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.     

用短期大风资料推算极值风速的一种方法

根据复合极值分布理论，试用二项—对数正态复合极值分布，利用海上短期实测大风资料求算海面多年一遇极值风速，并以此作为基础值，以沿岸站长年代大风经验公式计算风速为订正值，基础值与订正值的叠加作为海面多年一遇工程设计风速。该方法计算结果与皮尔逊Ⅲ型、泊松—龚贝尔复合极值分布计算结果相近，较单纯由二项—对数正态分布计算稳定度增大。     

Submarine fan environment inferred from turbidite thickness distributions

Recent studies of turbidite bed thickness distributions have demonstrated power-law as well as log-normal statistical distributions. The different distributions may reflect different fan processes and environments and, therefore, could be used as a quantitative method to help identify those environments, including those devoid of sequential patterns. The cumulative distributions of well-known turbidite deposits spanning a range of interpreted fan subenvironments are used to illustrate the potential correlation between cumulative distribution and environments. Assuming that power-law distributions may, for some systems, be the primary input signal, one-dimensional modelling allows semi-quantitative characterization of the effects of different fan processes such as erosion and bed amalgamation. Environments indicative of different fan processes may be characterized based on the degree to which processes have acted as a 'filter' to modify the assumed power-law distribution systematically. This model of the effect of fan processes on the power-law distribution is used to help to account for bed thickness distributions observed in several field sites.     

Prediction leaching of potassium using the convective–dispersive and the convective log-normal transfer function models

There is increasing concern about soil enrichment with K⁺ and subsequent potential losses following long-term application of poor quality water to agricultural land. Different models are increasingly being used for predicting or analyzing water flow and chemical transport in soils and groundwater. The convective–dispersive equation (CDE) and the convective log-normal transfer function (CLT) models were fitted to the potassium (K⁺) leaching data. The CDE and CLT models produced equivalent goodness of fit. Simulated breakthrough curves for a range of CaCl₂ concentration based on parameters of 15 mmol l⁻¹ CaCl₂ were characterised by an early peak position associated with higher K⁺ concentration as the CaCl₂ concentration used in leaching experiments decreased. In another method, the parameters estimated from 15 mmol l⁻¹ CaCl₂ solution were used for all other CaCl₂ concentrations, and the best value of retardation factor (R) was optimised for each data set. A better prediction was found. With decreasing CaCl₂ concentration the value of R is required to be more than that measured (except for 10 mmol l⁻¹ CaCl₂), if the estimated parameters of 15 mmol l⁻¹ CaCl₂ are used. The two models suffer from the fact that they need to be calibrated against a data set, and some of their parameters are not measurable and cannot be determined independently.     

Bayesian estimation of isotopic age differences

Isotopic dating is subject to uncertainties arising from counting statistics and experimental errors. These uncertainties are additive when an isotopic age difference is calculated. If large, they can lead to no significant age difference by classical statistics. In many cases, relative ages are known because of stratigraphic order or other clues. Such information can be used to establish a Bayes estimate of age difference which will include prior knowledge of age order. Age measurement errors are assumed to be log-normal and a noninformative but constrained bivariate prior for two true ages in known order is adopted. True-age ratio is distributed as a truncated log-normal variate. Its expected value gives an age-ratio estimate, and its variance provides credible intervals. Bayesian estimates of ages are different and in correct order even if measured ages are identical or reversed in order. For example, age measurements on two samples might both yield 100 ka with coefficients of variation of 0.2. Bayesian estimates are 22.7 ka for age difference with a 75% credible interval of [4.4, 43.7] ka.This paper was presented at Emerging Concepts, MGUS-87 Conference, Redwood City, California, 13–15 April 1987.