Modeling Uncertainty in the Earth Sciences E-Book

Jef Caers

• Herausgeber: John Wiley & Sons
• Kategorie: Wissenschaft und neue Technologien
• Sprache: Englisch

Seitenzahl: 341

Veröffentlichungsjahr: 2011

Beschreibung

Modeling Uncertainty in the Earth Sciences highlights the various issues, techniques and practical modeling tools available for modeling the uncertainty of complex Earth systems and the impact that it has on practical situations. The aim of the book is to provide an introductory overview which covers a broad range of tried-and-tested tools. Descriptions of concepts, philosophies, challenges, methodologies and workflows give the reader an understanding of the best way to make decisions under uncertainty for Earth Science problems.

The book covers key issues such as: Spatial and time aspect; large complexity and dimensionality; computation power; costs of 'engineering' the Earth; uncertainty in the modeling and decision process. Focusing on reliable and practical methods this book provides an invaluable primer for the complex area of decision making with uncertainty in the Earth Sciences.

Leseprobe

Contents

Cover

Title Page

Copyright

Preface

Acknowledgements

Chapter 1: Introduction

1.1 Example Application

1.2 Modeling Uncertainty

Chapter 2: Review on Statistical Analysis and Probability Theory

2.1 Introduction

2.2 Displaying Data with Graphs

2.3 Describing Data with Numbers

2.4 Probability

2.5 Random Variables

2.6 Bivariate Data Analysis

Chapter 3: Modeling Uncertainty: Concepts and Philosophies

3.1 What is Uncertainty?

3.2 Sources of Uncertainty

3.3 Deterministic Modeling

3.4 Models of Uncertainty

3.5 Model and Data Relationship

3.6 Bayesian View on Uncertainty

3.7 Model Verification and Falsification

3.8 Model Complexity

3.9 Talking about Uncertainty

3.10 Examples

Chapter 4: Engineering the Earth: Making Decisions Under Uncertainty

4.1 Introduction

4.2 Making Decisions

4.3 Tools for Structuring Decision Problems

Chapter 5: Modeling Spatial Continuity

5.1 Introduction

5.2 The Variogram

5.3 The Boolean or Object Model

5.4 3D Training Image Models

Chapter 6: Modeling Spatial Uncertainty

6.1 Introduction

6.2 Object-Based Simulation

6.3 Training Image Methods

6.4 Variogram-Based Methods

Chapter 7: Constraining Spatial Models of Uncertainty with Data

7.1 Data Integration

7.2 Probability-Based Approaches

7.3 Variogram-Based Approaches

7.4 Inverse Modeling Approaches

Chapter 8: Modeling Structural Uncertainty

8.1 Introduction

8.2 Data for Structural Modeling in the Subsurface

8.3 Modeling a Geological Surface

8.4 Constructing a Structural Model

8.5 Gridding the Structural Model

8.6 Modeling Surfaces through Thicknesses

8.7 Modeling Structural Uncertainty

Chapter 9: Visualizing Uncertainty

9.1 Introduction

9.2 The Concept of Distance

9.3 Visualizing Uncertainty

Chapter 10: Modeling Response Uncertainty

10.1 Introduction

10.2 Surrogate Models and Ranking

10.3 Experimental Design and Response Surface Analysis

10.4 Distance Methods for Modeling Response Uncertainty

Chapter 11: Value of Information

11.1 Introduction

11.2 The Value of Information Problem

Chapter 12: Example Case Study

12.1 Introduction

12.2 Solution

12.3 Sensitivity Analysis

Index

This edition first published 2011 © 2011 by John Wiley & Sons Ltd

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Library of Congress Cataloguing-in-Publication Data

Caers, Jef. Modeling uncertainty in the earth sciences / Jef Caers. p. cm. Includes index. ISBN 978-1-119-99263-9 (cloth) – ISBN 978-1-119-99262-2 (pbk.) 1. Geology–Mathematical models. 2. Earth sciences–Statistical methods. 3. Three-dimensional imaging in geology. 4. Uncertainty. I. Title. QE33.2.M3C34 2012 551.01′5195–dc22 2011008403

A catalogue record for this book is available from the British Library.

First Impression 2011

Preface

26 June 2010: CNN headlines

Tropical storm plus oil slick equal uncertainty

Decision question: “Will BP evacuate the clean-up crew knowing that evacuation requires at least three days, with the consequence of more oil spilling in the Gulf from the deep-water well, or, will BP leave the crew, possibly exposing them to tropical storm Alex, which may or may not become a hurricane?” A simple question: what is the best decision in this case?

Whether Earth Science modeling is performed on a local, regional or global scale, for scientific or engineering purposes, uncertainty is inherently present due to lack of data and lack of understanding of the underlying phenomena and processes taking place. This book highlights the various issues, techniques and practical modeling tools available for modeling uncertainty of complex Earth systems, as well as the impact it has on practical geo-engineering decision problems.

Modeling has become a standard tool in the Earth Sciences. Atmospheric scientists build climate models, seismologists build models of the deep Earth's structure, and hydrogeologists build models of aquifers. Many books and papers have been written on modeling, spread over many subdisciplines of mathematics and the Earth Sciences. Often, one or at most a few models are built to test certain hypothesis and assumptions, to validate or test certain engineering actions taken in the real world, or to attempt to describe physical processes as realistic as possible. The issue of uncertainty (historic, present or future) is often mentioned, but more as a side note; it is still rarely used for quantitative and predictive purposes. Very few books have uncertainty in Earth Sciences modeling as a primary topic; to date, no book to my knowledge discusses this at the level an undergraduate student in the Earth Sciences can actually comprehend and master. Professionals that are not academics often get lost in the myriad of technical details, limitations and assumptions of models of uncertainty in highly technical journal publications or books.

Therefore, in 2009, I decided to teach an entirely new class at Stanford University termed “Modeling Uncertainty in the Earth Sciences,” as part of the curriculum for Earth Science senior undergraduate and first year graduate students (geology, geophysics and reservoir engineers) as well as related fields (such as civil and environmental engineering and Earth systems studies). The focus of this class is not to build a single model of the Earth or of its physical processes for whatever purpose and then “add on” something related to uncertainty, but to build directly a model of uncertainty for practical decision purposes. The idea is not to start from a single estimate of a certain phenomenon and then “jiggle” the numbers a bit to get some confidence statement about that estimate. The idea is to have students think in terms of uncertainty directly, not in terms of a single climate, seismological or hydrological model or any single guess, from the beginning. The quest for a new syllabus was on.

In many discussions I had with various colleagues from various disciplines in the Earth Sciences, as well as from my decade-long experience as Director of the Stanford Center for Reservoir Forecasting, I had come to the conclusion that any modeling of uncertainty is only relevant if made dependent on the particular decision question or practical application for which such modeling is called for. This, I understand, is a rather strong statement. I strongly believe there is no “value” (certainly not in dollar terms) in spending time or resources in building models of uncertainty without focusing on what impact this uncertainty will have on the decision question at hand: do we change climate-related policies? Do we tax CO2? Do we clean a contaminated site? Where do we drill the next well? and so on.

Let's consider this more closely: if uncertainty on some phenomenon would be “infinite”, that is, everything imaginable is possible, but that uncertainty has no impact on a certain decision question posed, then why bother building any model of uncertainty in the first place, it would be a waste of time and resources! While this is an extreme example, any model approach that first builds a model of uncertainty about an Earth phenomenon and then only considers the decision question is likely to be highly inefficient and possibly also ineffective. It should be stressed that there is a clear difference between building a model of the Earth and building a model of uncertainty of the Earth. For example, building a single model of the inner Earth from earthquake data has value in terms of increasing our knowledge about the planet we live on and getting a better insight into how our planet has evolved over geological time, or will evolve in the short and long term. A model of uncertainty would require the seismologist to consider all possibilities or scenarios of the Earth structure, possibly to its finest detail, which may yield a large set of possibilities because the earthquake data cannot resolve meter or kilometer-scale details at large depths. Constructing all these possibilities is too difficult given the large~computation times involved in even getting a single model. However, should the focus be on how a seismological study can determine future ground motion in a particular region and the impact on building structures, then many prior geological scenarios or subsurface possibilities may not need to be considered. This would make the task of building a model of uncertainty efficient computationally and effective in terms of the application envisioned. Knowing what matters is therefore critical to building models of uncertainty and an important topic in this book.

Thinking about uncertainty correctly or at least in a consistent fashion is tricky. This has been my experience with students and advanced researchers alike. In fact, the matter of uncertainty quantification borders the intersection of science and philosophy. Since uncertainty is related to “lack of knowledge” about what is being modeled, the immediate rather philosophical question of “what is knowledge?” arises. Even with a large amount of data, our knowledge about the universe is, by definition, limited because we are limited human beings who can only observe that which we are able to observe; we can only comprehend that which we are able to comprehend. Our “knowledge” is in constant evolution: just consider Newtonian physics, which was considered a certainty until Einstein discovered relativity resulting in the collapse of traditional mathematics and physics at that time. While this may seem a rather esoteric discussion, it does have practical consequence on how we think about uncertainty and how we approach uncertainty, even for daily practical situations. Often, uncertainty is modeled by including all those possibilities that cannot be excluded from the observations we have. I would call this the “inclusion” approach to modeling uncertainty: a list or set of alternative events or outcomes that are consistent with the information available is compiled. That list/set is a perfectly valid model of uncertainty. In this book, however, I will often argue for an “exclusion” approach to thinking about uncertainty, namely to start from all possibilities that can be imagined and then exclude those possibilities that can be rejected by any information available to us. Although the inclusion and exclusion approaches may lead to the same quantification of uncertainty, it is more likely that the exclusion approach will provide a more realistic statement of uncertainty in practice. It is a more conservative approach, for it is typical human behavior to tend to agree on including less than the remainder of possibilities after exclusion. In a group of peers we tend to agree quicker on what to include, but tend to disagree on what to exclude. In the exclusion approach one focuses primordially on all imaginable possibilities, without being too much biased from the beginning by information, data or other experts. In this way we tend to end up with having less (unpleasant) surprises ultimately. Nevertheless, at the same time, we need to recognize that both approaches are limited by the set of solutions that can be imagined, and hence by our own human knowledge of the universe, no matter what part of the universe (earth or atmosphere, for example) is being studied.

My personal practical experience with modeling uncertainty lies in the subsurface arena. The illustration example and case studies in this book contain a heavy bias towards this area. It is a difficult area for modeling uncertainty, since the subsurface is complex, the data are sparse or at best indirect, a medium exists that can be porous and/or fractured. Many applications of modeling uncertainty in the subsurface are very practical in nature and relevant to society: the exploration and extraction of natural resources, including groundwater; the storage of nuclear material and gasses such as natural gas or carbon dioxide to give a few examples. Nevertheless, this book need not be read as a manual for modeling uncertainty in the subsurface; rather, I see modeling of the subsurface as an example case study as well as illustration for modeling uncertainty in many applications with similar characteristics: complex medium, complex physics and chemistry, highly computationally complex, multidisciplinary and, most importantly, subjective in nature, but requiring a consistent repeatable approach that can be understood and communicated among the various fields of science involved. Many of the tools, workflows and methodologies presented in this book could apply to other modeling areas that have elements in common with subsurface modeling: the modeling of topology and geometry of surfaces and the modeling of spatial variation of properties (whether discrete or continuous), the assessment of response functions and physical simulation models, such as provided through physical laws. As such, the main focus of application of this book is in the area of “geo-engineering”. Nevertheless, many of the modeling tools can be used for domains such as understanding fault geometries, sedimentary systems, carbonate growth systems, ecosystems, environmental sciences, seismology, soil sciences and so on.

The main aim of this book is therefore twofold: to provide an accessible, introductory overview of modeling uncertainty for the senior undergraduate or first year graduate student with interest in Earth Sciences, Environmental Sciences or Mineral and Energy Resources, and to provide a primer reading for professionals interested in the practical aspects of modeling uncertainty. As a primer, I will provide a broad rather than deep overview. The book is therefore not meant to provide an exhaustive list of all available tools for modeling uncertainty. Such book would be encyclopedic in nature and would distract the student and the first reader from the main message and most critical issues. Conceptual thinking is emphasized over theoretical understanding or encyclopedic knowledge.

Many theoretical details of the inner workings of certain methodologies are left for other, more specialized books. In colleges or universities one is used to emphasizing learning on how things work exactly (for example, how to solve a matrix with Gaussian elimination); as a result, often, why a certain tool is applied to solve a certain problem in practice is lost in the myriad of technical details and theoretical underpinnings. The aim, therefore, is to provide an overview of modeling uncertainty, not some limited aspect of it in great detail, and to understand what is done, why it is done that way and not necessarily how exactly it works (similarly, one needs to know about Gaussian elimination and what this does, but one doesn't need to remember exactly how it works unless one is looking to improve its performance). A professional will rarely have time to know exactly the inner working of all modeling techniques or rarely be involved in the detailed development of these methods. This is a book for the user, the designer of solutions to engineering problems, to create an intelligence of understanding around such design; the book is not for the advanced developer, the person who needs to design or further enhance a particular limited component in the larger workflow of solving issues related to uncertainty.

Therefore, in summary: what this book does not provide:

An encyclopedic overview of modeling uncertainty.A textbook with exercises.A detailed mathematical manifest explaining the inner workings of each technique.A cook-book with recipes on how to build models of uncertainty.Exhaustive reference lists on every relevant paper in this area.

What this book does attempt to provide:

A personal view on decision-driven uncertainty by the author.An intuitive, conceptual and illustrative overview on this important topic that cuts through the mathematical forest with the aim of illuminating the essential philosophies and components in such modeling.Methods, workflows and techniques that have withstood the test in the real world and are implemented in high quality commercial or open source software.A focus on the subsurface but with a qualification in various sections towards other applications.Some further suggest reading, mostly at the same level of this book.Teaching materials, such as slides in PDF, homework, software, and data, as well as additional material, are provided on http://uncertaintyES.stanford.edu

Acknowledgements

Many people have contributed to this book: through discussion, by providing ideas, supplying figures and other materials. First and foremost, I want to thank the students of Energy 160/260, “Modeling Uncertainty in the Earth Sciences”. A classroom setting at Stanford University is the best open forum any Author could wish for. Their comments and remarks, their critical thinking has given me much insight into what is important, what strikes a chord but also where potential pitfalls in understanding lie. I would also like to thank Gregoire Mariethoz and Kiran Pande for their reviews. Reidar Bratvold provided me an early version of his book on “Making good decisions” and the discussion we had were most insightful to writing chapter 4. I thank my co-author of chapter 8, Guillaume Caumon for his contribution to structural modeling and uncertainty. Many elements of that chapter were done with the help of Nicolas Cherpeau and using the gOcad (Skua) software supplied by Paradigm. Kwangwon Park and Celine Scheidt were invaluable in writing chapters 9 and 10 on the distance-based uncertainty techniques. In that regard, I am also thankful to Schlumberger for supplying to Petrel/Ocean software that was used in some of the case studies. Esben Auken supplied useful comments to the introductory case study in Chapter 1. Mehrdad Honarkhah helped me in constructing the case example of Chapter 12 that was used as one of the projects in my course. As a teaching assistant, he went above and beyond to call of duty to make the first version of this course successful. I would also like to thank Alexandre Boucher for the use and development of the S-GEMS software as well as the supplying the figure for the artwork on the cover. Sebastien Strebelle, Tapan Mukerji, Flemming Jrgensen, Tao Sun, Holly Michael, Wikimedia and NOAA supplied essential figure materials in the book. I would like to thank the member companies of the SCRF consortium (Stanford Center for Reservoir Forecasting) for their financial support. I also would like to thank my best friends and colleagues, Margot Gerritsen and Steve Gorelick for their enthusiasm and support, in so many other things than just the writing. Finally, I want to thank Wiley-Blackwell, and in particular Izzy Canning, for giving me the opportunity to publish this work and for making the experience a smooth one!

1

Introduction

1.1 Example Application

1.1.1 Description

To illustrate the need for modeling uncertainty and the concepts, as well as tools, covered in this book, we start off with a virtual case study. “Virtual” meaning that the study concerns an actual situation in an actual area of the world; however, the data, geological studies and, most importantly, the practical outcomes of this example should not be taken as “truth,” which is understandably so after reading the application case.

Much of the world's drinking water is supplied from groundwater sources. Over the past several decades, many aquifers have been compromised by surface-borne contaminants due to urban growth and farming activities. Further contamination will continue to be a threat until critical surface recharge locations are zoned as groundwater protection areas. This can only be successfully achieved if the hydraulically complex connections between the contaminant sources at the surface and the underlying aquifers are understood.