of the precessional cycle through a combination of continued subsidence and slower aggradation on the floodplain than on the channel belt (Fig. 7). That space appears to have been created at a rate that was paced by astronomical climate change, such that avulsion was triggered by climate change at the time super-elevation was reached. In this scenario, one would expect avulsion to be instigated during the orbital extremes or somewhere in the transitional stages towards the orbital extreme (Mann & Meltzer, 2007).
Jones & Schumm (1999) suggested that increases in flood magnitude and frequency can cause more rapid floodplain aggradation and, thus, increase the susceptibility of a channel to avulsion and also enhance the probability of a triggering event. Similarly, Sinha et al. (2005) concluded that avulsion of the Baghmati River in India appears to have been instigated by major floods. Consequently, the present authors hypothesize that regional avulsions were triggered during periods dominated by high magnitude floods, whereas more typical floodplain deposition took place during periods of lesser floods (Fig. 7).
Orbital climate change causing avulsion–overbank cyclicity
In the previous paragraphs, a mechanistic pathway of allogenic climate change was synthesized causing Willwood overbank–avulsion cyclicity. The regular cyclicity in four distinct stratigraphic sections and the match in time scales make a link with the climatic precession cycle tentative. However, the impact of the precession cycle on the Eocene Bighorn Basin is not well-known. In the following, the orbital cycle to climate pathway is discussed.
Orbital cyclicity of Earth's axis and orbit produces significant insolation differences (Berger et al., 1992). Precession extremes can generate insolation differences up to 20%, depending on latitude and season. The resulting climate impact on Earth's surface, or in the depositional environment, depends on local climate and, thus, land–sea configuration has a great influence. No temperature or precipitation data were available covering a complete precession cycle from the early Eocene Bighorn Basin. In the studied section, palaeosol proxies are hard to apply across a precession cycle because one part of the cycle is characterized by sandy mudrocks showing no or very incipient soil formation.
Lawrence et al. (2003) modelled realistic precession extremes with Eocene-like boundary conditions. These authors found that mean annual temperature and precipitation in the western interior of North America were not significantly affected by the precession cycle, but their model results show a summer temperature increase of 5°C, a ca 50% decrease in autumn precipitation, and ca 40% lower annual net moisture (precipitation – evaporation) availability in this region during precession minima relative to precession maxima.
Other studies show that precession cycles do affect the strength of monsoonal systems through their impact on summer insolation. For example, Tuenter et al. (2007) found that, in the Asian and African monsoon systems, the summer monsoonal system strengthens during precession minima because summer insolation is increased. If the modern North American monsoon becomes stronger, summer thunderstorms are more frequent and generate larger floods (e.g. Mann & Meltzer, 2007), ideal for triggering river avulsion. In contrast, if the system weakens, the magnitude and frequency of summer floods decline. Increased floods are related to warmer periods, such as the last precession minimum (Mann & Meltzer, 2007).
The precession modelling of Lawrence et al. (2003) and monsoonal studies (Tuenter et al., 2007; Mann & Meltzer, 2007) produce results that are contradictory, and a direct phase relation between overbank–avulsion cyclicity and orbital parameters cannot be readily deduced. For now, the higher seasonality leading to extreme summer and winter seasons during precession minima is the most likely candidate for triggering the regional avulsion phase. Another unknown is whether the trigger for regional avulsion occurred in exact phase with precession extremes or if triggering occurred somewhere in the transitional stages between extremes.
Rhythmic alternations of overbank and regional avulsion deposits occur at precession and probably eccentricity time scales in the sedimentary successions of the Willwood Formation, Bighorn Basin, Wyoming (USA); this strongly suggests that these overbank–avulsion cycles were driven by astronomical climate change. Changes in rainfall on Milankovitch time scales causing peak discharges may have affected the recurrence time of river avulsion, which is, in principle, an autogenic process. This means that the rate at which accommodation space was created by tectonic subsidence, which ultimately controls the recurrence time of super-elevation of the channel belt, was probably at a pace that allowed orbital climate change to control the timing of river avulsion. The present authors hypothesize that times of extreme floods triggered regional avulsion, with the intervals in between being more stable.
Regional avulsion is important because of its influence on alluvial stratigraphy and, thus, on the shape, size and connectivity of sandstone reservoirs and aquifers. Recent work (Hajek et al., 2010, 2012) indicates that the channel sandstones in some fluvial units display a non-random distribution, which is attributed to avulsion behaviour that was autogenic in nature. This study shows that the organization of floodplain deposits in the Willwood Formation is not random; however, these results suggest that autogenically controlled avulsion patterns were tuned by climate forcing. The Willwood Formation resulted from progradational avulsion, which produces floodplain deposits consisting of both overbank fines and avulsion deposits. The effects of orbital forcing could be common in the fluvial stratigraphic record, especially in fluvial systems dominated by progradational avulsion.
We thank Peter van den Berg, and Beryl, Winston and Tom Churchill for invaluable logistical support and field assistance. Frits Hilgen is thanked for invaluable discussions and for making this project possible by funding to HA through Dutch Science Foundation (NWO-ALW) award 818.01.002. HA was also supported by a personal NWO-ALW VENI award. MJK was supported by NSF award EAR0718740. The authors do not have any conflict of interest.