Seismic AmplitudeAn Interpreters Handbook

The oil and gas industries now routinely use seismic amplitudes inexploration and production as they yield key information on lithology andfluid fill, enabling interpretation of reservoir quality and likelihood ofhydrocarbon presence. The modern seismic interpreter must be able todeploy a whole range of sophisticated geophysical techniques, such as seismicinversion, AVO (amplitude variation with offset), and rock physicsmodelling, as well as integrating information from other geophysicaltechniques and well data.This accessible yet authoritative book provides a complete framework for

seismic amplitude interpretation and analysis, in a practical manner thatallows easy application independent of any commercial software products.Springing from the authors extensive industry expertise and experience ofdelivering practical courses on the subject, it guides the interpreter througheach step, introducing techniques with practical observations and helping toevaluate interpretation confidence.

Seismic Amplitude is an invaluable day-to-day tool for graduate studentsand industry professionals in geology, geophysics, petrophysics, reservoirengineering, and all subsurface disciplines making regular use of seismicdata.

Rob Simm is a Senior Geophysical Adviser for Cairn Energy PLC, and hasworked in the oil and gas industry since 1985. He spent the early part of hiscareer working as a seismic interpreter for British independent oil companiesincluding Britoil, Tricentrol and Enterprise Oil. After working inexploration, production and field equity teams, Dr Simm established his ownconsultancy (Rock Physics Associates Ltd) in 1999, providing project andtraining services to oil and gas companies. He runs an internationallyrenowned training course on The Essentials of Rock Physics for SeismicAmplitude Interpretation.

Mike Bacon is a Principal Geoscientist for Ikon Science Ltd, having workedfor 30 years in the oil industry with Shell, Petro-Canada and Ikon Science.During that time he has interpreted seismic data from various basins aroundthe world, with particular emphasis on extracting useful information fromseismic amplitudes. Dr Bacon has served as Publications Officer of the EAGE(European Association of Geoscientists and Engineers), chairing the editorialboard of the journal First Break. He has also co-authored a number ofpractical texts, including, with Rob Simm and Terry Redshaw, 3-D SeismicInterpretation (Cambridge University Press, 2003).

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Seismic Amplitude:An Interpreters Handbook

Rob SimmCairn Energy PLC

Mike BaconIkon Science Ltd

University Printing House, Cambridge cb2 8bs, United Kingdom

Published in the United States of America by Cambridge University Press, New York

Cambridge University Press is part of the University of Cambridge.

It furthers the Universitys mission by disseminating knowledge in the pursuit ofeducation, learning and research at the highest international levels of excellence.

www.cambridge.orgInformation on this title: www.cambridge.org/9781107011502

Rob Simm and Mike Bacon 2014

This publication is in copyright. Subject to statutory exceptionand to the provisions of relevant collective licensing agreements,no reproduction of any part may take place without the writtenpermission of Cambridge University Press.

First published 2014

Printed in the United Kingdom by XXXX

A catalogue record for this publication is available from the British Library

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isbn 978-1-107-01150-2 Hardback

Cambridge University Press has no responsibility for the persistence or accuracyof URLs for external or third-party internet websites referred to in this publication,and does not guarantee that any content on such websites is, or will remain,accurate or appropriate.

Contents

Preface ixAcknowledgments x

1 Overview 11.1 Introduction 1

1.2 Philosophy, definitions and scope 1

1.3 The practice of seismic rock physics 2

2 Fundamentals 32.1 Introduction 3

2.2 Seismic basics 3

2.2.1 Seismic geometry 3

2.2.2 Gathers and stacks 3

2.3 Modelling for seismic interpretation 6

2.3.1 The convolutional model, waveletsand polarity 7

2.3.2 Isotropic and elastic rock properties 10

2.3.3 Offset reflectivity 14

2.3.4 Types of seismic models 17

2.3.5 Relating seismic data to models 19

3 Seismic wavelets and resolution 233.1 Introduction 23

3.2 Seismic data: bandwidth and phase 23

3.3 Zero phase and minimum phase 24

3.4 Change of wavelet shape with depth 25

3.5 Idealised wavelets 28

3.6 Wavelet shape and processing 29

3.6.1 Q compensation 29

3.6.2 Zero phasing 29

3.6.3 Bandwidth improvement 30

3.7 Resolution 32

3.7.1 The problem of interference 32

3.7.2 Simple models of interference 32

3.7.3 Estimating vertical resolution from seismic 33

3.7.4 The effect of wavelet shape on resolution 34

3.7.5 Lateral resolution 35

3.8. Detectability 37

4 Well to seismic ties 384.1 Introduction 38

4.2 Log calibration depth to time 38

4.2.1 Velocities and scale 38

4.2.2 Drift analysis and correction 39

4.3 The role of VSPs 40

4.4 Well tie approaches using synthetics 43

4.4.1 Well tie matching technique 43

4.4.2 Adaptive technique 47

4.5 A well tie example 47

4.6 Well tie issues 50

4.6.1 Seismic character and phase ambiguity 50

4.6.2 Stretch and squeeze 51

4.6.3 Sense checking and phase perception 53

4.6.4 Importance of tie accuracy in horizonmapping 56

4.6.5 Understanding offset scaling 56

4.6.6 Use of matching techniques to measure animproving tie 57

5 Rock properties and AVO 585.1 Introduction 58

5.2 AVO response description 58

5.2.1 Positive or negative AVO and the sign of theAVO gradient 58

5.2.2 AVO classes and the AVO plot 58

5.2.3 Introducing the AVO crossplot 59

5.2.4 Examples of AVO responses 59

5.3 Rock property controls on AVO 61

5.3.1 Ranges of parameters for common sedimentaryrocks 61

5.3.2 The role of compaction 62

5.3.3 The effect of fluid fill 63

5.3.4 The effects of rock fabric and pore geometry 69

5.3.5 Bed thickness and layering 72

5.3.6 The effects of pressure 77

5.3.7 Anisotropy 83

v

5.4 The rock model and its applications 89

5.4.1 Examples of rock model applications 90

5.5 Rock properties, AVO reflectivity andimpedance 92

5.5.1 AVO projections, coordinate rotations andweighted stacks 93

5.5.2 Angle-dependent impedance 99

5.5.3 Bandlimited impedance 103

5.6 Seismic noise and AVO 106

6 Seismic processing issues 1116.1 Introduction 111

6.2 General processing issues 112

6.2.1 Initial amplitude corrections 112

6.2.2 Long-wavelength overburdeneffects 113

6.2.3 Multiple removal 114

6.2.4 Migration 115

6.2.5 Moveout correction 115

6.2.6 Final scaling 116

6.2.7 Angle gathers and angle stacks 117

6.3 Data conditioning for AVO analysis 118

6.3.1 Spectral equalisation 119

6.3.2 Residual moveout removal 119

6.3.3 Amplitude scaling with offset 121

6.3.4 Supergathers 123

6.3.5 Gradient estimation and noise reduction 124

7 Amplitude and AVO interpretation 1267.1 Introduction 126

7.2 AVO and amplitude scenarios 126

7.2.1 Class II/III hydrocarbon sands and Class Iwater sands 127

7.2.2 Class III hydrocarbon and water sands 128

7.2.3 Class IV hydrocarbon and water sands 130

7.2.4 Class IIp hydrocarbon sands, Class I watersands 131

7.2.5 Class I hydrocarbon sands, Class I watersands 133

7.2.6 Multi-layered reservoirs 134

7.2.7 Hydrocarbon contacts 136

7.2.8 Carbonates 145

7.2.9 Fractured reservoirs 147

8 Rock physics for seismic modelling 1508.1 Introduction 150

8.2 Rock physics models and relations 151

8.2.1 Theoretical bounds 151

8.2.2 Empirical models 152

8.2.3 Gassmanns equation 159

8.2.4 Minerals, fluids and porosity 163

8.2.5 Dry rock relations 169

8.2.6 Contact models 174

8.2.7 Inclusion models 176

8.3 Requirements for a rock physics study 178

8.3.1 Data checklist 178

8.3.2 Acoustic logs 179

8.4 Data QC and log edits 181

8.4.1 Bad hole effects 181

8.4.2 Vp and Vs from sonic waveform analysis 183

8.4.3 Log prediction 186

8.4.4 Borehole invasion 188

8.4.5 Sonic correction for anisotropy in deviatedwells 191

8.5 Practical issues in fluid substitution 192

8.5.1 Shaley sands 192

8.5.2 Laminated sands 194

8.5.3 Low porosity and permeabilitysandstones 195

8.6 Rock characterisation and modellingissues 196

9 Seismic trace inversion 1989.1 Introduction 198

9.2 Deterministic inversion 199

9.2.1 Recursive inversion 199

9.2.2 Sparse spike inversion 199

9.2.3 Model-based inversion 200

9.2.4 Inversion issues 204

9.2.5 Inversion QC checklist 209

9.2.6 Bandlimited vs broadband 209

9.2.7 Inversion and AVO 209

9.2.8 Issues with the quantitative interpretation ofdeterministic inversions 213

9.3 Stochastic inversion 214

10 Seismic amplitude applications 22210.1 Introduction 222

10.2 Litho/fluid-facies from seismic 222

10.3 Reservoir properties from seismic 224

10.3.1 Reservoir properties from deterministicinversion 224

10.3.2 Simple regression, calibration anduncertainty 226

Contents

vi

10.3.3 Reservoir property mapping using geostatisticaltechniques 229

10.3.4 Net pay estimation from seismic 230

10.4 Time-lapse seismic 236

10.5 Amplitudes in prospect evaluation 247

10.5.1 An interpreters DHI checklist 247

10.5.2 A Bayesian approach to prospectrisking 248

10.5.3 Risking, statistics and other sensechecks 250

10.6 Seismic amplitude technology in reservesestimation 252

References 254Index 270

Contents

vii

Preface

The past twenty years have witnessed significantdevelopments in the way that seismic data are usedin oil and gas exploration and production. Arguablythe most important has been the use of 3D seismic,not only to map structures in detail but also to inferreservoir properties from an analysis of seismic ampli-tude and other attributes. Improvements in seismicfidelity coupled with advances in the understandingand application of rock physics have made quantitativedescription of the reservoir and risk evaluation basedon seismic amplitude not only a possibility but anexpectation in certain geological contexts. It is probablyno exaggeration to say that the interpreter has entered anew era in which rock physics is the medium not onlyfor the interpretation of seismic amplitude but also forthe integration of geology, geophysics, petrophysicsand reservoir engineering. For conventional oil andgas reservoirs, the technology has reached a sufficientstate of maturity that it is possible to describe effectivegeneric approaches to working with amplitudes, anddocumenting this is the purpose of this book.

The inter-disciplinary nature of Seismic RockPhysics presents a challenge for interpreters (bothold and new) who need to develop the appropriateknowledge and skills but it is equally challenging forthe asset team as a whole, who need to understandhow information derived from seismic might beincorporated into project evaluations. This book pro-vides a practical introduction to the subject and aframe of reference upon which to develop a moredetailed appreciation. It is written with the seismicinterpreter in mind as well as students and other oiland gas professionals. Mathematics is kept to a min-imum with the express intention of demonstrating thecreative mind-set required for seismic interpretation.To a large extent the book is complementary toother Cambridge University Press publications suchas 3-D Seismic Interpretation by Bacon et al. (2003),Exploration Seismology by Sheriff and Geldart (1995),The Rock Physics Handbook by Mavko et al. (1998)and Quantitative Seismic Interpretation by Avsethet al. (2005).

ix

Acknowledgements

In large part the material and ideas presented in thisbook are based around the training course TheEssentials of Rock Physics for Seismic Interpretation,provided to the industry since 1999 by Rock PhysicsAssociates Ltd and Nautilus Ltd (now part of the RPSgroup) and latterly by Ikon Science Ltd. Many col-leagues, past and present, too numerous to mentionindividually, have indirectly contributed to the work.Special thanks are due to John Chamberlain for dis-cussions, help and guidance and to Roy White formuch lively and informative discussion. RachelAdams at Dreamcell Ltd laboured tirelessly and withgreat patience over the illustrations. The followingsoftware providers are also thanked: Ikon ScienceLtd for use of RokDoc software and Senergy foruse of Interactive Petrophysics software.

We are grateful to the following for permission toreproduce proprietary or copyright material: AAPGfor Figs. 3.20, 5.30 and 8.45; Apache Corporationfor Fig. 7.15; APPEA for Figs. 7.18, 7.20 and 10.2;Dr P. Avseth for Fig. 5.8; Baird Petrophysical forFigs. 2.6, 2.7, 2.9, 2.21 and 5.69; CGG for Fig. 9.10;Dr P. Connolly for Figs. 5.75, 9.36 and 10.21; CSEGfor Figs. 4.6, 6.4, 10.7 and 10.8; CUP for Figs. 2.28,5.18 and 8.7; EAGE for Figs. 2.5, 3.1, 3.6, 3.9, 3.19,3.22, 4.20, 4.28, 5.56, 6.1, 6.16, 7.9, 7.13, 7.32, 7.36,8.28, 8.43, 8.56, 8.58, 8.59, 8.60, 8.61, 9.12, 9.14, 9.15,9.24, 9.29, 9.30, 9.32, 9.33, 9.34, 9.35, 10.12, 10.14,10.15, 10.16, 10.20, 10.26, 10.32, 10.34 and 10.35;Elsevier for Fig. 5.43; Dr M. Floricich and ProfessorC. Macbeth for Fig. 10.30; Dr A. Francis for Figs. 9.11,10.4 and 10.5; Dr G. Drivenes for Fig. 7.27; theGeological Society of London for Figs. 4.30, 4.31,

7.23, 7.29 and 10.33; Dr S. Helmore for Fig. 3.14;Ikon Science for Figs. 9.25 and 9.26; the IndonesianPetroleum Association for Fig. 6.3; Dr H. Ozdemir forFig. 9.15; Dr C. Pearse for Fig. 7.31; Dr T. Ricketts forFig. 10.29a; Dr B. Russell for Fig. 7.4; Rashid Petrol-eum Company for Figs. 5.26 and 7.1; Rock PhysicsAssociates Ltd for Figs. 2.1, 2.2, 2.3, 2.4, 2.8, 2.11,2.12, 2.13, 2.14, 2.16, 2.19, 2.20, 2.22, 2.23, 2.25,2.26, 2.27, 2.28, 2.29, 3.2, 3.3, 3.4, 3.5, 3.7, 3.8, 3.10,3.12, 3.16, 3.17, 3.18, 4.1, 4.9, 4.10, 4.11, 4.21, 4.22,4.23, 4.24, 4.25, 4.26, 4.29, 5.1, 5.3, 5.4, 5.5, 5.6, 5.7,5.9, 5.10, 5.11, 5.12, 5.14, 5.17, 5.29, 5.34, 5.36, 5.38,5.40, 5.41, 5.45, 5.50, 5.53, 5.54, 5.55, 5.57, 5.58, 5.61,5.73, 5.74, 6.5, 6.7, 6.10, 6.11, 7.2, 7.3, 7.5, 7.12, 7.21,8.4, 8.9, 8.10, 8.11, 8.12, 8.15, 8.16, 8.17, 8.18, 8.19,8.21, 8.22, 8.24, 8.25, 8.26, 8.27, 8.29, 8.30, 8.32,8.35, 8.36, 8.37, 8.38, 8.44, 8.46, 8.47, 8.48, 8.50,8.52, 8.53, 9.2, 9.4, 9.6, 9.7, 9.9, 9.13, 9.16, 9.17, 9.18,9.19, 9.20, 9.21, 9.23, 10.13 and 10.36; Schlumbergerfor Fig. 8.42; SEG for Figs. 3.11, 3.13, 3.21, 4.7,4.8, 4.27, 5.2, 5.20, 5.21, 5.25, 5.33, 5.44, 5.46,5.48, 5.51, 5.52, 5.66, 5.77, 6.2, 6.6, 6.8, 6.9, 6.12,6.13, 6.15, 6.17, 7.6, 7.7, 7.8, 7.11, 7.14, 7.16, 7.30,7.33, 7.34, 7.35, 7.37, 7.38, 8.2, 8.3, 8.5, 8.6, 8.20,8.31, 8.33, 8.34, 8.39, 8.40, 8.51, 8.57, 8.63, 9.5, 9.8,9.9, 9.23, 10.1, 10.3, 10.10, 10.17, 10.19, 10.23, 10.27,10.31, 10.37, 10.38, 10.39, 10.40 and 10.41; SIPfor Fig. 2.24; SPE for Figs. 5.35, 8.55, 9.31, 10.6,10.11, 10.24 and 10.29b; Dr J. Smith for Fig. 8.14;Springer for Figs. 5.71 and 9.9; SPWLA for Fig. 8.13;Dr R Staples for Fig. 10.28; Western Geco forFigs. 7.22 and 7.24; Professor R. White for Fig. 4.12;John Wiley for Fig. 8.54; World Oil for Fig. 10.25.

x

Chapter

1Overview

1.1 IntroductionThis book is about the physical interpretation ofseismic amplitude principally for the purpose offinding and exploiting hydrocarbons. In appropriategeological scenarios, interpretations of seismic ampli-tude can have a significant impact on the bottomline. At all stages in the upstream oil and gas businesstechniques based on the analysis of seismic amplitudeare a fundamental component of technical evaluationand decision making. For example, an understandingof seismic amplitude signatures can be critical to therecognition of direct hydrocarbon indicators (DHIs)in the exploration phase as well as the evaluation ofreservoir connectivity or flood front monitoring inthe field development phase. Given the importance ofseismic amplitude information in prospect evaluationand risking, all technical disciplines and exploration/asset managers need to have a familiarity with thesubject.

1.2 Philosophy, definitions and scopeThe central philosophy is that the seismic interpreterworking in exploration and appraisal needs to makephysical models to aid the perception of what to lookfor and what to expect from seismic amplituderesponses in specific geological settings. This usuallyinvolves the creation of synthetic seismic models forvarious rock and fluid scenarios based on availablewell log data. In rank exploration areas the uncertain-ties are generally such that only broad concepts,assumptions and analogies can be used. By contrast,in field development settings where data are readilyavailable, physical modelling can lead to a quantifica-tion of reservoir properties from seismic (with associ-ated error bars!).

Fundamental to this process of applying models inseismic interpretation is the integration of data from avariety of disciplines including geology, geophysics,

petrophysics and reservoir engineering. The coreaspect of the data integration is rock physics, whichcan be defined as the study of the relationshipsbetween measurements of elastic parameters (madefrom surface, well, and laboratory equipment), theintrinsic properties of rocks (such as mineralogy, por-osity, pore shapes, pore fluids, pore pressures, permea-bility, viscosity, and stress sensitivity) and overall rockarchitecture (such as laminations and fractures) (Sayersand Chopra, 2009). Rock physics effectively providesthe rock and fluid parameters for seismic models.

Pennington (1997) describes the careful andpurposeful use of rock physics data and theory in theinterpretation of seismic observations and calls thisapproach Seismic Petrophysics. Others commonlyrefer to it simply as Rock Physics (sensu lato), SeismicRock Physics (Wang, 2001) or Quantitative Interpret-ation (QI). The mind-set which drives the approach isnot new of course but modern data has provided a newcontext. More than ever before there is an opportunity,paraphrasing Sheriff (1980), to reveal the meaning ofthe wiggles. There are numerous workers, past andpresent, to whom the authors are indebted and whosenames occur frequently in the following pages.

The book describes the theory of seismic reflectiv-ity (Chapter 2) and addresses the key issues thatunderpin a seismic interpretation such as phase,polarity and seismic to well ties (Chapters 3 and 4).On these foundations are built a view of how contrastsin rock properties give rise to variations in seismicreflectivity (Chapter 5). Seismic data quality is an allimportant issue, controlling to a large extent the con-fidence in an interpretation, and this is addressed,from an interpreters perspective, in Chapter 6.Examples of fluid and rock interpretations usingAmplitude Versus Offset (AVO) techniques are pre-sented in Chapter 7 for a variety of geological contexts.The key rock physics components that drive seismicmodels are documented in Chapter 8, whilst the 1

concept of seismic trace inversion is introduced inChapter 9. Chapter 10 outlines some key applicationsof seismic amplitudes such as the description of reser-voir properties from seismic and the use of amplitudeinformation in prospect evaluation and reservesdetermination.

1.3 The practice of seismic rock physicsThe practice of seismic rock physics depends to alarge extent on the application. In some cases, simplyfluid substituting the logs in a dry well and generatingsynthetic gathers for various fluid fill scenarios maybe all that is needed to identify seismic responsesdiagnostic of hydrocarbon presence. On the otherhand, generating stochastic inversions for reservoirprediction and uncertainty assessment will require acomplete rock physics database in which the elasticproperties of various lithofacies and their distribu-tions are defined in an effective pressure context.Either way, the amount of knowledge required tomaster the art of seismic rock physics is a dauntingprospect for the seismic interpreter.

The broad scope of the subject inevitably meansthat geophysicists need to work closely with petro-physicists, geologists and engineers. Often this iseasier said than done. To quote Ross Crain (2013):Geophysicists engaged in seismic interpretationseldom use logs to their full advantage. This sad stateis caused, of course, by the fact that most geophysi-cists are not experts in log analysis. They rely heavilyon others to edit the logs and do the analysis for them.But, many petrophysicists and log analysts have noidea what geophysicists need from logs, or even howto obtain the desired results.

Effectively, the use of rock physics in seismicinterpretation blurs the distinctions between subsur-face disciplines. This book introduces the subjectfrom a practical viewpoint with a description of howit works and how connections are made between thevarious disciplines. Whilst there is good practice,there is no single workflow to follow. It is hoped thatthe perspective presented here will be a source ofencouragement to those eager to learn the trade aswell as providing ideas for creative hydrocarbonexploration and development.

Overview

2

Chapter

2Fundamentals

2.1 IntroductionInterpreting seismic amplitudes requires an under-standing of seismic acquisition and processing as wellas modelling for describing and evaluating acousticbehaviour. Separate books have been written abouteach of these subjects and there is certainly more tosay on these issues than can be presented here. Theaim of this chapter is to provide a framework of basicinformation which the interpreter requires in order tostart the process of seismic amplitude interpretation.

2.2 Seismic basics2.2.1 Seismic geometrySeismic data are acquired with acoustic sources andreceivers. There are numerous types of seismic geom-etry depending on the requirements of the survey andthe environment of operation. Whether it is on landor at sea the data needed for seismic amplitude analy-sis typically require a number of traces for each sub-surface point, effectively providing measurementsacross a range of angles of incidence. The marineenvironment provides an ideal setting for acquiringsuch data and a typical towed gun and streamerarrangement is illustrated in Fig. 2.1a. Each shot sendsa wave of sound energy into the subsurface, and eachreceiver on the cable records energy that has beenreflected from contrasts in acoustic hardness (orimpedance) associated with geological interfaces. Itis convenient to describe the path of the sound energyby rays drawn perpendicular to the seismic wavefront;this in turn clarifies the notion of the angle of inci-dence ( in Fig. 2.1a). Usually, the reflectionsrecorded on the near receivers have lower angles ofincidence than those recorded on the far receivers.

Figure 2.1b illustrates the recorded signal from theblue and red raypaths shown in Fig. 2.1a. The signalrecorded at each receiver is plotted against time (i.e. thetravel time from source to receiver), and the receiver

traces are ordered by increasing sourcereceiverdistance, usually referred to as offset. Plotting the tracesfor all receivers for one particular source positionprovides a shot gather display. In Fig. 2.1 the reflectedenergy is shown as a wiggle display and the shape of thereflection signal from the isolated boundary describesthe shape of the seismic pulse (the wavelet) at theboundary. Owing to the difference in travel path, thearrival time of the reflection from the geologicalboundary increases with offset and, usually, the rela-tion between travel time and offset is approximatelyhyperbolic. The amplitude of the reflection from theboundary is related to the contrast in acoustic param-eters across the boundary, but is also affected by dis-tance travelled, mainly because the energy becomesspread out over a larger area of wavefront. This phe-nomenon has commonly been referred to as sphericaldivergence, although it is now evident that wavefrontshave shapes between spherical and elliptical. An object-ive of seismic processing is to produce traces where theamplitudes are related only to the contrasts at thereflecting boundary, and all other effects along thepropagation path are removed (this is often referredto as true amplitude processing). This can be difficultfor land data, where there may be large differencesfrom one trace to the next, related to the effectivenessof the coupling of sources and receivers to the surface,as well as rapid lateral variation in the properties of theshallow zone immediately below the surface.

2.2.2 Gathers and stacksDuring seismic acquisition, each shot is recorded bymany receivers. Figure 2.2 illustrates that each receiveris recording reflections from different subsurface loca-tions for any given shot. The shot gather thereforemixes together energy from different subsurface loca-tions, and is of little direct use for interpretation. If theEarth is made up of relatively flat-lying layers thenthe various traces relating to sourcereceiver pairs

3

which share a common midpoint (CMP) will alsoshare common subsurface reflection points. Theseare typically brought together to form a CMP gather(Fig. 2.2) and form the basis for further analysis. If thesubsurface is not a simple stack of plane layers, it isstill possible to create a gather for a common reflec-tion point provided that the subsurface geometry andseismic velocities can be determined reasonablyaccurately from the data. This is an aspect of seismicmigration, which attempts to position subsurfacereflectors in their true spatial location. There areseveral different approaches to migration, and a vastliterature exists on the subject. Jones (2010) gives auseful overview. For the purpose of this narrative it isassumed that a gather has been produced in which allthe traces are related to the same subsurface point atany given reflection time.

In order for the gathers to be interpretable, theyneed to be processed. Figure 2.3 gives a generalisedoverview of some of the steps involved. A time-varyinggain is applied to remove the effects of wavefrontdivergence, a mute is applied to remove unwantedsignal (typically high-amplitude near-surface directand refracted arrivals visible on the further offsets atany given time), and pre-stack migration is applied tobring traces into the correct geometrical subsurfacelocation. As shown on the left-hand side of Fig. 2.3,the reflection time of any particular interface on theraw gather becomes later with increasing offset, dueto the increased path length. An important step isthe application of time-varying time shifts to eachtrace so as to line up each reflection horizontallyacross the gather, as shown on the right-hand side ofFig. 2.3. This is needed in conventional processing

Near Far

Shotreceiver offset

Time

Receiver cable

ii

a)

b)

Figure 2.1 Marine seismic geometry 1; (a) source and receiver configuration showing wavefronts, rays (perpendicular to wavefronts) andangle of incidence increasing with offset (b) a shot gather representation of the recorded energy. For a horizontal layered case the reflectionsform a hyperbola on the gather. Note that the amplitude of a reflection on the gather is related to the rock contrast across the boundaryand the decrease in amplitude due to wavefront divergence.

Fundamentals

4

because the next step will be to stack the data bysumming the traces of the gather along lines of con-stant time, i.e. along horizontal lines in the display ofFig. 2.3. This has the important effect of enhancingsignal and suppressing noise. Accurate horizontalalignment across the gather is also important for thestudy of amplitude variation with offset (AVO)

described later in this chapter and in Chapter 5. Theprocess of time-shifting to flatten the reflections iscalled moveout correction. A commonly used term isnormal moveout (NMO), which refers to the specificcase where there is no dip on the reflector.

Figure 2.4 illustrates a stacking methodology thatis popular for seismic AVO analysis. Seismic sections

Corrected and processed gather

Offset

Raw gather

Offset

Offset

TWT

TWT

TWT

TWT

Offset

Outer mute

Apply gain function to remove effect of wavefront divergence

Remove noise and mute out unwanted data

Apply spatial geometric corrections (pre-stack migration)

Calculate velocities to flatten gather (Moveout)

Figure 2.3 Key steps in the processing of seismic gathers.

a) b)

Figure 2.2 Marine seismic geometry 2; (a) acquisition; each shot is recorded at a variety of receivers depending on the depth and the angleof reflection and (b) the common midpoint (CMP); if it is assumed that the Earth is flat the data can be arranged according to reflectionlocation, i.e. different sourcereceiver pairs sampling the same position in the subsurface. For more complex velocity overburden sophisticatedimaging solutions are required.

Rob Simm and Mike Bacon

5

have been created by stacking the near-offset data andthe far-offset data separately, giving an immediatevisual impression of AVO effects but also providinginformation that can be analysed quantitatively (see

Chapters 5 and 7). In this particular case, the differ-ence between near and far trace data is unusually largebut it illustrates the point that where there is only afull stack section available (i.e. created by addingtogether all the traces of the gather) the interpretermay be missing valuable information.

2.3 Modelling for seismicinterpretationPropagation of seismic energy in the Earth is a com-plex phenomenon. Figure 2.5 shows some of thenumerous factors related to geology and acquisition.The goal of course is to relate seismic amplitude torock property contrasts across reflecting boundariesbut there are several other factors besides geology thatalso have an influence on amplitude. Some of theseare associated with the equipment used for the survey;these include variability of source strength andcoupling from shot to shot, variability of sensitivityand coupling from one receiver to another, the direc-tivity of the receiver array (i.e. more sensitive at some

Near stack (210-1800m)

Far stack (1960-3710m)

100ms

a)

b)

Figure 2.4 Offset stacking example; (a) near stack, 2101800 moffset, (b) far stack, 19603710 m offset. Note that the choice ofoffsets is dependent on the offset range available and the depth ofthe target. In this case the offsets have been selected to avoidstacking across a zone of phase reversal.

Instrumentresponse

Arraydirectivity Scattering

Reflector curvature and rugosity

Absorption Multiples Wavefrontdivergence

Reflectioncoefficient

Reflector interference

Geophonesensitivity

Source strengthand coupling

Superimposednoise

Azimuthalanisotropy

Small scalehorizontal

layeringElasticity &isotropy

Vertical polar anisotropy

Fractures

AVO

Figure 2.5 Factors affecting seismic amplitude (modified after Sheriff, 1975).

Fundamentals

6

angles of incidence than others) and the imperfectfidelity of the recording equipment. Marine seismichas the advantage that sources and receivers are veryrepeatable in their characteristics. This is not true forland data, where the coupling of source and receiversto the ground may be quite variable from one shot toanother, depending on surface conditions. However,these effects can be estimated and allowed for by theseismic processor.

Some amplitude effects are features of the subsur-face that are of little direct interest and ideally wouldbe removed from the data during processing if pos-sible; these include divergence effects, multiples, scat-tering, reflection curvature and rugosity, and generalsuperimposed noise. Depending on the individualdata set, it may be quite difficult to remove thesewithout damaging the amplitude response of interest.For example, processors often have difficulty inattenuating multiple energy whilst preserving thefidelity of the geological signal. Other effects on seis-mic amplitude, for example related to absorption andanisotropy, might be useful signal if their origin werebetter understood. The processor clearly faces a toughchallenge to mitigate the effects of unwanted acquisi-tion and transmission factors and enhance the geo-logical content of the data.

Interpretation of seismic amplitudes requires amodel. A first order aspect of the seismic model isthat the seismic trace can be regarded as the convolu-tion of a seismic pulse with a reflection coefficientrelated to contrasting rock properties across rockboundaries. This idea is an essential element in seismicprocessing as well as seismic modelling. Given that theseismic processor attempts to remove unwantedacquisition and propagation effects and provide adataset in which the amplitudes have correct relativescaling, the interpreters approach to modelling tends(at least initially) to focus on primary geological signalin a target zone of interest. Of course, one eye shouldbe on the look out for noise remaining in the sectionthat has not been removed (such as multiple energyand other forms of imaging effects). The presenceof such effects might dictate more complex (andmore time consuming) modelling solutions and canoften negate the usefulness of the seismic amplitudeinformation.

From a physical point of view the geological com-ponent of seismic reflectivity can be regarded ashaving various levels of complexity. For the most part,the geological component can be described in simple

physical terms. In the context of the small stresses andstrains related to the passage of seismic waves, rockscan be considered perfectly elastic (i.e. they recovertheir initial size and shape completely when externalforces are removed) and obey Hookes Law (i.e. thestrain or deformation is directly proportional to thestress producing it). An additional assumption is thatrocks are to first order isotropic (i.e. rocks have thesame properties irrespective of the direction in whichthe properties are measured). Experience has shownthat in areas with relatively simple layered geologythis isotropic/elastic model is very useful, being thebasis of well-to-seismic ties (Chapter 4) and seismicinversion (Chapter 9).

There are, however, complexities that should notbe ignored. These complexities can broadly be char-acterised as (a) signal-attenuating processes such asabsorption and scattering and (b) anisotropic effects,related to horizontal sedimentary layering (verticalpolar isotropy) and vertical fracture effects (azimuthalanisotropy) (see Section 5.3.7). One effect of absorp-tion is to attenuate the seismic signal causing changesin wavelet shape with increasing depth and this isusually taken into account. Attenuation is difficult tomeasure directly from seismic but at least theoreticallythis information could have a role in identifying thepresence of hydrocarbons (e.g. Chapman et al., 2006;Chapman, 2008). Whilst there is a good deal of theor-etical understanding about anisotropy (Thomsen,1986; Lynn, 2004), there is currently limited know-ledge of how to exploit it for practical explorationpurposes. One problem is the availability of data withwhich to parameterise anisotropic models. Practicalseismic analysis in which anisotropic phenomenaare exploited has so far been restricted to removinghorizontal layering effects on seismic velocities andmoveout in seismic processing (i.e. flattening gathersparticularly at far offsets) (Chapter 6) and definingvertical fracture presence and orientation (Chapter 7).

2.3.1 The convolutional model, waveletsand polarityThe cornerstone of seismic modelling is the convolu-tional model, which is the idea that the seismic tracecan be modelled as the convolution of a seismic pulsewith a reflection coefficient series. In its simplest formthe reflection coefficient is related to change in acousticimpedance, where the acoustic impedance (AI) is theproduct of velocity (V) and bulk density () (Fig. 2.6):

Rob Simm and Mike Bacon

7

R AI2 AI1AI2+AI1

, 2:1

where AI1 is the acoustic impedance on the incidentray side of the boundary and AI2 is the acousticimpedance on the side of the transmitted ray. Reflect-ivity can be either positive or negative. In the modelof Fig. 2.6 the top of the limestone (interface 6) ischaracterised by a positive reflection whilst the top ofthe gas sand (interface 1) is characterised by a negativereflection.

It should be noted that the equation above isrelevant for a ray which is normally incident on aboundary. The change in reflectivity with incidentangle (i.e. offset dependent reflectivity) will be dis-cussed in more detail later in this chapter. A usefulapproximation that derives from the reflectivity equa-tion and which describes the relationship betweenreflectivity and impedance is:

R0:5ln AI: 2:2Effectively, the amount of reflected energy determineshow much energy can be transmitted through thesection. Following the normal incidence modeldescribed above, the transmission coefficient(at normal incidence) is defined by

T 2AI1=AI2+AI1: 2:3Given the boundary conditions of pressure continuityand conservation of energy it can be shown that the

amount of reflected energy is proportional to R2,whereas the transmitted energy is proportional to(AI2/AI1) T. Thus, less energy is transmitted throughboundaries with high AI contrasts (e.g. such as a hardsea floor or the top of a basalt layer). In extreme cases,lateral variations in AI contrasts can result in unevenamplitude scaling deeper in the section.

Transmission effects are important in understand-ing the general nature of recorded seismic energy.ODoherty and Anstey (1971) noted that seismicamplitudes at depth appear to be higher than can beaccounted for with a simple (normal incidence)model of reflection and transmission at individualboundaries. It was concluded that seismic reflectionenergy is being reinforced by reflections from thinlayers for which the top and base reflections haveopposite sign (Anstey and ODoherty, 2002). Thecumulative effects of many cyclical layers can be sig-nificant and this may provide an explanation for theobservation that reflections tend to parallel chrono-stratigraphic boundaries.

To generate a synthetic seismogram requiresknowledge of the shape of the seismic pulse as wellas a calculated reflection coefficient series. A recordedseismic pulse typically has three dominant loops, therelative amplitudes of which can vary according to thenature of the source, the geology and the processesapplied to the data (Chapter 3). Assuming that noattempt has been made to shape the wavelet or changeits timing, a time series representation of the recordedwavelet will start at time zero (i.e. the wavelet iscausal). Figure 2.7 shows the reflection coefficientseries from Fig. 2.6 convolved with a recorded seismicpulse, illustrating how the synthetic trace is the add-ition of the individual reflections.

With regard to the polarity representation of thewavelet shown in Fig. 2.7, reference is made to therecommendation of a SEG committee on polarity pub-lished by Thigpen et al. (1975). It states that an upwardgeophone movement or increase in pressure on ahydrophone should be recorded as a negative numberand displayed as a trough (SEG standard polarity)(Fig. 2.8). This definition is almost universally adheredto in seismic recording. The implication is that areflection from a positive reflection coefficient (a posi-tive or hard reflection), will start with a trough. Notethat a positive reflection is the interpreters referencefor describing polarity. Figure 2.7 conforms, therefore,to the SEG standard polarity convention withpositive reflections such as the top of the limestone

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45

6

RcLithology- +

Vp AI (Vp )

Figure 2.6 The reflection coefficient as defined by thedifferentiation of the acoustic impedance log (re-drawn andmodified after Anstey, 1982).

Fundamentals

8

starting with a trough and negative reflections (suchas the top of the gas sand) starting with a peak.

One problem with causal wavelets (amongstothers) is that there is a time lag between the positionof the boundary and the energy associated with areflection from the boundary, making it difficult tocorrelate the geology with the seismic. Thus, there is arequirement for processing the seismic wavelet to asymmetrical form which concentrates and correctly

aligns the energy with the position of geologicalboundaries. Figure 2.9 shows the same synthetic butnow with a symmetrical wavelet. It is now muchclearer which loops in the seismic the interpreterneeds to pick for the various geological boundaries.

The polarity conventions in common usage thatapply to symmetrical wavelets have been defined bySheriff and Geldart (1995), again with reference to apositive reflection. If a positive reflection is represented

soft

hardpeak

trough

(Thigpen et al,1975) (Sheriff & Geldart,1982)

(Brown, 2001)

- +

twt

Impedance

Symmetrical (processed)

wavelet

Causal (recorded)

wavelet

American Polarity

European Polarity

SEG STANDARD POLARITY

GEOLOGICAL INTERFACE MODEL

POSITIVE STANDARD POLARITY

NEGATIVE STANDARD POLARITY

0

Figure 2.8 Seismic polarity conventions.

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45

Individual reflectionsRcLithology Synthetic seismogram

6

Impedance1 2 3 4 5 6- +

two-

way

tim

e

Figure 2.7 Synthetic seismogram usinga causal (i.e. recorded) wavelet with SEGstandard polarity (re-drawn and modifiedafter Anstey, 1982).

Rob Simm and Mike Bacon

9

as a peak (i.e. positive number) then this is referred to aspositive standard polarity, whereas if it is representedas a trough (i.e. negative number) it is referred to asnegative standard polarity (Fig. 2.8). Historically theusage of these two conventions has been broadly geo-graphical and they have been referred to as Americanand European (Brown, 2001, 2004). In addition, theseconventions are sometimes informally referred torespectively as SEG normal and SEG reverse polarity.It is evident, however, that the use of normal andreverse terms can easily lead to confusion and it isrecommended that their use should be avoided.

From the point of view of seismic amplitude andAVO studies it is recommended that positive stand-ard polarity be used as it lessens the potential confu-sion in the representation of amplitude data.Following this convention will mean that AVO plotswill be constructed with positive numbers represent-ing positive reflections and integration type processes(such as coloured inversion (Chapter 5)) will producethe correct sense of change in bandlimited impedancetraces (i.e. negative to positive for a boundary with apositive reflection) (see Section 5.5.3).

With respect to colour, it is common for seismictroughs to be coloured red and peaks to be colouredblue or black. There are some notable exceptions,however. For example, in South Africa the tendencyhas been to adhere to positive standard polarity butcolouring the troughs blue and the peaks red. Withmodern software the interpreter is not restricted toblue and red and can choose from a whole range ofcolour options. For more discussion of the role ofcolour in seismic interpretation the reader is referredto Brown (2004) and Froner et al. (2013).

For the interpreter who inherits a seismic projectit is evident that polarity and colour coding issues (aswell as uncertainties concerning the processing of thedata) introduce significant potential for misunder-standing and error. It is critical that the interpreterdevelops a good idea of the shape of the seismicwavelet prior to detailed horizon picking (see Chap-ters 3 and 4).

2.3.2 Isotropic and elastic rock properties2.3.2.1 P and S velocities and bulk densitySeismic models for exploration purposes are con-structed using velocities and densities, principallyfrom wireline log data (Chapter 8). As will be shownin the following section the calculation of offsetreflectivity requires two types of velocity (compres-sional (P) and shear (S)) as well as the bulk density ().Figure 2.10 illustrates the P and S waves of interest in3D exploration. The P wave is characterised by par-ticle motion in the direction of wave propagation. TheS wave travels in the same direction as the P wave (andat approximately half the speed of the compressionalwave) but the particle motion is perpendicular to thedirection of wave propagation. Strictly speaking thisshear wave is the vertically polarised shear wave.Whilst it is only compressional waves that arerecorded in marine seismic the reason that shearinformation is important to the interpreter is becausechanges in amplitude with angle are related to thecontrast in the velocities of P waves and the verticallypolarised S wave. By contrast, in land exploration acomparison of vertically and horizontally polarisedshear waves (recorded with three component sensors)

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45

Individual reflectionsRcLithology Synthetic seismogram

6

Impedance1 2 3 4 5 6- +

two-

way

tim

eFigure 2.9 Synthetic seismogram usinga symmetrical wavelet with positivestandard polarity (re-drawn and modifiedafter Anstey, 1982). This illustrates theimportance of zero phase to theinterpreter; the main layer boundaries aremore easily identified with the processedsymmetrical wavelet compared to therecorded asymmetrical wavelet shownin Fig 2.7.

Fundamentals

10

can indicate the presence and orientation of fracturesin the subsurface (Lynn, 2004) (Chapters 5 and 7).

Bulk density b is a relatively simple parameter,being calculated as the weighted average of the dens-ities of the components (Fig. 2.11):

0 b=0 f e, 2:4where is the porosity and the fl and 0 parametersare the densities of the fluid in the pore space and ofthe rock matrix respectively. If more than one fluid ormineral is present the effective densities are calculatedsimply by weighting the various component densitiesaccording to their proportions. Equation (2.4) can bere-written to calculate porosity from bulk density:

b 0=0 f l: 2:5

2.3.2.2 Isotropic and elastic moduliUnfortunately it is insufficient simply to focus onvelocity and bulk density. Understanding the isotropicand elastic context of velocities and density is neces-sary in order to appreciate the rock physics tools at thedisposal of the seismic modeller. For example, whencalculating the effect of varying fluid fill on sandstonevelocities and densities (i.e. fluid substitution) it is

necessary to perform the calculation in terms of elas-tic moduli before the effect on velocities and densitycan be appreciated (see Chapter 8).

There are a variety of elastic parameters that canbe used to describe the isotropic and elastic behaviourof rocks. Table 2.1 provides a useful reference (fromSmidt, 2009), illustrating that two independent meas-urements can be used to calculate any other elasticparameter. Elastic moduli describe rock responses todifferent types of stress (i.e. force applied over a unitarea). The bulk modulus, for example, is the rockresponse to normal stress applied in all directions ona unit of rock (Fig. 2.12) and relates fractional volumechange V/V to the uniform compressive stress S:

K SV=V

: 2:6

As such the bulk modulus is an indicator of theextent to which the rock can be squashed. It is some-times encountered as its reciprocal, 1/K, called thecompressibility. The shear modulus () is the responseto a tangential or shearing stress and is defined by

shear stressshear strain

, 2:7

where the shear strain is measured through the shearangle (Fig. 2.12). As such the shear modulus indicatesthe rigidity of the rock or the resistance of the rockto a shaking motion. Most fluids are not able to resista shear deformation, so it is usually assumed that theshear modulus of fluids is zero.

P wave x

z

Undisturbed rock

Particlemotion

Compression Rarefaction

x

z

S wave x

z

Direction of propagation

Direction of propagation

Direction of propagation

Figure 2.10 Schematic illustration of P and S waves.

Figure 2.11 Density components of a rock with intergranularporosity.

Rob Simm and Mike Bacon

11

Table 2.1 Table of elastic constants for isotropic media (after Smidt, 2009). Note that moduli units GPa, Vkm/s, g/cc.Symbol E K or M (lambda) (mu) / Vp Vs Vp/Vs

Entity Youngsmodulus

Poissonsratio

Bulk modulus P wavemodulus

Lamparameter

Lamparameter

Lamimpedance

ratio

V-primary V-secondary Vp/Vs ratio

(E, ) E31 2

E1 1+1 2

E1+1 2

E21+

21 2

E1

1+1 2

s E

21+r

1 1=2

r

(E, ) 3 E6

33+E9 E 3

3 E9 E

3E9 E

3E 1

33+E9 E

s 3E

9 Er

3+EE

r

(E, ) E 22

E33 E

4 E3 E

E 23 E

4 E3 E

s

r 4 E3 E

r

(, ) 3(1 2)3

1 1+

3

1+321 21+

21 2

31 1+

s 31 221+

s 1

1=2 r

(, ) 2(1 + ) 21+31 2 2

1 1 2

21 2

21 1 2

s

r 1

1=2 r

(, )1+1 2

1+3

1

1 22

1

s 1 2

2

s 1 1=2

s

(, ) 93+

3 223+

+ 4/3 2/3 +4=3

r

r +4=3

s

(, )9

3

3 3 2 3( )/2 3 2

r 3

2

s 2 2=3

r

(, )3+2+

2+ + 2/3 + 2

+2

r

r +2

r

(Vp. Vs) V2s 3V2p 4V2s

V2p V2s

V2p 2V2s2 V2p V2s V2p 4V2s =3

V2p V2p 2V2s

V2s Vp

Vs

2 2

12

Some authors (e.g. Goodway et al., 1997) preferthe use of the Lam parameters ( and ) in prefer-ence to (K and ) believing that they offer greaterphysical insight. The Lam constant is given by

K 23

: 2:8

An important elastic parameter in AVO is Poissonsratio. Poissons ratio is the ratio of the fractionalchange in width to the fractional change in lengthunder uni-axial compression (Fig. 2.13). It can beshown that it is given by:

Poisson ratio w=wl=l

Transverse strainLongitudinal strain

3K 223K+ : 2:9

The contrast in Poissons ratio across an interface canhave a large control on the rate of change of ampli-tude with offset.

Elastic moduli are not generally measured directly,for example with downhole logging tools, but theycan be calculated from velocity and density measure-ments. Some key equations relating velocities anddensities to elastic properties are as follows:

Vp K+4=3

sor Vp

+2

s2:10

and

Vs

r, 2:11

where is the density of the material.It is evident from these equations that the com-

pressional velocity is a more complicated quantitythan the shear wave velocity, involving both bulkand shear moduli. Useful equations that illustratethe relationship between P and S velocities and Pois-sons ratio () are shown below:

VpVs

21 1 2

s2:12

22 2 , where

VpVs

2and 2 2

2 1 :

2:13The general relationship between Vp/Vs and Poissonsratio is shown in Fig. 2.14 together with typical ranges

V

w

l

Figure 2.13 Poissons ratio.

no change in volume

Shear stress = stress parallel to a surface

Normal stress (S) = Force (kg.m/sec2) / Area (m2)

a) b)

V

Figure 2.12 Volume and shape changesin rocks under stress; (a) change ofvolume with stress applied equally fromall directions, (b) change in shapeassociated with shear stress (e.g. stressesapplied parallel to bedding boundaries).

Rob Simm and Mike Bacon

13

for shales and sands with different fluid fill. Sandstend to have a lower Poissons ratio than shalesbecause quartz has a lower Vp/Vs ratio than mostother minerals. Rocks containing compressible fluids(oil and, especially, gas) have lower Vp and slightlyhigher Vs than their water-wet equivalent. This meansthat hydrocarbon sands will have a lower Poissonsratio than water-bearing sands.

2.3.3 Offset reflectivityThe isotropic and elastic behaviour of a P waveincident on a boundary at any angle is describedby the Zoeppritz (1919) equations (see Aki andRichards, 1980) (Fig. 2.15). The Zoeppritz equationsdescribe the partitioning of P and S wave energyinto reflected and transmitted components. The vari-ation of the P wave reflection coefficient with angleis the key parameter for most seismic interpretation,though S wave reflection coefficients sometimesneed to be considered, for example when interpret-ing marine seismic acquired with cables on the seafloor.

An example of a single boundary calculation usingthe Zoeppritz equations is shown in Fig. 2.15. Theresponse shown is for shale overlying dolonite, not atypical contrast of interest in hydrocarbon explor-ation but it illustrates an important point. TheP wave amplitude of the hard reflection initiallydecreases with increasing angle, but at a certain point

the amplitude increases sharply. This is associatedwith the point at which the transmitted P wave amp-litude is reduced to zero and refractions are generatedat the boundary. The angle at which these effectsoccur is called the critical angle. This may be thoughtof in terms of Snells Law that defines the relationshipbetween incident and transmission angles (Fig. 2.16).If the upper layer has lower velocity, then the criticalangle is given by:

c sin 1 Vp1Vp2

: 2:14

Beyond the critical angle, the reflected P wave isphase-shifted relative to the incident signal. It is pos-sible that critical angle energy from boundaries withhigh velocity contrast can be misinterpreted as ahydrocarbon effect so it is important that the inter-preter and processor do not include these data ingathers for AVO analysis. A seismic gather exampleof critical angle energy (at a shale/limestone interface)is shown in Fig. 2.17.

Unfortunately, the Zoeppritz equations are com-plicated and do not give an intuitive feel for howrock properties impact the change of amplitude withangle. For this reason several authors have derivedapproximations to the equations for estimating amp-litude as a function of angle for pre-critical angles.A popular three-term approximation was developedby Aki and Richards (1980). Various authors havere-formulated the approximation depending on thepurpose, but a useful starting point for the inter-preter is the formulation generally accredited toWiggins et al. (1983):

R A+B sin 2+C sin 2 tan 2, 2:15where

A 12

VpVp

+

B Vp2Vp

4 VsVP

2 VSVS

2 VS

VP

2

and C 12

VpVp

,

where Vp Vp1+Vp22 , Vs Vs1+Vs2

2 1+2

2,

Vs=Vp2 Vs1=Vp12+Vs2=Vp222

,

Poissons Ratio

V p/V

s

Gas sands

Water-wet sands and shales

00 0.1 0.2 0.3 0.4 0.5

1

2

3

4

5

6

7

Figure 2.14 Poissons ratio and Vp/Vs.

Fundamentals

14

Vp Vp2 Vp1, Vs Vs2 Vs1,and 2 1:

The first term (A) is the zero angle reflection coeffi-cient related to the contrast of acoustic impedance,whilst the second term (B) introduces the effect ofshear velocity at non-zero angles. A third term (C)determines the curvature of the amplitude responsenear to the critical angle (Fig. 2.18a). The interpretershould be aware that there are a variety of symbols forthe first and second terms used in the literature. For

example, the A term is commonly referred to as theintercept or by the symbols R0 or NI (for normalincidence), whilst the B term is referred to as thegradient (G) or slope. In the past, Shell and Hesscorporations have used the symbols L and M and R0and R1 respectively to refer to intercept and gradient(Fig. 2.18).

The third term can be dropped to give a two termapproximation generally accredited to Shuey (1985,although the equation does not actually appear in thepaper):

Critical angle Critical angle

Transmitted P

Reflected P

Transmitted S

Reflected S

0 30 60 90

0 30 60 90

0 30 60 90

0 30 60 90

0

0.5

1

0

0.5

1

0

0.5

1

0

0.5

1

Angle of incidence (degrees) Angle of incidence (degrees)

Critical angle Critical angle

Rela

tive

ener

gy

Rela

tive

ener

gy

Rela

tive

ener

gy

Rela

tive

ener

gy

Angle of incidence (degrees) Angle of incidence (degrees)

Figure 2.15 Partitioning of P wave energy at a shale/limestone interface as a function of incidence angle. The model uses the Zoeppritzequations for the calculation and the various components sum to one at all angles. Note that the critical angle defines the point at which thereis a dramatic rise in reflected P wave energy and a corresponding reduction of transmitted energy to zero. Appreciable S wave energy isgenerated beyond the critical angle. Not shown in the diagram is energy refracted along the boundary at the critical angle. Elastic values in themodel: shale Vp 2540 m/s, Vs 1150 m/s, density 2.35 g/cc; limestone Vp 3750 m/s, Vs 1950 m/s, density 2.4 g/cc. The modelwas calculated using the Crewes Energy Ratio Explorer software available at www.Crewes.org.

Rob Simm and Mike Bacon

15

R A+B sin 2: 2:16Shueys equation is a simple linear regression. For thepurpose of describing seismic amplitude variationthis approach to linearising AVO is applicable onlyover a limited range of angles. The angle at whichthe two-term approximation deviates from thethree-term and Zoeppritz solutions depends on the

contrasts across the boundary. It is generally safe toassume that the two-term approximation holds to anangle of incidence up to 30; for the case in Fig. 2.19the second and third order curves start to diverge ataround 40. If intercept and gradient are to be derivedfrom seismic then the interpreter needs to ensurethat only traces which show a linear change of ampli-tude with sin2 are used (Chapters 5 and 6).

The modern day importance of the Shuey equationis not as a predictor of seismic amplitudes at particularangles but as a tool for analysing AVO data for fluidand lithology effects (described in Chapters 5 and 7).Shueys equation played a key role in the developmentof seismic AVO analysis techniques in the 1980s and1990s. The simplicity of the equation meant that theregression coefficients A and B (intercept and gradient)could be fairly easily derived and a range of AVOattributes defined by various parameter combinations.

Another, rock property oriented, approximationto the Zoeppritz equations has been put forward byHilterman (2001):

R AI2 AI1AI2+AI1

cos 2+2 1

1 avg2sin 2: 2:17

This approximation is effectively the same as thetwo-term Shuey equation but has been rearranged to

Vp2, Vs2, 2

Vs1, Vs1, 1

Figure 2.16 Snells Law.

=

AI

Offset Offset

TWT

100ms timing lines

Figure 2.17. An example of critical angle energy on an NMOcorrected gather.

Sin2

+

-

0Rc

Critical angle

3rd term

2nd termBSlopeGradientRIM

1st termAR0NIInterceptL

Curvature component

Figure 2.18 The three components of the AkiRichards (1980)approximation to the Zoeppritz equations.

Fundamentals

16

highlight the fact that reflectivity is fundamentallyrelated to two rock properties, the acoustic impedancecontrast and the Poissons ratio contrast (see Chapter5 for rock property controls on acoustic impedanceand Poissons ratio).

2.3.4 Types of seismic modelsThere are a number of different types of models thatcan be generated to aid amplitude interpretation (Fig.2.20). For most applications these utilise relativelysimple primaries-only reflectivity. However, theremay be occasions when more sophisticated modellingis required. The key problem is that as the complexityor sophistication increases, the time and effort alsoincreases, often without any guarantees that it will beworth the effort. The user needs to select the rightdegree of complexity for the problem at hand.

2.3.4.1 Single interface modelThe simplest model (and sometimes the most import-ant aid to understanding) is the single interfacemodel, where Vp, Vs and for the upper and lowerlayers are input into an algorithm based on Zoeppritzor its approximations to produce the AVO plot, agraph of reflection coefficient versus incidence angle(Fig. 2.20a). This is often the best place to start. If thetarget comprises thick layers with significant contrastsat top and base, this simple model will give a goodidea of what to expect in real seismic data. However, it

is less helpful if there is complicated layering or grad-ational change in properties across a boundary.

2.3.4.2 Wedge modelThe wedge model (Fig. 2.20b) is a tool to describethe interaction of reflections from two converginginterfaces, and is therefore an important way to under-stand interference effects. In particular the wedgemodel is useful for determining vertical resolution(Chapter 3) and can also be used in simple approachesto net pay estimation (Chapter 10). However, like thesingle interface model the wedge model can be toosimplistic for practical purposes, particularly in areaswhere there are rapid vertical variations in lithology.

2.3.4.3 1D synthetics based on log dataThe synthetic seismogram uses wireline log data and awavelet to calculate either a single normal incidencetrace or a range of traces at different angles, simulat-ing the angle variation in a seismic gather. This typeof model is important when tying wells to seismic(Chapter 4) and when generating multi-layeredmodels with different fluid fill. One-dimensional(1D) synthetic models are useful in understandinghow the seismic response depends on the frequencycontent of the data (Chapter 3). Following theresponse of a layer of interest from the fully resolvedcase with a (perhaps unrealistic) high-bandwidthwavelet through the increasingly complex interferencepatterns that may arise as the bandwidth decreases is

Usual range of seismic acquisition angles

Refle

ctio

n co

effic

ient

Incidence angle

ShaleGas sand

Aki-R 2 term

Aki-R 3 term

Hilt. approx

0

0

-0.1

0.1

0.2

-0.2

-0.3

-0.4

-0.5

-0.610 20 30 40 50 60 70

Vp Vs AI PR2438 1006 2.252.25 5486 0.3972600 1700 1.85 4810 0.127

Figure 2.19 Comparison of AkiRichards two-term and three-termequations and Hilterman equation for anexample interface of a shale overlying agas sand.

Rob Simm and Mike Bacon

17

often instructive. This can be a useful way to appreci-ate which geological units can be resolved with thecurrent data and how much improvement in band-width (by new acquisition or reprocessing) would beneeded to resolve more detail (Fig. 2.21).

Sometimes, multi-layered models can be too com-plex, combining so many ingredients that it becomes

hard to understand how changes in individual layerproperties will affect the seismic response withoutconstructing a very large and unwieldy suite of models.

The 1D synthetics can be made more sophisti-cated by including propagation modes other thanprimaries-only, for example multiples and modeconversions (Kennett, 1983). In general this results

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45

RcLithology

6

Impedance- +

two-

way

tim

e

Synthetic seismogram with different pulse shapes

Figure 2.21 Synthetic seismogramswith varying symmetrical wavelet shapesfrom broad to sharp (re-drawn andmodified after Anstey, 1982).

Shale

SandAmpl.

Offset

-

+

0

Single Interface Model

Layered Model

Wedge Model

2D Modelc)

b)a)

d)

Figure 2.20 Types of seismic models; (a) single interface model, (b) three-layer wedge model, (c) 1D layered model, (d) 2D model calculatedat a given reflectivity angle.

Fundamentals

18

in longer computer run times and often requiresmore time to be spent preparing the log data (e.g. indevising a log blocking strategy). Given that in mostcases the seismic processor will have tried, withvarying success, to remove these events from thedata it may be that this type of modelling haslimited predictive value.

2.3.4.4 2D modelsTwo-dimensional (2D) models (Fig. 2.20) can beextremely useful for understanding the effects of lat-eral changes in rock properties and/or layer thick-nesses on the seismic signature. These types ofmodels are typically created using wireline well logdata interpolated along model horizons. Figure 2.20dshows an anticline with gas-bearing sands above a flatgaswater contact. Numerous effects are evident onthe section, including changes in the polarity and

amplitude of various reflectors at the contact as wellas the subtle nature of the interference effects as thefluid contact passes through the geological layering.These types of model can be generated for differentangles of incidence to explore which angle gives theclearest fluid response (Chapter 5).

2.3.5 Relating seismic data to modelsIn order to relate reflectivity models calculated atthe wells in terms of angle to seismic data whichhave been collected as a function of sourcereceiveroffset, a conversion scheme from offset to angle isrequired (Fig. 2.22). This requires use of a velocitymodel, usually constructed from velocity informationacquired in the course of seismic processing, i.e. incorrecting for moveout. If the geology can be approxi-mated as a set of horizontal layers then reflection

2500m300m

?

Amplitude varying with offset

Am

plitu

de

Offset (m)

0-20000-15000-10000-5000

050001000

1500020000

500 1000 1500 2000 2500 3000

Model from well dataAmplitude varying with angle

0

-0.2

-0.1

-0.3

0.2

0.3

0.1

0

0.05 0.1 0.15 0.2 0.25

Rc

a) b)

c)

TWT

Figure 2.22 The issue of relating offset to sin2; (a) corrected gather showing a reflection from the top of a thick gas sand, (b) offsetversus amplitude crossplot from the reflection shown on the gather, (c) modelled change of reflectivity as a function of sin2 based onwell data.

Rob Simm and Mike Bacon

19

time increases with offset approximately accordingto a hyperbolic relation (Fig. 2.23):

Tx T20+

x2

V2rms

s, 2:18

where Tx is the time at offset x, T0 is the time at zerooffset, and Vrms is the RMS average velocity from thesurface to the reflector concerned. Given the assump-tion that the overburden comprises a stack of layerswith velocity V and time thickness t, Vrms is given by:

Vrms X

V2i tiXti

vuut : 2:19In practice, stacking velocities are picked so that aftercorrecting for moveout the gather is flattened andmaximum coherence achieved (Fig. 2.24). Thesestacking velocities are a first order approximationfor RMS velocities (see Al-Chalabi (1974) for adetailed discussion).

The interval velocity between two reflections attimes T1 and T2 is given by the Dix (1955) equation:

Vi T2V2rms2 T1V2rms1

T2 T1

s: 2:20

This equation is usually applied to a time interval of atleast 200 ms to avoid instability arising from errors inthe RMS velocity estimates. Given the RMS velocitydown to a reflector and the interval velocity immedi-ately above it, it can be shown that an estimate of theincidence angle at offset x is given by:

sin 2 x2V2i

V2rms V2rmsT

20+x

2 , 2:21

where T0 is the zero offset travel time. Figure 2.25shows a moveout corrected gather with angle as acoloured background. An alternative approach thatmay be useful if velocity information is available(for example sonic and check-shot data from a well)is to calculate offset as a function of incidence angle,using Snells Law to follow the ray path through thelayers to the surface (Fig. 2.26). This requires a modelto be constructed for the near-surface where there islikely to be no well data available, but it can give moreaccurate angle estimates than those obtained fromstacking velocities. It is, however, not always clearhow to extrapolate well velocities away from a well,as the velocities may show some combination ofstratigraphic conformance (if there are big differencesin lithology between layers) and increase with depthdue to compaction. It is certainly important to takelarge changes in water depth into account. Ideally theangle conversions obtained from seismic velocitiesand from well velocities need to be checked againstone another and perhaps somehow combined; the

00

500

1000

1500

2000

2500

3000

1000 2000 3000 4000

Offset (m)TW

T

T0=2000ms Vrms=2000m/s

Figure 2.23 Reflection hyperbola.

Tim

e (m

s)3500

3000

2500

2000

1500

1000

2000

3000

4000

2000

3000

4000

Velocity (m/s) Offset (m)a) b)

Figure 2.24 Velocity analysis; (a) semblance plot showing lines ofequal velocity (black) and stack coherency for each velocity shownin colour (red high coherency), (b) corrected gather using velocitydefined by velocity picks (white trend shown in (a)) (courtesySeismic Image Processing Ltd).

Fundamentals

20

accuracy of the offset to angle conversion is often asignificant factor for generating partial stacks and forAVO analysis in general.

Once the offsets have been converted to anglesthen the data in the corrected gathers can be com-bined in a number of ways. Figure 2.27 illustrates the

calculation of intercept and gradient, using the two-term AVO equation. As suggested in the previoussection, care must be taken that for the angle range inquestion a two-term fit is appropriate. Before calculat-ing intercept and gradient, some data conditioningmay be needed as it is important that reflections areflat across the moveout corrected gather (Chapter 6).

An alternative to intercept/gradient calculation isto create angle stacks (i.e. stack the data according toangle ranges). For the purposes of seismic interpret-ation the available angle range is usually divided intotwo or three equal parts and separate stacks createdfor each. This maintains reasonable signal-to-noiseratio whilst maintaining the key elements of theAVO response. Typically, therefore, the interpreterwill have near, mid and far sub-stacks in addition tothe conventional full stack. It should be noted that thefull stack is seldom the product of adding togetherthe partial stacks. In most instances the full stack isthe processors best data quality stack and frequentlyhas a harsher mute of the outer traces of the gatherthan the far stack. There may be instances wheremore than three sub-stacks are generated, for examplein simultaneous inversion (Chapter 9).

Figure 2.26 Converting angle to offset using well velocity data;the simplest case is for a horizontal layered model and a straight rayassumption.

-30000

-20000

-10000

0

10000

Sin2

R0

Rc

Figure 2.27 Deriving intercept and gradient. Offsets have beenconverted into sin2 using a velocity model prior to fitting a robustlinear regression through the data.

15 20

10 5

3.0

2.5

2.0

1.5

1

.5

0210 3710Offset (m)

Two-

way

tim

e (s

ecs)

Figure 2.25 A gather displayed with incidence angle as colouredbackground.

Rob Simm and Mike Bacon

21

The sub-stacks can be loaded to a structural inter-pretation software package in just the same way as thefull stack. If the data processing is good the sub-stackswill look similar to the full stack but amplitudechanges (for example, an increase from near to fartraces) will be immediately apparent when sub-stacksare displayed side by side (Fig. 2.28). This gives theinterpreter a way to search through a 3D seismicsurvey to look for anomalous AVO behaviour, whichcan then be followed up by looking at CMP gathers.As will be discussed, AVO differences are often mademore apparent by combining the data from partialstacks using a weighting procedure (Chapter 5)

For the purpose of calibration of the angle stack toa well-based AVO plot or indeed for seismic inversionof individual stacks (Chapter 9), it can be considered

that each angle stack represents reflectivity at a par-ticular (effective) angle. Theoretically, the effectiveangle should be derived from the average of sin2across the sub-stack, but in practice (especially sincethe offset to angle transformation contains a degree ofuncertainty) it can usually be assumed to be the mid-point of the range of angles included.

The goal of quantitative interpretation is to relatechanges in seismic amplitude to changes in rock prop-erties. A key aspect of this is the scaling of the seismicamplitude to the reflection coefficient (Fig. 2.29). Thisis done principally through well ties (Chapter 4).Correct scaling is particularly critical for seismicinversion (Chapter 9), but problems with scaling canseriously compromise all quantitative amplitudeinterpretation.

Seismic Gather

Near traces

Far traces

5 15 35 5-15 15-35

Far Angle StackNear Angle Stack a) b) c)

Offset

Figure 2.28 Angle stacks; (a) seismic gather, (b) near angle (515) stack, (c) far angle (515) stack. Note that the actual angles stackedwill depend on the available angle range and the choice as to number of stacks required (after Bacon et al., 2003).

Vp1 , Vs1 , 1

AI Rc AI Rc

Vp2 , Vs2 , 2

Figure 2.29 Scaling: the key to seismic calibration; if the processor has been successful the amplitude is proportional to reflection coefficientfor a unique reflector. This is the key assumption in any inversion (Chapter 9) or quantitative amplitude interpretation.

Fundamentals

22

Chapter

3Seismic wavelets and resolution

3.1 IntroductionA fundamental aspect of any seismic interpretation inwhich amplitudes are used to map reservoirs is theshape of the wavelet. This chapter presents introduc-tory material relating to the nature of seismic wave-lets; how they are defined, described and manipulatedto improve interpretability. Seismic resolution, interms of recognising the top and base of a rock layer,is controlled by wavelet properties. However, owingto the high spatial sampling of modern 3D seismic,resolution in the broadest sense also includes thedetection of geological patterns and lineaments onamplitude and other attribute maps.

3.2 Seismic data: bandwidth andphaseThe seismic trace is composed of energy that has arange of frequencies. Mathematical methods of Four-ier analysis (e.g. Sheriff and Geldart, 1995) allow thedecomposition of a signal into component sinusoidalwaves, which in general have amplitude and phase thatvary with the frequency of the component. An exampleis the seismic wavelet of Fig. 3.1, which can be formedby adding together an infinite set of sine waves withthe correct relative amplitude and phase, of which afew representative examples are shown in the figure.The amplitude spectrum shows how the amplitude ofthe constituent sine waves varies with frequency. InFig. 3.1 there is a smooth amplitude variation with abroad and fairly flat central peak. This is often the caseas the acquisition and processing have been designedto achieve just such a spectrum. The bandwidth of thewavelet is usually described as the range of frequenciesabove a given amplitude threshold. With amplitudesthat have been normalised, such as those shown in Fig.3.1, a common threshold for describing bandwidth ishalf the maximum amplitude. In terms of the logarith-mic decibel scale commonly used to present amplitudedata this equates to 6 dB (i.e. 20 log10 0.5).

In practice, the amplitude spectrum is calculatedfrom the seismic trace using a Fourier transform overa given seismic window, usually several hundredmilliseconds long. It is assumed to first order thatthe Earth reflectivity is random and that the waveletis invariant throughout the window. The amplitudespectrum of the wavelet is then assumed to be a scaledversion of the amplitude spectrum of the seismictrace. Amplitude spectra are also commonly esti-mated over short seismic segments using a range ofdifferent approaches (e.g. Chakraborty and Okaya,1995). Such analysis is an essential component ofspectral decomposition techniques for use in detailedstratigraphic interpretation (e.g. Burnett et al. 2003).

In addition to the amplitude spectrum, the otherpiece of information that is needed to define the shapeof the wavelet uniquely is the relative shift of the sinewave at each frequency (i.e. the phase). The wavelet inFig 3.1 shows frequency components that have a peakaligned at time zero. Such awavelet is termed zero phase.As described in Chapter 2 a zero phase wavelet is idealfor the interpreter because it has a strong dominantcentral trough or peak at zero time. If this is the waveletin a processed seismic dataset, then an isolated subsur-face interface between layers of different impedance willbe marked by a correctly registered trough or peak(depending on the sign of the impedance contrast andthe polarity convention used). This makes it fairly easyto relate the seismic trace to the subsurface layering,even in thin-layered situations with overlapping reflec-tions. The interpretation is made more difficult if theseismic wavelet is not symmetrical but, for example, hasseveral loops with roughly the same amplitude; then theinterference between adjacent closely spaced reflectorswill be difficult to understand intuitively. The import-ance of zero phase wavelets to the interpreter becomesclear when considering well to seismic ties (Chapter 4).Zero phase is a condition that requires processing of theseismic data (see Section 3.6.2). 23

Phase can be thought of as a relative measure ofthe position of a sinusoidal wave relative to a refer-ence point, and is measured in terms of the phaseangle (Fig. 3.2). The sine waves in Fig 3.2 all havethe same frequency but are out of phase. At the timezero reference point, they vary from peak (red wave)to zero-crossing (blue wave) to trough (green wave) to

zero-crossing (brown wave). The turning wheel idea isuseful for describing the angular differences in phase.

Seismic wavelets can sometimes be approximatedas constant phase across the dominant bandwidth. Insuch a case (Fig. 3.3), the phase of each frequencycomponent is the same. Figure 3.3 shows a wavelet inwhich the phase is 90. Thus, a zero phase wavelet is aspecial case of a constant phase wavelet. Another caseoften seen is linear phase, where phase is relatedlinearly to frequency (Fig. 3.4). In effect, a waveletwith linear phase is equivalent to a time-shifted con-stant phase wavelet.

As will be discussed in detail below, the bandwidthand phase of the seismic signal emitted by the sourceis modified in its passage through the subsurface bythe earth filter (Fig. 3.5). Shallow targets will gener-ally have higher bandwidth than deeper targets.Higher bandwidth essentially means greater resolvingpower.

3.3 Zero phase and minimum phaseFrom the interpreters point of view the ideal waveletis zero phase, i.e. symmetrical and with the amplitudecentred on time zero. Real sound sources such asexplosives and airguns typically have minimum phasesignatures. Generally, a minimum phase wavelet isone that has no energy before time zero and has arapid build-up of energy. Each amplitude spectrumcan be characterised by a unique minimum phasewavelet (i.e. the wavelet that has most rapid build-upof energy for that given spectrum). It is possible tofind the minimum phase wavelet for a given spectrumusing methods based on the z transform (see e.g.Sheriff and Geldart 1995) but there is no intuitiveway to determine whether a given wavelet is min-imum phase or not. Conversely, to say that a datasetis minimum phase does not guarantee a particularshape. Figure 3.6 shows an example of two minimumphase wavelets with similar bandwidth but slightlydifferent rates of change of frequency in the low-frequency range. Thus, if an interpreter is told thatthe seismic data is minimum phase then it is not clearexactly what response should be expected from agiven interface. What is important is that the inter-preter is able to assess and describe wavelet shape inseismic data. Determining wavelet shape from seismicis described in Chapter 4.

A useful semi-quantitative description of waveletshape is in terms of a constant phase rotation of an

20 60

180

-180

0

Phas

e an

gle

Frequency Hz

0 3 6 12 24 40 72Hz

b) Phase spectrum

20 60

1

0

Frequency Hz

Am

plitu

de

c) Amplitude spectrum

Half peak amplitude point

Bandwidth (7-55Hz)

a) Zero phase wavelet and selected frequency components

Figure 3.1 Elements of seismic wavelets; (a) sinusoidal frequencycomponents, (b) phase spectrum, (c) amplitude spectrum (afterSimm and White, 2002).

Seismic wavelets and resolution

24

initially zero phase wavelet (Fig. 3.7). As the phaserotates, the relative amplitudes of the peak andtrough loops of the wavelet change. At a phase angleof 90 the two loops have the same amplitude. Notethat the description of phase is dependent on thereference polarity. It is most common to referencepolarity descriptions to positive standard polarity(Chapter 2).

3.4 Change of wavelet shapewith depthThe Earth filter can have significant effects on the amp-litude and phase spectrum of the wavelet. Figure 3.8shows an example where the seabed response corres-ponds to a 60 phase rotated zero phase wavelet,whereas at the target the optimum wavelet for the well

0

0

180

-180

90

180

270(-90)

Phase angle Time

Phase angleFrequency

Figure 3.2 Illustration of phase; showing several waveforms with the same frequency but different phase (i.e different timing of thewaveforms relative to the zero reference point). The turning wheel model describes the angular relations intrinsic to the advancement ofthe waveform.

Wavelet

Time Time

Frequency

Phase

180

-180

0

Decomposed into single frequency components Plot of phase against frequency

Time zero

Figure 3.3 Constant phase wavelet (+90) (J. Chamberlain, personal communication).

Robb Simm and Mike Bacon

25

tie is lower in frequency and roughly symmetrical with aphase of around 180.

These effects are controlled by attenuation, whichvaries with the lithology and state of consolidation.

Time-shiftedzero-phasewavelet

Time Time

Frequency

Phase

0

-360

-180

Decomposed into single frequency components

Plot of phase against frequency

Time zero

Time shift

Figure 3.4 Linear phase wavelet; illustrating that this phase behaviour is effectively associated with a time shift (J. Chamberlain, personalcommunication)

Earth Filter

Frequency

Am

plitu

de

Reflection

Refraction

Transmission

Attenuation

Source Signature

Frequency

Am

plitu

de

Seismic Trace Figure 3.5 Seismic bandwidth and the Earth filter.

50

100

150

0

50

100

150

0

18db/oct low-cut

100

10-1

10-2

0 50 100

Amplitude spectra

Frequency Hz

Am

plitu

de

a: blue b: red

18+24 db/oct low-cut a) b)

Figure 3.6 Two minimum phase wavelets with similar bandwidthbut slightly different low-cut responses (after Simm and White 2002).Note the marked differences in wavelet shape.

Seismic wavelets and resolution

26

Attenuation is parameterised by the quantity Qdefined as

Q 2=fraction of energy lost per cycle: 3:1Equation (3.1) implies that the effect of attenuation isto reduce amplitude at high frequencies more than atlow frequencies, because in any given subsurface paththere will be more cycles (i.e. wavelengths) at a higher

frequency than at a lower one. Attenuation also causesseismic wave propagation to be dispersive (i.e. theseismic velocity varies with frequency), and thuschanges to the phase spectrum depend on distancetravelled. For a Q value greater than about 10, velocityshould vary with frequency according to

C2 C1=C1 lnf 2=f 1Q

, 3:2

where c1 is the velocity at frequency f1 and c2 is thevelocity at frequency f2 (OBrien and Lucas, 1971). Anexample of a modelled effect of Q on wavelet phase isshown in Fig. 3.9. Essentially low values of Q will givegreater phase rotation for a given sediment thicknessthan higher values of Q.

Q can be measured on core samples in the labora-tory (e.g. Winkler, 1986), but it is not clear whetherthe results obtained are representative of in-situvalues. At the seismic scale the easiest way to measureQ is from a VSP (e.g. Stainsby and Worthington,1985; see also Chapter 4). The method comparesdirect (down-going) arrivals at two different depthsin a vertical well using vertical incidence geometry

450 -50

0

50

500TWT

Seabed Response

Extracted wavelet at 3000ms

Figure 3.8 Example of change in wavelet shape with depth.

0

120

-120

30

150

-90

60

180

-60

90

-150

-30

180

-60

60

-150

-30

90

-120

0

130

-90

30

150

Figure 3.7 Constant phase rotation of a zero phase wavelet a useful description for wavelet shape. Blue numbers are referenced to positivestandard polarity and red numbers are referenced to negative standard polarity. Note it is usual to use the positive standard convention whendescribing wavelet phase.

Robb Simm and Mike Bacon

27

(i.e. near-zero horizontal offset between source andreceiver). This sourcereceiver geometry is highlyfavourable, because raypaths for the top and base ofan interval are essentially coincident. Thus spectraldifferences between the arrivals can be reliablyassumed to be due only to the interval propertiesbetween the two depths.

Determining Q from VSPs is of course only pos-sible where there is a borehole, so it would be desir-able to extend lateral coverage by measuring Q fromsurface seismic. This is not easy to do and it is notroutine practice. Q cannot be derived from stackedtraces owing to mixing of traces with different pathlength, the spectral distortion due to moveou