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.

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. Overview
• Motivations and previous work
• Modelling approach
• Examples: current and future work
• Conclusion

3. Overview
• Motivations and previous work
• Modelling approach
• Examples: current and future work
• Conclusion
Note: JI = Joint Inversion

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. 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. 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. 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. 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. 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. 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. 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. 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. 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. 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. Overview
• Motivations and previous work
• Modelling approach
• Examples: current and future work
• Conclusion

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. 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. 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. Workflow Summary
Giraud et al. 2016

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. 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. Conditioning Petro. Const.
Conditioning using geology – synth. example
1 function per
cell
True rock
model
Statistical
geological
model
In one particular cell

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. 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. Overview
• Motivations and previous work
• Modelling approach
• Examples: current and future work
• Current and future work
• Conclusion

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. 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. 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. 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. 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. 2D Inversion results
Horizontal position (km) Depth (km)
Depth(km)
Depth(km)
True modelTrue model
NC
P
P
GP
GP
True model geometry

32. 2D Inversion results
Horizontal position (km) Depth (km)
Depth(km)
Depth(km)
True modelTrue model
NC
P
P
GP
GP

33. 2D Inversion results
Horizontal position (km) Depth (km)
Depth(km)
Depth(km)
True modelTrue model
NC
P
P
GP
GP

34. 2D Inversion results
Horizontal position (km) Depth (km)
Depth(km)
Depth(km)
True modelTrue model
NC
P
P
GP
GP

35. 2D Inversion results
Depth(km)
NC
P
P
GP
GP
Paper in prep.

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. Inversion results
In a nutshell
NC P P GP GP
Paper in prep.
Boxplot of likelihood

38. Inversion results
In a nutshell
NC P P GP GP
Paper in prep.
Boxplot of likelihood
Circle size
model fit

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. 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. Overview
• Motivations and previous work
• Modelling approach
• Examples: current and future work
• Conclusion and discussion

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. 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. 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. 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. 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. 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. Thank you for your attention
Questions (?)