Carl N. Drummond

Climatic forcing of carbon-oxygen isotopic covariance in temperate-region marl lakes.

Carbon and oxygen stable isotopic compositions of lacustrine carbonate from a southeastern Michigan marl lake display linear covariance over a range of 4.0% Peedee belemnite (PDB) in oxygen and 3.9% (PDB) in carbon. Mechanisms of delta 13 C-delta 18 O coupling conventionally attributed to lake closure in arid-region basins are inapplicable to hydrologically open lake systems. Thus, an alternative explanation of isotopic covariance in temperate region dimictic marl lakes is required. We propose that isotopic covariance is a direct record of change in regional climate. In short-residence-time temperate-region lake basins, summer meteoric precipitation is enriched in 18O relative to winter values, and summer organic productivity enriches epilimnic dissolved inorganic carbon in 13C. Thus, climate change toward longer summers and/or shorter winters could result in greater proportions of warm-month meteoric precipitation, longer durations of warm-month productivity, and net long-term enrichment in carbonate 18O and 13C. Isotopic covariance observed in the Michigan marl lake cores is interpreted to reflect postglacial warming from 10 to 3 ka followed by cooler mean annual temperature, a shift toward greater proportions of seasonal summer precipitation, a shortening of the winter season, or some combination of these three factors.

Stratal Thickness Frequencies and the Prevalence of Orderedness in Stratigraphic Sequences

Assuming the existence of discernable hierarchies in the thickness and/or temporal recurrence of stratal units within sedimentary sequences has become an increasingly important axiom of sequence and cyclostratigraphic studies, and multiple orders of stratigraphic cyclicity are now commonly associated with inferred durations and magnitudes of rhythmic variation in global sea level. Beyond the desire to establish an informal nomenclature relating stratigraphic thickness to periodicity of eustatic change, an assumption of stratigraphic orderedness also supports the inference that groups of sedimentary units with distinct modal dimensions in fact do occur with some generally distinct frequency in stratigraphic sequences. In contrast to such perceived patterns of stratigraphic order, many groupings of sedimentary units exhibit lognormal frequency distributions wherein most of the population has an exponentially increasing frequency of occurrence with linearly decreasing class size. Such thickness distributions typify a wide range of sedimentary entities, including individual lithofacies, formally named stratigraphic units, epoch-interval sedimentary sections, and cyclic peritidal lithofacies associations, as well as durations of unconformity-bounded stratigraphic sequences and the magnitudes and durations of presumed change in global sea level. These distributions indicate that most natural populations of sedimentary units comprise a non-modal series of increasing frequency with decreasing size. The importance of this statement lies in the fact that discrimination of stratigraphic hierarchies and their designation as nth-order cycles may constitute little more than the arbitrary subdivision of an uninterrupted stratigraphic continuum.

Facies Mosaics Across the Persian Gulf and Around Antigua—Stochastic and Deterministic Products of Shallow-Water Sediment Accumulation

ABSTRACT Among broadly different types of sedimentary successions, those that accumulate in nearshore settings are perhaps unique in that a very wide range of rock types recurs with high frequency over relatively short stratigraphic intervals. This vertical lithofacies heterogeneity suggests that deposition of any sedimentary unit at any site was short-lived, that many different sediment types existed within a complex mosaic over the depositional surface, and that this facies montage repeatedly moved across surfaces of accumulation in response to eustatic, sedimentologic, and/or tectonic forcing. Data on numbers and thicknesses of lithofacies units from several dozen such sequences define the size frequency distribution expected if horizons of lithologic change occur randomly within sedimentary successions. Walthers law suggests that the amount of vertical lithologic heterogeneity manifest in a sedimentary sequence should reflect the degree of lateral heterogeneity in sediment composition that existed across depositional surfaces. If so, this repetition should also be manifest in sizes and areal distributions of sediment patches constituting the depositional mosaic. In order to examine size frequency relations of sediment bodies across surfaces of sediment accumulation, we tabulated numbers and areal extents of lithotopes across two rather dissimilar settings, across the Persian Gulf and around the Caribbean island of Antigua. Although compositions and lateral extents of different sediment types exhibit broad lateral variation across interior to margin transects in either area, lithotope abundances and areal extents define frequency distributions that are in excellent agreement with those anticipated for a facies mosaic of elements whose mean linear widths constitute an exponential frequency distribution. These are the size frequency distributions one would expect if mosaic element boundaries occur randomly across regions of sediment accumulation, and suggest that distributions of lithotope areas from Holocene surfaces are directly analogous to lithofacies thickness frequencies from ancient successions. In addition to the fact that both of the size frequency distributions attest to the importance of stochastic processes during sediment deposition, they also afford numerical descriptors of abundances and areal extents of Holocene lithosomes that can then be used as controlling parameters in computational models of sediment accumulation. Importantly, results derived from such simulations are based not on inference of water depth varying in response to change in subsidence, sea level, and rate of sediment accumulation but on statistical attributes intrinsic to modern and ancient marginal marine successions.

Michigan hockey, meteoric precipitation, and rhythmicity of accumulation on peritidal carbonate platforms

On Saturday afternoon March 30, 1996, the University of Michigan hockey team won the 1996 National Collegiate Athletic Association Division I national championship. Durations between Wolverine goals, between opponent goals, and between all goals during the preceding 40-game regular season each describe an exponential distribution in which duration frequency depends only on number of shots on goal and probability of success. Compared to opponent scores, University of Michigan between-goal duration frequencies describe a trend having a steeper slope (University of Michigan shot better) and a higher intercept (University of Michigan took more shots). Over much of the past 100 yr, meteoric precipitation on Ann Arbor occurred during 11 949 days. Time durations of the 6401 precipitation episodes that occurred over this interval, as well as durations of contiguous days of precipitation and contiguous days of drought, each define an exponential distribution in which duration frequency is largely defined by total interval length (35 101 days) and probability of precipitation (34%). Roadcuts near Wytheville, Virginia, provide spectacular exposures of a 303.7-m-thick section of peritidal carbonate in the Middle to Upper Cambrian Elbrook and Conococheague Formations. Stratigraphic durations (thicknesses) of the 527 lithologic units within this sequence, of the 265 “cyclic” upward-shallowing lithofacies associations that can be designated over this interval, and of stratigraphic intervals between recurrences of like lithofacies, also define exponential distributions wherein frequency of stratigraphic recurrence is only dependent on the total thickness and net abundance of designated stratal elements. Frequency of goal scoring, and frequency and/or magnitude of meteoric precipitation can be described in terms of random, independent processes at short time scales. Similarly, exponential distributions of lithologic and “cyclic” thickness frequencies at Wytheville, Virginia (as well as in most other epicratonic peritidal sequences), indicate that meter-scale variation in carbonate deposition was predominantly controlled by stochastic (Poisson) processes that were largely unrelated to recurrent intrabasinal or extrabasinal forcing and/or to periodic (rhythmic) sediment accumulation.

On the Use of Cycle Thickness Diagrams as Records of Long-Term Sealevel Change during Accumulation of Carbonate Sequences

Analysis of variation in changing rates of accommodation space creation, as represented by stratigraphic thickness, has become an integral part of ongoing investigations into the origin of ancient, meter-scale, upward-shoaling, cyclic marine carbonates. Groupings of thicker than average and thinner than average cycles within long stratigraphic sections have been thought to represent the influence of long-term eustatic sealevel variation on rates of accommodation space creation under conditions of constant basin subsidence. Statistical analysis demonstrates that a large percentage of early Paleozoic cyclic carbonate sequences contain thickness distributions indistinguishable from those anticipated for random associations of cycles, and that only a few have characteristics commensurate with long-term changes in rate of accommodation space creation. Moreover, in those cases where some extraneous control is suggested, computational considerations readily demonstrate that change in subsidence rate and/or differential compaction could easily give rise to similar stratigraphic associations of cycle thickness. Even if it is accepted that long-term sealevel change has occurred during the accumulation of cyclic carbonates, significant time gaps and difficulty in recognizing and documenting thin cycles results in considerable uncertainty when attempting to use cycle thickness diagrams as records of long-term sealevel change.

Taphonomic Reworking and Stratal Organization of Tempestite Deposition

ABSTRACT Tempestite beds of the Ordovician Kope Formation of northern Kentucky provide an interesting subject for numerical simulation and stratigraphic analysis. Taphonomic characteristics of these shell-rich beds suggest that they were formed by multiple reworking and amalgamation events. If so, then storm-driven redepositional processes could have led to temporal condensation within the tempestite beds. Numerical simulation of tempestite formation indicates that storm-bed abundance is maximized by frequent, weak storm events, whereas shell degradation is increased by frequent, strong storms. Conversely, these stratigraphic and taphonomic parameters are insensitive to changes in storm intensity when such events are relatively uncommon. Additionally, the stratigraphic and taphonomic characteristics of tempestite formation are found to be largely insensitive to the abundance of shell material in the undisturbed shale. Lacunarity analysis of the vertical spacing of Kope Formation tempestite beds (grainstones and packstones) demonstrates stratal clustering. Such clustering was caused by either absolute or relative changes in storm intensity or frequency. Given the temporal scale of tempestite clustering within the Kope, changes in water depth across the shallow shelf--driven either by changes in sea level or sedimentation rate--is a likely mechanism by which such relative changes in storm processes occurred. Conversely, climatologic variability at the scale of tens to hundreds of thousands of years could drive absolute changes in storm intensity leading to stratigraphic clustering of tempestite beds.

An Analysis of the Bachelor of Science in Geology Degree as Offered in the United States

The Bachelor of Science in Geology degree is offered by nearly 300 universities and colleges in the United States. The curriculum of these degree programs is composed of three parts: core required and elective geology courses, cognate science requirements, and general education requirements. Analysis of the frequency of inclusion of courses in the required core has lead to the identification of four curricular patterns common to geology departments. Conversely, there is much more commonality in the cognate science requirements nationally in that two semesters of chemistry, physics, and calculus are required by two thirds of all Bachelor of Science programs. The structure and organization of general education requirements vary significantly as do the number of required credit hours embedded in the general education program. Analysis of the Bachelor of Science in Geology degree serves two important purposes: first, it provides a database upon which informed discussions of curricular content and accreditation standards can be made; second, it provides departments undergoing program review a basis for comparison with other institutions and national norms.

Biological mediation of stochastic peritidal carbonate accumulation

Exponential thickness frequencies of peritidal carbonate units in the Lower Ordovician Kindblade and West Spring Creek Formations at Ardmore, Oklahoma, are readily interpreted in a context of probabilities of upsection transition from one lithology to another. These largely reflect Poisson (random) processes of deposition from suspended load, traction load, and microbialitic accumulation. Although grainy to muddy particulate and cyanobacterial elements exhibit nearly equal ranges of unit thickness, carbonate generation and/or entrapment via algally mediated processes was less likely to lapse and therefore led to lower probability of transition to some other sediment type. The mean thickness of microbially bound units is roughly double those from the physical transport and deposition of particulate material. Greater persistence of algal accumulation probably related to intrinsically higher biologically induced rates of carbonate precipitation and/or binding by cyanobacteria. Stratigraphic intervals between successive occurrences of suspended load, traction load, and microbial units are also closely approximated by exponential frequency distributions for which regression slopes define probabilities of upsection recurrence of a particular sediment type. Values for grainy and algal carbonates are similar and are nearly twice that of muddy suspended-load units. Although biological processes resulted in significantly lower transition probabilities for thrombolitic bioherms and cryptalgal laminites, spatial dominance of carbonate mud across the region led to higher rates of stratigraphic recurrence and a volumetric dominance of muddy lithologies in the Ardmore sequence. Poissonian distributions of unit stratigraphic duration and recurrence suggest a significant component of haphazard variation in the type and amount of accumulated carbonate sediment. If deposition was influenced by extrabasinal forcing, such control must have been nearly random in both secular and spatial dimensions of water depth change. Stratigraphic durations and recurrences in this sequence more closely reflect the inherently stochastic nature of carbonate accumulation in epicratonic platformal settings than any influence of rhythmic eustatic forcing.

Teaching on the Edge of Chaos

Geology, as with all the natural sciences, has undergone a rapid transformation over the last half-century. Transitioning from an interval of largely descriptive science to the establishment of a unifying paradigm has resulted in an extremely rapid advance in our understanding of the Earth and its processes. For several decades plate tectonics has provided the foundation for all geological interpretation. While tectonics continues to be expanded and refined, a new method of observing and simulating nature has recently been developed. Currently, geology, like all other sciences is struggling to absorb the lessons of a new and growing field complexity study. Mark Buchanan, in his new book Ubiquity, describes how densely interconnected networks of relativity simple mathematical expressions can simulate natures complexity. While the physical sciences have embraced self-organization in its various forms, the historical sciences of evolutionary biology and geology are just beginning to explore the wide range of applications provided by this field of inquiry. As science educators, we are faced with two challenges when considering the growing field of complexity science. First, we need to study the theoretical advances and evaluate how we must modify our individual understanding of geology. In most cases the primary literature is accessible to non-specialists. As such, it is essential to understand how this new field is impacting our science. Beyond staying abreast of the growth of this new field, it is important for us to translate to our students the excitement of intellectual inquiry presented by the study of natures complexity. Students are naturally drawn to the most complex aspects of the geosciences; earthquakes, mass extinctions, and climate change are all examples of highly dynamic processes that are well suited to study with complexity models. Translating student interest to meaningful instruction is, as always, a difficult proposition for geoscience educators. Bringing complexity to the classroom presents some unique pedagogical problems for the geoscience educator. First, in order to be more than an exercise in show-and-tell, students must become actively engaged in the simulation of natural systems. Given that so many students have problems with unit conversions and elementary computation, suggesting that a time-rate-ofchange relationship be expressed in mathematical form could prove overwhelming to many introductory students. It is essential, however, that we demand numerical ability in our students. As such, simple exercises in complex systems provide a good process by which to introduce functional relationships and differential expressions. Given the iterative nature of most numerical models of complex systems, it is also necessary to introduce students to either spreadsheet calculation or simple programming formats. Likewise, the outcomes of experiments in complexity produce vast amounts of computational data and it is therefore necessary to introduce students to the basics of data presentation. Understanding graphical relationships is often a difficult skill for students to master, and complex systems provide an interesting way to have students construct and interpret visual data. Beyond these somewhat traditional learning outcomes associated with building complexity experiments into the geoscience curriculum, the most powerful pedagogical benefit to be gained is in the introduction of students to the concepts of model design, testing, and modification. In order for students to learn to think scientifically, they must be encouraged to become engaged in scientific discovery. Numerical simulation of complex systems provides both an exciting and low-cost technique for delivering the pleasures and problems of scientific research. Given the steadily declining numbers of students majoring in the sciences, the geosciences particularly, it is clear the future health of our profession demands that we do all we can to attract more and better students to our classrooms. I am convinced that todays students require, in fact demand, a rich and challenging learning environment. While it certainly remains necessary, it is no longer sufficient to pull out a tray of silicate minerals for student observation or drone on about the virtues of the township and range system in our introductory labs. Rather, we must embrace the pedagogical opportunities presented by the scientific discoveries of self-organization and complexity science. As such, I strongly encourage educators to prepare and submit manuscripts describing how they are using problems associated with modeling complexity in their classrooms. This field of study is too exciting, too important, and too beautiful to not explore with our students.

Exploring the Statistics of Sedimentary Bed Thicknesses - Two Case Studies

Analysis of stratigraphic sections typically consists of recognition and interpretation of lateral and vertical heterogeneities in sedimentary rock. Qualitatively, significant information is obtained by careful observation of changes in various lithologic components (grain composition, size, texture, sorting) as well as the presence or absence of a wide range of sedimentary structures (ripples, cross-stratification, desiccation cracks). Taken together, these physical manifestations of conditions within the depositional environment allow for construction of complexly detailed facies models of ancient sedimentary systems. However, modern stratigraphic analysis is becoming increasingly concerned with more than the construction of facies models. Such transcendent analytical effort represents a further refinement of past attempts at quantification of processes of deposition. To date, the principal approaches to quantitative stratigraphic analysis have been statistical – and the datatype upon which the most effort has been placed is bed thickness. As such, evaluation of several commonly used analytical techniques provides an important background to, and overview of, the statistical analysis of bed thicknesses. By providing students with an introduction to the statistical foundations of modern stratigraphy, it is possible to greatly enhance understanding of both stratal architecture as well as the relationships between depositional process and the stratigraphic record.