Abstract
The heterogeneity of hydrofacies is represented as spatial variability on different scales, and it has a significant impact on the behavior of groundwater flow and pollutant transport. However, effectively characterizing hydrofacies heterogeneity on different scales remains one of the most challenging problems in hydrogeology. In this study, an upscaling hydrofacies simulation (UHS) framework is proposed by integrating the upscaling borehole generalization (UBG) approach and transition probability geostatistics (TPG). A new UBG approach for generating virtual boreholes with equivalent hydrofacies information based on relatively high-density borehole lithological data is proposed, and the TPG is used to delineate the multiscale facies distribution. The results show that the UBG approach can significantly reduce borehole data volume while retaining the key equivalent hydrofacies information on a coarser scale. The UHS method can well characterize the overall distribution of equivalent hydrofacies on coarser scales, with the minor-component hydrofacies underestimated and the major-component hydrofacies overestimated to a lesser extent, and more equivalent facies appearing in strong heterogeneous areas. These results demonstrate that the UHS method can provide valuable capacity insights and advantages in characterizing hydrofacies heterogeneity on different scales using such high-density borehole lithological data.
Résumé
L’hétérogénéité des hydrofaciès est représentée comme une variabilité spatiale à différentes échelles, et elle a un impact significatif sur le comportement de l’écoulement des eaux souterraines et du transport des polluants. Cependant, la caractérisation efficace de l’hétérogénéité des hydrofaciès à différentes échelles reste l’un des grands défis en hydrogéologie. Dans cette étude, un cadre de simulation d’hydrofaciès à grande échelle (UHS) est proposé en intégrant l’approche de généralisation des forages à grande échelle (UBG) et la géostatistique des probabilités de transition (TPG). Une nouvelle approche UBG pour générer des forages virtuels avec des informations d’hydrofaciès équivalentes basées sur des données lithologiques de forages à densité relativement élevée est proposée, et la TPG est utilisée pour délimiter la distribution des faciès multiéchelle. Les résultats montrent que l’approche UBG peut réduire de manière significative le volume de données des forages tout en conservant les informations clés sur les hydrofaciès équivalents à une échelle plus grossière. La méthode UHS peut bien caractériser la distribution globale des hydrofaciès équivalents à des échelles plus grossières, avec une sous-estimation des hydrofaciès à composantes mineures et une surestimation des hydrofaciès à composantes majeures dans une moindre mesure, et plus de faciès équivalents apparaissant dans les zones très hétérogènes. Ces résultats démontrent que la méthode UHS peut fournir de précieuses informations sur son potentiel et offrir des avantages dans la caractérisation de l’hétérogénéité des hydrofaciès à différentes échelles en utilisant des données lithologiques de forage à haute densité.
Resumen
La heterogeneidad de las hidrofacies se representa como variabilidad espacial a diferentes escalas, y tiene un impacto significativo en el comportamiento del flujo de aguas subterráneas y el transporte de contaminantes. Sin embargo, la caracterización efectiva de la heterogeneidad de las hidrofacies a diferentes escalas sigue siendo uno de los problemas más desafiantes en hidrogeología. En este estudio, se propone un marco de simulación de hidrofacies a escala creciente (UHS) mediante la integración del enfoque de generalización de perforaciones a escala creciente (UBG) y la geoestadística de probabilidad de transición (TPG). Se propone un nuevo enfoque UBG para generar sondeos virtuales con información equivalente de hidrofacies basada en datos litológicos de sondeos de densidad relativamente alta, y se utiliza la TPG para delinear la distribución de facies multiescala. Los resultados muestran que el enfoque UBG puede reducir significativamente el volumen de datos de sondeos, conservando al mismo tiempo la información clave de las hidrofacies equivalentes a una escala más amplia. El método UHS puede caracterizar bien la distribución global de las hidrofacies equivalentes en escalas más amplias, subestimando en menor medida las hidrofacies de componentes menores y sobreestimando en menor medida las hidrofacies de componentes mayores, y apareciendo más facies equivalentes en áreas fuertemente heterogéneas. Estos resultados demuestran que el método UHS puede proporcionar valiosos conocimientos y ventajas en la caracterización de la heterogeneidad de las hidrofacies a diferentes escalas utilizando datos litológicos de sondeos de alta densidad.
摘要
水相的非均质性表现为不同尺度上的空间变异性，且对地下水流和污染物运移行为产生显著影响。然而，有效表征不同尺度上的水相非均质性仍然是水文地质学中最具挑战性的问题之一。本研究将升尺度钻孔数据综合法(UBG)和转移概率地质统计学(TPG)相结合，提出了升尺度水相模拟(UHS)框架。基于相对高密度的钻孔岩性资料，结合等效水相信息，本研究提出了一种新的UBG方法，并利用TPG来表征多尺度水相分布。结果显示，UBG方法可以显著减少钻孔数据量，同时在更大的尺度上保留关键等效水相信息。UHS方法在较大的尺度上能较好地刻画等效水相的整体分布，次要组分水相被低估，主要组分水相被较小程度地高估，强非均质区出现较多的等效相。上述结果表明，UHS方法在利用高密度钻孔岩性数据表征不同尺度上的水相非均质性方面提供了有价值的见解和优势。
Resumo
A heterogeneidade de hidrofácies é representada como variabilidade espacial em diferentes escalas, e possui um impacto significante no comportamento do fluxo das águas subterrâneas e transporte de poluentes. Entretanto, a caracterização efetiva da heterogeneidade de hidrofácies em diferentes escalas permanece como um dos problemas mais desafiadores na hidrogeologia. Neste estudo, é proposta uma estrutura de simulação de hidrofácies com aumento de escala (SHAE) com a integração do aumento de escala generalizado de dados de poços (AEGP) e geoestatística de probabilidade de transição (GTP). Uma nova abordagem AEGP para geração de dados virtuais de poços artesianos com informação de hidrofácies equivalente baseado em dados litológicos de poços artesianos relativamente robustos é proposta, e a GTP é utilizado para delinear a distribuição multiescalar das fácies. Os resultados demonstram que a abordagem AEGP pode reduzir significativamente o volume de dados de poços artesianos, ao mesmo tempo que retém a informação da hidrofácie equivalente principal em uma escala mais grosseira. O método SHAE pode caracterizar bem a distribuição generalizada das hidrofácies equivalentes em escala mais grosseira, com as hidrofácies das componentes menores subestimadas e as hidrofácies das componentes maiores superestimadas em menor extensão, e mais fácies equivalentes aparentes em áreas fortemente heterogêneas. Estes resultados demonstram que o método SHAE pode fornecer valiosos conhecimentos sobre a capacidade e vantagens na caracterização da heterogeneidade de hidrofácies em diferentes escalas, utilizando dados litológicos de poços artesianos robustos.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
Bakshevskaya VA, Pozdnyakov SP (2013) Methods of modeling hydraulic heterogeneity of sedimentary formations. Water Res 40(7):767–775. https://doi.org/10.1134/s0097807813070026
Ballio F, Guadagnini A (2004) Convergence assessment of numerical Monte Carlo simulations in groundwater hydrology. Water Resour Res 40(4), Artn W04603. https://doi.org/10.1029/2003wr002876.
Bianchi M, Pedretti D (2018) An entrogram-based approach to describe spatial heterogeneity with applications to solute transport in porous media. Water Resour Res 54(7):4432–4448. https://doi.org/10.1029/2018WR022827
Bianchi M, Kearsey T, Kingdon A (2015) Integrating deterministic lithostratigraphic models in stochastic realizations of subsurface heterogeneity: impact on predictions of lithology, hydraulic heads and groundwater fluxes. J Hydrol 531:557–573. https://doi.org/10.1016/j.jhydrol.2015.10.072
Bimonte S, Bertolotto M, Gensel J, Boussaid O (2012) Spatial OLAP and map generalization: model and algebra. Int J Data Warehous Min 8(1):24–51
Binley A, Hubbard SS, Huisman JA, Revil A, Robinson DA, Singha K, Slater LD (2015) The emergence of hydrogeophysics for improved understanding of subsurface processes over multiple scales. Water Resour Res 51(6):3837–3866. https://doi.org/10.1002/2015WR017016
Blessent D, Therrien R, Lemieux J-M (2011) Inverse modeling of hydraulic tests in fractured crystalline rock based on a transition probability geostatistical approach. Water Resour Res 47(12):W12530. https://doi.org/10.1029/2011wr011037
Blöschl G, Sivapalan M (1995) Scale issues in hydrological modelling: a review. Hydrol Process 9(3–4):251–290
Burstedde C, Fonseca JA, Kollet S (2018) Enhancing speed and scalability of the ParFlow simulation code. Comput Geosci 22(1):347–361. https://doi.org/10.1007/s10596-017-9696-2
Carle SF (1997) Implementation schemes for avoiding artifact discontinuities in simulated annealing. Math Geol 29(2):231–244
Carle SF (1999) T-PROGS: transition probability geostatistical software (version 2.1), Hydrologic Sciences Graduate Group, University of California, Davis
Carle SF, Fogg GE (1996) Transition probability-based indicator geostatistics. Math Geol 28(4):453–476
Carle SF, Fogg GE (1997) Modeling spatial variability with one and multidimensional continuous-lag Markov chains. Math Geol 29(7):891–918
Carle SF, Fogg GE (2020) Integration of soft data into geostatistical simulation of categorical variables. Front Earth Sci 8, Artn 565707. https://doi.org/10.3389/Feart.2020.565707
Chang CM, Yeh HD (2010) Nonstationary stochastic analysis of flow in a heterogeneous unconfined aquifer subject to spatially-random periodic recharge. J Hydrol 395(3–4):163–168
Chen J, Hu YG, Li ZL, Zhao RL, Meng LQ (2009) Selective omission of road features based on mesh density for automatic map generalization. Int J Geogr Inf Sci 23(8):1013–1032
Curtis ZK, Li SG, Liao HS, Lusch D (2018) Data-driven approach for analyzing hydrogeology and groundwater quality across multiple scales. Groundwater 56(3):377–398. https://doi.org/10.1111/gwat.12584
Curtis ZK, Liao HS, Li SG, Sampath PV, Lusch DP (2019) A multiscale assessment of shallow groundwater salinization in Michigan. Groundwater 57(5):784–806. https://doi.org/10.1111/gwat.12873
Dafflon B, Irving J, Holliger K (2009) Simulated-annealing-based conditional simulation for the local-scale characterization of heterogeneous aquifers. J Appl Geophys 68(1):60–70
Dai ZX, Keating E, Bacon D, Viswanathan H, Stauffer P, Jordan A, Pawar R (2014) Probabilistic evaluation of shallow groundwater resources at a hypothetical carbon sequestration site. Scientific Reports 4, Artn 4006
Dehkordy FM, Briggs MA, Day-Lewis FD, Singha K, Krajnovich A, Hampton TB, Zarnetske JP, Scruggs C, Bagtzoglou AC (2019) Multi-scale preferential flow processes in an urban streambed under variable hydraulic conditions. J Hydrol 573:168–179. https://doi.org/10.1016/j.jhydrol.2019.03.022
dell’Arciprete D, Bersezio R, Felletti F, Giudici M, Comunian A, Renard P (2012) Comparison of three geostatistical methods for hydrofacies simulation: a test on alluvial sediments. Hydrogeol J 20(2):299–311. https://doi.org/10.1007/s10040-011-0808-0
Dendumrongsup N, Tartakovsky DM (2021 Probabilistic reconstruction of hydrofacies with support vector machines. Water Resour Res 57(5), Artn e2021WR029622. https://doi.org/10.1029/2021WR029622.
Deutsch JL, Deutsch CV (2014) A multidimensional scaling approach to enforce reproduction of transition probabilities in truncated plurigaussian simulation. Stoch Env Res Risk A 28(3):707–716. https://doi.org/10.1007/s00477-013-0783-1
Deutsch CV, Journel AG (1992) GSLIB, geostatistical software library and user’s guide. Oxford University Press, New York
Dewandel B, Marechal JC, Bour O, Ladouche B, Ahmed S, Chandra S, Pauwels H (2012) Upscaling and regionalizing hydraulic conductivity and effective porosity at watershed scale in deeply weathered crystalline aquifers. J Hydrol 416:83–97. https://doi.org/10.1016/j.jhydrol.2011.11.038
Dey S, Dhar A (2020) On proper orthogonal decomposition (POD) based reduced-order modeling of groundwater flow through heterogeneous porous media with point source singularity. Adv Water Resour 144, Artn 103703. https://doi.org/10.1016/j.advwatres.2020.103703
Engdahl NB, Weissmann GS (2010) Anisotropic transport rates in heterogeneous porous media. Water Resour Res 46, Artn W02507. https://doi.org/10.1029/2009WR007910
Engdahl NB, Vogler ET, Weissmann GS (2010) Evaluation of aquifer heterogeneity effects on river flow loss using a transition probability framework. Water Resour Res 46, Artn W01506. https://doi.org/10.1029/2009WR007903
Fitts CR (2002) Groundwater science, 1st edn. Elsevier, San Diego
Fleckenstein JH, Fogg GE (2008) Efficient upscaling of hydraulic conductivity in heterogeneous alluvial aquifers. Hydrogeol J 16(7):1239–1250. https://doi.org/10.1007/s10040-008-0312-3
Freeze AR (1975) A stochastic-conceptual analysis of one-dimensional groundwater flow in nonuniform homogeneous media. Water Resour Res 11(5):725–741
Gleeson T, Paszkowski D (2014) Perceptions of scale in hydrology: what do you mean by regional scale? Hydrol Sci J 59(1):99–107
Guadagnini A, Guadagnini L, Tartakovsky DM, Winter CL (2003) Random domain decomposition for flow in heterogeneous stratified aquifers. Stoch Env Res Risk A 17(6):394–407. https://doi.org/10.1007/s00477-003-0157-1
Guo WL, Yang QK, Wang HJ, Li R (2012) DEM multi-scale representation based on wavelet multiresolution analysis. J Food Agric Environ 10(3–4):1346–1349
Guo ZL, Fogg GE, Brusseau ML, LaBolle EM, Lopez J (2019) Modeling groundwater contaminant transport in the presence of large heterogeneity: a case study comparing MT3D and RWhet. Hydrogeol J 27(4):1363–1371. https://doi.org/10.1007/s10040-019-01938-9
He Y, Hu KL, Li BG, Chen DL, Sutter HC, Huang YF (2009) Comparison of sequential indicator simulation and transition probability indicator simulation used to model clay content in microscale surface soil. Soil Sci 174(7):395–402. https://doi.org/10.1097/SS.0b013e3181aea77c
He X, Koch J, Sonnenborg TO, Jorgensen F, Schamper C, Refsgaard JC (2014) Transition probability-based stochastic geological modeling using airborne geophysical data and borehole data. Water Resour Res 50(4):3147–3169. https://doi.org/10.1002/2013WR014593
Herr M, Schäfer G, Spitz K (1989) Experimental studies of mass transport in porous media with local heterogeneities. J Contam Hydrol 4(2):127–137. https://doi.org/10.1016/0169-7722(89)90017-X
Jones NL, Walker JR, Carle SF (2005) Hydrogeologic unit flow characterization using transition probability geostatistics. Ground Water 43(2):285–289. https://doi.org/10.1111/j.1745-6584.2005.0007.x
Kalbermatten M, Van De Ville D, Turberg P, Tuia D, Joost S (2012) Multiscale analysis of geomorphological and geological features in high resolution digital elevation models using the wavelet transform. Geomorphology 138(1):352–363
Klemeš V (1983) Conceptualization and scale in hydrology. J Hydrol 65(1–3):1–23. https://doi.org/10.1016/0022-1694(83)90208-1
Klingbeil R, Kleineidam S, Asprion U, Aigner T, Teutsch G (1999) Relating lithofacies to hydrofacies: outcrop-based hydrogeological characterisation of Quaternary gravel deposits. Sediment Geol 129(3–4):299–310
Koch J, He X, Jensen KH, Refsgaard JC (2014) Challenges in conditioning a stochastic geological model of a heterogeneous glacial aquifer to a comprehensive soft data set. Hydrol Earth Syst Sci 18(8):2907–2923. https://doi.org/10.5194/hess-18-2907-2014
Langousis A, Kaleris V, Kokosi A, Mamounakis G (2018) Markov based transition probability geostatistics in groundwater applications: assumptions and limitations. Stoch Env Res Risk A 32(7):2129–2146. https://doi.org/10.1007/s00477-017-1504-y
Larsen F, Tran LV, Van Hoang H, Tran LT, Christiansen AV, Pham NQ (2017) Groundwater salinity influenced by Holocene seawater trapped in incised valleys in the Red River delta plain. Nat Geosci 10(5):376. https://doi.org/10.1038/NGEO2938
Le PVV, Kumar P, Valocchi AJ, Dang HV (2015) GPU-based high-performance computing for integrated surface-subsurface flow modeling. Environ Model Softw 73:1–13. https://doi.org/10.1016/j.envsoft.2015.07.015
Lee SY, Carle SF, Fogg GE (2007) Geologic heterogeneity and a comparison of two geostatistical models: sequential Gaussian and transition probability-based geostatistical simulation. Adv Water Resour 30(9):1914–1932. https://doi.org/10.1016/j.advwatres.2007.03.005
Li WD (2007) A fixed-path Markov chain algorithm for conditional simulation of discrete spatial variables. Math Geol 39(2):159–176. https://doi.org/10.1007/s11004-006-9071-7
Liao HS, Li LX, Li SG (2004) Advancement of stochastic modeling for non-stationary groundwater transport and interaction between small-scale heterogeneity and large-scale non-uniformity. Shuili Xuebao 35(10):13–21
Liao HS, Curtis ZK, Sampath PV, Li SG (2020) Simulation of flow in a complex aquifer system subjected to long-term well network growth. Groundwater 58(2):301–322. https://doi.org/10.1111/gwat.12918
Liao QZ, Lei G, Zhang DX, Patil S (2019) Analytical solution for upscaling hydraulic conductivity in anisotropic heterogeneous formations. Adv Water Resour 128:97–116. https://doi.org/10.1016/j.advwatres.2019.04.011
Ma L, Deng H, Yan YS, Deng YP, Zhao WD, Tan XH, Qian JZ (2022) Hydrofacies simulation based on transition probability geostatistics using electrical resistivity tomography and borehole data. Hydrogeol J 30(7):2117–2134. https://doi.org/10.1007/s10040-022-02539-9
Malenda HF, Sutfin NA, Guryan G, Stauffer S, Rowland JC, Williams KH, Singha K (2019) From Grain to Floodplain: evaluating heterogeneity of floodplain hydrostatigraphy using sedimentology, geophysics, and remote sensing. Earth Surf Process Landf 44(9):1799–1815. https://doi.org/10.1002/esp.4613
MDEQ, GLMD (2003) General geology of Michigan. Michigan Gov. https://www.michigan.gov/-/media/Project/Websites/egle/Documents/Programs/OGMD/Catalog/04/GIMDL-GGGM.pdf?rev=ae187fc807c0454e9638dd5ef61e6d19. Accessed February 2023
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, Artn W05527. https://doi.org/10.1029/2009wr008414
Muller JC, Lagrange JP, Weibel R (1995) GIS and generalisation: methodology and practice. Taylor & Francis, London
Park YJ, Sudicky EA, McLaren RG, Sykes JF (2004) Analysis of hydraulic and tracer response tests within moderately fractured rock based on a transition probability geostatistical approach. Water Resour Res 40(12). https://doi.org/10.1029/2004wr003188
Proce CJ, Ritzi RW, Dominic DF, Dai Z (2004) Modeling multiscale heterogeneity and aquifer interconnectivity. Ground Water 42(5):658–670
Ritzi RW Jr (2000) Behavior of indicator variograms and transition probabilities in relation to the variance in lengths of hydrofacies. Water Resour Res 36(11):3375–3381
Rubin Y, Lunt IA, Bridge JS (2006) Spatial variability in river sediments and its link with river channel geometry. Water Resour Res 42(6):W06D16. https://doi.org/10.1029/2005WR004853
Sampath PV, Liao HS, Curtis ZK, Herbert ME, Doran PJ, May CA, Landis DA, Li SG (2016) Understanding fen hydrology across multiple scales. Hydrol Process 30(19):3390–3407. https://doi.org/10.1002/hyp.10865
Shi LS, Zeng LZ, Zhang DX, Yang JZ (2012) Multiscale-finite-element-based ensemble Kalman filter for large-scale groundwater flow. J Hydrol 468:22–34. https://doi.org/10.1016/j.jhydrol.2012.08.003
Skøien JO, Blöschl G, Western AW (2003) Characteristic space scales and timescales in hydrology. Water Resour Res 39(10):1304. https://doi.org/10.1029/2002WR001736
Song XH, Chen XY, Ye M, Dai ZX, Hammond G, Zachara JM (2019) Delineating facies spatial distribution by integrating ensemble data assimilation and indicator geostatistics with level-set transformation. Water Resour Res 55(4):2652–2671. https://doi.org/10.1029/2018WR023262
Sun AY, Ritzi RW, Sims DW (2008) Characterization and modeling of spatial variability in a complex alluvial aquifer: implications on solute transport. Water Resour Res 44(4):W04402. https://doi.org/10.1029/2007WR006119
Tsai FTC (2006) Enhancing random heterogeneity representation by mixing the kriging method with the zonation structure. Water Resour Res 42(8), Artn W08428. https://doi.org/10.1029/2005wr004111.
Walker JR (2002) Application of transition probability geostatistics for indicator simulations involving the MODFLOW model. Brigham Young University, Provo, UT
Wang JY, Cheng Y (2004) The multiple character of spatial data and automated generalization. Hydrographic Survey Chart 24(4):1–3. https://doi.org/10.3969/j.issn.1671-3044.2004.04.001
Ware JM, Wilson ID, Ware JA (2003) A knowledge based genetic algorithm approach to automating cartographic generalisation. Knowl-Based Syst 16(5–6):295–303
Webber T, Costa JFCL, Salvadoretti P (2013) Using borehole geophysical data as soft information in indicator kriging for coal quality estimation. Int J Coal Geol 112:67–75
Weissmann GS, Fogg GE (1999) Multi-scale alluvial fan heterogeneity modeled with transition probability geostatistics in a sequence stratigraphic framework. J Hydrol 226(1–2):48–65
Weissmann GS, Carle SF, Fogg GE (1999) Three-dimensional hydrofacies modeling based on soil surveys and transition probability geostatistics. Water Resour Res 35(6):1761–1770
Woodbury AD, Sudicky EA (1991) The geostatistical characteristics of the Bordon Aquifer. Water Resour Res 27(4):533–546. https://doi.org/10.1029/90wr02545
Ye M, Khaleel R (2008) A Markov chain model for characterizing medium heterogeneity and sediment layering structure. Water Resour Res 44(9):W09427. https://doi.org/10.1029/2008WR006924
Zarlenga A, Fiori A, Russo D (2018) Spatial variability of soil moisture and the scale issue: a geostatistical approach. Water Resour Res 54(3):1765–1780. https://doi.org/10.1002/2017WR021304
Zhan LT, Hu YT, Zou LC, Xu WJ, Ye ZY, Chen RQ, Zhuang DY, Li JL, Chen YM (2022) Effects of multiscale heterogeneity on transport in three-dimensional fractured porous rock with a rough-walled fracture network. Comput Geotech 148, Artn 104836. https://doi.org/10.1016/j.compgeo.2022.104836.
Zhang H, Harter T, Sivakumar B (2006) Nonpoint source solute transport normal to aquifer bedding in heterogeneous, Markov chain random fields. Water Resour Res 42(6):W06403. https://doi.org/10.1029/2004WR003808
Zhang Y, Fogg GE (2003) Simulation of multi-scale heterogeneity of porous media and parameter sensitivity analysis. Sci China Series E-Technol Sci 46(5):459–474. https://doi.org/10.1360/02ye0098
Zhou ML, Soga K, Yamamoto K (2020) Upscaling techniques for fully coupled THM simulation and application to hydrate gas production tests. Comput Geotech 124, Artn 103596. https://doi.org/10.1016/j.compgeo.2020.103596.
Zhu L, Dai ZX, Gong HL, Gable C, Teatini P (2016) Statistic inversion of multi-zone transition probability models for aquifer characterization in alluvial fans. Stoch Env Res Risk A 30(3):1005–1016. https://doi.org/10.1007/s00477-015-1089-2
Funding
This study was supported by the National Natural Science Foundation of China (No. 42072276; No. 41831289)
Author information
Authors and Affiliations
Corresponding authors
Ethics declarations
The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.
Additional information
Publisher’s note
Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.
Supplementary information
ESM 1
(PDF 2203 kb)
Rights and permissions
Springer Nature or its licensor (e.g. a society or other partner) holds exclusive rights to this article under a publishing agreement with the author(s) or other rightsholder(s); author self-archiving of the accepted manuscript version of this article is solely governed by the terms of such publishing agreement and applicable law.
About this article
Cite this article
Ma, L., Liao, H., Qian, J. et al. Upscaling equivalent hydrofacies simulation based on borehole data generalization and transition probability geostatistics. Hydrogeol J 31, 985–1004 (2023). https://doi.org/10.1007/s10040-023-02621-w
Received:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s10040-023-02621-w