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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
Overview
• Motivations and previous work • Modelling approach• Examples: current and future work• Conclusion
Overview
• Motivations and previous work• Modelling approach• Examples: current and future work• Conclusion
Note: JI = Joint Inversion
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
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.gifImage 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?
Previous workPetrophysics 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
Previous workPetrophysics 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 constraintsFrom 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
Previous workPetrophysics 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
Previous workPetrophysics 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
Previous work
Structural information: Derive covariance matrix
Explore & update geological model space given structural constraints
Test against geophysicsin probabilistic framework
Zhou J., Revil A. and Jardani A. 2016, Stochastic structure-constrained image-guided inversionof geophysical data, Geophysics 81(2), P.E89-E101.
Zhou et al. 2016Geology and geophysics Geop
Geol
Petro
Previous workGeology 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 inversionof geophysical data, Geophysics 81(2), P.E89-E101.
Geop
Geol
Petro
Previous workmultiple 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)
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:
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
Overview
• Motivations and previous work • Modelling approach• Examples: current and future work• Conclusion
Use of geology
Monte Carlo PerturbationGeological rules
Geol data
𝑝𝑘 ,𝑖
Measurement with uncertainty
Set of geologically plausible models
from best guess modelStatistical geological model
Paper in prep.
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
¿¿
Integrate Petrophysics and Geology in geophysics
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
Workflow Summary
Giraud et al. 2016
Cost functionJoint cost function (least-square)
𝜃 (𝒎 )=(𝒅−𝒈 (𝒎 ) )𝑇𝑪𝒅−1 (𝒅−𝒈 (𝒎 ) )+ (𝒎−𝒎0 )𝑇𝑪𝒎
−1 (𝒎−𝒎0 )
𝒈 (𝒎 )=[ ¿𝒈𝒈 (𝒎 )¿𝒈𝒎 (𝒎 )] ,𝒎=[𝒎𝒈 ,𝒎𝒎 ]𝑇 ,𝒅=[𝒅𝒈 ,𝒅𝒎 ]𝑇 ,𝑪𝒅=[𝑪𝒅
𝒈 00 𝑪𝒅
𝒎] ,𝑪𝒎=[𝑪𝒎𝒈 0
0 𝑪𝒎𝒎] ,𝑪𝒑=[𝑪𝒑
𝒈 00 𝑪𝒑
𝒎]
𝑷 (𝒎 )=∑𝑘=1
𝑛 𝑓
¿¿
Petrophysical constraint
With:
Paper in prep.
Conditioning Petro. Const.
Geology-Petrophysics Constraint
𝑷 (𝒎 )=∑𝑘=1
𝑛 𝑓
¿¿
Global Petrophysical constraint
Resulting geol. model from simulations
Petro. statistics
One function applied to the entire model
Paper in prep.
Conditioning Petro. Const.Conditioning using geology – synth. example
1 function per cell
True rock model
Statistical geological model
In one particular cell
Model optimizationModel update: fixed-point method
𝒎𝑘+ 1=𝒎𝑘+[𝑮𝑘𝑇𝑪𝑑
− 1𝑮𝑘+𝑪𝒎−𝟏+ 𝑱𝑘𝑇𝑪𝑝
−1 𝑱𝑘 ]−1 [𝑮𝑘𝑇𝑪𝑑
− 1 (𝒅0−𝒈 (𝒎𝑘))−𝑪𝐦−𝟏 (𝒎𝑘−𝒎0 )+ 𝑱𝑘𝑇𝑪𝐩
−𝟏 (𝑷𝒎𝒂𝒙−𝑷 (𝒎𝑘)) ] Quasi-Newton Damping not necessary No Tikhonov
Posterior analysis
¿ Joint Petro – Geol likelihood
+ Fisher information
+ use of score to derive indicators
Paper in prep.
Sensitivity analysisValidation 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
Incr
easi
ng d
egre
e of
inte
grat
ion
NC
P
P
GP
GP
No Constraints
Global Petrophysics
Global Petrophysics
Geology & Petrophysics
Geology & Petrophysics
Overview
• Motivations and previous work • Modelling approach• Examples: current and future work• Current and future work• Conclusion
Joint inversionProof of concept
Testing joint inversion workflowModel 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 DataMagnetic dataJoint Inversion Prior and constraints
(1)
(2)
(1)
Petrophysical constraint
Giraud et al. 2016a
Magnetics
Gravity
True model
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 constP
Petro conditioningGP
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
True model in cube view
True model – section view
Statistic geological model – Mansfield geological data
More complex modelRock 1
Rock 2
Rock 3
Rock 4
Rock 5
Rock 6
Top viewRock type
Rock type
Paper in prep.
2D Inversion results
Horizontal position (km)
Kg/m³ SIGravity – true model Magnetic – true model
Depth (km)
Dep
th (k
m)
Dep
th (k
m)
NC
P
GP
GP
Geometries of gravity and magnetic models do not match.Test case on synthetic geophysical data using geological model.
2D Inversion results
Horizontal position (km) Depth (km)
Dep
th (k
m)
Dep
th (k
m)
True modelTrue model
NC
P
P
GP
GP
True model geometry
2D Inversion results
Horizontal position (km) Depth (km)
Dep
th (k
m)
Dep
th (k
m)
True modelTrue model
NC
P
P
GP
GP
2D Inversion results
Horizontal position (km) Depth (km)
Dep
th (k
m)
Dep
th (k
m)
True modelTrue model
NC
P
P
GP
GP
2D Inversion results
Horizontal position (km) Depth (km)
Dep
th (k
m)
Dep
th (k
m)
True modelTrue model
NC
P
P
GP
GP
2D Inversion resultsD
epth
(km
)NC
P
P
GP
GP
Paper in prep.
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
Inversion results In a nutshell
NC P P GP GP
Paper in prep.
Boxplot of likelihood
Inversion results In a nutshell
NC P P GP GP
Paper in prep.
Boxplot of likelihood
Circle size
model fit
MagneticsQ: 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. 1998² Pirajno and Occhipinti 2000
deposits possible deposits
cross-section modified from ²
Yerrida basin: case study
Magnetics
Area location (modified from¹)
¹ Pirajno et al. 1998² 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
Overview
• Motivations and previous work • Modelling approach• Examples: current and future work• Conclusion and discussion
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
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
AcknowledgementsFor 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
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.
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.
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.
Thank you for your attention
Questions (?)
