Use of high-resolution geophysical data to characterize heterogeneous aquifers: influence of data integration method on hydrological predictions

The integration of geophysical data into the subsurface characterization problem has been shown in many cases to significantly improve hydrological knowledge by providing information at spatial scales and locations that is unattainable using conventional hydrological measurement techniques. The investigation of exactly how much benefit can be brought by geophysical data in terms of its effect on hydrological predictions, however, has received considerably less attention in the literature. Here, we examine the potential hydrological benefits brought by a recently introduced simulated annealing (SA) conditional stochastic simulation method designed for the assimilation of diverse hydrogeophysical data sets. We consider the specific case of integrating crosshole ground-penetrating radar (GPR) and borehole porosity log data to characterize the porosity distribution in saturated heterogeneous aquifers. In many cases, porosity is linked to hydraulic conductivity and thus to flow and transport behavior. To perform our evaluation, we first generate a number of synthetic porosity fields exhibiting varying degrees of spatial continuity and structural complexity. Next, we simulate the collection of crosshole GPR data between several boreholes in these fields, and the collection of porosity log data at the borehole locations. The inverted GPR data, together with the porosity logs, are then used to reconstruct the porosity field using the SA-based method, along with a number of other more elementary approaches. Assuming that the grid-cell-scale relationship between porosity and hydraulic conductivity is unique and known, the porosity realizations are then used in groundwater flow and contaminant transport simulations to assess the benefits and limitations of the different approaches.

DNA-DNA interactions in bacteriophage capsids are responsible for the observed DNA knotting.

Recent experiments showed that the linear double-stranded DNA in bacteriophage capsids is both highly knotted and neatly structured. What is the physical basis of this organization? Here we show evidence from stochastic simulation techniques that suggests that a key element is the tendency of contacting DNA strands to order, as in cholesteric liquid crystals. This interaction favors their preferential juxtaposition at a small twist angle, thus promoting an approximately nematic (and apolar) local order. The ordering effect dramatically impacts the geometry and topology of DNA inside phages. Accounting for this local potential allows us to reproduce the main experimental data on DNA organization in phages, including the cryo-EM observations and detailed features of the spectrum of DNA knots formed inside viral capsids. The DNA knots we observe are strongly delocalized and, intriguingly, this is shown not to interfere with genome ejection out of the phage.

Quantitative integration of high-resolution hydrogeophysical data through Monte-Carlo-type conditional simulations

Geophysical techniques can help to bridge the inherent gap with regard to spatial resolution and the range of coverage that plagues classical hydrological methods. This has lead to the emergence of the new and rapidly growing field of hydrogeophysics. Given the differing sensitivities of various geophysical techniques to hydrologically relevant parameters and their inherent trade-off between resolution and range the fundamental usefulness of multi-method hydrogeophysical surveys for reducing uncertainties in data analysis and interpretation is widely accepted. A major challenge arising from such endeavors is the quantitative integration of the resulting vast and diverse database in order to obtain a unified model of the probed subsurface region that is internally consistent with all available data. To address this problem, we have developed a strategy towards hydrogeophysical data integration based on Monte-Carlo-type conditional stochastic simulation that we consider to be particularly suitable for local-scale studies characterized by high-resolution and high-quality datasets. Monte-Carlo-based optimization techniques are flexible and versatile, allow for accounting for a wide variety of data and constraints of differing resolution and hardness and thus have the potential of providing, in a geostatistical sense, highly detailed and realistic models of the pertinent target parameter distributions. Compared to more conventional approaches of this kind, our approach provides significant advancements in the way that the larger-scale deterministic information resolved by the hydrogeophysical data can be accounted for, which represents an inherently problematic, and as of yet unresolved, aspect of Monte-Carlo-type conditional simulation techniques. We present the results of applying our algorithm to the integration of porosity log and tomographic crosshole georadar data to generate stochastic realizations of the local-scale porosity structure. Our procedure is first tested on pertinent synthetic data and then applied to corresponding field data collected at the Boise Hydrogeophysical Research Site near Boise, Idaho, USA.

The contribution of patch topology and demographic parameters to PVA predictions: the case of the European tree frog

Population viability analyses (PVA) are increasingly used in metapopulation conservation plans. Two major types of models are commonly used to assess vulnerability and to rank management options: population-based stochastic simulation models (PSM such as RAMAS or VORTEX) and stochastic patch occupancy models (SPOM). While the first set of models relies on explicit intrapatch dynamics and interpatch dispersal to predict population levels in space and time, the latter is based on spatially explicit metapopulation theory where the probability of patch occupation is predicted given the patch area and isolation (patch topology). We applied both approaches to a European tree frog (Hyla arborea) metapopulation in western Switzerland in order to evaluate the concordances of both models and their applications to conservation. Although some quantitative discrepancies appeared in terms of network occupancy and equilibrium population size, the two approaches were largely concordant regarding the ranking of patch values and sensitivities to parameters, which is encouraging given the differences in the underlying paradigms and input data.

The population genetics of clonal and partially clonal diploids.

The consequences of variable rates of clonal reproduction on the population genetics of neutral markers are explored in diploid organisms within a subdivided population (island model). We use both analytical and stochastic simulation approaches. High rates of clonal reproduction will positively affect heterozygosity. As a consequence, nearly twice as many alleles per locus can be maintained and population differentiation estimated as F(ST) value is strongly decreased in purely clonal populations as compared to purely sexual ones. With increasing clonal reproduction, effective population size first slowly increases and then points toward extreme values when the reproductive system tends toward strict clonality. This reflects the fact that polymorphism is protected within individuals due to fixed heterozygosity. Contrarily, genotypic diversity smoothly decreases with increasing rates of clonal reproduction. Asexual populations thus maintain higher genetic diversity at each single locus but a lower number of different genotypes. Mixed clonal/sexual reproduction is nearly indistinguishable from strict sexual reproduction as long as the proportion of clonal reproduction is not strongly predominant for all quantities investigated, except for genotypic diversities (both at individual loci and over multiple loci).

Ruin Theory with Excess of Loss Reinsurance and Reinstatements

The present paper studies the probability of ruin of an insurer, if excess of loss reinsurance with reinstatements is applied. In the setting of the classical Cramer-Lundberg risk model, piecewise deterministic Markov processes are used to describe the free surplus process in this more general situation. It is shown that the finite-time ruin probability is both the solution of a partial integro-differential equation and the fixed point of a contractive integral operator. We exploit the latter representation to develop and implement a recursive algorithm for numerical approximation of the ruin probability that involves high-dimensional integration. Furthermore we study the behavior of the finite-time ruin probability under various levels of initial surplus and security loadings and compare the efficiency of the numerical algorithm with the computational alternative of stochastic simulation of the risk process. (C) 2011 Elsevier Inc. All rights reserved.

quantiNemo: an individual-based program to simulate quantitative traits with explicit genetic architecture in a dynamic metapopulation.

quantiNemo is an individual-based, genetically explicit stochastic simulation program. It was developed to investigate the effects of selection, mutation, recombination and drift on quantitative traits with varying architectures in structured populations connected by migration and located in a heterogeneous habitat. quantiNemo is highly flexible at various levels: population, selection, trait(s) architecture, genetic map for QTL and/or markers, environment, demography, mating system, etc. quantiNemo is coded in C++ using an object-oriented approach and runs on any computer platform. Availability: Executables for several platforms, user's manual, and source code are freely available under the GNU General Public License at http://www2.unil.ch/popgen/softwares/quantinemo.

Environmental data mining and modeling based on machine learning algorithms and geostatistics

The paper presents some contemporary approaches to spatial environmental data analysis. The main topics are concentrated on the decision-oriented problems of environmental spatial data mining and modeling: valorization and representativity of data with the help of exploratory data analysis, spatial predictions, probabilistic and risk mapping, development and application of conditional stochastic simulation models. The innovative part of the paper presents integrated/hybrid model-machine learning (ML) residuals sequential simulations-MLRSS. The models are based on multilayer perceptron and support vector regression ML algorithms used for modeling long-range spatial trends and sequential simulations of the residuals. NIL algorithms deliver non-linear solution for the spatial non-stationary problems, which are difficult for geostatistical approach. Geostatistical tools (variography) are used to characterize performance of ML algorithms, by analyzing quality and quantity of the spatially structured information extracted from data with ML algorithms. Sequential simulations provide efficient assessment of uncertainty and spatial variability. Case study from the Chernobyl fallouts illustrates the performance of the proposed model. It is shown that probability mapping, provided by the combination of ML data driven and geostatistical model based approaches, can be efficiently used in decision-making process. (C) 2003 Elsevier Ltd. All rights reserved.

Interacting populations in heterogeneous environments

To optimally manage a metapopulation, managers and conservation biologists can favor a type of habitat spatial distribution (e.g. aggregated or random). However, the spatial distribution that provides the highest habitat occupancy remains ambiguous and numerous contradictory results exist. Habitat occupancy depends on the balance between local extinction and colonization. Thus, the issue becomes even more puzzling when various forms of relationships - positive or negative co-variation - between local extinction and colonization rate within habitat types exist. Using an analytical model we demonstrate first that the habitat occupancy of a metapopulation is significantly affected by the presence of habitat types that display different extinction-colonization dynamics, considering: (i) variation in extinction or colonization rate and (ii) positive and negative co-variation between the two processes within habitat types. We consequently examine, with a spatially explicit stochastic simulation model, how different degrees of habitat aggregation affect occupancy predictions under similar scenarios. An aggregated distribution of habitat types provides the highest habitat occupancy when local extinction risk is spatially heterogeneous and high in some places, while a random distribution of habitat provides the highest habitat occupancy when colonization rates are high. Because spatial variability in local extinction rates always favors aggregation of habitats, we only need to know about spatial variability in colonization rates to determine whether aggregating habitat types increases, or not, metapopulation occupancy. From a comparison of the results obtained with the analytical and with the spatial-explicit stochastic simulation model we determine the conditions under which a simple metapopulation model closely matches the results of a more complex spatial simulation model with explicit heterogeneity.

Coev-web: a web platform designed to simulate and evaluate coevolving positions along a phylogenetic tree.

BACKGROUND: Available methods to simulate nucleotide or amino acid data typically use Markov models to simulate each position independently. These approaches are not appropriate to assess the performance of combinatorial and probabilistic methods that look for coevolving positions in nucleotide or amino acid sequences. RESULTS: We have developed a web-based platform that gives a user-friendly access to two phylogenetic-based methods implementing the Coev model: the evaluation of coevolving scores and the simulation of coevolving positions. We have also extended the capabilities of the Coev model to allow for the generalization of the alphabet used in the Markov model, which can now analyse both nucleotide and amino acid data sets. The simulation of coevolving positions is novel and builds upon the developments of the Coev model. It allows user to simulate pairs of dependent nucleotide or amino acid positions. CONCLUSIONS: The main focus of our paper is the new simulation method we present for coevolving positions. The implementation of this method is embedded within the web platform Coev-web that is freely accessible at http://coev.vital-it.ch/, and was tested in most modern web browsers.

A pseudo-spectral method for the simulation of poro-elastic seismic wave propagation in 2D polar coordinates using domain decomposition

We present a novel numerical approach for the comprehensive, flexible, and accurate simulation of poro-elastic wave propagation in 2D polar coordinates. An important application of this method and its extensions will be the modeling of complex seismic wave phenomena in fluid-filled boreholes, which represents a major, and as of yet largely unresolved, computational problem in exploration geophysics. In view of this, we consider a numerical mesh, which can be arbitrarily heterogeneous, consisting of two or more concentric rings representing the fluid in the center and the surrounding porous medium. The spatial discretization is based on a Chebyshev expansion in the radial direction and a Fourier expansion in the azimuthal direction and a Runge-Kutta integration scheme for the time evolution. A domain decomposition method is used to match the fluid-solid boundary conditions based on the method of characteristics. This multi-domain approach allows for significant reductions of the number of grid points in the azimuthal direction for the inner grid domain and thus for corresponding increases of the time step and enhancements of computational efficiency. The viability and accuracy of the proposed method has been rigorously tested and verified through comparisons with analytical solutions as well as with the results obtained with a corresponding, previously published, and independently bench-marked solution for 2D Cartesian coordinates. Finally, the proposed numerical solution also satisfies the reciprocity theorem, which indicates that the inherent singularity associated with the origin of the polar coordinate system is adequately handled.

On the problematic of reserving and stochastic loss models

Abstract Traditionally, the common reserving methods used by the non-life actuaries are based on the assumption that future claims are going to behave in the same way as they did in the past. There are two main sources of variability in the processus of development of the claims: the variability of the speed with which the claims are settled and the variability between the severity of the claims from different accident years. High changes in these processes will generate distortions in the estimation of the claims reserves. The main objective of this thesis is to provide an indicator which firstly identifies and quantifies these two influences and secondly to determine which model is adequate for a specific situation. Two stochastic models were analysed and the predictive distributions of the future claims were obtained. The main advantage of the stochastic models is that they provide measures of variability of the reserves estimates. The first model (PDM) combines one conjugate family Dirichlet - Multinomial with the Poisson distribution. The second model (NBDM) improves the first one by combining two conjugate families Poisson -Gamma (for distribution of the ultimate amounts) and Dirichlet Multinomial (for distribution of the incremental claims payments). It was found that the second model allows to find the speed variability in the reporting process and development of the claims severity as function of two above mentioned distributions' parameters. These are the shape parameter of the Gamma distribution and the Dirichlet parameter. Depending on the relation between them we can decide on the adequacy of the claims reserve estimation method. The parameters have been estimated by the Methods of Moments and Maximum Likelihood. The results were tested using chosen simulation data and then using real data originating from the three lines of business: Property/Casualty, General Liability, and Accident Insurance. These data include different developments and specificities. The outcome of the thesis shows that when the Dirichlet parameter is greater than the shape parameter of the Gamma, resulting in a model with positive correlation between the past and future claims payments, suggests the Chain-Ladder method as appropriate for the claims reserve estimation. In terms of claims reserves, if the cumulated payments are high the positive correlation will imply high expectations for the future payments resulting in high claims reserves estimates. The negative correlation appears when the Dirichlet parameter is lower than the shape parameter of the Gamma, meaning low expected future payments for the same high observed cumulated payments. This corresponds to the situation when claims are reported rapidly and fewer claims remain expected subsequently. The extreme case appears in the situation when all claims are reported at the same time leading to expectations for the future payments of zero or equal to the aggregated amount of the ultimate paid claims. For this latter case, the Chain-Ladder is not recommended.

Integration of local-scale hydrological and regional-scale geophysical based on a nonlinear Bayesian sequential simulation approach

Significant progress has been made with regard to the quantitative integration of geophysical and hydrological data at the local scale. However, extending the corresponding approaches to the regional scale represents a major, and as-of-yet largely unresolved, challenge. To address this problem, we have developed a downscaling procedure based on a non-linear Bayesian sequential simulation approach. The basic objective of this algorithm is to estimate the value of the sparsely sampled hydraulic conductivity at non-sampled locations based on its relation to the electrical conductivity, which is available throughout the model space. The in situ relationship between the hydraulic and electrical conductivities is described through a non-parametric multivariate kernel density function. This method is then applied to the stochastic integration of low-resolution, re- gional-scale electrical resistivity tomography (ERT) data in combination with high-resolution, local-scale downhole measurements of the hydraulic and electrical conductivities. Finally, the overall viability of this downscaling approach is tested and verified by performing and comparing flow and transport simulation through the original and the downscaled hydraulic conductivity fields. Our results indicate that the proposed procedure does indeed allow for obtaining remarkably faithful estimates of the regional-scale hydraulic conductivity structure and correspondingly reliable predictions of the transport characteristics over relatively long distances.

Simulated-annealing-based conditional simulation for the local-scale characterization of heterogeneous aquifers

Simulated-annealing-based conditional simulations provide a flexible means of quantitatively integrating diverse types of subsurface data. Although such techniques are being increasingly used in hydrocarbon reservoir characterization studies, their potential in environmental, engineering and hydrological investigations is still largely unexploited. Here, we introduce a novel simulated annealing (SA) algorithm geared towards the integration of high-resolution geophysical and hydrological data which, compared to more conventional approaches, provides significant advancements in the way that large-scale structural information in the geophysical data is accounted for. Model perturbations in the annealing procedure are made by drawing from a probability distribution for the target parameter conditioned to the geophysical data. This is the only place where geophysical information is utilized in our algorithm, which is in marked contrast to other approaches where model perturbations are made through the swapping of values in the simulation grid and agreement with soft data is enforced through a correlation coefficient constraint. Another major feature of our algorithm is the way in which available geostatistical information is utilized. Instead of constraining realizations to match a parametric target covariance model over a wide range of spatial lags, we constrain the realizations only at smaller lags where the available geophysical data cannot provide enough information. Thus we allow the larger-scale subsurface features resolved by the geophysical data to have much more due control on the output realizations. Further, since the only component of the SA objective function required in our approach is a covariance constraint at small lags, our method has improved convergence and computational efficiency over more traditional methods. Here, we present the results of applying our algorithm to the integration of porosity log and tomographic crosshole georadar data to generate stochastic realizations of the local-scale porosity structure. Our procedure is first tested on a synthetic data set, and then applied to data collected at the Boise Hydrogeophysical Research Site.