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Stochastic Seismic Inversion using Waveform and Traveltime Data and
Its Application toTime-lapse Monitoring
Youli Quan & Jerry M. HarrisStanford University
November 12, 2008
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• Introduction • Motivations• Kalman filter
• Seismic inversion with EnKF
• An example of CO2 storage monitoring
• Conclusions
Outline
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• 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
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Amplitude Traces Impedance Traces
-0.2 0 0.2
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SeismicInversion
• Images of seismic inversion may be more meaningful for interpretation.
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• 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.
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• Seismic monitoring
- To integrate time-lapse seismic data - Dynamic imaging
• Reservoir characterization
- Integration of sonic logs and seismic data
Motivations to Use EnKF
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• Dynamic imaging
• Integration of sonic logs and seismic data
Kalman Filter
)( )()1()()1( tttt Gmdkmm
)(ˆ )()()( sonicseismicsonic Gmdkmm
1)( RGCGCGk TTKalman gain
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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
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)(md g
m dPoststack
Full waveform Convolution
Define observation function
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Create model ensemble
ii εmm 0
0 1000 2000 3000 4000 5000 60000
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1.4x 10
-3
Velocity (m/s)
f(m)
m0
],...,[ 1 NmmM
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Create data ensemble
ii γdd
],...,[ 1 NddD
-1000 -500 0 500 10000
1
2
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4x 10
-3
Aplitudef(m
)
m0d
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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
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• 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
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• 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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Distance(m)
Dep
th(m
)
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Distance(m)D
epth
(m)
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Distance(m)
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th(m
)
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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.
Distance(m)
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)
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Distance(m)
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th(m
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Distance(m)
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Distance(m)
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A Simple Synthetic Test
“Observed” data calculated by convolution
Distance(m)
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th(m
)
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Distance(m)D
epth
(m)
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Distance(m)
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Distance(m)
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Inversion with Waveform Data
Inversion with Waveform and Travel Time Data
Use constant initial model
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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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Tim
e (s
ec)
0
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Samples of the shot gathers calculated using the finite difference
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Distance(m)
Dep
th(m
)
220 380 580 780
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Tim
e (s
ec)
Distance (m)100 300 500 700 900
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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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Distance (m)200 400 600 800
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v (m/s)Distance (m)
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th (m
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Time-lapse velocity models inverted using EnKF
time=0 time=3 months time= 1 year time=3 years
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Vp differences between time-lapse models and base modelD
epth
(m)
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epth
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dv(m/s)
time=3 months time= 1 year time=3 years
True
Inverted
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2000 3000 4000 5000
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Velocity (m/s)
Dep
th (m
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TrueInit.Inv.
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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-0.5 0 0.5
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Amplitude
Dep
th (m
)
GivenConv.
A comparison between “observed” data and modeled data
Solid line: “Observed” seismic trace Dotted line: Modeled seismic trace from inverted model
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• 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
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• 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