Frequency Distribution Of Thickness Research Articles

Mississippian (Lower Carboniferous) Facies Heterogeneity and Distribution within the Mixed Carbonate-Siliciclastic Reservoirs of the Midcontinent STACK Play, Oklahoma, USA

Summary The objective of this study is to evaluate facies heterogeneity, including both lateral and vertical distributions within the mixed carbonate and siliciclastic reservoirs of the Mississippian System (Lower Carboniferous). This research and statistical approach will aid in future investigations related to determining optimal landing zones, enhancing completion designs, and providing geologic insight into fracture driven well interference studies to increase production efficiency. This study integrates well log, petrographic, sedimentologic, and conventional core analyses along a set of transects across the Anadarko Basin and includes the development of core-based facies logs. Statistical analysis indicates that the Mississippian System in the STACK play of the Anadarko Basin is fundamentally a highly layered rhythmic succession in which a variety of carbonate rock types, siliciclastic rock types, and chert tend to form couplets with siltstone. Thickness-frequency distributions and Markov chain analysis indicate that sediment thickness and lithologic transitions were stochastically regulated and that lithologic cyclicity is not apparent. Overall lithologic trends indicate a transition from carbonate to sandstone in the midramp and from carbonate to mudstone and siltstone in the outer ramp. Stratal geometry defines a series of south-prograding clinoforms, and detailed analysis of vertical trends in the distribution of mudstone, siltstone, sandstone, chert, and carbonate facilitates identification of shoaling-upward parasequences that can be correlated regionally.

Statistical characterization of a confined submarine fan system: The Pennsylvanian Lower Atoka Formation, Ouachita Mountains, USA

AbstractCurrent knowledge of submarine fan deposits has historically relied heavily on qualitative field and subsurface observations and interpretations, but recent studies using statistical analyses have enhanced the understanding of submarine fan sub‐environments, including the degree of confinement, stratigraphic patterns and potential control factors. The purpose of this study is to improve the quantitative understanding of synorogenic submarine fan deposition at foreland basin settings with a statistical approach. A suite of statistical methods is integrated and developed (Hurst Statistics/rescaled range analysis, bed thickness frequency distribution analysis, Markov Chains and time‐series analysis), and applied to the well‐understood Pennsylvanian lower Atoka submarine fan system in the Ouachita Mountains, United States, for this purpose. The results of the Hurst Statistics and bed thickness analyses corroborate qualitative interpretations that: (i) the lower Atoka is lobe‐dominated; and (ii) the south‐eastern (wedge top) portion of the system is more strongly confined than the northern (foredeep) portion. The Markov Chains and time‐series analyses reveal the prevalence (56% of the measured sections) of stratigraphic orderliness and cyclicity; these results are used to discuss potential control signals, which are otherwise difficult to distinguish, on the turbidite sandstone recurrence cycles. The results of this study demonstrate that these integrated statistical methods can be utilized to quantify depositional interpretations and extract hidden information using outcrops with limited exposures.

Supraglacial debris thickness variability: impact on ablation and relation to terrain properties

Abstract. Shallow ground-penetrating radar (GPR) surveys are used to characterize the small-scale spatial variability of supraglacial debris thickness on a Himalayan glacier. Debris thickness varies widely over short spatial scales. Comparison across sites and glaciers suggests that the skewness and kurtosis of the debris thickness frequency distribution decrease with increasing mean debris thickness, and we hypothesize that this is related to the degree of gravitational reworking the debris cover has undergone and is therefore a proxy for the maturity of surface debris covers. In the cases tested here, using a single mean debris thickness value instead of accounting for the observed small-scale debris thickness variability underestimates modelled midsummer sub-debris ablation rates by 11 %–30 %. While no simple relationship is found between measured debris thickness and morphometric terrain parameters, analysis of the GPR data in conjunction with high-resolution terrain models provides some insight into the processes of debris gravitational reworking. Periodic sliding failure of the debris, rather than progressive mass diffusion, appears to be the main process redistributing supraglacial debris. The incidence of sliding is controlled by slope, aspect, upstream catchment area and debris thickness via their impacts on predisposition to slope failure and meltwater availability at the debris–ice interface. Slope stability modelling suggests that the percentage of the debris-covered glacier surface area subject to debris instability can be considerable at glacier scale, indicating that up to 32 % of the debris-covered area is susceptible to developing ablation hotspots associated with patches of thinner debris.

The Varve Interpolation Program 3.0.0 - A unique and easy to use tool for incompletely varved sediments

Abstract Annually laminated (varved) sediments are particularly interesting for palaeo-environmental reconstruction, since they allow independent, high resolution chronological control. But often varved archives contain intervals in which seasonal layers did not form every year. To construct independent varve chronologies from such archives varve interpolation is required. Here, a significantly advanced Varve Interpolation Program (VIP) is presented, which uses a novel approach to interpolate varves. Through probability distribution fitting the varve thickness frequency distribution of an interval is approximated and used for interpolation. The new approach is superior in many respects to the approach used in the original VIP 1.0.0, but retains all the advantages, such as objectivity, reproducibility and the fact that it does not rely on well varved intervals. The program is designed for common log-normally distributed varve thickness frequency distributions. It is realised in Matlab, but comes with a graphical user interface, which allows easy handling and requires no prior knowledge about Matlab. The program can be run fully automated, but also allows manual control of settings. While the accuracy of the results depends on the characteristics of the data and the degree of varve formation/preservation, the application examples presented here show that under suitable conditions accuracies in the range of 2% can be achieved.

Calculation of the sun protection factor of sunscreens with different vehicles using measured film thickness distribution — Comparison with the SPF in vitro

The sun protection factor (SPF) depends on UV filter composition, and amount and type of vehicle of the applied sunscreen. In an earlier work, we showed that the vehicle affected the average thickness of sunscreen film that is formed upon application to a skin substrate and that film thickness correlated significantly with SPF in vitro. In the present study, we quantitatively assess the role for sunscreen efficacy of the complete film thickness frequency distribution of sunscreen measured with an oil-in-water cream, an oil-in-water spray, a gel, a water-in-oil, and an alcoholic spray formulation. A computational method is employed to determine SPF in silico from calculated UV transmittance based on experimental film thickness and thickness distribution, and concentration and spectral properties of the UV filters. The investigated formulations exhibited different SPFs in vitro and different film thickness distributions especially in the small thickness range. We found a very good agreement between SPF in silico and SPF in vitro for all sunscreens. This result establishes the relationship between sun protection and the film thickness distribution actually formed by the applied sunscreen and demonstrates that variation in SPF between formulations is primarily due to their film forming properties. It also opens the possibility to integrate the influence of vehicle into tools for in silico prediction of the performance of sunscreen formulations. For this, the use of the Gamma distribution was found to be appropriate for describing film thickness distribution.

Stranding Moso and Guadua Bamboo. Part I: Strand Production and Size Classification

Giant timber bamboos, such as moso (Phyllostachys pubescens) and guadua (Guadua angustifolia) are potentially well-suited to the production of engineered strand-based structural composite building materials. There is no information available for guadua, but moso bamboo is known to produce good-quality, strand-based composites. However, economically viable commercial production of these composites is hindered by the lack of an efficient, automated method for converting culm stock to strands, and very little technical information is available regarding strand production and quality. In this study, moso and guadua culm characteristics and tissue re-saturation behavior likely to affect stranding were measured and compared. Strand size classification and the thickness and width distributions from stranding re-saturated moso and guadua quartered culm pieces using a CAE 6/36 single-blade disk flaker were determined. While node frequency was lower in guadua than in moso, the diaphragms and embedded wall tissue were much thicker and tougher, with strong negative effects on strand quality. When cut to a target thickness of 0.65 mm, moso bamboo produced strand thickness frequency distributions close to those found in sampled mill strands of trembling aspen, while guadua caused high wear on blades and yielded a greater proportion of excessively thick, broken, and very rough strands.

Film thickness frequency distribution of different vehicles determines sunscreen efficacy

Sun protection factor (SPF) frequently differs between sunscreens containing the same composition of ultraviolet (UV) filters that primarily define sunscreen efficacy. We tested the hypothesis that the thickness frequency distribution of the sunscreen film is also responsible for and can explain the divergence in the measured SPF. For this, we developed a method to measure film thickness from the difference of topography before and after application of of sunscreen on pig ear epidermal membrane. The influence of five vehicle formulations and of application pressure and spreading time on mean thickness ( ), to median ratio, and SPF in vitro was investigated. The vehicle had a significant impact, low vehicle viscosity resulting in a smaller , larger to median ratio, and lower SPF in vitro than high viscosity; continuous oil phase produced the largest and SPF values. A long spreading time reduced and SPF and increased application pressure reduced SPF. There was a positive correlation between and SPF in vitro, underlining the relevance of film thickness for interpreting UV protection differences of formulations with the same filter composition. This work demonstrated a strong influence of vehicle and application conditions on sunscreen efficacy arising from differences in film thickness distribution.

Layer morphology analysis of sputter-eroded silicon gratings using Rutherford backscattering

The possibility to simulate Rutherford backscattering (RBS) spectra from arbitrary laterally inhomogeneous sample structures was implemented in the SIMNRA code. Layer morphology is modeled by a layer thickness frequency distribution. This method was used to monitor the evolution of the surface morphology of a one dimensional silicon grating on top of a tantalum interlayer in situ. The Si grating was sputtered by argon and carbon ion beams at an incident energy of 6 keV at two different angles of incidence parallel to the grid lines. After each sputtering step the surface was investigated by RBS. The Si grid lines undergo a change of their morphology due to sputtering erosion. The morphology change depends on the sputtering angle and is different for Ar and C bombardment. Sputtering with C leads to the formation of a protective C layer on top, which was confirmed by additional NRA measurements. The results of the RBS measurements were confirmed by scanning electron micrographs of sample cross-sections produced by focused ion beam cross-sectioning.

宮崎県日南海岸沿いに分布する新第三系宮崎層群青島層の重力流堆積物とその層序パターンの特異性

The Neogene Aoshima Formation of the Miyazaki Group, well exposed along the Nichinan coast, has been considered to be a turbidite succession deposited at a forearc basin, although the thickness-frequency distributions and the sedimentary facies of the formation are in disagreement with those of typical turbidite successions. In this study, we investigated the depositional system and the sedimentary environments of the formation, on the basis of the facies of sediment-gravity flow deposits and stratigraphic variations of bed-thickness distributions. From the results, we can classify the sediment-gravity flow deposits of the formation into the following types; Type G: sedimentary structures containing grading beds, whose wavelength is in the range of 0.5-5m; Type I: inverse grading structures composed of a finer lower unit with climbing-ripple cross lamination or HCS-mimics, and a coarser upper unit with massive sandstones; and Type M: massive structureless sandstones. Individual sediment-gravity flow deposits can be correlated over 10 km using key-tuff markers along palaeocurrent directions. Stratigraphic fluctuations of the hemipelagic-mudstone thickness and sediment-gravity flow thickness show that the formation along the Aoshima Island consists of a lower progradational system indicated by a thinning-upward trend of hemipelagic mudstones and an upper system dominated by lobate sand bodies characterized by the cyclic sedimentation of thick-sediment-gravity flow deposits. These results indicate that the depositional setting of the formation is a deep-offshore basin of a fandelta along the south-east coast of the Kyushu Island.

Frequency Distribution of Thickness of Sediments Bounded by Cenozoic Biostratigraphic Events in Wells Drilled Offshore Norway and along the Northwestern Atlantic Margin

Sampling for microfossils in exploratory wells in basins with hydrocarbon potential is subject to considerable uncertainty, mainly because the samples usually are small and subject to caving. Biostratigraphic events defined on fossil taxa include their last occurrences of which the depths along the wells generally can be measured with precision. The RASC method for ranking and scaling of stratigraphic events produces an average basin-wide optimum sequence and zonation that can be used for correlation of strata between wells. In this optimum sequence the fossil events are ordered according to their occurrences in geological time. Depth differences between successive events in the optimum sequence satisfy a frequency distribution that is of interest for potentially increasing stratigraphic resolution. In this article the depth difference frequency distribution is modeled for three large Cenozoic microfossil data sets consisting of 30 wells in the North Sea Basin, 27 wells on the Labrador Shelf and Grand Banks, and 11 wells in the western Barents Sea. The shapes of the three frequency distributions satisfy bilateral gamma distributions with similar parameters. These distributions are fitted by the construction of straightlines on normal Q–Q plots of square root transformed average-corrected depth differences. The gamma distribution model is approximately satisfied except for small negative and positive depth differences, which have anomalous frequencies because of the discrete sampling method used in exploratory well-drilling to collect microfossils. It implies not only comparable average stratigraphic order of events, but also comparable average sedimentation rates in the three Cenozoic basins selected for study.

Bone microarchitecture in males with corticosteroid-induced osteoporosis

Microarchitectural changes in trabecular bone were analyzed by microcomputed tomography (microCT) and histomorphometry in 24 patients with corticosteroid-induced osteoporosis. The microCT images revealed a reduction in trabecular thickness only on frequency distribution curves, with no increase in trabecular separation. Trabecular plate thinning and perforations were easily identified. Corticosteroid-induced osteoporosis (CSIOP) is mediated by direct actions of the drug on bone cells. The result is a decrease in trabecular bone mass and a reduction in trabecular thickness, but connectivity is believed to remain rather well preserved. Twenty-four transiliac bone biopsies from patients with CSIOP were studied conjointly by histomorphometry [with two-dimensional (2D) architectural descriptors] and microCT (with 3D analysis of trabecular characteristics, including trabecular thickness and separation). The frequency distribution of thickness and separation were compared with data obtained in nine control subjects. 2D histomorphometry revealed a decrease in bone volume and trabecular thickness in the bone biopsies of the CSIOP patients when compared to those of the controls. MicroCT appeared to be able to identify the reduction in thickness only when the frequency distribution of trabecular thickness was computed. No difference for the curves of the frequency distribution of trabecular separation was evidenced between patients and controls. MicroCT and 2D histomorphometric results were correlated, but 2D analysis appeared to be more sensitive. However, microCT identified a very specific thinning of the trabecular plates in their center that corresponds to the earlier stages of perforations. Trabecular plate thinning can be observed and perforations occur on very thin plates in CSIOP patients.

On the frequency distribution of turbidite thickness

The frequency distribution of turbidite thickness records information on flow hydrodynamics, initial sediment volumes and source migration and is an important component of petroleum reservoir models. However, the nature of this thickness distribution is currently uncertain, with log‐normal or negative‐exponential frequency distributions and power‐law cumulative frequency distributions having been proposed by different authors. A detailed analysis of the Miocene Marnoso Arenacea Formation of the Italian Apennines shows that turbidite bed thickness and sand‐interval thickness within each bed have a frequency distribution comprising the sum of a series of log‐normal frequency distributions. These strata were deposited predominantly in a basin‐plain setting, and bed amalgamation is relatively rare. Beds or sand intervals truncated by erosion were excluded from this analysis. Each log‐normal frequency distribution characterizes bed or sand‐interval thickness for a given basal grain‐size or basal Bouma division. Measurements from the Silurian Aberystwyth Grits in Wales, the Cretaceous Great Valley Sequence in California and the Permian Karoo Basin in South Africa show that this conclusion holds for sequences of disparate age and variable location. The median thickness of these log‐normal distributions is positively correlated with basal grain‐size. The power‐law exponent relating the basal grain‐size and median thickness is different for turbidites with a basal A or B division and those with only C, D and E divisions. These two types of turbidite have been termed ‘thin bedded’ and ‘thick bedded’ by previous workers. A change in the power‐law exponent is proposed to be related to: (i) a transition from viscous to inertial settling of sediment grains; and (ii) hindered settling at high sediment concentrations. The bimodal thickness distribution of ‘thin‐bedded’ and ‘thick‐bedded’ turbidites noted by previous workers is explained as the result of a change in the power‐law exponent. This analysis supports the view that A and B divisions were deposited from high‐concentration flow components and that distinct grain‐size modes undergo different depositional processes. Summation of log‐normal frequency distributions for thin‐ and thick‐bedded turbidites produces a cumulative frequency distribution of thickness with a segmented power‐law trend. Thus, the occurrence of both log‐normal and segmented power‐law frequency distributions can be explained in a holistic fashion. Power‐law frequency distributions of turbidite thickness have previously been linked to power‐law distributions of earthquake magnitude or volumes of submarine slope failure. The log‐normal distribution for a given grain‐size class observed in this study suggests an alternative view, that turbidite thickness is determined by the multiplicative addition of several randomly distributed parameters, in addition to the settling velocity of the grain‐sizes present.

Depositional Cyclicity in the Lower Devonian Helderberg Group of New York State.

The Helderberg Group of New York State, consisting of a wide range of shallow water carbonate lithologies, contains one of the finest and most complete stratigraphic records of Lower Devonian earth history. High-frequency spatial and temporal rhythmicity of carbonate accumulation in the Helderberg Group has been evaluated by examining thickness frequency distributions of individual sedimentation units in flasered ribbon rock and of individual lithofacies elements. These distributions provide important insights into the sedimentation processes that ultimately controlled stratal thicknesses. Observed thickness frequencies are closely approximated by the exponential end member of the gamma distribution, wherein flaser and lithofacies thickness frequency over each stratigraphic interval is dependent only on net sequence length and the number of stratal elements. Exponentially distributed thickness frequencies would be expected if lithologic change were a Poisson process, that is, if horizons of lithologic change occurred more or less randomly throughout. Such Poisson variation in lithologic thickness suggests a general absence of regularly recurrent high-frequency depositional forcing of stratal thicknesses during accumulation. At the individual flaser-bedded and lithofacies scale, deposition was primarily a stochastic rather than a deterministic process. Thickness distributions of supposedly shallowing-upward lithofacies associations, and magnitudes of sea-level rise inferred from lithologic change across shallowing cycle boundaries, exhibit similar skewed distributions of thickness/magnitude recurrence in Helderberg Group sections. These also are readily interpreted as generally Poisson processes of carbonate accumulation. Skewed frequency distributions of either cycle thickness or water depth change result from the grouping of a small number of elements from an exponential population of randomly distributed sizes. Modal (albeit skewed) cycle thickness distributions are simply an artifact of cycle definition and need not bear any relation to periodic extrabasinal forcing mechanisms. We conclude that thicknesses of flasered bedding units and lithofacies in the Helderberg Group largely reflect the more or less incidental migration of Lower Devonian depositional subenvironments across New York State during sediment accumulation. Stratigraphic extents of shallowing-upward lithofacies associations and apparent punctuated deepening across shallowing "cycle" tops are little different from chance groupings of stratal units randomly drawn from an exponential population. If any sea-level control is manifest in these patterns of sediment accumulation, it must have been nearly haphazard with respect to both secular recurrence and magnitude of eustatic change.

Poisson processes of carbonate accumulation on Paleozoic and Holocene platforms

ABSTRACT Cambro-Ordovician carbonate lithofacies units in the Elbrook and Conococheague formations exposed at Wytheville, Virginia, as well as those in many other Phanerozoic peritidal sequences, exhibit exponential thickness frequency distributions. That is, occurrence frequency decreases exponentially with linear increase in unit thickness. Such distributions are characteristic of waiting times between independent Poisson events. This relative frequency of spaces of different size between horizons of lithologic change is what one would expect if the horizons were distributed randomly throughout carbonate successions. Abundances of different lithologies, both as net stratigraphic thickness and as number of occurrences, also decreases exponentially among successively rare sediment types, with each lithology being about 60% as plentiful as the next more abundant rock type. Relations between net thickness and number of occurrences for each facies define a linear trend coincident with a mean thickness for all Wytheville units of 0.48 m, a relation indicating that thickness distribution is independent of facies type. Similar relations are apparent for the horizontal extent of carbonate sediment bodies from the Holocene Florida-Bahama platform. Areal extents of individual facies units (lithotopes) are described by a frequency distribution in agreement with that anticipated for a population of equidimensional facies elements whose diameter distribution follows an exponential frequency distribution. Although regional gradients in sediment texture and composition are also apparent along most transects from platform margin to interior, such frequency distributions indicate that lateral extents of individual sediment reflect a largely stochastic distribution of facies boundaries across this Holocene surface. Lithotope abundances also yield trends of exponentially decreasing dominance among successively subordinate facies, with each being about 70% as extensive the next more abundant sediment type. Relations between areas and abundances for all lithotopes define a covariant trend corresponding to a mean area of 2.2 103 km2 for all Florida-Bahamas lithotopes. We consider several numerical models of stochastic carbonate accumulation; although not demonstrably unique, scenarios incorporating the sequential superposition of randomly placed coniform lithotopes result in thickness and area frequency distributions that are the same as those observed in ancient and modern platform deposits. Such simulations of Poisson processes of sediment accumulation are in general agreement with stochastic models of lithologic heterogeneity that have been more widely applied to petroleum reservoirs and groundwater aquifers. To the as yet unknown degree that peritidal lithofacies area and thickness are correlated, data from Paleozoic and Holocene platforms suggest that carbonate units should exhibit length/height ratios of approximately 105. Given the decimeter scale over which facies are designated in most Paleozoic peritidal successions, these relations predict mean lateral extents on the order of several tens of kilometers, a value in general agreement with the few data that exist on spatial continuities of peritidal lithotopes in Paleozoic carbonate sequences.

Aperiodic accumulation of cyclic peritidal carbonate

Tabulation of thickness data on nearly 3000 Proterozoic and Paleozoic peritidal carbonate cycles indicates that metre-scale facies associations exhibit exponential thickness frequency distributions. Because carbonate deposition occurs during infilling of available space between sea level and the surface of the preceding cycle, and because the rate of generation of accommodation space is ultimately determined by rates of platform subsidence, thicknesses of individual cycles must record the duration of time since deposition of underlying units. Exponential thickness distributions therefore require either that upward-shoaling carbonates record aperiodic accumulation, or that any periodic forcing manifest during sedimentation has been masked by the vagarious nature of depositional processes. Such a conclusion is contrary to interpretation of such carbonate units as originating from high-frequency eustatic change. In addition, exponential thickness distributions and sequence thickness structures are replicated when assuming a random probability of carbonate deposition under conditions of constant subsidence. The nature of cycle thickness distributions therefore invalidates virtually any endeavor to derive an average depositional period from mean cycle thicknesses, and refutes the use of such estimates as proxy records of past sea-level oscillation frequency, whether they are related to Milankovitch-band climate forcing or to any other periodic process.

Myelin sheath thickness and conduction latency groups in the cat optic nerve.

In many animals, the optic nerve has multiple conduction latency groups of fibres yet displays a unimodal frequency distribution of fibre sizes. An attempt has been made to resolve this discrepancy in the cat. Examination of teased preparations of fixed cat optic nerve fibres by polarizing interference light microscopy indicated that a fibre's size may change abruptly along its length. Furthermore, the diameters of single nerve fibres followed for distances of up to 30 mum in serial transverse sections of cat optic nerve showed variations of up to 100% of a fibre's average diameter over that distance. On the other hand, the myelin sheath thickness of these fibres appeared to be relatively constant along any one fibre. A population of cat optic nerve fibres which had a unimodal axon diameter frequency distribution was found to have a myelin sheath thickness frequency distribution with five modes. These modes have been interpreted as indicating the existence of five groups of fibres in the cat optic nerve. Four of these groups may be related to four negative peaks seen in the antidromic compound action potential recorded at the margin of the cat optic disc following stimulation of the optic chiasm. The fifth myelin thickness group appears to represent the slowly conducting fibres which do not make an obvious contribution to the antidromic compound action potential. It is concluded that for the cat optic nerve, the conduction latency groups seen in the compound action potential may be more directly correlated with the frequency distribution of fixed nerve myelin thickness than with the frequency distribution of fixed nerve fibre diameter.

Transportation of detrital materials on the lunar surface: evidence from Apollo 15

ABSTRACTThe thickness frequency distribution of stratigraphic layers intersected by the Apollo 15 deep core suggests that the majority of impact events reworking the lunar soil are small and produce ejecta blankets with an average thickness of less than 1·D5 cm. The energy frequency distribution of the meteorites producing the layers may be bimodal. The impacting meteorites produce both normal and reverse graded beds which appear to be the end products of two depositional mechanisms. First, the normally graded beds appear to be produced in base surges as escaping gases fluidize the flowing debris and larger particles move downwards in response to Stokes Law. Second, if the gas loss from the base surge is excessive the fluidization may cease and inertial grain flow dominates. In this situation the beds are reverse graded as larger particles move under dispersive pressure to the region of minimum shear stress at the upper boundary of the base surge. The same processes also produce measurable shape sorting of the particles in the beds.

Forest Windthrows and Their Influence on Soil Morphology

AbstractThe variability in thickness of the O and A2 horizons was studied on a sandy loam forest soil in the Great Lakes‐St. Lawrence Region of southern Ontario. Horizon thicknesses were recorded in 1.3 cm (0.5 inch) classes for each 10.2 cm (4 inches) of horizontal distance on the faces of each soilpit. Soilpits were located both subjectively on windthrows and randomly in the study area. Thickness frequency distributions for O horizons were normal and for the A2 horizons Poisson‐like. Both were independent of recent fire history and sampling method. It may be inferred that the disturbance by windthrow is infrequent in relation to O horizon formation, but frequent relative to A2 horizon development. Microtopographic position had a slight effect; thicknesses in top positions being somewhat less than for bottom positions. Horizon distortions related to windthrow disturbance were recorded for only 19% of the soil profiles sampled.

Stratigraphic Sections, Bedding Sequences, and Random Processes

Both dependent and independent random processes can be used to study and synthesize stratigraphic sections and bedding sequences. Synthetic stratigraphic sections can be modeled to fit any geologic problem with a good correspondence between the synthetic and actual stratigraphic sections. To synthesize a sedimentary sequence, one needs only a transition procedure to go from one lithology or bedding type to another, and frequency distributions of thickness for the various lithologies. A sedimentation process with a "memory" is termed Markovian; if the past has no influence on either present or future sedimentation, it is called an independent trials process.

29—Merino Staple Crimp: The Relationship of Staple ‘Character’ and Variability of Fiber Thiickness

No significant relationship was found between excellenc of staple ‘character’ and uniformity of fibre thickness, and hence of fibre length, within the staple, nor did the presence of an extremely coarse group of fibres in the frequency distribution of thickness appear to have any influence on the staple structure in respect to ‘character.’