Use of unit response functions for management of regional multilayered aquifers: application to the North Aquitaine Tertiary system (France)

Although there are many numerical applications used in aquifer management, few methodologies seem to be sufficiently adapted to provide solutions for regional-scale problems. Their applications for multilayered aquifers are also too limited. A new groundwater management tool adapted to such large physical systems has been developed, using the unit response function (URF) approach. This tool is based on the link between a numerical groundwater flow model and a mathematical optimisation tool. Pre- and post processing are based on a geographical information system (GIS). The developed tool has been applied to a real management case—the regional Aquitaine multilayered aquifer (France). A representative hydrodynamic model was built using MODFLOW 2000 code. First tests show that the linearity condition needed for the application of URF methodology is respected despite the high complexity of the system. Two management scenarios were tested. Optimal solutions thus obtained allow for viable exploitation alternatives to be proposed, which integrate complex environmental constraints.

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Résumé Malgré un nombre important d’applications existant dans le domaine de la gestion des aquifères, peu de méthodologies semblent adaptées pour proposer des solutions à des problèmes réels de dimension régionale. Leurs application pour des systèmes multicouches sont souvent trop limitées. Un outil de gestion adapté à ces systèmes de large taille a été développé, basé sur la théorie des Fonctions de Réponses Unitaires (FRU). Cet outil est basé sur le couplage d’un modèle numérique d’écoulement et d’un code d’optimisation mathématique. Les entrées et sorties du modèle sont réalisées à l’aide d’un Système d’Information Géographique (SIG). L’outil développé est appliqué à un cas de gestion réel—le système aquifère régional multicouche aquitain (France). Un modèle hydrodynamique représentatif a été construit, basé sur le code MODFLOW 2000. Les premiers tests montrent que les conditions de linéarité nécessaires à l’application de la méthode FRU sont respectées, malgré l’importante complexité du système. Deux scénarii de gestion sont testés. Les solutions optimales ainsi obtenues permettent de proposer des solutions d’exploitation alternatives viables, intégrant des contraintes environnementales complexes.

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Resumen Aunque hay muchas aplicaciones numéricas usadas en la gestión de acuíferos, unas pocas metodologías parecen estar adaptadas suficientemente para dar las soluciones a los problemas de escala regional. También son limitadas sus aplicaciones para los acuíferos multicapa. Se ha desarrollado una nueva herramienta para el manejo del agua subterránea, adaptada a tales sistemas físicos grandes, usando el avance de la Función de Respuesta Unitaria (URF). Esta herramienta se basa en la combinación entre un modelo numérico de flujo de agua subterránea y una herramienta de optimización matemática. El pre-proceso y el post-proceso se basan en un Sistema de Información Geográfico (GIS). La herramienta desarrollada se ha aplicado a un caso real de manejo en el acuífero regional multicapa de Aquitania (Francia). Se construyó un modelo hidrodinámico representativo, que usó el código MODFLOW 2000. Las primeras pruebas muestran que la condición de linearidad, necesaria para la aplicación de la metodología URF, se respeta a pesar de la complejidad alta del sistema. Se probaron dos escenarios de manejo. Las soluciones óptimas así obtenidas permiten la proyección de alternativas viables de explotación, las cuales integran restricciones medioambientales complejas.

     

Optimisation of an idealised ocean model,stochastic parameterisation of sub-grid eddies

An optimisation scheme is developed to accurately represent the sub-grid scale forcing of a high dimensional chaotic ocean system. Using a simple parameterisation scheme, the velocity components of a 30 km resolution shallow water ocean model are optimised to have the same climatological mean and variance as that of a less viscous 7.5 km resolution model. The 5 day lag-covariance is also optimised, leading to a more accurate estimate of the high resolution response to forcing using the low resolution model.The system considered is an idealised barotropic double gyre that is chaotic at both resolutions. Using the optimisation scheme, we find and apply the constant in time, but spatially varying, forcing term that is equal to the time integrated forcing of the sub-grid scale eddies. A linear stochastic term, independent of the large-scale flow, with no spatial correlation but a spatially varying amplitude and time scale is used to represent the transient eddies. The climatological mean, variance and 5 day lag-covariance of the velocity from a single high resolution integration is used to provide an optimisation target. No other high resolution statistics are required. Additional programming effort, for example to build a tangent linear or adjoint model, is not required either.The focus of this paper is on the optimisation scheme and the accuracy of the optimised flow. However the forcing can provide insights in the design of deterministic and stochastic parameterisations. In the present study, we found that the stochastic parameterisation correcting the model variance is associated with the spatial pattern of eddy-decorrelation timescales rather than the spatial pattern of the amplitude of the variance. The method can be applied in future investigations into the physical processes that govern barotropic turbulence and it can perhaps be applied to help understand and correct biases in the mean and variance of a more realistic coarse or eddy-permitting ocean model. The method is complementary to current parameterisations and can be applied at the same time without modification.     

Parametric design of sailing hull shapes

The author presents an original algorithm aimed at automatically generating the hull shape of a sailing yacht starting from an initial set of parameters. The procedure consists of two steps. First one keel line and a Designed Water Line (DWL in the following) are faired according to a set of parameters, say length of water line, canoe body draft, stem angle and some adimensional coefficients. This information is then used to fair the hull surface, which must in turn fulfil more prerequisites (parameters like displaty cement, floatation area and related coefficients). The hull is defined by means of a B-spline surface, the fairing of which is ensured by allowing for all the imposed objectives and constraints. An optimisation technique based upon the gradient method ensures that a reliable solution is obtained in a very short time.     

Probabilistic reliability analysis of multiple slopes with genetic algorithms

Uncertainty estimation and consideration in engineering is an important practice to design reliable structures especially in geotechnics since the level of control with regards to the material parameters is relatively low. The definition of reliability indices to approximate the probability of failure allows for a better assessment of stability with fewer computations than using alternative methods. Nonetheless, yet an optimisation problem needs to be solved. In this work, a genetic algorithm is developed to solve this optimisation problem considering the limit equilibrium method to search for multiple critical failures. Study cases are presented to illustrate the capabilities of the method.     

Design optimisation of Propeller Boss Cap Fins for enhanced propeller performance

Economic pressures and regulatory requirements have brought about a great interest in improving ship propulsion efficiency. This can be exercised by installing Energy Saving Devices (ESD) such as Propeller Boss Cap Fins (PBCF). This paper demonstrates an approach for optimising PBCF by using Computational Fluid Dynamics (CFD) analysis. The conducted Reynolds-averaged Navier-Stokes (RANS) CFD open water model tests were validated by comparison with experimental data until the simulation was deemed satisfactory within the capabilities and limitations of the model. A design and optimisation procedure was defined to analyse the impact of ESDs on propeller efficiency and then used to evaluate the influence of alternative geometric parameters and locations of the PBCF on the hub. This analysis was done at full scale using high fidelity CFD-based RANS methods. Outcomes of the study include a design and optimisation process that can be used for the analysis of other ESDs on the market. The influences of various PBCF geometry were examined with optimal solutions presented for the analysis case. Results indicated a net energy efficiency improvement of 1.3% contributing to a substantial minimisation of cost and energy consumption. A reduction in the hub vortex was also clearly identified and presented.     

Calibration of an elasto-plastic constitutive model by a constrained optimisation procedure

The presented paper deals with a constrained optimisation technique for the calibration of elasto-plastic model parameters in a rational and objective manner. The procedure consists in finding a set of model parameters which minimise the difference between the experimental data and the numerical simulations defined by an objective function. For this purpose, an optimisation routine, termed ParaID, has been developed which combines the quasi-Newton and stochastic methods. The optimisation technique was employed to calibrate a multi-mechanism elasto-plastic constitutive model. Using the results of three isotropically consolidated drained triaxial compression tests, a comparison between numerical and experimental results clearly shows the capability of the optimisation procedure to determine the model parameters correctly.     

Optimisation of arrays of flap-type oscillating wave surge converters

In this paper a finite array of hinged flap-type wave energy converters are modelled using a mathematical approach. These are illustrative of the Oyster device of Aquamarine Power Ltd.¹ A novel semi-analytic solution method is presented for a set of boundary-value problems involving the scattering and radiation of waves by thin barriers used to model the device hydrodynamics. The approach makes use of the geometry to apply Fourier transforms, deriving non-singular integral equations in terms of the jumps in pressure across the flaps. These are then solved numerically using a highly efficient Galerkin expansion method. The focus of the results is on optimisation. We suggest optimal parameters for a single device, identifying flap length as crucial to device performance. This optimisation is then carried through to arrays with optimal arrangements and spacings being determined for a model sea state. Here, the lateral displacement of the devices emerges as a critical factor in optimal array configuration.     

Three‐dimensional potential field data inversion with L0 quasinorm sparse constraints

The quantitative explanation of the potential field data of three‐dimensional geological structures remains one of the most challenging issues in modern geophysical inversion. Obtaining a stable solution that can simultaneously resolve complicated geological structures is a critical inverse problem in the geophysics field. I have developed a new method for determining a three‐dimensional petrophysical property distribution, which produces a corresponding potential field anomaly. In contrast with the tradition inverse algorithm, my inversion method proposes a new model norm, which incorporates two important weighting functions. One is the L0 quasi norm (enforcing sparse constraints), and the other is depth‐weighting that counteracts the influence of source depth on the resulting potential field data of the solution. Sparseness constraints are imposed by using the L0 quasinorm on model parameters. To solve the representation problem, an L0 quasinorm minimisation model with different smooth approximations is proposed. Hence, the data space (N) method, which is much smaller than model space (M), combined with the gradient‐projected method, and the model space, combined with the modified Newton method for L0 quasinorm sparse constraints, leads to a computationally efficient method by using an N × N system versus an M × M one because N ? M. Tests on synthetic data and real datasets demonstrate the stability and validity of the L0 quasinorm spare norms inversion method. With the aim of obtaining the blocky results, the inversion method with the L0 quasinorm sparse constraints method performs better than the traditional L2 norm (standard Tikhonov regularisation). It can obtain the focus and sparse results easily. Then, the Bouguer anomaly survey data of the salt dome, offshore Louisiana, is considered as a real case study. The real inversion result shows that the inclusion the L0 quasinorm sparse constraints leads to a simpler and better resolved solution, and the density distribution is obtained in this area to reveal its geological structure. These results confirm the validity of the L0 quasinorm sparse constraints method and indicate its application for other potential field data inversions and the exploration of geological structures.     

A two‐phase automatic static correction method

Statics are an effective approach to correct for complex velocity variations in the near surface, but so far, to a large extent, a general and robust automatic static correction method is still lacking. In this paper, we propose a novel two‐phase automatic static correction method, which is capable of handling both primary wave statics (PP statics) and converted‐wave statics (S‐wave statics). Our method is purely data driven, and it aims at maximizing stacking power in the target zone of the stack image. Low‐frequency components of the data are analysed first using an advanced genetic algorithm to estimate seed statics and the time structure for an event of interest, and then the original full‐band data are further aligned via the back‐and‐forth coordinate descent method using the seed statics as initial values and the time structure for event alignment guidance. We apply our new method to two field datasets, i.e., one for 2D PP static correction and the other for 3D S‐wave static correction.     

Markov chain Monte Carlo (MCMC) sampling methods to determine optimal models,model resolution and model choice for Earth Science problems

We present an overview of Markov chain Monte Carlo, a sampling method for model inference and uncertainty quantification. We focus on the Bayesian approach to MCMC, which allows us to estimate the posterior distribution of model parameters, without needing to know the normalising constant in Bayes' theorem. Given an estimate of the posterior, we can then determine representative models (such as the expected model, and the maximum posterior probability model), the probability distributions for individual parameters, and the uncertainty about the predictions from these models. We also consider variable dimensional problems in which the number of model parameters is unknown and needs to be inferred. Such problems can be addressed with reversible jump (RJ) MCMC. This leads us to model choice, where we may want to discriminate between models or theories of differing complexity. For problems where the models are hierarchical (e.g. similar structure but with a different number of parameters), the Bayesian approach naturally selects the simpler models. More complex problems require an estimate of the normalising constant in Bayes' theorem (also known as the evidence) and this is difficult to do reliably for high dimensional problems. We illustrate the applications of RJMCMC with 3 examples from our earlier working involving modelling distributions of geochronological age data, inference of sea-level and sediment supply histories from 2D stratigraphic cross-sections, and identification of spatially discontinuous thermal histories from a suite of apatite fission track samples distributed in 3D.