Mathematical Geosciences

, Volume 49, Issue 8, pp 947–964 | Cite as

Pseudo-outcrop Visualization of Borehole Images and Core Scans

  • Evgeny M. Mirkes
  • Alexander N. Gorban
  • Jeremy Levesley
  • Peter A. S. ElkingtonEmail author
  • James A. Whetton


A pseudo-outcrop visualization is demonstrated for borehole and full-diameter rock core images to augment the ubiquitous unwrapped cylinder view and thereby assist nonspecialist interpreters. The pseudo-outcrop visualization is equivalent to a nonlinear projection of the image from borehole to earth frame of reference that creates a solid volume sliced longitudinally to reveal two or more faces in which the orientations of geological features indicate what is observed in the subsurface. A proxy for grain size is used to modulate the external dimensions of the plot to mimic profiles seen in real outcrops. The volume is created from a mixture of geological boundary elements and texture, the latter being the residue after the sum of boundary elements is subtracted from the original data. In the case of measurements from wireline microresistivity tools, whose circumferential coverage is substantially <100 %, the missing circumferential data are first inpainted using multiscale directional transforms, which decompose the image into its elemental building structures, before reconstructing the full image. The pseudo-outcrop view enables direct observation of the angular relationships between features and aids visual comparison between borehole and core images, especially for the interested nonspecialist.


Wellbore Microresistivity Image Inpainting 



The authors acknowledge the help of John Winship, Technical Advisor at Weatherford Laboratories, UK, for providing core scans.


  1. Assous S, Elkington P, Whetton J (2014) Microresistivity borehole image inpainting. Geophysics 79:D31–D39. doi: 10.1190/geo2013-0188.1 CrossRefGoogle Scholar
  2. Cangelosi R, Goriely A (2007) Component retention in principal component analysis with application to cDNA microarray data. Biol Direct 2:2. doi: 10.1186/1745-6150-2-2 CrossRefGoogle Scholar
  3. Chen J, Wang B (2010) High quality solid texture synthesis using position and index histogram matching. Vis Comput 26:253–262. doi: 10.1007/s00371-009-0408-3 CrossRefGoogle Scholar
  4. Criminisi A, Pérez P, Toyama K (2004) Region filling and object removal by exemplar-based image inpainting. IEEE Trans Image Process 13:1200–1212. doi: 10.1109/TIP.2004.833105 CrossRefGoogle Scholar
  5. Elad M, Starck JL, Querre P, Donoho DL (2005) Simultaneous cartoon and texture image inpainting using morphological component analysis (MCA). Appl Comput Harmon Anal 19:340–358. doi: 10.1016/j.acha.2005.03.005 CrossRefGoogle Scholar
  6. Francos JM, Friedlander B (1998) Parameter estimation of two-dimensional moving average random fields. IEEE Trans Signal Process 46:2157–2165. doi: 10.1109/78.705427 CrossRefGoogle Scholar
  7. Fu HC, Zou CC, Li N, Xiao CW, Zhang CS, Wu XN, Liu RL (2016) A quantitative approach to characterize porosity structure from borehole electrical images and its application in a carbonate reservoir in the Tazhong area, Tarim basin. SPE Reserv Eval Eng. doi: 10.2118/179719-PA
  8. Hurley NF, Zhang T (2011) Method to generate full-bore images using borehole images and multipoint statistics. SPE Reserv Eval Eng 14:204–214. doi: 10.2118/120671-PA CrossRefGoogle Scholar
  9. Joubert JB, Millot P, Montaggioni P, Dymmock S, Andonof L, Kadri N, Torres D (2016) Understanding wireline borehole image workflows from the wellsite to the end user. First Break 34:65–78Google Scholar
  10. Keogh E, Chu S, Hart D, Pazzani M (2004) Segmenting time series: a survey and novel approach. In: Last M, Kandel A, Bunke H (eds) Data mining in time series databases. World Scientific, Singapore, pp 1–22Google Scholar
  11. Nelder JA, Mead R (1965) A simplex method for function minimization. Comput J 7:308–313. doi: 10.1093/comjnl/7.4.308 CrossRefGoogle Scholar
  12. Ojeda S, Vallejos R, Bustos O (2010) A new image segmentation algorithm with applications to image inpainting. Comput Stat Data Anal 54:2082–2093. doi: 10.1016/j.csda.2010.03.021 CrossRefGoogle Scholar
  13. Portilla J, Simoncelli EP (2000) A parametric texture model based on joint statistics of complex wavelet coefficients. Int J Comput Vis 40:49–70. doi: 10.1023/A:1026553619983 CrossRefGoogle Scholar
  14. Rider M, Kennedy M (2011) The geological interpretation of well logs, 3rd edn. Rider-French Consulting Limited, SutherlandGoogle Scholar
  15. Starck JL, Elad M, Donoho DL (2005) Image decomposition via the combination of sparse representations and a variational approach. IEEE Trans Image Process 14:1570–1582. doi: 10.1109/TIP.2005.852206 CrossRefGoogle Scholar
  16. Takeda H, Farsiu S, Milanfar P (2007) Kernel regression for image processing and reconstruction. IEEE Trans Image Process 16:349–366. doi: 10.1109/TIP.2006.888330 CrossRefGoogle Scholar
  17. Urs RD, Da Costa JP, Germain C (2014) Maximum-likelihood based synthesis of volumetric textures from a 2D sample. IEEE Trans Image Process 23:1820–1830. doi: 10.1109/TIP.2014.2307477 CrossRefGoogle Scholar
  18. Wang H, Wellmann J, Li Z, Wang X, Liang R (2017) A segmentation approach for stochastic geological modeling using hidden Markov random fields. Math Geosci 49:145–177. doi: 10.1007/s11004-016-9663-9 CrossRefGoogle Scholar
  19. Woiselle A, Starck JL, Fadili J (2011) 3-d data denoising and inpainting with the low-redundancy fast curvelet transform. J Math Imaging Vis 39:121–139. doi: 10.1007/s10851-010-0231-5 CrossRefGoogle Scholar
  20. Xu C, Torres-Verdín C (2013) Pore system characterization and petrophysical rock classification using a bimodal Gaussian density function. Math Geosci 45:753–771. doi: 10.1007/s11004-013-9473-2 CrossRefGoogle Scholar
  21. Zhang T, Du Y (2014) A multiple-point geostatistical reconstruction method of porous media using soft data and hard data. J Comput Inf Syst 10:7213–7224. doi: 10.12733/jcis11741 Google Scholar
  22. Zhang T, Gelman A, Laronga R (2016) Structure and texture-based fullbore image reconstruction. Math Geosci 48:1–21. doi: 10.1007/s11004-016-9649-7 CrossRefGoogle Scholar

Copyright information

© International Association for Mathematical Geosciences 2017

Authors and Affiliations

  1. 1.Department of MathematicsUniversity of LeicesterLeicesterUK
  2. 2.WeatherfordLoughboroughUK

Personalised recommendations