Stochastic Seismic Inversion using Waveform and Traveltime Data and

Its Application toTime-lapse Monitoring

Youli Quan & Jerry M. HarrisStanford University

November 12, 2008

• Introduction • Motivations• Kalman filter

• Seismic inversion with EnKF

• An example of CO2 storage monitoring

• Conclusions

Outline

• Seismic inversion recovers subsurface elastic properties (e.g., acoustic impedance and velocity) from seismic data.

• Inversion using both waveform and traveltime improves the estimation of velocity.

• Estimation of absolute velocity helps quantitative interpretation of seismic data.

Introduction

Amplitude Traces Impedance Traces

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SeismicInversion

• Images of seismic inversion may be more meaningful for interpretation.

• Deterministic inversion methods normally need less computation.

• Stochastic inversion uses more computing power but can integrate other information (e.g., sonic logs.)

• Ensemble Kalman Filter (EnKF) is a stochastic method used in this study for seismic inversion.

• Seismic monitoring

- To integrate time-lapse seismic data - Dynamic imaging

• Reservoir characterization

- Integration of sonic logs and seismic data

Motivations to Use EnKF

• Dynamic imaging

• Integration of sonic logs and seismic data

Kalman Filter

)( )()1()()1( tttt Gmdkmm

)(ˆ )()()( sonicseismicsonic Gmdkmm

1)( RGCGCGk TTKalman gain

Seismic Inversion with EnKF

],...,[ 1 NddD

],...,[ 1 NmmM

• Define observation function

• Create model & data ensembles using their probability distributions

)(md g

d – poststack seismic data in this case

)(md g

m dPoststack

Full waveform Convolution

Define observation function

Create model ensemble

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Create data ensemble

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• Estimate model parameters with EnKF

)]([ )()1()()1( tttt g MDKMM

K can be simply calculated from the ensemble covariance

It can handle large model and non-linear inverseThis is a Monte Carlo approach

)1/()]()][([ NEE TMMMMC

)1/()]()][([ NEE TDDDDR

)(Mg

and observation function

• CO2 sequestration provides a possible solution for reducing the green gas emission to the atmosphere.

• For safety and operational reasons, we need to monitor the containment of the CO2 storage in the subsurface.

An Example of CO2 Storage Monitoring

CO2 Sequestration

• Find model parameters from unmineable coalbeds in Powder River Basin

• Build a stationary geology model

• Run flow simulation with GEM

• Convert flow simulation results to time-lapse seismic velocity models

Creation of Time-lapse Models

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Four time-lapse P-wave velocity modes created based on CO2 flow simulation in the coalbeds. A: time=0; B: time=3 months; C: time=1 year; D: time=3 years.

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A Simple Synthetic Test

“Observed” data calculated by convolution

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Inversion with Waveform Data

Inversion with Waveform and Travel Time Data

Use constant initial model

A Full Waveform Synthetic Test

• Run FD for time-lapse Vp models derived from flow simulation.

• Process complete shot gathers and get depth and time images.

• Extract wavelet.

• Use convolution as the modeling in the inversion.

• Perform seismic inversion with EnKF.

• Compare the inverted Vp with given models.

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Samples of the shot gathers calculated using the finite difference

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Depth image Time image

Reflector 1 2 3 4 5

Depth (m) 270 310 550 670 750

Time (sec) 0.1675 0.1918 0.3340 0.4173 0.4595

Traveltime picks used for the inversion

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Time-lapse velocity models inverted using EnKF

time=0 time=3 months time= 1 year time=3 years

Vp differences between time-lapse models and base modelD

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A comparison between true model and inverted model

Solid black line: Ture model; Dash-dot blue line: inverted model;Dotted yellow line: Initial model; At distance x=500m

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Amplitude

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A comparison between “observed” data and modeled data

Solid line: “Observed” seismic trace Dotted line: Modeled seismic trace from inverted model

• The ensemble Kalman filter is a useful tool for stochastic seismic inversion, especially for dynamic inversion in seismic monitoring (field data tests will be done.)

• Integrating travetime data into the inversion makes the estimation of absolute velocity possible.

• Fast forward modeling and true amplitude processing are essential.

Conclusions

• We would like to thank the sponsors (ExxonMobil, General Electric, Schlumberger, and Toyota) of Global Climate & Energy Project at Stanford University for their support to this study.

• Eduardo Santos, Yemi Arogunmati, and Tope Akinbehinje helped for the creation of time-lapse velocity models.

Acknowledgements