1. Youli Quan & Jerry M. Harris
Stochastic Seismic Inversion using Waveform and Traveltime Data and Its Application to Time-lapse Monitoring
Youli Quan & Jerry M. Harris
Stanford University
November 12, 2008

2. Outline Seismic inversion with EnKF
Introduction
Motivations
Kalman filter
Seismic inversion with EnKF
An example of CO2 storage monitoring
Conclusions

3. Introduction
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.
Why Seismic Inversion
Why use waveform and travel time
Quantitative interpretation: fluid saturation

4. Images of seismic inversion may be more meaningful for interpretation.
Amplitude Traces
Impedance Traces
Seismic
Inversion
Amplitude traces show layer boundaries.
Inversion results show properties within layers

5. 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.
How to do seismic inversion
Stochastic inversion gives higher vertical resolution

6. Motivations to Use EnKF
Seismic monitoring
- To integrate time-lapse seismic data
- Dynamic imaging
Reservoir characterization
- Integration of sonic logs and seismic data
Similar to other stochastic methods, to Integrate sonic logs and seismic data for regular reservoir characterization
But also, to use Ensemble kalman filter comes seismic monitoring

7. Kalman Filter Dynamic imaging
Integration of sonic logs and seismic data
We propose to use Kalman filter. G – observation matrix,
K is calculated from model covariance and measurement error and G, K=
Difficulties: large number of model parameters, model covariance, nonlinearity
Therefore we use ensemble Kalman filter, a Monte Carlo implementation of Kalman filter
Combine both
Kalman gain

8. Seismic Inversion with EnKF
Define observation function
Create model & data ensembles using their probability distributions
m could be impedance, velocity, or even porosity and permeability
g could be convolution, FD shot gather + migration, flow simulation + rock physics+ FD s
d – poststack seismic data in this case

9. Define observation function
1. Illustration with sketches
Poststack
Full waveform
Convolution

10. Create model ensemble …

11. Create data ensemble d …

12. Estimate model parameters with EnKF
K can be simply calculated from the ensemble covariance …
and observation function
It can handle large model and non-linear inverse
This is a Monte Carlo approach

13. An Example of CO2 Storage Monitoring
CO2 Sequestration
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.
1. We use CO2 monitoring as an example to demonstrate our method, though it can also be used for general stationary reservoir characterization using surface reflection seismic data and sonic logs.

14. Creation of Time-lapse Models
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
1. We use CO2 monitoring as an example to demonstrate our method, though it can also be used for general stationary reservoir characterization using surface reflection seismic data and sonic logs.

15. …
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.

16. “Observed” data calculated by convolution
A Simple Synthetic Test
“Observed” data calculated by convolution …

17. Inversion with Waveform Data
Inversion with Waveform and Travel Time Data …
Use constant initial model

18. 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. …

19. Samples of the shot gathers calculated using the finite difference…

20. Traveltime picks used for the inversion
Depth image
Time image …
Traveltime picks used for the inversion
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

21. Time-lapse velocity models inverted using EnKF
time= time=3 months time= 1 year time=3 years
That I have been used and developed of many software applications of earth sciences
GEM: Generalized Equation-of-State Model), GPRS: General Purpose Research Simulator
Gassmann fluid substitution, Vp-Porosity templates, Vp-Vs regressions
This looks like a list for interview presentation, but it is not.

22. Vp differences between time-lapse models and base model
True
Inverted
That I have been used and developed of many software applications of earth sciences
GEM: Generalized Equation-of-State Model), GPRS: General Purpose Research Simulator
Gassmann fluid substitution, Vp-Porosity templates, Vp-Vs regressions
This looks like a list for interview presentation, but it is not.
time=3 months time= 1 year time=3 years

23. A comparison between true model and inverted model
That I have been used and developed of many software applications of earth sciences
GEM: Generalized Equation-of-State Model), GPRS: General Purpose Research Simulator
Gassmann fluid substitution, Vp-Porosity templates, Vp-Vs regressions
This looks like a list for interview presentation, but it is not.
Solid black line: Ture model; Dash-dot blue line: inverted model;
Dotted yellow line: Initial model; At distance x=500m

24. A comparison between “observed” data and modeled data
That I have been used and developed of many software applications of earth sciences
GEM: Generalized Equation-of-State Model), GPRS: General Purpose Research Simulator
Gassmann fluid substitution, Vp-Porosity templates, Vp-Vs regressions
This looks like a list for interview presentation, but it is not.
Solid line: “Observed” seismic trace
Dotted line: Modeled seismic trace from inverted model

25. Conclusions
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. …

26. Acknowledgements
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.
ExxonMobil, General Electric, Schlumberger, and Toyota