Environmental Earth Sciences

, 75:1487 | Cite as

2D probabilistic prediction of sparsely measured earth properties constrained by geophysical imaging fully accounting for tomographic reconstruction ambiguity

  • Abduljabbar AsadiEmail author
  • Peter Dietrich
  • Hendrik Paasche
Original Article


Many hydrological, environmental, or engineering exploration tasks require predicting spatially continuous scenarios of sparsely measured borehole logging data. We present a methodology to probabilistically predict such scenarios constrained by ill-posed geophysical tomography. Our approach allows for transducing tomographic reconstruction ambiguity into the probabilistic prediction of spatially continuous target parameter scenarios. It is even applicable to data sets where petrophysical relations in the survey area are non-unique, i.e., different facies related petrophysical relations may be present. We employ static two-layer artificial neural networks (ANNs) for prediction and additionally evaluate, whether the training performance of the ANNs can be used to rank geophysical tomograms, which are mathematically equal reconstructions of physical parameter distributions in the ground. We illustrate our methodology using a realistic synthetic database for maximal control about the prediction performance and ranking potential of the approach. For doing so, we try to link geophysical radar and seismic tomography as input parameters to porosity of the ground as target parameter of ANN. However, the approach is flexible and can cope with any combination of geophysical tomograms and hydrologic, environmental or engineering target parameters. Ranking of equivalent geophysical tomograms based on additional borehole logging data is found to be generally possible, but risks remain that the ranking based on the ANN training performance does not fully coincide with the closeness of geophysical tomograms to ground truth. Since geophysical field data sets do usually not offer control options similar to those used in our synthetic database, we do not recommend the utilization of recurrent ANNs to learn weights for the individual geophysical tomograms used in the prediction procedure.


Geophysics Petrophysics Probabilistic prediction Tomography ANN Global search inversion 


  1. Angioni T, Rechtien RD, Cardimona SJ, Luna R (2003) Crosshole seismic tomography and borehole logging for engineering site characterization in Sikeston. Tectonophysics 368:119–137CrossRefGoogle Scholar
  2. Archie GE (1942) The electrical resistivity log as an aid in determining some reservoir characteristics. Trans Am Inst Mineral Met 146:54–62Google Scholar
  3. Asadi A, Dietrich P, Paasche H (2016) 2D probabilistic prediction of sparsely measured geotechnical parameters constrained by tomographic ambiguity and measurement errors. In: Expanded abstracts of the 78th EAGE conference and exhibition, Vienna. doi: 10.3997/2214-4609.201601402
  4. Aster RC, Borchers B, Thurber CH (2005) Parameter Estimation and Inverse problems. Academic Press, CambridgeGoogle Scholar
  5. Bailly K, Milgram M (2009) Boosting feature selection for neural network based regression. Neural Netw 22:748–756CrossRefGoogle Scholar
  6. Balling R (2003) The maximin fitness function; multi-objective city and regional planning. In: Fonseca CM, Fleming PJ, Zitzler E, Deb K, Thiele L (eds) Second international conference on evolutionary multi-criterion optimization, Springer Lecture Notes in Computer Science, vol 2632, pp 1–15Google Scholar
  7. Ban JC, Chang CH (2013) The learning problem of multi-layer neural networks. Neural Netw 46:116–123CrossRefGoogle Scholar
  8. Binley A, Winship P, Middelton R (2001) High-resolution characterization of vadose zone dynamics using cross-borehole radar. Water Resour Res 37:2639–2652CrossRefGoogle Scholar
  9. Bodin T, Sambridge M (2009) Seismic tomography with the reversible jump algorithm. Geophys J Int 178:1411–1436CrossRefGoogle Scholar
  10. Bodin T, Sambridge M, Rawlinson N, Arroucau P (2012) Transdimensional tomography with unknown data noise. Geophys J Int 189:1536–1556CrossRefGoogle Scholar
  11. Boisclair CD, Gloaguen E, Marcotte D, Giroux B (2011) Heterogeneous aquifer characterization from ground-penetrating radar tomography and borehole hydrogeophysical data using nonlinear Bayesian simulations. Geophysics 76:J13–J25CrossRefGoogle Scholar
  12. Bosch M, Mukerji T, Gonzalez FE (2010) Seismic inversion for reservoir properties combining statistical rock physics and geostatistics: a review. Geophysics 75:165–176CrossRefGoogle Scholar
  13. Breiman L, Friedman JH (1985) Estimating optimal transformations for multiple regression and correlation. J Am Stat Assoc 80:580–598CrossRefGoogle Scholar
  14. Cassiani G, Böhm G, Vesnaver A, Nicolich R (1998) A geostatistical framework for incorporating seismic tomography auxiliary data into hydraulic conductivity. J Hydrol 206:58–74CrossRefGoogle Scholar
  15. Cawley GC, Janacek GJ, Haylock MR, Dorling SR (2007) Predictive uncertainty in environmental modelling. Neural Netw 20:537–549CrossRefGoogle Scholar
  16. Chen J, Hubbard S, Rubin Y (2001) Estimating the hydraulic conductivity at the South Oyster Site from geophysical tomographic data using Bayesian techniques based on the normal linear regression. Water Resour Res 37:1603–1613CrossRefGoogle Scholar
  17. Dafflon B, Irving J, Holliger K (2009) Simulated-annealing-based conditional simulation for the local-scale characterization of heterogeneous aquifers. J Appl Geophys 68:60–70CrossRefGoogle Scholar
  18. Duan S, Hu X, Dong Z, Wang L, Mazumder P (2015) Memristor-based cellular nonlinear/neural network: design, analysis, and applications. IEEE Trans Neural Netw Learn Syst 26:1202–1213CrossRefGoogle Scholar
  19. Ezzedine S, Rubin Y, Chen J (1999) Bayesian method for hydrogeological site characterization using borehole and geophysical survey data: theory and application to the Lawrence Livermore National. Water Resour Res 35:2671–2683CrossRefGoogle Scholar
  20. Frénay B, Doquire G, Verleysen M (2013) Is mutual information adequate for feature selection in regression? Neural Netw 48:1–7CrossRefGoogle Scholar
  21. Friedel S (2003) Resolution, stability and efficiency of resistivity tomography estimated from a generalized invers approach. Geophys J Int 153:305–316CrossRefGoogle Scholar
  22. Ganivada A, Sankar Ray S, Pal SK (2013) Fuzzy rough sets, and a granular neural network for unsupervised feature selection. Neural Netw 48:91–108CrossRefGoogle Scholar
  23. Gassmann F (1951) Über die Elastizität poröser Medien. Vierteljahresschrift der Naturforsch. Ges., Zürich, vol 96, pp 1–22Google Scholar
  24. Gloaguen E, Chaouteau M, Marcotte D, Chaouis R (2001) Estimation of hydraulic conductivity of an unconfined aquifer using cokriging of GPR and Hydrostratigraphic data. J Appl Geophys 47:135–152CrossRefGoogle Scholar
  25. Hornik K (1991) Approximation capabilities of multilayer feedforward networks. Neural Netw 4:251–257CrossRefGoogle Scholar
  26. Hubbard S, Chen J, Peterson J, Majer E, Williams K, Swift D, Mailliox B, Rubin Y (2001) Hydrogeological characterization of the D.O.E. bacterial transport site in Oyster Virginia using geophysical data. Water Resour Res 37:2431–2456CrossRefGoogle Scholar
  27. Jain AK, Mao J, Mohiuddin KM (1996) Artificial neural networks: a tutorial. IEEE Comput 29:31–44CrossRefGoogle Scholar
  28. Jing X (2012) Robust adaptive learning of feedforward neural networks via LMI optimizations. Neural Netw 31:33–45CrossRefGoogle Scholar
  29. Kennedy J, Eberhart RC (1995) Particle swarm optimization. In: Proceedings of IEEE international conference on neural networks, Piscataway, 1942–1948Google Scholar
  30. Khoshdel H, Riahi MA (2011) Multi attribute transform and neural network in porosity estimation of an offshore oil field—a case study. J Petrol Sci Eng 78:740–747CrossRefGoogle Scholar
  31. Kiranyaz S, Ince T, Yildirim AG (2009) Evolutionary artificial neural networks by multi-dimensional particle swarm optimization. Neural Netw 22:1448–1462CrossRefGoogle Scholar
  32. Knödel K, Krummel H, Lange G (1997) Handbuch zur Erkundung des Untergrundes von Deponien und Altlasten. Springer, BerlinGoogle Scholar
  33. Leite EP, de Souza Filho CR (2009) Artificial neural networks applied to mineral potential mapping for copper-gold mineralizations in the Carajás Mineral Province, Brazil. Geophys Prospect 57:1049–1065CrossRefGoogle Scholar
  34. Leite EP, Vidal AC (2011) 3D porosity prediction from seismic inversion and neural networks. Comput Geosci 37:1174–1180CrossRefGoogle Scholar
  35. Leray P, Gallinari P (2002) Feature selection with neural networks. Behaviormetrika 26:145–166CrossRefGoogle Scholar
  36. Liu H, Motoda H (1998) Feature transformation and subset selection. IEEE Intell Syst 13:26–28Google Scholar
  37. Liu H, Motoda H (2001) Feature extraction, construction and selection: a data mining perspective. Kluwer Academic Publishers, BostonCrossRefGoogle Scholar
  38. Miche Y, Sorjamaa A, Bas P, Simula O, Jutten C, Lendasse A (2010) OP-ELM: optimally pruned extreme learning machine. IEEE Trans Neural Netw 21:158–162CrossRefGoogle Scholar
  39. Mitchell M (1998) An introduction to genetic algorithms. MIT Press, CambridgeGoogle Scholar
  40. Paasche H (2015) Fully non-linear self-organizing inversion of cross-borehole tomographic data. In: Near Surface Geoscience—21st European meeting of environmental and engineering geophysics, ItalyGoogle Scholar
  41. Paasche H (2017a) Translating tomographic ambiguity into the probabilistic inference of hydrologic and engineering target parameters. Geophysics (submitted)Google Scholar
  42. Paasche H (2017b) Probabilistic inference of spatially continuous geotechnical parameter fields by means of sparse calibration data and geophysical tomography. Geophys Prospect (submitted)Google Scholar
  43. Paasche H, Tronicke J (2007) Cooperative inversion of 2D geophysical data set: a zonal approach based on fuzzy c-means cluster analysis. Geophysics 72:35–39CrossRefGoogle Scholar
  44. Paasche H, Tronicke J, Holliger K, Green AG, Maurer HR (2006) Integration of diverse physical-property models: subsurface zonation and petrophysical parameter estimation based on fuzzy c-means cluster analyses. Geophysics 71:H33–H44CrossRefGoogle Scholar
  45. Pham DL (2001) Spatial models for fuzzy clustering. Comput Vis Image Underst 84:285–297CrossRefGoogle Scholar
  46. Poulton MM (2002) Neural networks as an intelligence amplification tool: a review of applications. Geophysics 67:979–993CrossRefGoogle Scholar
  47. Quan H, Srinivasan D, Khosravi A (2014) Short-term load and wind power forecasting using neural network-based prediction intervals. IEEE Trans Neural Netw Learn Syst 25:303–315CrossRefGoogle Scholar
  48. Raeesi M, Moradzadeh A, Doulati Ardejani F, Rahimi M (2012) Classification and identification of hydrocarbon reservoir lithofacies and their heterogeneity using seismic attributes, logs data and artificial neural networks. J Petrol Sci Eng 82:151–165CrossRefGoogle Scholar
  49. Raymer DS, Hunt ER, Gardner JS (1980) An improved sonic transit time-to-porosity transform. In: Proceeding of SPWLA 21st ann. Meeting, paper PGoogle Scholar
  50. Razavi S, Tolson BA (2011) A new formulation for feedforward neural networks. IEEE Trans Neural Netw 22:1588–1598CrossRefGoogle Scholar
  51. Roy L, Sen MK, McIntosh K, Stoffa PL, Nakamura Y (2005) Joint inversion of first arrival seismic travel-time and gravity data. J Geophys Eng 2:277–289CrossRefGoogle Scholar
  52. Ruggeri P, Irving J, Gloaguen E, Holliger K (2013) Regional scale integration of multiresolution hydrological and geophysical data using a two-step Bayesian sequential simulation approach. Geophys J Int 194:289–303CrossRefGoogle Scholar
  53. Rumpf M, Tronicke J (2014) Predicting 2D geotechnical parameter fields in near-surface sedimentary environments. J Appl Geophys 101:95–107CrossRefGoogle Scholar
  54. Schön JH (1998) Physical properties of rocks: fundamentals and principles of petrophysics. Pergamon Press, OxfordGoogle Scholar
  55. Schwarzbach C, Börner RU, Spitzer K (2005) Two-dimensional inversion of direct current resistivity data using a parallel, multi-objective genetic algorithm. Geophys J Int 162:685–695CrossRefGoogle Scholar
  56. Seteiono R, Liu H (1997) Neural-network feature selector. IEEE Trans Neural Netw 8:354–362Google Scholar
  57. Topp GC, Davis JL, Annan AP (1980) Electromagnetic determination of soil water content: measurements in coaxial transmission lines. Water Resour Res 16:574–582CrossRefGoogle Scholar
  58. Tronicke J, Holliger K (2005) Quantitative integration of hydrogeophysical data: conditional geostatistical simulation for characterizing heterogeneous alluvial aquifers. Geophysics 70:H1–H10CrossRefGoogle Scholar
  59. Tronicke J, Paasche H, Böniger U (2012) Crosshole traveltime tomography using particle swarm optimization: a near-surface field example. Geophysics 77:R19–R32CrossRefGoogle Scholar
  60. Van der Baan M, Jutten C (2000) Neural networks in geophysical applications. Geophysics 65:1032–1047CrossRefGoogle Scholar
  61. Velis DR (2001) Traveltime inversion for 2D anomaly structures. Geophysics 66:1481–1487CrossRefGoogle Scholar
  62. Verikas A, Bacauskiene M (2002) Feature selection with neural networks. Pattern Recognit Lett 23:1323–1335CrossRefGoogle Scholar
  63. Wharton RP, Hazen GA, Rau RN, Best DL (1980) Advancements in electromagnetic propagation logging. In: SPE 9267 American institute of mining metallurgical and petroleum engineersGoogle Scholar
  64. Widrow B, Greenblatt A, Kim Y, Park D (2013) The No-Prop algorithm: a new learning algorithm for multilayer neural networks. Neural Netw 37:182–188CrossRefGoogle Scholar
  65. Wu X, Rozycki P, Wilamowski BM (2015) A hybrid constructive algorithm for single-layer feedforward networks learning. IEEE Trans Neural Netw Learn Syst 26:1659–1668CrossRefGoogle Scholar
  66. Wyllie MRJ, Gregory AR, Grander LW (1956) Elastic wave velocities in heterogeneous and porous media. Geophysics 26:41–70CrossRefGoogle Scholar
  67. Yamamoto T (2001) Imaging the permeability structure within the near-surface sediments by acoustic crosswell tomography. J Appl Geophys 47:1–11CrossRefGoogle Scholar
  68. Yan H, Yang J (2015) Locality preserving score for joint feature weights learning. Neural Netw 69:126–134CrossRefGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2016

Authors and Affiliations

  • Abduljabbar Asadi
    • 1
    Email author
  • Peter Dietrich
    • 1
  • Hendrik Paasche
    • 1
  1. 1.Department Monitoring and Exploration TechnologiesUFZ - Helmholtz Centre for Environmental ResearchLeipzigGermany

Personalised recommendations