How do basin margins record long-term tectonic and climatic changes?

Sediment supply is considered as the de facto carrier of signals of environmental change from upstream to downstream reaches of sediment-routing systems (Romans et al., 2016; Sharman et al., 2019). However, sediment supply is difficult to measure, especially over long (>10⁶ yr) geologic time scales (Allen et al., 2013). In contrast, the stratigraphic record of sedimentary basins contains a voluminous, albeit fragmentary (Paola et al., 2018), record of Earth history (Paola, 2000; Allen, 2008a). In spite of decades of research on either the controls on sediment generation and transport (e.g., Densmore et al., 2007; Armitage et al., 2011) or basin-margin development (e.g., Payton, 1977; Wilgus et al., 1988), there has been less work on the relationship between the two and their coupled response to tectonic and climatic forcings (Carvajal et al., 2009). We designed a series of numerical models to better understand the long-term (10⁶–10⁷ yr) relationship between sediment supply and basin stratigraphic evolution under different forcing mechanisms. Our main research questions are:

• (1) How do patterns in sediment supply compare to the basin-margin stratigraphic evolution as measured by the progradation rate of a basin margin?

• (2) How does basin-margin evolution respond to changes in tectonic uplift and precipitation in the source area within a catchment?

• (3) Do downstream external controls, such as subsidence and eustasy, attenuate or alter the signals from the source area?

Results from this study can be used to reconstruct the tectonic and climatic histories of ancient basin-margin records and their source areas.

We model a continental-scale source-to-sink system analogous to the Himalaya-Indus system (Clift et al., 2001) (Fig. 1A) during deep geologic time (i.e., >500 km river stream length, >2 km basin relief, and 10⁶–10⁷ yr model time scale). We choose to model such a system because its response time (10⁵ yr) is shorter than the period of long-term the tectonic and climatic forcings we study (10⁶ yr), where response time is the time for a landscape to respond to a forcing and return to a steady state (Allen, 2008b). Castelltort and Van Den Driessche (2003) calculated the response time of the Himalaya-Indus system to range between 124 and 440 k.y. We divide the source-to-sink system into three domains: source (erosion dominated), transfer (limited erosion and sedimentation), and sink (sedimentation dominated) (Schumm, 1977) (Fig. 1). The entire model domain is 1500 km long and 500 km wide. The source domain is 200 km long with 200 m initial relief and spatially uniform uplift. The transfer domain is 400 km long with an initial slope of 0.03°. The sink domain is 900 km long and 2300 m deep.

We designed eight model runs of variable uplift and precipitation without changes in subsidence and eustasy (Tables S1 and S2 in the Supplemental Material¹). We designed another six model runs to evaluate the role of subsidence and eustasy. The duration of each model run is 30 m.y. with 0.5 m.y. time step, divided into two periods of 15 m.y. During the initial period, all of the models evolve with 250 m/m.y. uplift and 1 m/yr precipitation to achieve a steady state in sediment supply. The steady state results from the balance between uplift and erosion (Willett and Brandon, 2002). During the second period, we double or halve either uplift or precipitation in models 1–4, and double or halve both variables in models 5–8. This experimental design and ranges of uplift and precipitation are similar to catchment-alluvial fan systems modeled by Densmore et al. (2007) and Armitage et al. (2011). In models 9–14, either uplift or precipitation is doubled from the first to second period. We use a back-tilted or fore-tilted subsidence geometry during the second period of models 9, 10, 12, and 13. The maximum subsidence rate is 100 m/m.y. (based on Xie and Heller [2009] and Allen and Allen [2013]), which gradually decreases to 0 m/m.y. away from the point of maximum subsidence (Fig. 1B). We gradually and steadily raise sea level by 150 m, without any subsidence, during the second period of models 11 and 14. We report the sediment discharge by summing the erosion in the source area, and the average and standard deviation of basin-margin progradation rates are measured by tracking the shelf-edge position. These rates are in steady states when they are approximately constant during experiment runs.

In all cases of changing uplift and precipitation without changes in subsidence and eustasy, the trend of sediment supply from source-area erosion is similar to basin-margin progradation (Fig. 2). Changing uplift under constant precipitation results in gradual changes in sediment supply and basin-margin progradation. Sediment supply and margin progradation take ∼9 m.y. to adjust to new steady states. For example, doubling the uplift rate in model 1 increases the average basin-margin progradation rate from ∼21 km/m.y. at 15 m.y. to ∼43 km/m.y. at 24 m.y. Changing precipitation under constant uplift results in more rapid changes in sediment supply and basin-margin progradation (Fig. 2). Following an initial pulse of sediment supply and rapid margin progradation, they return to their initial steady states. When both uplift and precipitation change, sediment supply and margin progradation quickly respond, and then gradually adjust to new steady states (Fig. 2). For example, in model 7, with decreasing uplift and increasing precipitation, the average basin-margin progradation rate abruptly increases from ∼21 km/m.y. at 15 m.y. to ∼30 km/m.y. at 16 m.y., followed by a slow decrease to ∼10 km/m.y. at 24 m.y. The standard deviation of margin progradation in models 1–8 is ∼10 km/m.y. (Fig. 2C). There are also short-term variations in the time series of average margin progradation rate in all of the models (<1 km/m.y.), in contrast with lower variability in sediment supply.

Sediment supply and margin progradation exhibit similar trends because almost all of the sediment eroded from the source area is deposited in the sink; that is, (1) there are no relative sea-level changes in models 1–8, so there is limited storage of sediment on the shelf, and (2) the transfer domain does not sequester much sediment (Fig. 2A). In model 1, the depositional volume in the transfer domain is ∼7 × 10³ km³, which is <1% of the volume in the sink domain (∼9 × 10⁵ km³). The temporal and spatial variability of margin progradation is a result of autogenically controlled sediment routing across the transfer domain (e.g., avulsion) and the sediment storage and release on the coastal plain and shelf (Kim et al., 2006; Harris et al., 2016).

Changing uplift results in gradual (over several million years) changes in sediment supply and margin progradation. When uplift rate increases (Animation S1 in the Supplemental Material), a fault forms at the boundary between the source domain and the transfer domain. The steep fault initiates erosion on the basinward side of the source domain. It takes several million years for a wave of knickpoints to propagate upstream from the fault and establish a new topographic steady state (Equation 1; Whipple and Tucker, 1999). When uplift rate decreases (Animation S2), larger erosion is focused on the ridges between channels. It takes several million years for the ridges to erode and establish a new topographic steady state. The largest changes in erosion rates are within the channels (Fig. S1). Erosion of ridges between channels is slower to respond to changes in uplift.

Precipitation results in rapid changes in sediment supply and margin progradation because precipitation influences the entire catchment simultaneously, resulting in an abrupt change in erosion over the entire source domain (Equation 2) (Bonnet and Crave, 2003; Armitage et al., 2013; Sharman et al., 2019). When precipitation increases (Animation S3), larger erosion rates are initially located along the ridges between channels until the ridges are eroded to a level at which uplift balances with erosion. When precipitation decreases, there is an initial uniform decrease in erosion rates across the source domain. Subsequent erosion then propagates upstream by headward erosion of knickpoints originating at the fault between the source and transfer domains. Contrary to the experiments with changing uplift, in these experiments of changing precipitation, the largest changes in erosion are focused along the ridges between channels (Fig. S1). This is because the high-relief ridges need more change in elevation to achieve the new topographic steady state compared to the channels.

We compare models 1 and 3 with models 9–14 to study how subsidence and eustasy influence basin-margin progradation (Fig. 3). Changes in uplift and precipitation are the same in these models, but models 9–14 include changes in subsidence or eustasy between 15 and 30 m.y. (Fig. 1B). We focus our analysis on experimental scenarios with acceleration of margin progradation under rising relative sea level (the combined effects of subsidence and eustasy) because we are interested in the potential for attenuation of uplift and precipitation signals. The basin margins in models 9–14 prograde slower than those in models 1 and 3 (Fig. 3C). However, under changing precipitation, models 12–14 show the same magnitude of abrupt margin progradation as model 3. Models 9 and 10, under increasing uplift, show smaller increases in margin progradation compared to model 1. Margin progradation in models 1 and 11 is similar.

To further evaluate the influence of subsidence and eustasy, we systematically changed both variables (Fig. 3D). We increased subsidence rates from 50 to 500 m/m.y. at 50 m/m.y. increments in back-tilted models, and from 20 to 200 m/m.y. at 20 m/m.y. increments in fore-tilted models (Xie and Heller, 2009; Allen and Allen, 2013). We increased eustasy from 30 to 300 m at 30 m increments over 15 m.y. We modeled such a large amplitude of eustatic rise in order to achieve a clear, measurable result of depositional response; in reality, long-term (10⁶–10⁷ yr) Cretaceous–Cenozoic eustatic changes tend to be <150 m (Miller et al., 2005). These models mimic the results of models 9–14: increasing precipitation results in an abrupt increase in margin progradation, in spite of relative sea-level rise, but the signal of increasing uplift is attenuated in the record of basin-margin progradation (Fig. 3D). Moreover, subsidence, compared to eustasy, more strongly attenuates the signal of changing uplift.

Uplift signals are attenuated in models 9–14 because relative sea-level rise created space for deposition across the subaqueous shelf. So, a portion of the sediment supply from erosion of the source area is deposited in route to the basin margin and, as a result, cannot contribute to margin progradation. However, increasing precipitation can create a large enough amount of sediment to overwhelm space for sediment deposition on the shelf and prograde the basin margin.

Our experiments provide guidelines for interpreting long-term (10⁶–10⁷ yr) uplift and precipitation changes from the record of basin-margin progradation. Our results are especially applicable to field cases in which the role of relative sea-level change on margin progradation is negligible. Changing relative sea level can control the rate of margin progradation (e.g., models 9–14). However, for the cases of (1) accelerating margin progradation under rising relative sea level, and (2) decelerating margin progradation under falling relative sea level, the role of relative sea level can be ruled out. In these cases, margin progradation is controlled by the changes of source-area uplift and/or precipitation. For example, the Cretaceous Colville Basin (Alaska, USA) shows a basinward-shallowing foreland-basin geometry with back-tilting subsidence, where the space available for sediment deposition decreases from proximal to distal (Houseknecht, 2019) (Fig. S2A; see other examples in the Supplemental Material). This decreasing space should accelerate margin progradation. However, the basin-margin progradation rate decreases from ∼52 km/m.y. during 115–107 Ma to ∼13 km/m.y. during 107–98 Ma (Lease and Houseknecht, 2017). The large (75%) decrease of progradation rate under decreasing space for deposition indicates a possible decrease in source-area uplift after 107 Ma (cf. model 2 of Fig. 2).

These results highlight the similarity between source-area erosion and basin-margin deposition and further illustrate that erosion, sediment supply, and basin-margin progradation respond differently to source-area uplift and precipitation (Fig. 2). Changing uplift results in a gradual transition of margin progradation to a new steady state. The largest changes in erosion are focused within channels. Changing precipitation results in an abrupt change in margin progradation, followed by a return to the initial steady state. The largest changes in erosion are focused along the ridges between channels. Furthermore, our experiments on the influence of relative sea-level change underscore the importance of the competition between sediment supply, subsidence, and eustasy in basin-margin evolution (Helland-Hansen and Hampson, 2009) (Fig. 3). Long-term, large-magnitude relative sea-level change can attenuate signals of catchment uplift by trapping sediment on the subaqueous shelf. Subsidence can have a greater impact than eustasy on signal attenuation because it is of larger magnitude. However, precipitation forcings can change the sediment supply fast enough to overwhelm relative sea-level changes temporarily. Therefore, the precipitation signal is more likely to be preserved, and well-constrained basin-margin records, especially those with three-dimensional control, can be used to reconstruct their tectonic and climatic histories. We build on the idea of using the basin-margin progradation rate as an indicator of the magnitude of sediment supply (e.g., Carvajal et al., 2009; Petter et al., 2013), and our modeling results go further to suggest that basin-margin progradation can be used to understand controls on changes in sediment supply.

We are grateful for the support from the State of Texas Advanced Oil and Gas Resource Recovery (STARR) program and the Quantitative Clastics Laboratory (QCL) consortium at the Bureau of Economic Geology (The University of Texas at Austin). The manuscript was greatly improved by the comments of G. Hampson, T. Salles, and editor J. Schmitt.