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

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Abstract

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.

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References

  • Angioni T, Rechtien RD, Cardimona SJ, Luna R (2003) Crosshole seismic tomography and borehole logging for engineering site characterization in Sikeston. Tectonophysics 368:119–137

    Article  Google Scholar 

  • Archie GE (1942) The electrical resistivity log as an aid in determining some reservoir characteristics. Trans Am Inst Mineral Met 146:54–62

    Google Scholar 

  • 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

  • Aster RC, Borchers B, Thurber CH (2005) Parameter Estimation and Inverse problems. Academic Press, Cambridge

    Google Scholar 

  • Bailly K, Milgram M (2009) Boosting feature selection for neural network based regression. Neural Netw 22:748–756

    Article  Google Scholar 

  • 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 1–15

  • Ban JC, Chang CH (2013) The learning problem of multi-layer neural networks. Neural Netw 46:116–123

    Article  Google Scholar 

  • Binley A, Winship P, Middelton R (2001) High-resolution characterization of vadose zone dynamics using cross-borehole radar. Water Resour Res 37:2639–2652

    Article  Google Scholar 

  • Bodin T, Sambridge M (2009) Seismic tomography with the reversible jump algorithm. Geophys J Int 178:1411–1436

    Article  Google Scholar 

  • Bodin T, Sambridge M, Rawlinson N, Arroucau P (2012) Transdimensional tomography with unknown data noise. Geophys J Int 189:1536–1556

    Article  Google Scholar 

  • 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–J25

    Article  Google Scholar 

  • Bosch M, Mukerji T, Gonzalez FE (2010) Seismic inversion for reservoir properties combining statistical rock physics and geostatistics: a review. Geophysics 75:165–176

    Article  Google Scholar 

  • Breiman L, Friedman JH (1985) Estimating optimal transformations for multiple regression and correlation. J Am Stat Assoc 80:580–598

    Article  Google Scholar 

  • Cassiani G, Böhm G, Vesnaver A, Nicolich R (1998) A geostatistical framework for incorporating seismic tomography auxiliary data into hydraulic conductivity. J Hydrol 206:58–74

    Article  Google Scholar 

  • Cawley GC, Janacek GJ, Haylock MR, Dorling SR (2007) Predictive uncertainty in environmental modelling. Neural Netw 20:537–549

    Article  Google Scholar 

  • 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 37:1603–1613

    Article  Google Scholar 

  • Dafflon B, Irving J, Holliger K (2009) Simulated-annealing-based conditional simulation for the local-scale characterization of heterogeneous aquifers. J Appl Geophys 68:60–70

    Article  Google Scholar 

  • 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 26:1202–1213

    Article  Google Scholar 

  • 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 35:2671–2683

    Article  Google Scholar 

  • Frénay B, Doquire G, Verleysen M (2013) Is mutual information adequate for feature selection in regression? Neural Netw 48:1–7

    Article  Google Scholar 

  • Friedel S (2003) Resolution, stability and efficiency of resistivity tomography estimated from a generalized invers approach. Geophys J Int 153:305–316

    Article  Google Scholar 

  • Ganivada A, Sankar Ray S, Pal SK (2013) Fuzzy rough sets, and a granular neural network for unsupervised feature selection. Neural Netw 48:91–108

    Article  Google Scholar 

  • Gassmann F (1951) Über die Elastizität poröser Medien. Vierteljahresschrift der Naturforsch. Ges., Zürich, vol 96, pp 1–22

  • 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 47:135–152

    Article  Google Scholar 

  • Hornik K (1991) Approximation capabilities of multilayer feedforward networks. Neural Netw 4:251–257

    Article  Google Scholar 

  • 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 37:2431–2456

    Article  Google Scholar 

  • Jain AK, Mao J, Mohiuddin KM (1996) Artificial neural networks: a tutorial. IEEE Comput 29:31–44

    Article  Google Scholar 

  • Jing X (2012) Robust adaptive learning of feedforward neural networks via LMI optimizations. Neural Netw 31:33–45

    Article  Google Scholar 

  • Kennedy J, Eberhart RC (1995) Particle swarm optimization. In: Proceedings of IEEE international conference on neural networks, Piscataway, 1942–1948

  • 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 78:740–747

    Article  Google Scholar 

  • Kiranyaz S, Ince T, Yildirim AG (2009) Evolutionary artificial neural networks by multi-dimensional particle swarm optimization. Neural Netw 22:1448–1462

    Article  Google Scholar 

  • Knödel K, Krummel H, Lange G (1997) Handbuch zur Erkundung des Untergrundes von Deponien und Altlasten. Springer, Berlin

    Google Scholar 

  • 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 57:1049–1065

    Article  Google Scholar 

  • Leite EP, Vidal AC (2011) 3D porosity prediction from seismic inversion and neural networks. Comput Geosci 37:1174–1180

    Article  Google Scholar 

  • Leray P, Gallinari P (2002) Feature selection with neural networks. Behaviormetrika 26:145–166

    Article  Google Scholar 

  • Liu H, Motoda H (1998) Feature transformation and subset selection. IEEE Intell Syst 13:26–28

    Google Scholar 

  • Liu H, Motoda H (2001) Feature extraction, construction and selection: a data mining perspective. Kluwer Academic Publishers, Boston

    Book  Google Scholar 

  • Miche Y, Sorjamaa A, Bas P, Simula O, Jutten C, Lendasse A (2010) OP-ELM: optimally pruned extreme learning machine. IEEE Trans Neural Netw 21:158–162

    Article  Google Scholar 

  • Mitchell M (1998) An introduction to genetic algorithms. MIT Press, Cambridge

    Google Scholar 

  • 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, Italy

  • Paasche H (2017a) Translating tomographic ambiguity into the probabilistic inference of hydrologic and engineering target parameters. Geophysics (submitted)

  • Paasche H (2017b) Probabilistic inference of spatially continuous geotechnical parameter fields by means of sparse calibration data and geophysical tomography. Geophys Prospect (submitted)

  • Paasche H, Tronicke J (2007) Cooperative inversion of 2D geophysical data set: a zonal approach based on fuzzy c-means cluster analysis. Geophysics 72:35–39

    Article  Google Scholar 

  • 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–H44

    Article  Google Scholar 

  • Pham DL (2001) Spatial models for fuzzy clustering. Comput Vis Image Underst 84:285–297

    Article  Google Scholar 

  • Poulton MM (2002) Neural networks as an intelligence amplification tool: a review of applications. Geophysics 67:979–993

    Article  Google Scholar 

  • 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 25:303–315

    Article  Google Scholar 

  • 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 82:151–165

    Article  Google Scholar 

  • Raymer DS, Hunt ER, Gardner JS (1980) An improved sonic transit time-to-porosity transform. In: Proceeding of SPWLA 21st ann. Meeting, paper P

  • Razavi S, Tolson BA (2011) A new formulation for feedforward neural networks. IEEE Trans Neural Netw 22:1588–1598

    Article  Google Scholar 

  • 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 2:277–289

    Article  Google Scholar 

  • 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 194:289–303

    Article  Google Scholar 

  • Rumpf M, Tronicke J (2014) Predicting 2D geotechnical parameter fields in near-surface sedimentary environments. J Appl Geophys 101:95–107

    Article  Google Scholar 

  • Schön JH (1998) Physical properties of rocks: fundamentals and principles of petrophysics. Pergamon Press, Oxford

    Google Scholar 

  • 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 162:685–695

    Article  Google Scholar 

  • Seteiono R, Liu H (1997) Neural-network feature selector. IEEE Trans Neural Netw 8:354–362

    Google Scholar 

  • Topp GC, Davis JL, Annan AP (1980) Electromagnetic determination of soil water content: measurements in coaxial transmission lines. Water Resour Res 16:574–582

    Article  Google Scholar 

  • Tronicke J, Holliger K (2005) Quantitative integration of hydrogeophysical data: conditional geostatistical simulation for characterizing heterogeneous alluvial aquifers. Geophysics 70:H1–H10

    Article  Google Scholar 

  • Tronicke J, Paasche H, Böniger U (2012) Crosshole traveltime tomography using particle swarm optimization: a near-surface field example. Geophysics 77:R19–R32

    Article  Google Scholar 

  • Van der Baan M, Jutten C (2000) Neural networks in geophysical applications. Geophysics 65:1032–1047

    Article  Google Scholar 

  • Velis DR (2001) Traveltime inversion for 2D anomaly structures. Geophysics 66:1481–1487

    Article  Google Scholar 

  • Verikas A, Bacauskiene M (2002) Feature selection with neural networks. Pattern Recognit Lett 23:1323–1335

    Article  Google Scholar 

  • Wharton RP, Hazen GA, Rau RN, Best DL (1980) Advancements in electromagnetic propagation logging. In: SPE 9267 American institute of mining metallurgical and petroleum engineers

  • Widrow B, Greenblatt A, Kim Y, Park D (2013) The No-Prop algorithm: a new learning algorithm for multilayer neural networks. Neural Netw 37:182–188

    Article  Google Scholar 

  • Wu X, Rozycki P, Wilamowski BM (2015) A hybrid constructive algorithm for single-layer feedforward networks learning. IEEE Trans Neural Netw Learn Syst 26:1659–1668

    Article  Google Scholar 

  • Wyllie MRJ, Gregory AR, Grander LW (1956) Elastic wave velocities in heterogeneous and porous media. Geophysics 26:41–70

    Article  Google Scholar 

  • Yamamoto T (2001) Imaging the permeability structure within the near-surface sediments by acoustic crosswell tomography. J Appl Geophys 47:1–11

    Article  Google Scholar 

  • Yan H, Yang J (2015) Locality preserving score for joint feature weights learning. Neural Netw 69:126–134

    Article  Google Scholar 

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Authors and Affiliations

  1. Department Monitoring and Exploration Technologies, UFZ - Helmholtz Centre for Environmental Research, Permoserstr. 15, 04318, Leipzig, Germany

    Abduljabbar Asadi, Peter Dietrich & Hendrik Paasche

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  1. Abduljabbar Asadi
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  2. Peter Dietrich
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Correspondence to Abduljabbar Asadi.

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Asadi, A., Dietrich, P. & Paasche, H. 2D probabilistic prediction of sparsely measured earth properties constrained by geophysical imaging fully accounting for tomographic reconstruction ambiguity. Environ Earth Sci 75, 1487 (2016). https://doi.org/10.1007/s12665-016-6288-8

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