Advertisement

Hydrogeology Journal

, Volume 23, Issue 5, pp 883–900 | Cite as

Integrating aerial geophysical data in multiple-point statistics simulations to assist groundwater flow models

  • Neil E. M. DicksonEmail author
  • Jean-Christophe Comte
  • Philippe Renard
  • Julien A. Straubhaar
  • Jennifer M. McKinley
  • Ulrich Ofterdinger
Paper

Abstract

The process of accounting for heterogeneity has made significant advances in statistical research, primarily in the framework of stochastic analysis and the development of multiple-point statistics (MPS). Among MPS techniques, the direct sampling (DS) method is tested to determine its ability to delineate heterogeneity from aerial magnetics data in a regional sandstone aquifer intruded by low-permeability volcanic dykes in Northern Ireland, UK. The use of two two-dimensional bivariate training images aids in creating spatial probability distributions of heterogeneities of hydrogeological interest, despite relatively ‘noisy’ magnetics data (i.e. including hydrogeologically irrelevant urban noise and regional geologic effects). These distributions are incorporated into a hierarchy system where previously published density function and upscaling methods are applied to derive regional distributions of equivalent hydraulic conductivity tensor K. Several K models, as determined by several stochastic realisations of MPS dyke locations, are computed within groundwater flow models and evaluated by comparing modelled heads with field observations. Results show a significant improvement in model calibration when compared to a simplistic homogeneous and isotropic aquifer model that does not account for the dyke occurrence evidenced by airborne magnetic data. The best model is obtained when normal and reverse polarity dykes are computed separately within MPS simulations and when a probability threshold of 0.7 is applied. The presented stochastic approach also provides improvement when compared to a previously published deterministic anisotropic model based on the unprocessed (i.e. noisy) airborne magnetics. This demonstrates the potential of coupling MPS to airborne geophysical data for regional groundwater modelling.

Keywords

Aerial magnetics Multiple-point statistics Heterogeneity Groundwater flow UK 

Intégration de données géophysiques aéroportées dans des simulations statistiques à points multiples pour aider à la réalisation de modèles d’écoulement d’eaux souterraines

Résumé

Le processus de prise en compte de l’hétérogénéité a fait des progrès considérables dans le domaine de la recherche en statistique, principalement dans le cadre de l’analyse stochastique et le développement de statistiques à points multiples (MPS). Parmi les techniques MPS, la méthode d’échantillonnage direct (DS) est testée pour déterminer sa capacité à délimiter les hétérogénéités à partir de données géophysiques magnétiques aéroportées dans un aquifère régional gréseux intersecté par des dykes volcaniques de faible conductivité hydraulique dans le Nord de l’Irlande (Royaume Uni). L’utilisation de deux images d’apprentissage bidimensionnelles et à deux variables aide à la création de distributions spatiales probabilistes d’hétérogénéités d’intérêt hydrogéologique, malgré des données magnétiques relativement bruitées (par du bruit urbain hydrogéologique et par des effets géologiques régionaux). Ces distributions sont intégrées dans un système hiérarchisé au sein duquel une fonction de densité et des méthodes de changement d’échelle préalablement publiéessont appliquées pour déterminer les distributions régionales du tenseur de conductivité hydraulique équivalent K. Plusieurs modèles K, déterminés par plusieurs réalisations stochastiques de MPS sur des localisations de dykes, sont appliqués dans des modèles d’écoulements d’eaux souterraines et évalués en comparant les charges hydrauliques modélisées avec les observations de terrain. Les résultats montrent une amélioration significative de la calibration du modèle par rapport à un modèle d’un aquifère homogène simpliste et isotrope qui ne prend pas en considération l’occurrence des dykes mis en évidence par les données magnétiques aéroportées. Le meilleur modèle est obtenu lorsque les dykes de polarité normale et inversée sont pris en compte séparément avec des simulations MPS et quand un filtre de probabilité d’une valeur de 0.7 est appliqué. Cette approche stochastique présentée fournit également une amélioration lorsqu’elle est comparée à un modèle déterministe anisotrope publié précédemment, basé sur des données magnétiques aéroportées non traitées (c’est-à-dire bruitées). Cela démontre le potentiel du couplage de la méthode MPS à des données géophysiques aéroportées pour la modélisation hydrogéologique régionale.

Integración de datos geofísicos aéreos en simulaciones estadísticas de múltiples puntos para ayudar a los modelos de flujo de agua subterránea

Resumen

El proceso para explicar la heterxogeneidad ha logrado avances significativos en la investigación estadística, primariamente en el marco del análisis estocástico y el desarrollo de la estadística de múltiples puntos (MPS). Entre las técnicas de MPS, se probó el método de muestreo directo (DS) para determinar su habilidad para delinear la heterogeneidad a partir de datos magnéticos aéreos en un acuífero regional de areniscas instruido por diques volcánicos de baja permeabilidad en Irlanda del Norte, Reino Unido. El uso de dos imágenes de entrenamiento bidimensionales bivariadas ayuda para crear una distribución de probabilidad espacial de heterogeneidades de interés hidrogeológico, a pesar de los datos magnéticos relativamente ‘ruidosos’ (es decir que incluye el ruido urbano hidrogeológicamente irrelevante y efectos geológicos regionales). Estas distribuciones son incorporadas en un sistema jerárquico donde se aplican las funciones de densidad previamente publicadas de métodos de generalización de la escala para deducir las distribuciones regionales del tensor equivalente de conductividad hidráulica K. Se calculan varios modelos de K, según lo determinado por varias realizaciones estocásticas de ubicaciones de diques MPS, dentro de los modelos de flujo de agua subterránea y se evalúan comparando las cargas hidráulicas modeladas con observaciones de campo. Los resultados muestran una mejora significativa en la calibración del modelo cuando se los compara con modelos simples de un acuífero isotrópico y homogéneo que no tienen en cuenta la ocurrencia de diques evidenciados por los datos magnéticos aéreos. El mejor modelo se obtiene cuando las polaridades normal e inversa de los diques son calculadas separadamente dentro de las simulaciones MPS y cuando se aplica un umbral de probabilidad de 0.7. La aproximación estocástica presentada también proporciona mejoras cuando se la compara con un modelo anisotrópico determinístico previamente publicado basado en datos magnéticos aéreos no procesados (es decir ruidosos). Esto demuestra el potencial de acoplar MPS a datos geofísicos aéreos para el modelado regional de agua subterránea.

整合多点统计学模拟中航空地球物理资料以支撑地下水流模型

摘要

在统计研究中,主要在随机分析和多点统计学开发框架内,论述非均质性的过程取得了重要进展。在多点统计学技术中,检测了直接采样法,以确定其根据英国北爱尔兰一个受到低透水性火山岩脉入侵的区域砂岩含水层航空磁测数据描述非均质性的能力。尽管磁性资料相当“嘈杂”(即包括与水文地质方面无关的城市噪音和区域地质影响),但两个二维二变量训练图像的使用为创建水文地质方面的非均质性空间概率分布提供了帮助。这些分布数据整合到一个分级体系中,在这个分级系统中,应用过去刊出的密度函数法和升级法导出等同的水力传导率张量K的区域分布。由多点统计学几个随机完成的岩脉位置确定的几个K模型在地下水流模型内进行了计算,并通过对比模拟的水头和室外观测结果进行了评价。结果显示,与没有解释航空磁性资料已证明的岩脉赋存的、过分简单的均质和各相同性含水层模型相比,模型校正有很大的改进。在多点统计学模拟内分别计算正反极岩脉时,并且概率阈值设定为0.7时,获得了最好的模型。与过去刊出的基于未处理的(即嘈杂的)航空磁性、确定性的各相向性的模型相比,所论述的随机方法也进行了改进。这展示了多点统计学与航空地球物理资料相结合进行区域地下水模拟的潜力。

Integrando dados geofísicos aéreos em simulações estatísticas multi-ponto para auxiliar modelos de fluxo de águas subterrâneas

Resumo

O processo de explicar a heterogeneidade teve avanço significativo na pesquisa estatística, primeiramente no âmbito da análise estocástica e desenvolvimento da estatística multi-ponto (EMP). Em meio às técnicas de EMP, o método de amostragem direta (AD) é testado para determinar sua habilidade em delinear heterogeneidade de dados magnéticos aéreos em um aquífero sedimentar regional com intrusão de diques vulcânicos de baixa permeabilidade na Irlanda do Norte, Reino Unido. O uso de duas imagens bidimensionais de treinamento bivariantes auxilia na criação de distribuições espaciais de probabilidade das heterogeneidades de interesse hidrogeológico, apesar do relativo ruído dos dados magnéticos (p. ex., incluindo ruídos urbanos hidrogeologicamente irrelevantes e efeitos geológicos regionais). Essas distribuições são incorporadas à um sistema hierárquico onde funções de densidade previamente publicadas e métodos de aumento de escala são aplicados para derivar distribuições regionais do tensor K de condutividade hidráulica equivalente. Diversos modelos K, como determinados pelas diversas realizações estocásticas de EMP dos locais de diques, são computados em modelos de fluxo de águas subterrâneas e avaliados pela comparação de cargas modeladas com observações de campo. Os resultados demonstram uma significativa melhora na calibração do modelo quando comparado à um modelo de aquífero simplistamente homogêneo e isotrópico que não considera a ocorrência de diques evidenciados nos dados magnéticos aerotransportados. O melhor modelo é obtido quando as polaridades normais e reversas dos diques são computadas separadamente nas simulações EMP e quando um limite de probabilidade de 0.7 é aplicado. A presente abordagem estocástica também proporcionou melhora quando comparada ao modelo determinístico anisotrópico publicado previamente, baseado em dados magnéticos aerotransportados não processados (ou seja, com ruídos). Isso demonstra o potencial da integração de EMP aos dados geofísicos aerotransportados para modelagem regional das águas subterrâneas.

Notes

Acknowledgements

Neil Dickson was funded through a PhD studentship in Queen’s University, Belfast, from the Northern Irish Department of Education and Learning (DEL). We acknowledge two anonymous reviewers as well as the associate editor A. McDonald and the editor E. Screaton for valuable comments that contributed to improving the final manuscript.

References

  1. Abdollahifard MJ, Faez K (2014) Fast direct sampling for multiple-point stochastic simulation. Arab J Geosci 7:1927–1939. doi: 10.1007/s12517-013-0850-4 CrossRefGoogle Scholar
  2. Allard D, Comunian A, Renard P (2012) Probability aggregation methods in geoscience. Math Geosci 44(5):545–581. doi: 10.1007/s11004-012-9396-3 CrossRefGoogle Scholar
  3. Anderson MP (1997) Characterization of geological heterogeneity. In: Dagan G, Neuman SP (eds) Subsurface flow and transport: a stochastic approach. Cambridge University Press, New York, pp 23–43CrossRefGoogle Scholar
  4. Andersen TR, Poulsen SE, Christensen S, Jørgensen F (2013) A synthetic study of geophysics-based modelling of groundwater flow in catchments with a buried valley. Hydrogeol J 21:491–503. doi: 10.1007/s10040-012-0924-5 CrossRefGoogle Scholar
  5. Bennett JRP (1976) The Lagan Valley: hydrogeological study. Open File Report 57, Geological Survey of Northern Ireland, BelfastGoogle Scholar
  6. Betts NL (1982) Synoptic climatology of Northern Ireland, chapter 1. In: Cruickshank JG, Wilcox DN (eds) Northern Ireland: environment and natural resources. The Queen’s University of Belfast, University Road, Belfast, Northern Ireland, pp 9–42Google Scholar
  7. Blouin M, Martel R, Gloaguen E (2013) Accounting for aquifer heterogeneity from geological data to management tools. Groundwater 51(3):421–431. doi: 10.1111/j.1745-6584.2012.00982.x Google Scholar
  8. Brunner P, Hendricks Franssen H-J, Kgotlhang L, Bauer-Gottwein P, Kinzelbach W (2007) How can remote sensing contribute in groundwater modelling? Hydrogeol J 15:5–18. doi: 10.1007/s10040-006-0127-z CrossRefGoogle Scholar
  9. Burns C, Comte J-C, Gaffney L, Ofterdinger U, Young M (2010) Characterization of the effect of dyke swarms on groundwater flow in a sedimentary coastal aquifer by combined geophysical and hydrogeological modelling.P paper presented at American Geophysical Union, Fall Meeting 2010, San Francisco, Abstract no. H11E-0842, AGU, Washington, DCGoogle Scholar
  10. Caers J, Strebelle S, Payrazyan K (2003) Stochastic integration of seismic data and geologic scenarios: a West Africa submarine channel saga. Lead Edge 22(3):192–196CrossRefGoogle Scholar
  11. Cardwell WT, Parsons RL (1945) Average permeabilities of heterogeneous oil sands. Trans Am Inst Min Metall Pet Eng 160(1):34–42. doi: 10.2118/945034-G Google Scholar
  12. Chacksfield BC (2010) A preliminary interpretation of Tellus airborne magnetic and electromagnetic data for Northern Ireland, British Geological Survey Internal Report, IR/07/041, BGS, Nottingham, UK, 51 ppGoogle Scholar
  13. Chen Y, Durlofsky LJ, Gerritsen M, Weh XH (2003) A coupled local-global upscaling approach for simulating flow in highly heterogeneous formations. Adv Water Resour 26:1041–1060. doi: 10.1016/S0309-1708(03)00101-5 CrossRefGoogle Scholar
  14. Comte J-C, Ofterdinger U, Wilson C, Burns C (2012) Role hydrogéologique des dykes volcaniques au sein de l’aquifère cotier des grès de Belfast (Irlande du Nord) et implications pour la gestion de la resource [Hydrogeological role of volcanic dykes in the coastal sandstone aquifer of Belfast (Northern Ireland) and implications for the management of resources]. Paper presented at the Dix-huitièmes journées techniques du Comité Francais d’Hydrogéologie de l’Association Internationale des Hydrogéologues, Ressources et gestion des aquifères littoraux, Cassis, France, March 2012Google Scholar
  15. Comunian A, Renard P, Straubhaar J, Bayer P (2011) Three-dimensional high resolution fluvio-glacial aquifer analog, part 2: geostatistical modeling. J Hydrol 405:10–23. doi: 10.1016/j.jhydrol.2011.03.037 CrossRefGoogle Scholar
  16. Comunian A, Renard P, Straubhaar J (2012) 3D multiple-point statistics simulation using 2D training images. Comput Geosci 40:49–65. doi: 10.1016/j.cageo.2011.07.009 CrossRefGoogle Scholar
  17. Cooper MR, Anderson H, Walsh JJ, Van Dam CL, Young ME, Earls G, Walker A (2012) Palaoegene Alpine tectonics and Icelandic plume-related magmatism and deformation in Northern Ireland. J Geol Soc Lond 169:29–36. doi: 10.1144/0016-76492010-182 CrossRefGoogle Scholar
  18. Cordua KS, Hansen TM, Mosegaard K (2012) Monte Carlo full-waveform inversion of crosshole GPR data using multiple-point geostatistical a priori information. Geophysics 77(2):H19–H31. doi: 10.1190/geo2011-0170.1 CrossRefGoogle Scholar
  19. Cronin AA, Elliot T, Yang Y, Kalin RM (2000) Geochemical modelling and isotope studies in the Sherwood Sandstone Aquifer, Lagan Valley, Northern Ireland. In: Dassargues A (ed) Tracers and modelling in hydrogeology. IAHS, Oxfordshire, UK, pp 425–432Google Scholar
  20. Cronin AA, Barth JAC, Elliot T, Kalin RM (2005) Recharge velocity and geochemical evolution for the Permo-Triassic Sherwood Sandstone, Northern Ireland. J Hydrol 315:308–324. doi: 10.1016/j.jhydrol.2005.04.016 CrossRefGoogle Scholar
  21. de Laco S, Maggio S (2011) Validation techniques for geological patterns simulations based on variogram and multiple-point statistics. Math Geosci 43:483–500. doi: 10.1007/s11004-011-9326-9 CrossRefGoogle Scholar
  22. de Marsily G (1986) Quantitative hydrogeology: groundwater hydrology for engineers. Academic, LondonGoogle Scholar
  23. de Marsily G, Delay F, Teles V, Schafmeister MT (1998) Some current methods to represent the heterogeneity of natural media in hydrogeology. Hydrogeol J 6:115–130CrossRefGoogle Scholar
  24. de Marsily G, Delay F, Gonçalvès J, Renard P, Teles V, Violette S (2005) Dealing with spatial heterogeneity. Hydrogeol J 13:161–183. doi: 10.1007/s10040-004-0432-3 CrossRefGoogle Scholar
  25. de Vries LM, Carrera J, Falivene O, Gratacós O, Slooten LJ (2009) Application of multiple point geostatistics to non-stationary images. Math Geosci 41:29–42. doi: 10.1007/s11004-008-9188-y CrossRefGoogle Scholar
  26. Delhomme JP (1978) Kriging in the hydrosciences. Adv Water Resour 1(5):251–266. doi: 10.1016/0309-1708(78)90039-8 CrossRefGoogle Scholar
  27. Delhomme JP (1979) Spatial variability and uncertainty in groundwater flow parameters: a geostatistical approach. Water Resour Res 15(2):269–280. doi: 10.1029/WR015i002p00269 CrossRefGoogle Scholar
  28. Dewandel B, Maréchal JC, Bour O, Ladouche B, Ahmed S, Chandra S, Pauwels H (2012) Upscaling and regionalizing K and effective porosity at watershed scale in deeply weathered crystalline aquifers. J Hydrol 416–417:83–97. doi: 10.1016/j.jhydrol.2011.11.038 CrossRefGoogle Scholar
  29. Dickson NEM, Comte J-C, McKinley JM, Ofterdinger US (2014) Coupling ground and airborne geophysical data with upscaling techniques for regional groundwater modelling of heterogeneous aquifers: case study of a sedimentary aquifer intruded by volcanic dykes in Northern Ireland. Water Resour Res 50(10):7984–8001. doi: 10.1002/2014WR015320 CrossRefGoogle Scholar
  30. Diersch HJG (2002) FEFLOW reference manual. Wasy GmbH, Institute for Water Resources Planning and Systems Research, BerlinGoogle Scholar
  31. Elsheikh A, Abdelsalam MG, Mickus K (2011) Geology and geophysics of the West Nubian Paleolake and the Northern Darfur Megalake (WNPL-NDML): implication for groundwater resources in Darfur, northwestern Sudan. J Afr Earth Sci 61:82–93. doi: 10.1016/j.jafrearsci.2011.05.004 CrossRefGoogle Scholar
  32. Fay DQM, Young ME, Walker ASD (2010) Ground magnetometer survey of dykes in Co. Down. Paper presented at 53rd Irish Geological Research Meeting (IGRM) Ulster Museum, BelfastGoogle Scholar
  33. Friedel MJ, de Souza Filho OA, Iwashita F, Silva AM, Yoshinaga S (2012) Data-driven modeling for groundwater exploration in fractured crystalline terrain, northeast Brazil. Hydrogeol J 20:1061–1080. doi: 10.1007/s10040-012-0855-1 CrossRefGoogle Scholar
  34. Gibson PJ, Lyle P, Thomas N (2009) Magnetic characteristics of the Cuilcagh dykes, Co. Fermanagh, Northern Ireland. Ir J Earth Sci 27:1–9. doi: 10.3318/IJES.2009.27.1 Google Scholar
  35. Gondwe BRN, Lerer S, Stisen S, Marín L, Rebolledo-Vieyra M, Merediz-Alonso G, Bauer-Gottwein P (2010) Hydrogeology of the south-eastern Yucatan Peninsula: new insights from water level measurements, geochemistry, geophysics and remote sensing. J Hydrol 389:1–17. doi: 10.1016/j.jhydrol.2010.04.044 CrossRefGoogle Scholar
  36. GSNI (2007) TELLUS airborne magnetic maps. Geological Survey of Northern Ireland, BelfastGoogle Scholar
  37. Guardiano FB, Srivastava RM (1993) Multivariate geostatistics: beyond bivariate moments. In: Soares A (ed) Geostatistics: Troia ’92, vol 1. Kluwer, Dordrecht, The Netherlands, pp 133–144Google Scholar
  38. Hartley JJ (1935) The underground water resources of Northern Ireland. Institution of Civil Engineers, BelfastGoogle Scholar
  39. Hermans TJ (2013) Integration of near-surface geophysical, geological and hydrogeological data with multiple-point geostatistics in alluvial aquifers. Faculty of Applied Sciences, Univ. Of Liege, BelgiumGoogle Scholar
  40. Hermans T, Caers J, Nguyen F (2014) Assessing the probability of training image-based geological scenario using geophysical data. In: Pardo-Iguzquiza E, Gaurdiola-Albert C, Heredia J, Moreno-Merino L, Dura JJ, Vargas-Guzman JA (eds) Mathematics of planet Earth: proceedings of the 15th Annual Meeting of the International Association for Mathematical Geosceiences. Springer, New York, pp 679–682Google Scholar
  41. Huysmans M, Dassargues A (2009) Application of multiple-point geostatistics on modelling groundwater flow and transport in a cross-bedded aquifer (Belgium). Hydrogeol J 17:1901–1911. doi: 10.1007/s10040-009-0495-2 CrossRefGoogle Scholar
  42. Huysmans M, Darrargues A (2011) Direct multiple-point geostatistical simulation of edge properties for modeling thin irregularly shaped surfaces. Math Geosci 43:521–536. doi: 10.1007/s11004-011-9336-7 CrossRefGoogle Scholar
  43. Jha SK, Mariethoz G, Kelly BFJ (2013) Bathymetry fusion using multiple-point geostatistics: novelty and challenges in representing non-stationary bedforms. Environ Model Softw 50:66–76. doi: 10.1016/j.envsoft.2013.09.001 CrossRefGoogle Scholar
  44. Kalin RM, Roberts C (1997) Groundwater Resources in the Lagan Valley Sandstone Aquifer, Northern Ireland. JCIWEM 11:133–139Google Scholar
  45. Kalin R, Yang Y, Cronin A (1998) Regional groundwater modelling of the Sherwood Sandstone Aquifer in the Lagan ValleyGoogle Scholar
  46. Klingbeil R, Kleineidam S, Asprion U, Aigner T, Teutsch G (1999) Relating lithofaces to hydrofacies: outcrop-based hydrogeological characterisation of Quaternary gravel deposits. Sediment Geol 129(3–4):299–310. doi: 10.1016/S0037-0738(99)00067-6 CrossRefGoogle Scholar
  47. Lochbühler T, Pirot G, Straubhaar J, Linde N (2014) Conditioning of multiple-point statistics facies simulations to tomographic images. Math Geosci 46:625–645. doi: 10.1007/s11004-013-9484-z CrossRefGoogle Scholar
  48. Lyle P (1980) A petrological and geochemical study of the Tertiary Basaltic rocks of Northeast Ireland. J Earth Sci Roy Dublin Soc 2(2):137–152Google Scholar
  49. Manning PI, Robbie JH, Wilson HE (1970) Geology of Belfast and the Lagan Valley: memoir for 1:63360 geological sheet 36 (Northern Ireland), 2nd edn. H. M. Stationery Office, BelfastGoogle Scholar
  50. Mariethoz G, Renard P (2010) Reconstruction of incomplete data sets or images using direct sampling. Math Geosci 42:245–268. doi: 10.1007/s11004-010-9270-0 CrossRefGoogle Scholar
  51. Mariethoz G, Renard P, Straubhaar J (2010) The direct sampling method to perform multiple-point geostatistical simulations. Water Resour Res 46(11), W11536. doi: 10.1029/2008WR007621 Google Scholar
  52. Matheron G (1962) Traité de géostatistique appliquée [Treaty of applied geostatistics]. Technip, ParisGoogle Scholar
  53. Matheron G (1965) Les variables régionalisées et leur estimation: une application de la théorie des fonctions aléatoires aux sciences de la nature [Regionalized variables and their estimation: an application of the theory of random functions for natural sciences]. Masson, ParisGoogle Scholar
  54. Matheron G (1967) Eléments pour une théories des milieux poreux [Elements for a theory of porous media]. Masson, ParisGoogle Scholar
  55. McCabe M (2008) Glacial geology and geomorphology: the landscapes of Ireland. Dunedin Academic, Edinburgh, 274 ppGoogle Scholar
  56. McNeill GW, Cronin AA, Yang Y, Elliot T, Kalin RM (2000) The Triassic Sherwood Sandstone aquifer in Northern Ireland: constraint of a groundwater flow model for resource management. In: Robins NS, Misstear BD (eds) Groundwater in The Celtic regions: studies in hard rock and Quaternary hydrogeology. The Geological Society, London, pp 179–190Google Scholar
  57. Meerschman E, Pirot G, Mariethoz G, Straubhaar J, Van Meirvenne M, Renard P (2013) A practical guide to performing multiple-point statistical simulations with the direct sampling algorithm. Comput Geosci 52:307–324. doi: 10.1016/j.cageo.2012.09.019 CrossRefGoogle Scholar
  58. Meerschman E, Van Meirvenne M, Mariethoz G, Islam MM, de Smedt P, Van de Vijver E, Saey T (2014) Using bivariate multiple-point statistics and proximal soil sensor data to map fossil ice-wedge polygons. Geoderma 213:571–577. doi: 10.1016/j.geoderma.2013.01.016 CrossRefGoogle Scholar
  59. Michael HA, Li H, Boucher A, Sun T, Caers J, Gorelick SM (2010) Combining geologic-process models and geostatistics for conditional simulation of 3-D subsurface heterogeneity. Water Resour Res 46, W05527. doi: 10.1029/2009WR008414 Google Scholar
  60. Noetinger B, Artus V, Zargar G (2005) The future of stochastic and upscaling methods in hydrogeology. Hydrogeol J 13:184–201. doi: 10.1007/s10040-004-0427-0 CrossRefGoogle Scholar
  61. Okazaki K, Mogi T, Utsugi M, Ito Y, Kunishima H, Yamazaki T, Takahashi Y, Hashimoto T, Ymamaya Y, Ito H, Kaieda H, Tsukuda K, Yuuki Y, Jomori A (2011) Airborne electromagnetic and magnetic surveys for long tunnel construction design. Phys Chem Earth 36(16):1237–1246. doi: 10.1016/j.pce.2011.05.008 CrossRefGoogle Scholar
  62. Pirot G, Renard P, Straubhaar J (2014) Simulation of braided river elevation model time series with multiple-point statistics. Geomorphology 214:148–156. doi: 10.1016/j.geomorph.2014.01.022 CrossRefGoogle Scholar
  63. Rasmussen P, Sonnenborg TO, Goncear G, Hinsby K (2013) Assessing impacts of climate change, sea level rise, and drainage canals on saltwater intrusion to coastal aquifer. Hydrol Earth Syst Sci 17:421–443. doi: 10.5194/hess-17-421-2013 CrossRefGoogle Scholar
  64. Remy N, Boucher A, Wu J (2009) Applied geostatistics with SGeMS: a user’s guide. Cambridge University Press, New York, 264 ppCrossRefGoogle Scholar
  65. Renard P (2007) Stochastic hydrogeology: what professionals really need? Ground Water 45(5):531–541. doi: 10.1111/j.1745-6584.2007.00340.x CrossRefGoogle Scholar
  66. Renard P, de Marsily G (1997) Calculating equivalent permeability: a review. Adv Water Resour 5–6:253–278. doi: 10.1016/S0309-1708(96)00050-4 CrossRefGoogle Scholar
  67. Rezaee H, Mariethoz G, Koneshloo M, Asghari O (2013) Multiple-point geostatistical simulation using the bunch-pasting direct sampling method. Comput Geosci 54:293–308. doi: 10.1016/j.cageo.2013.01.020 CrossRefGoogle Scholar
  68. Rezaee H, Asghari O, Koneshloo M, Ortiz JM (2014) Multiple-point geostatistical simulation of dykes: application at Sungun porphyry copper system, Iran. Stoch Environ Res Risk Assess. doi: 10.1007/s00477-014-0857-8 Google Scholar
  69. Robins NS (1996) Hydrogeology of Northern Ireland. Environment and Heritage Service, HMSO for the British Geological Society, London, 60 ppGoogle Scholar
  70. Rubin Y, Hubbard SS (eds) (2005) Hydrogeophysics, vol 50. In: Water science and technology library, Springer, Dordrecht, The Netherlands, 523 ppGoogle Scholar
  71. Straubhaar J, Renard P, Mariethoz G, Froidevaux R, Besson O (2011) An improved parallel multiple-point algorithm using a list approach. Math Geosci 43:305–328. doi: 10.1007/s11004-011-9328-7 CrossRefGoogle Scholar
  72. Strebelle S (2001) Sequential simulation drawing structures from training images. PhD Thesis, Stanford University, Standford, CAGoogle Scholar
  73. Strebelle S (2002) Conditional simulation of complex geological structures using multiple-point statistics. Math Geol 34(1):1–22CrossRefGoogle Scholar
  74. Sulzbacher H, Wiederhold H, Siemon B, Grinat M, Igel J, Burschil T, Günther T, Hinsby K (2012) Numerical modelling of climate change impacts on freshwater lenses on the North Sea Island of Borkum using hydrological and geophysical methods. Hydrol Earth Syst Sci 16:3621–3642. doi: 10.5194/hess-16-3621-2012 CrossRefGoogle Scholar
  75. Virdee TS, Kottegoda NT (1984) A brief review of kriging and its application to optimal interpolation and observation well selection. Hydrol Sci J 29(4):367–387. doi: 10.1080/02626668409490957 CrossRefGoogle Scholar
  76. Wen X-H, Gómez-Hernández JJ (1996) Upscaling hydraulic conductivities in heterogeneous media: an overview. J Hydrol 183(1–2):9–32. doi: 10.1016/S0022-1694(96)80030-8 Google Scholar
  77. Whitehouse NJ, Roe HM, McCarron S, Knight J (eds) (2008) North of Ireland: field guide. Quaternary Research Association, London, 286 ppGoogle Scholar
  78. Wilson RL (1959) Remanent magnetism of late Secondary and early Tertiary igneous rocks. Philos Mag 4:750–755. doi: 10.1080/14786435908243271 CrossRefGoogle Scholar
  79. Wilson RL (1970) Palaeomagnetic stratigraphy of Tertiary lavas from Northern Ireland. Geophys J R Astron Soc 20:1–9. doi: 10.1111/j.1365-246X.1970.tb06744.x CrossRefGoogle Scholar
  80. Wilson HE (1972) Regional geology of Northern Ireland. HMSO, Belfast, 115 ppGoogle Scholar
  81. Wilson C (2011) Analysis of the effect of volcanic dykes on groundwater flow in the Sherwood Sandstone aquifer: impacts on piezometry, salinity, and attenuation of the tidal signal. MSc Thesis, Queen’s Univ., Belfast, IrelandGoogle Scholar
  82. Yang YS, Cronin AA, Elliot T, Kalin RM (2004) Characterising a heterogeneous hydrogeological system using groundwater flow and geochemical modelling. J Hydraul Res 42:147–155. doi: 10.1080/00221680409500058 CrossRefGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2015

Authors and Affiliations

  • Neil E. M. Dickson
    • 1
    Email author
  • Jean-Christophe Comte
    • 1
    • 2
  • Philippe Renard
    • 3
  • Julien A. Straubhaar
    • 3
  • Jennifer M. McKinley
    • 4
  • Ulrich Ofterdinger
    • 1
  1. 1.School of Planning, Architecture and Civil EngineeringQueen’s University BelfastBelfastUK
  2. 2.School of GeosciencesUniversity of AberdeenOld AberdeenUK
  3. 3.Centre d’HydrogéologieUniversité de NeuchâtelNeuchâtelSwitzerland
  4. 4.School of Geography, Archaeology and PalaeoecologyQueen’s University BelfastBelfastUK

Personalised recommendations