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Integration of geological and petrophysical constraints in geophysical joint inversion

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Jeremie Giraud's PhD research being conducted at the Centre for Exploration Targeting, University of Western Australia is investigating the use of probabilistic geological models and statistical distributions of petrophysics to constrain joint potential field inversion.

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  • nice way to perturb geology foliation uncertainty measures into 3D
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Integration of geological and petrophysical constraints in geophysical joint inversion

  1. 1. Integration of geological and petrophysical constraints in geophysical joint inversion Jérémie Giraud*, Mark Jessell, Mark Lindsay, Evren Pakyuz-Charrier and Roland Martin CET, Friday 5 August, 2016 3D Interest Group Meeting
  2. 2. Overview • Motivations and previous work • Modelling approach • Examples: current and future work • Conclusion
  3. 3. Overview • Motivations and previous work • Modelling approach • Examples: current and future work • Conclusion Note: JI = Joint Inversion
  4. 4. Geoscience integration in exploration scenarios Petrophysics Geophysics Geology Petrophysics Geophysics geology  Use of complementarity: Common realization space  Statistical framework, Quantitative approach  Estimate uncertainty  Reduce the risk
  5. 5. Geoscience integration in exploration scenarios Petrophysics: Rock properties Geophysics: bulk Physical prop. of medium Geology: Structure & rock type Refs: Hatfield K. L., Evans A. J. and Harvey P. K. 2002, Defining petrophysical units of the Palmer Deep sites from let 178, Proceedings of the Ocean Drilling Program, Scientific Results. Ocean Drilling Program, pp1-17. Anticline: http://facweb.bhc.edu/academics/science/harwoodr/GEOL101/Study/Images/Anticline.gif Image geophy: http://www.earthexplorer.com/2013/images/VOXI-3Dmap.jpg from http://explorationgeophysics.info/?cat=8 ? ?  How to use each technique, in an integrated workflow?
  6. 6. Previous work Petrophysics and geophysics (JI) Prior information: Categorical model, can be deformed  Constraint: force a relationship between model values,  Localised: inside each facies Use of prior information From Zhang J. and Revil A. 2015, 2D joint inversion of geophysical data using petrophysical clustering and facies deformation, Geophysics 80(5), M69-M88. Zhang J. and Revil A. 2015 Geop Geol Petro Resistivity vs density
  7. 7. Previous work Petrophysics and geophysics Values of rock properties are modified to fit geophysical data Prior information Zhang J. and Revil A. 2015  Geometry of geology can be deformed,  Little constraint on geology, localised constraints From Zhang J. and Revil A. 2015, 2D joint inversion of geophysical data using petrophysical clustering and facies deformation, Geophysics 80(5), M69-M88. Geop Geol Petro
  8. 8. Previous work Petrophysics and geophysics (JI) Prior information  Force inverted model to form clusters around specified values  Centre of clusters known  Limited statistics  Minimum information on geology necessary Sun J. and Li Y., 2016, Joint inversion of multiple geophysical data using guided fuzzy c-means clustering, Geophysics 81(3), P.ID37-ID57. Sun J. and Li Y., 2016 Geop Geol Petro Global constraint, applied to the entire model Tested on more complex models by Carter-McAuslan et al. 2015
  9. 9. Previous work Petrophysics and geophysics Sun J. and Li Y., 2016, Joint inversion of multiple geophysical data using guided fuzzy c-means clustering, Geophysics 81(3), P.ID37-ID57. Sun J. and Li Y., 2016 Geop Geol Petro
  10. 10. Previous work Structural information: Derive covariance matrix  Explore & update geological model space given structural constraints  Test against geophysics in probabilistic framework Zhou J., Revil A. and Jardani A. 2016, Stochastic structure-constrained image-guided inversion of geophysical data, Geophysics 81(2), P.E89-E101. Zhou et al. 2016 Geology and geophysics Geop Geol Petro
  11. 11. Previous work Geology and geophysics  Only one geophysical dataset inverted for  Little use of petrophysics, large number of trials, use of geology in categorical fashion categorical Modified from Zhou et al. 2016 Zhou J., Revil A. and Jardani A. 2016, Stochastic structure-constrained image-guided inversion of geophysical data, Geophysics 81(2), P.E89-E101. Geop Geol Petro
  12. 12. Previous work multiple geophysical datasets  Common approach: structural similarity between mode  Inverting several geophysical datasets at the same time Assumption: geometries of the different models do match. Abubakar et al. 2012 Q: how to integrate petrophysics, quantitative geology and petrophysics while honouring all? Abubakar A., Gao G., Habashy T. M. and Liu J. 2012, Joint inversion approaches for geophysical electromagnetic and elastic full-waveform data, Inverse Problems 28, p.1-19, Doi: doi:10.1088/0266-5611/28/5/055016 Geop Geol Petro (initially introduced by Gallardo and Meju 2003)
  13. 13. Previous work Geology  great improvement to reduce ill-determination Petrophysics: statistics of measurements not always honoured; use of constitutive equations requires very high level of prior information Petrophysics Geophysics  Structural constraints, good improvement to enforce structural similarity between models Hypothesis may not be robust in some cases  great improvement, reduce non-uniqueness Mostly use of discrete/fixed topology or use of best guess models, which can be depend on user expertise Geop Geol Petro State of the art in integrating:
  14. 14. Integration Aims Geology  Petrophysics: constraints that respect statistics of measurements Petrophysics Geophysics  Invert several datasets simultaneously  Account for geology’s AND petrophysics’ statistics  Robust to discrepancy between geometry of different models  Capture and reproduce the statistics  Robust to more complex scenarios & &  Not categorical/discrete description => Statistical description Geop Geol Petro Next steps
  15. 15. Overview • Motivations and previous work • Modelling approach • Examples: current and future work • Conclusion
  16. 16. Use of geology Monte Carlo Perturbation Geological rules Geol data 𝑝 𝑘,𝑖 Measurement with uncertainty Set of geologically plausible models ≠ from best guess model Statistical geological model Paper in prep.
  17. 17. Use of petrophysics Categorical, discrete clusters Statistical framework P1 P2 P1 P2 PDFs  Geological differentiation that does not fit reality  Can reproduce statistics of measurements 𝑷 𝒎 = 𝑘=1 𝑛 𝑓 𝜔 𝑘 𝐍(𝒎|𝝁 𝒌, 𝝈 𝒌  Integrate Petrophysics and Geology in geophysics
  18. 18. Use of geophysics  Reproduce statistics of measurements  In agreement with geological data  Reproduce the observed physics of the medium Prior information Starting model (guess given state of knowledge) Geophysical data Image of data: http://www.earthexplorer.com/2010-11/images/2_Santos-Basin-b.jpg Geophysical inversion Updated model Constraints: External sources of info
  19. 19. Workflow Summary Giraud et al. 2016
  20. 20. Cost function Joint cost function (least-square) 𝜃 𝒎 = 𝒅 − 𝒈 𝒎 𝑇 𝑪 𝒅 −1 𝒅 − 𝒈 𝒎 + 𝒎 − 𝒎0 𝑇 𝑪 𝒎 −1 𝒎 − 𝒎0 + 𝑷 𝒎𝒂𝒙 − 𝑷(𝐦 𝑇 𝑪 𝒑 −1 𝑷 𝒎𝒂𝒙 − 𝑷(𝐦 𝒈 𝒎 = 𝒈 𝒈 𝒎 𝒈 𝒎 𝒎 , 𝒎 = 𝒎 𝒈, 𝒎 𝒎 𝑇 , 𝒅 = 𝒅 𝒈, 𝒅 𝒎 𝑇 , 𝑪 𝒅 = 𝑪 𝒅 𝒈 0 0 𝑪 𝒅 𝒎 , 𝑪 𝒎 = 𝑪 𝒎 𝒈 0 0 𝑪 𝒎 𝒎 , 𝑪 𝒑 = 𝑪 𝒑 𝒈 0 0 𝑪 𝒑 𝒎 𝑷 𝒎 = 𝑘=1 𝑛 𝑓 𝜔 𝑘 𝐍(𝒎|𝝁 𝒌, 𝝈 𝒌 Petrophysical constraint With: Paper in prep.
  21. 21. Conditioning Petro. Const. Geology-Petrophysics Constraint 𝑷 𝒎 = 𝑘=1 𝑛 𝑓 𝜔 𝑘 𝐍(𝒎|𝝁 𝒌, 𝝈 𝒌 Global Petrophysical constraint Resulting geol. model from simulations Petro. statistics One function applied to the entire model Paper in prep.
  22. 22. Conditioning Petro. Const. Conditioning using geology – synth. example 1 function per cell True rock model Statistical geological model In one particular cell
  23. 23. Model optimization Model update: fixed-point method 𝒎 𝑘+1 = 𝒎 𝑘 + 𝑮 𝑘 𝑇 𝑪 𝑑 −1 𝑮 𝑘 + 𝑪 𝒎 −𝟏 + 𝑱 𝑘 𝑇 𝑪 𝑝 −1 𝑱 𝑘 −1 𝑮 𝑘 𝑇 𝑪 𝑑 −1 𝒅0 − 𝒈(𝒎 𝑘 − 𝑪 𝐦 −𝟏 𝒎 𝑘 − 𝒎0  Quasi-Newton  Damping not necessary  No Tikhonov Posterior analysis 𝑳 𝒎 = 𝑷(𝒎|𝒎 𝒈𝒆𝒐𝒍 Joint Petro – Geol likelihood + Fisher information + use of score to derive indicators Paper in prep.
  24. 24. Sensitivity analysis Validation of the workflow: step-by-step integration Single domain: Unconstrained inversion Single domain: petrophysics only Joint inversion: Petrophysics only Single domain: Geology and Petrophysics Joint inversion: Geology and Petrophysics Increasingdegreeofintegration NC P P GP GP No Constraints Global Petrophysics Global Petrophysics Geology & Petrophysics Geology & Petrophysics
  25. 25. Overview • Motivations and previous work • Modelling approach • Examples: current and future work • Current and future work • Conclusion
  26. 26. Joint inversion Proof of concept Testing joint inversion workflow Model confidence Constrained inversion Geological prior knowledge Prior information and constraints for joint inversion Joint inversion Petrophysical data Petrophysical constraints Petrophysical constraints Constrained inversion Model confidence Geology-derived petrophysical constraints Geology-derived petrophysical constraints Colour legend: Gravity Data Magnetic data Joint Inversion Prior and constraints (1) (2) (1) Petrophysical constraint Giraud et al. 2016a Magnetics Gravity True model
  27. 27. Joint inversion Sensitivity to integration level Constrained Single domain Joint inversion Density contrast mag. susc. No const Petro const JI petro conditioning NC P GP Giraud et al. 2016a JI petro const P Petro conditioningGP
  28. 28. Joint inversion Starting model for JI Joint inversion Clustering: separate domain, non-constrained vs JI  Correlation between  Petrophysics honoured  Likelihood increased Giraud et al. 2016b
  29. 29. True model in cube view True model – section view Statistic geological model – Mansfield geological data More complex model Rock 1 Rock 2 Rock 3 Rock 4 Rock 5 Rock 6 Top view Rock type Rock type Paper in prep.
  30. 30. 2D Inversion results Horizontal position (km) Kg/m³ SIGravity – true model Magnetic – true model Depth (km) Depth(km) Depth(km) NC P GP GP Geometries of gravity and magnetic models do not match. Test case on synthetic geophysical data using geological model.
  31. 31. 2D Inversion results Horizontal position (km) Depth (km) Depth(km) Depth(km) True modelTrue model NC P P GP GP True model geometry
  32. 32. 2D Inversion results Horizontal position (km) Depth (km) Depth(km) Depth(km) True modelTrue model NC P P GP GP
  33. 33. 2D Inversion results Horizontal position (km) Depth (km) Depth(km) Depth(km) True modelTrue model NC P P GP GP
  34. 34. 2D Inversion results Horizontal position (km) Depth (km) Depth(km) Depth(km) True modelTrue model NC P P GP GP
  35. 35. 2D Inversion results Depth(km) NC P P GP GP Paper in prep.
  36. 36. Inversion results  Colour scale: likelihood  Contour lines: petrophysical distribution  Geology + Petrophysics Increasing geological plausibility  Joint inversion: increase consistency between inverted models NC P P GP Paper in prep. GP
  37. 37. Inversion results In a nutshell NC P P GP GP Paper in prep. Boxplot of likelihood
  38. 38. Inversion results In a nutshell NC P P GP GP Paper in prep. Boxplot of likelihood Circle size model fit
  39. 39. Magnetics Q: How does it dip? How sure are we?  Integrated workflow: 3D Geology, Petro, Geophysics  Quantification of uncertainty and risk Area location (modified from¹) ¹ Pirajno et al. 1998 ² Pirajno and Occhipinti 2000 deposits possible deposits cross-section modified from ² Yerrida basin: case study
  40. 40. Magnetics Area location (modified from¹) ¹ Pirajno et al. 1998 ² Pirajno and Occhipinti 2000 deposits possible deposits cross-section modified from ² Yerrida basin: case study Q: How does it dip? How sure are we?  Integrated workflow: 3D Geology, Petro, Geophysics  Quantification of uncertainty and risk
  41. 41. Overview • Motivations and previous work • Modelling approach • Examples: current and future work • Conclusion and discussion
  42. 42. Conclusion  Tested on “complex” synthetic (statistically true geologically) - Integration gives better results - Obtain results with low model misfit  Higher degree of integration than other workflows  Respect the statistics  Consistent with geology  Honours geophysics  (tried to) address some of the weaknesses of previous work
  43. 43. Discussion  Investigate bigger models, more complex  Start investigating a case study – Compare with traditional exploration – Quantify uncertainty / risk – Identify new prospects?  Petrophysics: rock types not always very differentiated – geological useful to mitigate this  Possibility to add another geophysical method
  44. 44. Acknowledgements For interesting discussions – Jeff Shragge – Des Fitzgerald – Chris Wijns – André Revil And to Geological Survey of Victoria for releasing the geological data of the Mansfield area
  45. 45. References (1/2) and useful papers • Abubakar A., Gao G. and Liu J. 2012, Joint Inversion approaches for geophysical electromagnetic and elastic full-waveform data, Inverser Problems 28. • Bosch M., Bertorelli G., Alvarez G., Moreno A. and Colmenares R. 2015, Reservoir uncertainty description via petrophysical inversion of seismic data, The Leading Edge 34(9), 1018-1026. • Gallardo L. and Meju M. A. 2003, Characterization of heterogeneous near-surface materials by joint 2D inversion of dc resistivity and seismic data, Geophysical Research Letters 30(13), p.1-1 – p.1-4. • Carter-McAuslan A., Lelievre P. and Colin G. Farquharson 2015, A study of fuzzy c-means coupling for joint inversion, using seismic tomography and gravity test scenarios, Geophysics 80(1), P. W1-W15. • Dell’Aversana P., Bernasconi G., Miotti F. and Rovetta D. 2011, Joint inversion of rock properties from sonic, resistivity and density well-log measurements, Geophysical Prospecting 59, 1144-1154. • Guillen A., Calcagno P., Courrioux G., Joly A. and Ledru P. 2008, Geological modelling from field data and geological knowledge Part II. Modelling validation using gravity and magnetic data inversion, Physics of Earth and Planetary Interiors 71, 158-169. • Sun J. and Li Y. 2015, Multidomain petrophysically constrainted inversion and geology differentiation using guided fuzzy c-means clustering, Geophysicis 80(4), P. ID1-ID18. • Sun, J., and Li, Y., 2012, Joint inversion of multiple geophysical data: A petrophysical approach using guided fuzzy c-means clustering: SEG Las Vegas 2012 Annual Meeting, 1 -5. • Martin R., Monteiller V., Komatitsch D, Perrouty S., Jessell M. W., Bonvalot S. and Lindsay M. D. 2013, Gravity inversion using wavelet-based compression on parallel hybrid GPU/CPU systems: application to South-West Ghana, Geophysical Journal International 195(3), 1594-1619.
  46. 46. References (2/2) and useful papers • Bosch M. 1999, Lithologic tomography: from plural geophysical data to lithology estimation, journal of geophysical research 104, 749-766. • Fregoso E. and Gallardo L. 2009, Cross-gradients joint 3D inversion with applications to gravity and magnetic data, Geophysics 74(4), P.L31-42. • Garofalo F., Sauvin G., Socco L. V. and Lecompte I. 2015, Joint inversion of seismic and electric data applied to 2D media, Geophysicis 80(4), P. EN93-EN104. • Wellmann J. F., Finsterle S. and Croucher A. 2013, Integrating structural geological data into the inverse modelling framework of iTOUGH2, Computers & Geosciences 65, 95-109. • Lindsay M., Jessell M. W., Ailleres L., Perrouty S., de Kemp E. and Betts P.G. 2013, Geodiversity: Exploration of 3D geological model space, Tectonophysics 594, 27-37. • Medina E., Miotti F., Ratti S., Sangewar S., Andreis D. L. and Giraud J. 2015, SEG Annual Meeting Extended Abstracts. • Sun J. and Li Y. 2015, Multidomain petrophysically constrainted inversion and geology differentiation using guided fuzzy c-means clustering, Geophysicis 80(4), P. ID1-ID18. • Zhou J., Revil A. and Jardani A. 2016, Stochasic structure-constrained image-guided inversion of geophysical data, Geophysics 81(2), E89-E101. • Zhang J. and Revil A. 2015, 2D joint inversion of geophysical data using petrophysical clustering and facies deformation, Geophysics 80(5), M69-M88.
  47. 47. Conference papers related to presented results • Giraud. J., Jessell, M., Lindsay, M., Martin, R., Pakyuz-Charrier, E., Ogarko, V. Uncertainty reduction of gravity and magnetic inversion through the integration of petrophysical constraints and geological data, EGU General Assembly 2016, Vienna, Geophysical research abstracts. • Giraud. J., Jessell, M., Lindsay, M., Martin, R., Pakyuz-Charrier, E., Ogarko, V. Geophysical joint inversion using statistical petrophysical constraints and prior information, ASEG-PESA 2016: Adelaide, Extended Abstract. • Giraud. J., Jessell, M., Lindsay, M., M., Pakyuz-Charrier, E., Martin, M. Integrated geophysical joint inversion using petrophysical constraints and geological modelling, SEG Annual Meeting 2016, Dallas, Extended Abstract.
  48. 48. Thank you for your attention Questions (?)

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