Christian-Albrechts-Universität Kiel 24.03.2015 - DGG-Tagung Hannover A combined elastic waveform...

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

Daniel Wehner - DGG-Tagung 2015 Hannover

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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

Christian-Albrechts-Universität Kiel 24.03.2015 - DGG-Tagung Hannover A combined elastic waveform...

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