Peter M. Sadler

Sediment Accumulation Rates and the Completeness of Stratigraphic Sections

A compilation of nearly 25,000 rates of sediment accumulation shows that they are extremely variable, spanning at least 11 orders of magnitude. Much of this variation results from compiling rates determined for different time spans: there is a systematic trend of falling mean rate with increasing time span. The gradients of such trends vary with environment of deposition. Although measurement error and compaction contribute to these regressions, they are primarily the consequence of unsteady, discontinuous sedimentation. The essential character of the unsteadiness may be cyclic or random, but net accumulation is characterized by fluctuations whose magnitudes increase with increasing recurrence interval. Ratios of median long- to short-term accumulation rates provide a measure of the expected completeness of sedimentary stratigraphic sections, at the time scale of the short-term rate. Expected completeness deteriorates as finer time scales are considered.

Calibrating the End-Permian Mass Extinction

High-precision geochronologic dating constrains probable causes of Earths largest mass extinction. The end-Permian mass extinction was the most severe biodiversity crisis in Earth history. To better constrain the timing, and ultimately the causes of this event, we collected a suite of geochronologic, isotopic, and biostratigraphic data on several well-preserved sedimentary sections in South China. High-precision U-Pb dating reveals that the extinction peak occurred just before 252.28 ± 0.08 million years ago, after a decline of 2 per mil (‰) in δ13C over 90,000 years, and coincided with a δ13C excursion of −5‰ that is estimated to have lasted ≤20,000 years. The extinction interval was less than 200,000 years and synchronous in marine and terrestrial realms; associated charcoal-rich and soot-bearing layers indicate widespread wildfires on land. A massive release of thermogenic carbon dioxide and/or methane may have caused the catastrophic extinction.

Classical confidence intervals and Bayesian probability estimates for ends of local taxon ranges

The observed local range of a fossil taxon in a stratigraphic section is almost certainly a truncated version of the true local range. True endpoints are parameters that may be estimated using only the assumption that fossil finds are distributed randomly between them. If thickness is rescaled so that true endpoints lie at 0 and 1, the joint distribution of gap lengths between fossil finds is given by the Dirichlet distribution. Observed ends of the range are maximum likelihood estimators of true endpoints, but they are biased seriously. Extension of the observed range at each end by a distance equal to the average gap length yields unbiased point estimators. Classical statistics can generate confidence intervals for ends of the taxon range; but with Bayesian inference, the probability that true endpoints lie in a certain region can be stated. For a 95% confidence level (classical) or a 95% probability (Bayesian), the range extensions exceed the observed range if the range is established on less than six finds; if only two finds are used, such range extensions are an order of magnitude longer than the observed range. Evidently the standard biostratigraphic practice that identifies zonal boundaries as horizons rather than confidence intervals may not be justified at the resolution of typical fossiliferous sections.

The Ordovician Period

Abstract: Rapid and sustained biotic diversification reached its highest levels in the Paleozoic. A prolonged “hot-house” climate through Early Ordovician, cooling through Middle Ordovician and changing to “ice-house” conditions in Late Ordovician, global glaciation, oceanic turnover and mass extinction at end of period, strong fluctuations in eustatic sea level, appearance and diversification of pandemic planktonic graptolites and conodonts important for correlation, moderate to strong benthic faunal provincialism, re-organization and rapid migration of tectonic plates surrounding the Iapetus Ocean and migration of the South Pole from North Africa to central Africa all characterize the Ordovician Period. All seven Ordovician stages have formalized GSSPs.

High-resolution, early Paleozoic (Ordovician-Silurian) time scales

For much of the geologic time scale, resolving power appears to be limited by the duration of biostratigraphic zones and subzones. Yet these zones exploit the appearance and disappearance events of only a small fraction of the species they span. Computer algorithms can sequence an order of magnitude more events and make explicit the uncertainties that arise when calibrating the resulting time line. An illustrative case history builds an Ordovician and Silurian time scale from the geologic record of the entire graptolite clade—over 1900 species from more than 400 localities and sections worldwide. The same approach can be applied to any stratigraphic interval with detailed biostratigraphic observations. It provides the foundation for time scales and paleobiologic time lines. Using logic similar to graphic correlation, optimizing algorithms search for a composite sequence of species first- and last-appearance events that minimizes the implied shortcomings of all the field observations. The algorithms minimize the number of species coexistences that are implied, but never observed, and the net adjustments needed to bring local range charts into agreement with a single composite sequence of events. After total section thicknesses have been rescaled to help normalize for variation in depositional rate, mean stratigraphic thicknesses are used to scale the intervals between adjacent events in the composite sequence. The resulting scaled composite sequence is converted to a relative geologic time scale by identifying stage and zone boundaries within the sequence of graptolite events. This relative scale is, in turn, calibrated by dated volcanic ash beds that were incorporated in the search for the optimal sequence. These dated events are also used to test for linearity of the scaled composite. The final time scale has a potential resolving power of 0.02–0.1 m.y., more than ten times better than can be achieved by traditional zones. Graptolite zones vary widely in duration from as short as 0.1 m.y. to nearly 5.0 m.y. The mean duration of zones or zonal groupings calibrated here is 1.44 m.y. in the Ordovician and 0.91 m.y. in the Silurian. The average uncertainty in locating zone boundaries in a single composite sequence is about one-fourth of the mean zone duration. The variance resulting from differences in time scales developed from differing numbers of field observations and in response to changes in the optimization criteria gives a very conservative measure of the overall robustness of the method. These differences indicate an average uncertainty in the age of graptolite zone boundaries that is more nearly equal to the mean zone duration. For zone duration, the mean uncertainty amounts to about one-half of the length of an average zone.

Estimation of completeness of stratigraphical sections using empirical data and theoretical models

The completeness of a stratigraphical section is the fraction of time intervals of some specified length (t) that have left a record. A record is left when some sediment is deposited during the interval and is not subsequently eroded. A complete section contains no hiatuses longer than t. The completeness of a section varies with t and its accumulation rate varies with the length of the time span over which it is measured. Plots of measured accumulation rate against time span are an empirical means of estimating completeness. Simple theoretical models help extrapolate meagre data and identify bias. Completeness at time scale t can depend upon three general properties of the accumulation history: the age of the section, the long term net accumulation rate (drift) and the unsteadiness of the sedimentation rate. The way unsteadiness is measured depends upon the kinds of fluctuations that can be recognized in the accumulation rate. To describe random fluctuations a standard deviation of rates is sufficient. One dimensional Brownian motion is a model of random fluctuations that explains many aspects of stratigraphical completeness. Regular periodic fluctuations in accumulation rate may be described in terms of wavelength and amplitude. Completeness is an increasing function of t, drift and, in the periodic case, the wavelength of fluctuations; it decreases with increasing standard deviation of accumulation rate and the amplitude of periodic fluctuations. The completeness and thickness of stratigraphical sections are weakly positively associated.

Stochastic models for the completeness of stratigraphic sections

Properties of stratigraphic completeness are determined here from a Brownian motion model of sediment accumulation. This avoids flaws inherent in application of a discrete-time random walk to the time span, rather than thickness, of sediment layers. Both discrete and continuous models show that the concept of stratigraphic completeness is meaningful only when the time scale is specified. From the discrete model, not surprisingly, completeness improves with increasing relative frequency and average thickness of depositional increments and the error of completeness estimation should decrease for longer sections. The continuous model shows that two dimensionless products determine the probability that a given time interval will be recorded by some preserved sediment. The first is the ratio of the age of the interval to its time span; the second is the product of the square root of the time span and ratio of the mean to the standard deviation of accumulation rate. Expected completeness is the average of these probabilities for all successive intervals of the given time span. For long sections, completeness may be estimated from the second dimensionless product alone. The two dimensionless products are sufficient to predict the relationship of accumulation rate to time span, the distribution of bed thickness, and the weak association of completeness and section thickness.

A New Look at Sedimentation Rates and the Completeness of the Stratigraphic Record

Several recent papers have suggested that completeness of stratigraphic sections can be estimated by using the ratio of long-term sedimentation rates to short-term rates. We show that the median short-term sedimentation rates used in these papers are erroneous and are mostly an artifact arising from improper data manipulation. To demonstrate the artificial character of short-term median rates, we have generated a series of plots assuming a constant sedimentation rate with fixed variance and defined limits of measurement precision. These plots demonstrate that increasing variance in the time required to deposit sediments will result in spuriously high short-term median sedimentation rates. A new method for calculating median sedimentation rates, which eliminates the problem of spurious median rates, is then applied to make an improved estimate of expected completeness. Recalculated median values show that sedimentation rates for pelagic sediments are close to identical for both short-term and long-term time intervals. Applying this method to an expanded compilation of pelagic sedimentation rates confirms the near completeness of typical pelagic sequences. This undermines arguments for inherent temporal incompleteness as an explanation for the synchronous extinctions at the Cretaceous-Tertiary boundary. Finally, we suggest that median short-term sedimentation rates should not be used to assess completeness for individual sections. Problems with compaction, bioturbation, core smearing, uncertainties in radiometric age determinations, and the great variance inherent in sedimentation rates imply that median short-term sedimentation rates are suspect, however calculated. Sedimentation accumulation diagrams may find their greatest usefulness in estimating the completeness to be expected in a given depositional environment or in comparing completeness of one environment to another.

The expected duration of upward-shallowing peritidal carbonate cycles and their terminal hiatuses

Meter-scale accommodation cycles, which dominate the stratigraphic record of peritidal carbonate accumulation, might provide a time scale of unusually high resolution, but the duration of the hiatuses that cap the resulting cyclothems is difficult to determine. Thousands of rates of peritidal accumulation from many different carbonate sections have been combined, according to the length of the time span of measurement, to describe a hypothetical average section. Because all sections are interrupted by hiatuses, the average accumulation rate falls progressively with increasing time span and most steeply at the time spans that capture the highest proportion of hiatuses. The process of combining rates from many sections cancels local differences in the distribution of hiatuses. Only hiatuses that have similar spacing and duration in a majority of sections will stand out after compilation. The size and position of a pronounced inflection in the combined plot of accumulation rates against time span identifies a dominant cycle period of ∼100,000 yr, of which the terminal hiatus accounts for 80%-90%. The expected cyclothem is ∼10 m thick. Because peritidal accommodation cycles begin and end with the sediment surface at sea level, the expected cycle period can be estimated by finding the time span at which accommodation and accumulation rates balance. The maximum duration of the hiatus is the time span at which rates of subsidence and sea-level fall balance. Compilations of many empirical measurements were again employed to determine the relationship between time span and the rates of subsidence, sea- level change, and net accommodation. This second method confirms the results of the first and can be modified to predict the expected cyclothem in different climatic, tectonic, and depositional settings. Because Quaternary data dominate short-term rates, the hypothetical average section best describes a passive margin in an icehouse climate with strong glacio-eustatic fluctuations in sea level. After modification for an extreme greenhouse climate, devoid of ice caps, the second method predicts that 20,000-yr accommodation cycles will be preferentially recorded.The expected cyclothem is 2 m thick and accounts for about 50% of the cycle period. Increased subsidence rates, whether on active margins, in the initial phase of passive margin formation, or at the seaward edge of a platform, tend to extend the limit of cycle duration, increase cyclothem thickness, and partition less time to the bounding hiatus. Increased subsidence, however, raises the risk that the sediment surface will drown.

Scaling laws for aggradation, denudation and progradation rates: the case for time-scale invariance at sediment sources and sinks

Abstract Linear rates of sediment aggradation and fluvial incision are inverse functions of measurement interval, a generic consequence of unsteadiness in the underlying processes. This effect results from a one-dimensional approach–that is, vertical rates determined at a single location–and significantly complicates comparisons of rates at different timescales. Mass conservation imposes an important but underutilized constraint; sediment by-passing or eroded from one location must deposit somewhere else. Over the long term, sediment generation and deposition must balance. In principle, the effects of unsteadiness could be eliminated if the total volume of sediment eroded or deposited over different intervals could be measured. In practice, however, obtaining such three-dimensional data from an individual site is virtually impossible. Here, we advance from one- to two-dimensional rate data. We present two new global compilations of data: denudation rates of fluvial uplands; and lateral migration (progradation) rates of siliciclastic lowland and marine systems, from ripple to shelf-slope scale. Important new findings are: (1) upland denudation rates determined from specific sediment yield show little or no dependence of rate on time interval; (2) in the transfer zone between sediment source and sink, rates of erosion and deposition balance over all scales; and (3) progradation mirrors aggradation over all timescales. The product of progradation and aggradation is independent of timescale, implying that global sediment flux into the world’s oceans has been constant on the order of 100 m2/yr, from scales of months to tens of millions of years. Results show that global rates of denudation and accumulation are time invariant with appropriate spatial averaging; however, site-specific application remains a daunting challenge.