Stochastic estimation of facies using ground penetrating radar data

Explicitly defining large-scale heterogeneity is a necessary step of groundwater model calibration if accurate estimates of flow and transport are to be made. In this work, neural networks are used to estimate radar facies probabilities from ground penetrating radar (GPR) images, yielding stochastic facies-based models that honour the large-scale architecture of the subsurface. For synthetic GPR images, a neural network was able to correctly identify radar facies with an accuracy of approximately 90%. Manual interpretation of a set of 450 MHz GPR field data from the Borden aquifer resulted in the identification of four radar facies. Of these, a neural network was able to identify two facies with an accuracy of near 80% and one with an accuracy of 44%. The neural network was not able to identify the fourth facies, likely due to the choice of defining facies characteristics. Sequential indicator simulation was used to generate facies realizations conditioned to the radar facies probabilities. Numerical simulations indicate that significant improvements in the prediction of solute transport are possible when GPR is used to constrain the facies model compared to using well data alone, especially when data are sparse.This work was supported by funding to R. Knight under Grant No. DE-FG07–00ER15118-A000, Environmental Management Science Program, Office of Science and Technology, Office of Environment Management, United States Department of Energy (DOE). However, any opinions, findings, conclusions, or recommendations expressed herein are those of the authors and do not necessarily reflect the views of DOE. Further support was provided by a Stanford Graduate Fellowship to S. Moysey. The authors would also like to thank James Irving for his assistance with processing of the radar data.     

A revised burial dose estimation procedure for optical dating of youngand modern-age sediments

The presence of genuinely zero-age or near-zero-age grains in modern-age and very young samples poses a problem for many existing burial dose estimation procedures used in optical (optically stimulated luminescence, OSL) dating. This difficulty currently necessitates consideration of relatively simplistic and statistically inferior age models. In this study, we investigate the potential for using modified versions of the statistical age models of Galbraith et al. [Galbraith, R.F., Roberts, R.G., Laslett, G.M., Yoshida, H., Olley, J.M., 1999. Optical dating of single and multiple grains of quartz from Jinmium rock shelter, northern Australia: Part I, experimental design and statistical models. Archaeometry 41, 339–364.] to provide reliable equivalent dose (D_e) estimates for young and modern-age samples that display negative, zero or near-zero D_e estimates. For this purpose, we have revised the original versions of the central and minimum age models, which are based on log-transformed D_e values, so that they can be applied to un-logged D_e estimates and their associated absolute standard errors. The suitability of these ‘un-logged’ age models is tested using a series of known-age fluvial samples deposited within two arroyo systems from the American Southwest. The un-logged age models provide accurate burial doses and final OSL ages for roughly three-quarters of the total number of samples considered in this study. Sensitivity tests reveal that the un-logged versions of the central and minimum age models are capable of producing accurate burial dose estimates for modern-age and very young (<350 yr) fluvial samples that contain (i) more than 20% of well-bleached grains in their D_e distributions, or (ii) smaller sub-populations of well-bleached grains for which the D_e values are known with high precision. Our results indicate that the original (log-transformed) versions of the central and minimum age models are still preferable for most routine dating applications, since these age models are better suited to the statistical properties of typical single-grain and multi-grain single-aliquot D_e datasets. However, the unique error properties of modern-age samples, combined with the problems of calculating natural logarithms of negative or zero-Gy D_e values, mean that the un-logged versions of the central and minimum age models currently offer the most suitable means of deriving accurate burial dose estimates for very young and modern-age samples.     

Equivalent dose estimation of calcite using isothermal thermoluminescence signals

Thermoluminescence (TL) signals of calcite can be used to potentially date geological and archaeological events back to several million years. However, several issues, such as spurious TL signals appearing at temperatures above 300 °C, have hindered its application to a wide range of samples. A single-aliquot regenerative-dose (SAR) protocol for calcite with low-temperature measurements is proposed to measure the equivalent dose (D_e). It uses the isothermal TL (ITL) signals measured at around 225-240 °C, where a D_e vs. ITL temperature (D_e-T) plateau can be observed. The width of the temperature range of such a plateau can be sample dependent, as it relates to the proportional contributions of the signals from corresponding TL peaks. The signal at the ITL temperature plateau range largely corresponds to the TL signals of the 280 °C TL peak. D_e values obtained by the SAR-ITL protocol are in agreement with those of the multiple-aliquot additive-dose (MAA)-TL and MAA-ITL protocols. The absence of detectable anomalous fading of ITL signals at 235 °C in this and previous studies indicates that the signal is free of fading. Dose recovery tests confirm the suitability of the SAR-ITL protocol for D_e estimation. The SAR-ITL protocol measured with temperatures below 300 °C avoids the effects of spurious luminescence signals induced by high-temperature heating. The dose-response curves for ITL signals at 230-235 °C have large characteristic saturation doses (D₀) of ∼2000-2400 Gy. The SAR-ITL protocol for calcite thus has the potential to date geological and archaeological samples spanning the entire Quaternary period.     

Stochastic modeling of Iranian earthquakes and estimation of ground motion for future earthquakes in Greater Tehran

Strong-motion data from eight significant well-documented earthquakes in Iran have been simulated using a stochastic modeling technique for finite faults proposed by Beresnev and Atkinson [Bull Seismol Soc Am 87 (1997) 67–84; Seism Res Lett 69 (1998) 27–32]. The database consists of 61 three-component records from eight earthquakes of magnitude ranging from M 6.3 to M 7.4, recorded at hypocentral distances up to 200 km. The model predictions are in good agreement with available Iranian strong-motion data as evidenced by near-zero average of differences between logarithms of the observed and predicted values for all frequencies. The strength factor, sfact, a quantity that controls the high-frequency radiation from the source is determined, on an event-by-event basis, by fitting simulated to observed response spectra.     

Stochastic inverse method for estimation of geostatistical representation of hydrogeologic stratigraphy using borehole logs and pressure observations

An approach is presented for identifying statistical characteristics of stratigraphies from borehole and hydraulic data. The approach employs a Markov-chain based geostatistical framework in a stochastic inversion. Borehole data provide information on the stratigraphy while pressure and flux data provide information on the hydraulic performance of the medium. The use of Markov-chain geostatistics as opposed to covariance-based geostatistics can provide a more easily interpreted model geologically and geometrically. The approach hinges on the use of mean facies lengths (negative inverse auto-transition rates) and mean transition lengths (inverse cross-transition rates) as adjustable parameters in the stochastic inversion. Along with an unconstrained Markov-chain model, simplifying constraints to the Markov-chain model, including (1) proportionally-random and (2) symmetric spatial correlations, are evaluated in the stochastic inversion. Sensitivity analyses indicate that the simplifying constraints can facilitate the inversion at the cost of spatial correlation model generality. Inverse analyses demonstrate the feasibility of this approach, indicating that despite some low parameter sensitivities, all adjustable parameters do converge for a sufficient number of ensemble realizations towards their “true” values. This paper extends the approach presented in Harp et al. (doi:, 2008) to (1) statistically characterize the hydraulic response of a geostatistical model, thereby incorporating an uncertainty analysis directly in the inverse method, (2) demonstrate that a gradient-based optimization strategy is sufficient, thereby providing relative computational efficiency compared to global optimization strategies, (3) demonstrate that the approach can be extended to a 3-D analysis, and (4) introduce the use of mean facies lengths and mean transition lengths as adjustable parameters in a geostatistical inversion, thereby allowing the approach to be extended to greater than two category Markov-chain models.     

Stochastic modelling of multi-grain equivalent dose (De) distributions: Implications for OSL dating of sediment mixtures

A number of recent optically stimulated luminescence (OSL) studies have cited post-depositional mixing as a dominant source of equivalent dose (D_e) scatter across a range of sedimentary environments, including those previously considered ‘best suited’ for OSL dating. The potentially insidious nature of sediment mixing means that this problem may often only be identifiable by careful statistical analysis of D_e data sets. This study aims to address some of the important issues associated with the characterisation and statistical treatment of mixed D_e distributions at the multi-grain scale of analysis, using simulated D_e data sets produced with a simple stochastic model. Using this Monte Carlo approach we were able to generate theoretical distributions of single-grain D_e values, which were then randomly mixed together to simulate multi-grain aliquot D_e distributions containing a known number of mixing components and known corresponding burial doses. A range of sensitivity tests were undertaken using sediment mixtures with different aged dose components, different numbers of mixing components, and different types of dose component distributions (fully bleached, heterogeneously bleached and significantly overdispersed D_e distributions). The results of our modelling simulations reveal the inherent problems encountered when dating mixed sedimentary samples with multi-grain D_e estimation techniques. ‘Phantom’ dose components (i.e. discrete dose populations that do not correspond to the original single-grain mixing components) are an inevitable consequence of the ‘averaging’ effects of multi-grain D_e analysis, and prevent the correct number of mixing components being identified with the finite mixture model (FMM) for all of the multi-grain mixtures tested. Our findings caution against use of the FMM for multi-grain aliquot D_e data sets, even when the aliquots consist of only a few grains.     

Parallel calibration transfer and systematic effects in retrospective absorbed dose estimation using OSL

Parallel multiple aliquot calibration transfer is combined with the use of standardized optically stimulated luminescence signals and evaluation of single aliquot regenerative dose response characteristics, to produce a robust and efficient transfer protocol for mineral samples used in dating and retrospective dosimetry. Transfer was made from an IST-LPSR ⁶⁰Co primary air kerma standard to four Risø and Daybreak ⁹⁰Sr/⁹⁰Y irradiators, for quartz or polymineral grains of 90/100–160 μm or 160–250 μm diameter from seven samples. Grains were pretreated by activation, heating, or bleaching, and mounted on 0.5 mm thick aluminium or stainless steel disks, or 0.25 mm thick stainless steel cups. Multiple aliquot conversion coefficients based on parallel irradiations (mGy_60Co per s of ⁹⁰Sr/⁹⁰Y exposure) were corrected for non linearity in dose response using the regenerative measurements, and compared with “single aliquot” coefficients obtained directly from the regenerative, i.e. retrospectively measured, dose responses. Ratios of measured/given β exposure time provide controls: these were close to unity for activated and heated material, which exhibited predose sensitization, and vice versa for optically bleached samples. Parallel multiple aliquot calibration transfer, using OSL integrated over the main signal decay, was found to offer better accuracy and precision than retrospective single aliquot measurements, and was robust for polyminerals as well as quartz. Differences in conversion coefficient between grain-sizes and supports on a given irradiator ranged up to 25% and were specific to the irradiator-support-grainsize permutation. Geometric effects are quantitatively explained by the solid angle subtended at the source by the sample, and the effect of support material (and thickness) by differences in electron backscatter.     

Stochastic rainfall-runoff forecasting: parameter estimation,multi-step prediction,and evaluation of overflow risk

Probabilistic runoff forecasts generated by stochastic greybox models can be notably useful for the improvement of the decision-making process in real-time control setups for urban drainage systems because the prediction risk relationships in these systems are often highly nonlinear. To date, research has primarily focused on one-step-ahead flow predictions for identifying, estimating, and evaluating greybox models. For control purposes, however, stochastic predictions are required for longer forecast horizons and for the prediction of runoff volumes, rather than flows. This article therefore analyzes the quality of multistep ahead forecasts of runoff volume and considers new estimation methods based on scoring rules for k-step-ahead predictions. The study shows that the score-based methods are, in principle, suitable for the estimation of model parameters and can therefore help the identification of models for cases with noisy in-sewer observations. For the prediction of the overflow risk, no improvement was demonstrated through the application of stochastic forecasts instead of point predictions, although this result is thought to be caused by the notably simplified setup used in this analysis. In conclusion, further research must focus on the development of model structures that allow the proper separation of dry and wet weather uncertainties and simulate runoff uncertainties depending on the rainfall input.     

Scavenging of heavy metals from particulates by brown seaweed

Concentrations of Cu, As, Pb, Zn and Ag (but not Cd, Co, Fe, Mn and Hg) in the tissues of benthic algae (Fucus vesiculosus) correlate significantly with concentrations in sediment. Metals which complex most strongly with algal tissues show the strongest correlations of algal tissue and sediment. Scavenging these metals from particulates may be an important source of uptake by the algae. If so, concentrations of Cu, As, Pb, Zn and Ag in algal tissues may not be good indicators of concentrations of these metals in solution.     

Rapid equivalent dose estimation for eolian dune sands using a portable OSL reader and polymineralic standardised luminescence growth curves: Expedited sample screening for OSL dating

Portable optically stimulated luminescence (OSL) readers are robust devices that allow rapid determination of luminescence signals of polymineralic coarse-grained samples. To date, however, the utility of portable OSL readers has largely been confined to the construction of luminescence profiles that depict variations of luminescence signal intensities with depth. Because the luminescence signals used to construct such profiles are uncalibrated, it is neither practical to quantitatively compare portable OSL data from different sites nor is it possible to approximate sample ages. Such comparisons could be facilitated by converting portable OSL signals into equivalent doses (D_e). However, determining D_e requires the construction of unique growth curves for each sample; a laborious procedure that negates the rapidity associated with portable measurements. To circumvent that limitation, we construct standardised growth curves (SGCs) using normalized regeneration dose signals obtained using a portable OSL reader from the feldspar component of polymineralic sands from five disparate eolian dune sites in Alberta, Canada. Comparison of SGCs from different samples indicates general congruence and we merge these to construct a regionally applicable curve which we test by comparing the D_e obtained from given samples with that obtained using conventional OSL dating protocols. Results show that, though the uncertainties associated with the portable OSL data are high, the D_e values from the two approaches are linearly proportional. This direct variation enables portable OSL SGC D_e values to be used independently in reconnaissance studies that aim to screen samples for more detailed analysis using standard OSL methods. The affordability of portable OSL readers suggests that the approach could be attractive to researchers who do not have ready access to conventional OSL readers.     

Stochastic differential dynamic programming for multi-reservoir system control

: As with all dynamic programming formulations, differential dynamic programming (DDP) successfully exploits the sequential decision structure of multi-reservoir optimization problems, overcomes difficulties with the nonconvexity of energy production functions for hydropower systems, and provides optimal feedback release policies. DDP is particularly well suited to optimizing large-scale multi-reservoir systems due to its relative insensitivity to state-space dimensionality. This advantage of DDP encourages expansion of the state vector to include additional multi-lag hydrologic information and/or future inflow forecasts in developing optimal reservoir release policies. Unfortunately, attempts at extending DDP to the stochastic case have not been entirely successful. A modified stochastic DDP algorithm is presented which overcomes difficulties in previous formulations. Application of the algorithm to a four-reservoir hydropower system demonstrates its capabilities as an efficient approach to solving stochastic multi-reservoir optimization problems. The algorithm is also applied to a single reservoir problem with inclusion of multi-lag hydrologic information in the state vector. Results provide evidence of significant benefits in direct inclusion of expanded hydrologic state information in optimal feedback release policies.     

Stochastic differential dynamic programming for multi-reservoir system control

: As with all dynamic programming formulations, differential dynamic programming (DDP) successfully exploits the sequential decision structure of multi-reservoir optimization problems, overcomes difficulties with the nonconvexity of energy production functions for hydropower systems, and provides optimal feedback release policies. DDP is particularly well suited to optimizing large-scale multi-reservoir systems due to its relative insensitivity to state-space dimensionality. This advantage of DDP encourages expansion of the state vector to include additional multi-lag hydrologic information and/or future inflow forecasts in developing optimal reservoir release policies. Unfortunately, attempts at extending DDP to the stochastic case have not been entirely successful. A modified stochastic DDP algorithm is presented which overcomes difficulties in previous formulations. Application of the algorithm to a four-reservoir hydropower system demonstrates its capabilities as an efficient approach to solving stochastic multi-reservoir optimization problems. The algorithm is also applied to a single reservoir problem with inclusion of multi-lag hydrologic information in the state vector. Results provide evidence of significant benefits in direct inclusion of expanded hydrologic state information in optimal feedback release policies.     

Investigations of gram quantities of Atlantic and Pacific surface particulates

Particulates amounting to 0.1–2.0 g efficiently collected from large volumes of Atlantic and Pacific surface waters have been analyzed for carbonate, opal, quartz and several natural and man-made radioisotopes.The concentrations of particles range between 10 and 600 μg/kg. In the equatorial regions particle concentrations are low and similar in both the oceans. At higher latitudes (>30°N or S), the Atlantic waters, however, have higher concentrations of particles compared to those in the Pacific. The latitudinal distribution exhibits a north-south symmetry with higher concentrations in the 30°–60° belt. Based on the particulate abundance for CaCO₃ and opal and their sedimentation, we have estimated their production and in-situ integrated dissolution rates for a few regions.Radioisotopes having different source functions, namely¹⁴C and²³⁹Pu injected due to nuclear weapon tests,²³⁴Th,²³⁰Th and²²⁸Th produced in-situ in seawater,²³²Th which derives primarily from land,²¹⁰Pb introduced via wet precipitations and²²⁶Ra introduced through diffusion from deep-sea sediments have been measured in the particulates. The relative enrichment factors for these nuclides in particles vary as Th ? Pu > Pb > Ra. The atmospheric bomb fallout pattern is discernible in the surface particulates; the²³⁹Pu concentration increases with latitude in both the hemispheres; however, the values are about a factor of two lower in the southern hemisphere.The distribution pattern of radioisotopes is found to be complex, even for²³⁴Th whose source function in the oceans is uniform. In view of the differences in the source functions it becomes possible to delineate the principal geochemical/geophysical processes which determine the concentrations of these nuclides in surface waters.     

Stochastic earthquake source model for ground motion simulation

In the analysis and design of important structures with relatively long life spans, there is a need to generate strong motion data for possible large events. The source of an earthquake is characterized by the spatial distribution of slip on the fault plane. For future events, this is unknown. In this paper, a stochastic earthquake source model is developed to address this issue. Here, 1D and 2D stochastic models for slip distribution developed by Lavallée et al.(2006) are used. The random field associated with the slip distribution is heavy-tailed stable distribution which can be used for large events. Using 236 past rupture models, the spectral scaling parameter and the four stable or Levy's parameters against empirical relationship for known quantities like magnitude or fault length are developed. The model is validated with data from 411 stations of 1999 Chi-Chi earthquake. The simulated response spectrum showed good agreement to actual data. Further the proposed model is used to generate ground motion for the 1993 Killari Earthquake where strong motion data is not available. The simulated mean peak ground velocity was in turn related to the intensity(MSK) and compared against values in the literature.     

Stochastic overland flows

A theoretical solution framework to the nonlinear stochastic partial differential equations (SPDE) of the kinematic wave and diffusion wave models of overland flows under stochastic inflows/outflows, stochastic surface roughness field and stochastic state of flows was obtained. This development was realized by means of an eigenfunction representation of the time-space overland flow depths, and by transforming the problem into the phase space. By using Van Kampen's lemma and the cumulant expansion theory of Kubo-Van Kampen-Fox, the deterministic partial differential equation (PDE) for the evolutionary probability density function (pdf) of overland flow depths was finally obtained. Once this deterministic PDE is solved for the time-varying pdf of overland flow depths, then the time-space varying pdf of overland flow depths can be obtained by a transformation given in the text. In this solution framework it is possible to incorporate the stochastic dynamic behavior of the parameters and of the forcing functions of the overland flow process. For example, not only the individual rainfall duration and fluctuating rain intensity characteristics but also the sequential behavior of rainfall patterns is incorporated into the evolutionary probability density function of overland flow depths.     

Stochastic analysis of effective rate constant for heterogeneous reactions

A probability density function (pdf) formulation is applied to a heterogeneous chemical reaction involving an aqueous solution reacting with a solid phase in a batch. This system is described by a stochastic differential equation with multiplicative noise. Both linear and nonlinear kinetic rate laws are considered. An effective rate constant for the mean field approximation describing the change in mean concentration with time is derived. The effective rate constant decreases with increasing time eventually approaching zero as the system approaches equilibrium. This behavior suggests that a possible explanation for the observed discrepancy between laboratory measured rate constants on uniform grain sizes and field measurements may in part be caused by the heterogeneous distribution of grain sizes in natural systems. This work was supported in part by the US Department of Energy under the DOE/BES Program in the Applied Mathematical Sciences, Contract KC-07-01-01, and the Environmental Management Science Program, Office of Biological and Environmental Research. This work made use of shared facilities supported by SAHRA (Sustainability of Semi-Arid Hydrology and Riparian Areas) under the STC Program of the National Science Foundation under agreement EAR-9876800. Los Alamos National Laboratory is operated by the University of California for the US Department of Energy under contact W-7405-ENG-36.     

Regularized Bayesian estimation for GEV-B-splines model

Large observed datasets are not stationary and/or depend on covariates, especially, in the case of extreme hydrometeorological variables. This causes the difficulty in estimation, using classical hydrological frequency analysis. A number of non-stationary models have been developed using linear or quadratic polynomial functions or B-splines functions to estimate the relationship between parameters and covariates. In this article, we propose regularised generalized extreme value model with B-splines (GEV-B-splines models) in a Bayesian framework to estimate quantiles. Regularisation is based on penalty and aims to favour parsimonious model especially in the case of large dimension space. Penalties are introduced in a Bayesian framework and the corresponding priors are detailed. Five penalties are considered and the corresponding priors are developed for comparison purpose as: Least absolute shrinkage and selection (Lasso and Ridge) and smoothing clipped absolute deviations (SCAD) methods (SCAD1, SCAD2 and SCAD3). Markov chain Monte Carlo (MCMC) algorithms have been developed for each model to estimate quantiles and their posterior distributions. Those approaches are tested and illustrated using simulated data with different sample sizes. A first simulation was made on polynomial B-splines functions in order to choose the most efficient model in terms of relative mean biais (RMB) and the relative mean-error (RME) criteria. A second simulation was performed with the SCAD1 penalty for sinusoidal dependence to illustrate the flexibility of the proposed approach. Results show clearly that the regularized approaches leads to a significant reduction of the bias and the mean square error, especially for small sample sizes (n < 100). A case study has been considered to model annual peak flows at Fort-Kent catchment with the total annual precipitations as covariates. The conditional quantile curves were given for the regularized and the maximum likelihood methods.