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Cheolkyun Jeong May 2014 Abstract The main objective of this dissertation is to characterize reservoir models quantitatively using seismic data and geological information. Its key contribution is to develop a practical workflow to integrate seismic data and geological scenario uncertainty.

First, to address the uncertainty of multiple geological scenarios, we estimate the likelihood of all available scenarios using given seismic data. Starting with the probability given by geologists, we can identify more likely scenarios and less likely ones by comparing the pattern similarity of seismic data. Then, we use these probabilities to sample the posterior PDF constrained in multiple geological scenarios.

Identifying each geological scenario in metric space and estimating the probability of each scenario given particular data helps to quantify the geological scenario uncertainty.

Secondly, combining multiple-points geostatistics and seismic data in Bayesian inversion, we have studied some geological scenarios and forward simulations for seismic data. Due to various practical issues such as the complexity of seismic data and the computational inefficiency, this is not yet well established, especially for actual 3-D field datasets. To go from generating thousands of prior models to sampling the posterior, a faster and more computationally efficient algorithm is necessary. Thus, this dissertation proposes a fast approximation algorithm for sampling the posterior distribution of the Earth models, while maintaining a range of iv uncertainty and practical applicability.

Lastly, the proposed workflow has been applied in an actual reservoir. The field, still in the early stage, has limited well data, seismic data, and some geological observations. Accordingly, the proposed workflow can guide several processes, from selecting geological scenarios to suggesting a set of models for decision makers. The case study, applied in a turbidite reservoir in West Africa, demonstrates the quantitative seismic reservoir characterization constrained to geological scenarios. It contains a well log study, rock physics modeling, a forward simulation for generating seismic responses, and object-based prior modeling. As the result, we could pick some promising geological scenarios and its geological parameters from seismic data using distance-based pattern similarity. Next, based on the selected geological scenarios, Metropolis sampler using Adaptive Spatial Resampling (M-ASR) successfully sampled the posterior conditioned to all available data and geological scenario uncertainty.

v Acknowledgments I would be a person who believes the best is yet to come as Frank Sinatra said.

However, I have already tasted the best thing because living and studying at Stanford could never be better in any other places. My five years journey for a Ph.D. degree has been the most wonderful experience in my life. I have felt privileged to study in Stanford University with the greatest faculty and the smartest students. Recalling my past years I am fully indebted to all the people who have made this possible.

First and foremost, I would like to express my gratitude to Professor Tapan Mukerji for being an exceptional adviser. Like parents, he always taught me gently and precisely. Whenever I faced obstacles in my research, Tapan was there to rescue me. Whenever I made mistakes, Tapan corrected me with incredible patience. Also he was always approachable and open-minded for any discussion. He was not only a great teacher for my research but also a good mentor for my life. He encouraged me to approach various scientific investigations and help me in my life-changing events.

Without his guidance, encouragement, consistent support and brilliant ideas, this dissertation would have been impossible. I firmly believe that the opportunity to work with Tapan was the best of luck in my lifetime.

I want to thank Professor Jef Caers for providing me the incredible support and guidance. He always motivated and taught me how to make excellent scientific works.

Thanks to his endless research ideas and insightful advices, my work could reach the final destination. I really appreciate his help with my heart.

vi I would also like to express my gratitude to Professor Gary Mavko. His mentorship and remarkable classes have tremendously enriched my resources of research. His critical comments, feedback and ideas always helped me to shape and refine my PhD.

I wish to acknowledge the contributions of Céline Scheidt and Gregoire Mariethoz for co-working on my research. Thanks to their contributions and valuable comments, my research could move forward and be done. I express my sincere gratitude to my coauthors.

I also thank the members of my PhD committee: Roland Horne and Steve Graham. I have learned a lot of geology from Steve, both in class and discussion. The discussions with Steve and Eli Moises have been very helpful for my thesis. Also I acknowledge Tim McHargue and Ezequiel Gonzalez for their constructive comments.

I express a great deal of thanks to the SCRF program and its sponsors for the financial support during five years of my stay at Stanford. Along with that, I sincerely thank Thuy Nguyen for extraordinary administrative support.

I acknowledge Hess Corporation for providing us an excellent dataset from Equatorial Guinea, offshore West Africa. A special thanks to Steve Utchtyl and Scott Marler for support.

I acknowledge ConocoPhillips and Schlumberger for providing me the opportunities to learn real practice through their summer internship programs. Thanks to Claude, Lin, Mario, Yongshe, Sahyun, Selin, Denis, Jaideva and Vikas for their help during these internships.

I thank all the current and former students of SCRF. You all have enriched my life.

I hope we can share our life forever as a SCRF family. Sincerely, it was my honor to be a member of SCRF.

I am thankful to ERE Koreans: Jaehoon, Kwangwon, Hyungki, Yongduk, Wonjin, Sandy, Jieun, and Kyungjin. I am also very thankful to all KBSK members. You all

–  –  –

I also send my sincere gratitude to my previous professors who help to study here in Stanford: Joomyung Kang, Jonggeun Choe, and Changsoo Shin.

None of this could have been possible without the support of my family. I really appreciate my parents, Byungjoo Jeong and Hwasoon Lim, and sister, Heekyung. I also appreciate my parents-in-law. They have always been encouraging me and providing unconditional love and selfless support.

Lastly, I dedicate this dissertation to my wife, Yoojin Shin. Without her patience, encouragement and endless support, I would not be able to finish my PhD. I firmly believe I am really fortunate to share my life with her.

This dissertation is also dedicated to my holy God who led me here.

–  –  –




List of Tables

List of Figures

Chapter 1 Introduction

1.1 Objective

1.2 Motivation

1.2.1 Geological scenarios for spatial modeling

1.2.2 Seismic inverse modeling for reservoir characterization

1.3 Problems and challenges

1.3.1 How can we include geological information and quantify its uncertainty?... 6 1.3.2 How can we integrate seismic data and geological scenarios into a reservoir model?

1.3.3 What is the most appropriate process to apply the proposed workflow in actual reservoir cases?

1.4 Chapter descriptions

1.5 References

ix Chapter 2 Modeling Geological Scenario Uncertainty from Seismic Data using Pattern Similarity

2.1 Abstract

2.2 Introduction

2.3 Methodology

2.3.1 Distance-based approximation for uncertainty estimation

2.3.2 Pattern capturing (1): Multiple-Point Histogram (MPH)

2.3.3 Pattern capturing (2): Discrete Wavelet Transform (DWT)

2.3.4 Jensen-Shannon divergence for defining a distance

2.3.5 A pyramid of multiple resolution

2.4 Synthetic case study

2.5 Results

2.5.1 Case 1 (good quality seismic)

2.5.2 Case 2 (low quality seismic)

2.6 Conclusions

2.7 Acknowledgment

2.8 References

Chapter 3 A fast approximation for seismic inverse modeling: Adaptive Spatial Resampling

3.1 Abstract

3.2 Introduction

3. 3 Methodology

3.3.1 Seismic inverse modeling in a Bayesian framework

3.3.2 Rejection sampling

3.3.3 Iterative spatial resampling

3.3.4 Adaptive spatial resampling


3.4 Application of the methodology in 2D

3.4.1 2D section examples

3.4.2 Sensitivity of parameters

3.4.3 Case study 1: 2D acoustic impedance inversion

3.4.4 Case study 2: 2D seismograms inversion

3.4.5 Case study 3: Identifying a facies not observed in wells

3.5 A 3D seismic inversion compared to sequential approach

3.6 Conclusions

3.7 Acknowledgment

3.8 Reference

Chapter 4 Field Application to a Channelized Turbidite Reservoir in Equatorial Guinea, West Africa

4.1 Abstract

4.2 Introduction

4.3 Methodology

4.4 Field application

4.3.1 Seismic inversion in a Bayesian framework integrating seismic data and geological scenario uncertainty

4.4.1 Field introduction

4.4.2 Modeling a submarine canyon

4.5 Defining geological scenario uncertainty

4.5.1 Hierarchy of geological scenario uncertainty

4.5.2 Rockphysics uncertainty

4.5.3 Geometry uncertainty

4.5.4 Spatial distribution uncertainty

4.5.5 Forward simulation for seismic data prediction

4.6 Results

4.6.1 Modeling geological scenario uncertainty

xi 4.6.2 Seismic inverse modeling conditioned to the geological scenario uncertainty

4.7 Conclusions

4.8 Acknowledgement

4.9 References

Chapter 5 Conclusion

5.1 Summary

5.2 Future implications and visions

–  –  –

Table 2. 1: Comparison of features in the MPH and CHP algorithm

Table 2. 2: Multiple (16) geological scenarios using different parameter settings.

.... 32 Table 2. 3: Bayesian confusion matrix of MPH-based for Case 1

Table 2. 4: Bayesian confusion matrix of DWT-based for Case 1

Table 2. 5: Probability of each scenario given seismic data for the proposed approach and rejection sampling - Case 1

Table 2. 6: Bayesian confusion matrix of MPH-based for Case 2

Table 2. 7: Bayesian confusion matrix of DWT-based for Case 2

Table 2. 8: Probability of each scenario given seismic data for the approach and rejection sampling - Case 2

Table 3. 1: Comparison of input and output between the proposed inversion and sequential inversion.

–  –  –

xiv List of Figures Figure 2. 1: A schematic diagram of process converting patterns in seismic data into multiple-point histogram.

Figure 2. 2: Examples of multiple point histograms (MPH, left) and cluster-based histogram of patterns (CHP, right) projected in a 2D MDS map.

The result of CHP demonstrates the same or even better distinctions of each scenario in 2D while the computational time and cost is drastically less.

Figure 2. 3: Schematic diagram of 1D wavelet transform

Figure 2. 4: Schematic diagram of 2D wavelet transform

Figure 2. 5: A pyramid algorithm of multiple resolutions.

Original image (top) is 150x80 pixels; the second image (middle) is a half of the original, and the smallest image (bottom) is one third of the first image. A pyramid algorithm considers these all in a distance matrix using weights.

Figure 2. 6: Example of a few models (from scenario 1(top), 8(mid), and 11(bottom), left) and its forward simulated seismic data for high resolution (center) and low resolution (right)

xv Figure 2. 7: A process of estimating(|). First, generate 50 prior models from each scenario and project it in MDS map. Next, create the probability density function by using adaptive kernel density estimation, and estimate the probability of data location from the multi-dimensional pdf

Figure 2. 8: 2D representation of metric space (Case 1).

The reference is represented by a black cross.

Figure 2. 9: 2D representation of metric space (Case 2).

The reference is represented by a black cross.

Figure 3. 1: A flowchart of the McMC process with the Metropolis sampler.

In the resampling step for selecting conditioning points, the proposed ASR algorithm adaptively resamples a subset from the lastly accepted model instead of random selection in ISR

1 is randomly sampled to obtain the subset, which is used as conditioning data Figure 3. 2: Sketch of the Iterative Spatial Resampling method (ISR).

An initial model for generating next model 2. 2 displays similar local features as 1 due to the constraints imposed by the conditioning data, but represents a different realization from the prior multi-point geostatistical model

Figure 3. 3: The iteration of a Markov chain using ISR.

Left: generated facies models;

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