christian-albrechts-universität kiel 24.03.2015 - dgg-tagung hannover a combined elastic waveform...
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Christian-Albrechts-Universität Kiel 24.03.2015 - DGG-Tagung Hannover
A combined elastic waveform and gravity inversion for improved density model resolution applied to the Marmousi-II
model
Daniel Wehner, Daniel Köhn, Denise De Nil, Sabine Schmidt, Said al Hagrey, Hans-Jürgen Götze and
Wolfgang Rabbel
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Overview
• Motivation
• Gravity modelling
• Theory of FWI and Joint Inversion
• 2-step Joint Inversion applied to the Marmousi-II model
• Outlook
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True modified elastic 2D Marmousi-II model
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Initial model for FWI
smoothed versions of the true model
constant water-layer above constant halfspace
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Inversion with 2 Hz, 23 iterations
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Inversion with 2-5 Hz, 153 iterations
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Inversion with 2-5-10 Hz, 278 iterations
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Results for FWI with 2-5-10-20 Hz
Problem
wellresolved
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Results for Joint Inversion
True model
FWI alone
How do we get better resolution ?
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Solution?Integration of GRAVITY data into seismic FWI
workflow
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Solution?Integration of GRAVITY data into seismic FWI
workflow
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1. Gravity Modelling
Kernel K
Integration in existing FWI FD-Grid
Gravity of a prism
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1. Gravity Modelling• Cylindrical test model• distance between stations: 200 m
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1. Gravity Modelling• Marmousi-II test model• distance between stations: 200 m
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2. Objective Function• Objective function for FWI
• Minimizing the objective function by iteratively updating seismic velocities and densities with Quasi-Newton l-BFGS method (Nocedal & Wright, 2006; Brossier, 2011)
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2. Joint Objective Function• Modified objective function for Joint Inversion
• Minimizing the objective function by iteratively updating seismic velocities and densities with Quasi-Newton l-BFGS method (Nocedal & Wright, 2006; Brossier, 2011)
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3. Gradient• Gradient for the density (FWI) (Köhn et al., 2012)
Construction of the gradient by zero-lag correlation of forward wavefield and backpropagated data residual wavefield
• Gradient for the density (Gravity)
Construction of the gradient by the downward continuation of the gravity field residuals from the observation surface .
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Application: Step 1, pure seismic FWI
Inversion for allparameters
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Application: Step 2, inital model
v-models kept fixed
Inversion forthe density
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Application: Step 2, high λ
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Application: Step 2, high λ
long wavelength model
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Application: Step 2, low λ
Problem solved
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Results for Joint Inversion
True model
FWI alone
Joint Inversion
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Conclusion
Improvement
• good supplementation of seismic and gravity data
• good resolution of the density model due to introduction of long wavelength information by gravity data
Outlook
• estimate best weighting between seismic and gravity
• further regularization of gravity inversion
• inversion of gravity gradient data more sensitive to local structures
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Thank you very much for your attention
Acknowledgements:
• ANGUS+ research project funded by the German Federal Ministry of Education and Research (BMBF)
• MeProRisk-II research project funded by the Federal Ministry for the Environment, Nature Conservation, Building and Nuclear Safety (BMU)
• Inversions were performed on the NEC-HPC Linux-Cluster at Kiel University
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• Brossier, R. [2011] Two-dimensional frequency-domain visco-elastic full waveform inversion: Parallel algorithms, optimization and performance. Computers & Geosciences, 37(4),444-455.
• Köhn, D., De Nil, D., Kurzmann, A., Przebindowska, A. and Bohlen T. [2012] On the influence of model parametrization in elastic full waveform tomography. Geophysical Journal International, 191(1), 325-345.
• Nocedal, J. and Wright, S. [2006] Numerical Optimization. Springer, New York.
• Plessix, R.E. and Mulder, W.A. [2004] Frequency-domain finite-difference amplitude-preserving migration. Geophysical Journal International, 157(3), 975-987.
• Zhdanov, M.S., Liu, X., Wilson, G.A. and Wan, L. [2011] Potential field migration for rapid imaging of gravity gradiometry data. Geophysical Prospecting, 59, 1052-1071.
literature
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Comparison of density models for FWI
True model
FWI result
Absolute error
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Comparison of density models for Joint Inversion
True model
Joint Inversion result
Absolute error
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Comparison of density models for Joint Inversion
FWI result
Joint Inversion result
Absolute error
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Ambiguity between parameter classes
fromKöhn et al.
(2012)
CTS model
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Influence of inverse Hessian approximation
Inverse Hessian
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Influence of inverse Hessian approximation
Inverse Hessian (Plessix & Mulder, 2004)
minimum and maximum receiver positons ; source position
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Gravity gradient by adjoint operator
• adjoint operator for gravity (Zhdanov, 2011)
with and
• adjoint operator mirrors depth point at observation surface