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

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

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

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

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

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

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

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

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

Create model ensemble …

Create data ensemble d …

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

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.

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.

… 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.

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

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. …

Samples of the shot gathers calculated using the finite difference …

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

Time-lapse velocity models inverted using EnKF time=0 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.

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

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

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

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. …

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