52 Things Hooke

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52T H I N G S

E D I T E D B Y M AT T H A L L & E VA N B I A N C O

Y O U S H O U L D

K N O W A B O U T

GEOPHYSICS

an excerpt from


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A marvellous little book, full of nuggets of wisdom from the

whos who? of our industry. I highly recommend this book

to all young and aspiring geoscientists.

Dan Hampson

co-founder of HampsonRussell

This is a great book The contributing authors are among

the best known names in our profession. The subject each author

selects is an essential thing that we all need to know about

geophysics. I predict that when you get a copy of this

book in your hand, you will look at every page.

Bob A Hardage

President of SEG

I was grinning to myself as I read some of the comments. I liked the

informal tone and the down-to-earth advice. The bite-sized piecesof advice will be most useful to students starting out in the eld. Its

a fundamental truth that it is way more ecient to progress in your

discipline if you gaze at the horizon standing on the shoulders

of those who came before This book should make a

useful addition to any new geophysicists library!

Henry Posamentier

Seismic geomorphologist

Fascinating. In the current world of instant gratication this

provides rapid bites of insight into many aspects of geophysics,

seen through the eyes of some of the sciences best practitioners.

David MonkPresident-Elect of SEG


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First published in 2012 by Agile LibreNova Scotia, Canada. www.agilelibre.com

Copyright 2012 Agile LibreSome rights reserved.

Except where otherwise noted, the text and illustrations of the essays in this work arelicensed under the Creative Commons Attribution 3.0 Unported License. To view a copyof this license, visit http://creativecommons.org/licenses/by/3.0/ or send a letter to Cre-ative Commons, 444 Castro Street, Suite 900, Mountain View, California, 94041, USA.

e collection, preamble, design, and cover are copyright 2012 Agile Libre.All rights reserved.

Technical editors Matt Hall & Evan BiancotManaging editor Kara TurnerDesigner Neil Meister, MeisterWorkstIndexer Linda LeerCover design electr0nikatPrinting Amazon CreateSpace

We have done our best to ensure that the non-subjective parts of this book arefactually accurate. If you nd a typo or a factual inaccuracy please let us know [email protected]. While every precaution has been taken in the preparation inthis book, the publisher, editors, and contributors assume no responsibility fordamages resulting from the use of the information contained herein.

Library and Archives Canada Cataloguing in Publication

52 things you should know about geophysics / edited by Matt Hall and Evan Bianco

Includes bibliographical references and index.

ISBN 978-0-9879594-0-9

1. Geophysics. I. Hall, Matt, 1971- II. Bianco, Evan, 1982-

III. Title: Fifty-two things you should know about geophysics.

QC806.F54 2012 550 C2012-902408-2


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Contents by theme . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8

Introduction. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12

Essays

Anisotropy is not going away . . . . . . . . . . . . . . . . . . . . . .Vladimir Grechka 14

Beware the interpretation-to-data trap . . . . . . . . . . . . . . . . . . Evan Bianco 16

Calibrate your intuition . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .Taras Gerya 18

Dont ignore seismic attenuation. . . . . . . . . . . . . . . . . . . . . . . . . . Carl Reine 20

Dont neglect your math . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Brian Russell 22

Dont rely on preconceived notions . . . . . . . . . . . . . . . . . . . . Eric Andersen 24

Evolutionary understanding is the key to interpretation. . . . . Clare Bond 26

Explore the azimuths . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . David Gray 28

Five things I wish Id known . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .Matt Hall 30Geology comes rst. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .Chris Jackson 32

Geophysics is all around. . . . . . . . . . . . . . . . . . . . . . . . . . . . Jos M Carcione 34

How to assess a colourmap . . . . . . . . . . . . . . . . . . . . . . . . . . .Matteo Niccoli 36

Know your processing ow . . . . . . . . . . . . . . . . . . . . . . . . . .Duncan Emsley 38

Learn to program . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .Matt Hall 40

Leonardo was a geophysicist . . . . . . . . . . . . . . . . . . . . . . . . Jos M Carcione 42

Mind the quality gap. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Pavlo Cholach 44

My geophysical toolbox, circa 1973 . . . . . . . . . . . . . . . . . . . .Dave Mackidd 46

No more innovation at a snails pace . . . . . . . . . . . . . . . . . . . Paul de Groot 48

Old physics for new images . . . . . . . . . . . . . . . . . . . . . . . . . . . . Evan Bianco 50

One cannot live on geophysics alone . . . . . . . . . . . . . . . . . .Marian Hanna 52

Pick the right key surfaces . . . . . . . . . . . . . . . . . . . . . . . . . . . . Mihaela Ryer 54

Practise pair picking . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Evan Bianco 56P r a c t i s e s m a r t a u t o t r a c k i n g . . . . . . . . . . . . . . . . . . . . . . . . . . . . .Don Herron 58

Pre-stack is the way to go . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Marc Sbar 60

Prove it . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .Matt Hall 62

ContentsAlphabetical


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ALPHABETICAL

CONTENTS

Publish or perish, industrial style . . . . . . . . . . . . . . . . . . . . . . . . Sven Treitel 64

Recognize conceptual uncertainty and bias. . . . . . . . . . . . . . . . Clare Bond 66

Remember the bootstrap . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .Tooney Fink 68

Resolution on maps and sections . . . . . . . . . . . . . . . . . . . . . . . . . Rob Simm 70

See the big picture . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Brian Russell 72

Seek out the biostrat . . . . . . . . . Alex Cullum & Linn Margareth Johansen 74

Simplify everything. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . John Logel 76

Sweat the small stu . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Brian Russell 78

e evolution of workstation interpretation . . . . . . . . . . . . .Dave Mackidd 80

e

ne art of Mother Nature . . . . . . . . . . . . . . . . . . . . . . . . . . . . Chris Kent 82e idea of seismic attributes. . . . . . . . . . . . . . . . . . . . . . . . . . . . .Art Barnes 84

e last een years . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .Dave Mackidd 86

e magic of Fourier. . . . . . . . . . . . . . . . . . . . . . . . . . . Mostafa Naghizadeh 88

e magic of Lam . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .Bill Goodway 90

e scale of a wavelet . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .Brian Romans 92

e subtle eect of attenuation . . . . . . . . . . . . . . . . . Fereidoon Vasheghani 94

e unied AVO equation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Rob Simm 96

Use names to manage data . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .Don Herron 98

Use the rock physics bridge . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Per Avseth 100

We need integrative innovation. . . . . . . . . . . . . . . . . . . . . . . . .Maitri Erwin 102

Well tie basics. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Rachel Newrick 104

Well tie perfection . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Rachel Newrick 106

What I learned as a geophysicist wannabe. . . . . . . . . . . . . . Victoria French 108Where did the data come from? . . . . . . . . . . . . . . . . . . . . . . Rachel Newrick 110

Why you care about HashinShtrikman bounds . . . . . . . . . .Alan J Cohen 112

Wrong is good for you . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .Bert Bril 114

You are a geologist. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .Derik Kleibacker 116

List of contributors . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 118

Index . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 128


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50

At its core, seismology is concerned with how objects move when forces act

on them. Over 300 years ago, two gentlemen outlined everything we need to

know: Robert Hooke, with his law describing elasticity, and Isaac Newton with

his second law describing inertia. Anyone working with seismic data should

try to develop an intuitive understanding of their ideas and the equations that

manifest them.

For rocks, a rudimentary but useful analogy is to imagine a mass suspended

by a spring. Hooke discovered that when the spring is stretched, stress is

proportional to strain. In other words, the force vector F exerted by the

spring is proportional to the magnitude of the displacement vector u. e

proportionality constant k is called the stiness coecient, also known as

the spring constant:

kF u= -

is is the simplest form of Hookes law of elasticity. Importantly, it implies that

the stiness coecient is the dening property of elastic materials.

Newtons second law says that a body of mass m, has a resistance to acceleration

(that is, the second derivative of displacement with respect to time) under

an applied force F:

mF u= p

If displaced from equilibrium, a mass attached to the end of a spring will feel

two forces: a tensional force described by Hookes law, and an inertial force

from its motion, described by Newtons second law. e system of a mass and

a single spring yields simple harmonic motion, characterized by acceleration

being proportional to displacement but opposite in direction:

m ku u= -p

Simple harmonic motion has many applications in physics, but doesnt quitet the behaviour of rocks and seismic waves. A rock is bounded, like a mass

held under the opposing tension oftwo springs. In this case, there are two

tensional forces acting in the line along which the mass can oscillate. Writing

Old physics for new imagesEvan Bianco


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51

Rock properties dance upon the crests of

travelling waves, and they dance to

the tune of seismic rock physics.

30$,1):4

*$4

t"/"-:4*4

t."5)&."5*$4

out the forces in this system and doing a bit of calculus yields the well-known

wave equation:

m

ku u

2d=p

e wave equation says the acceleration of the mass with respect to time is pro-

portional to the acceleration of the mass with respect to space, a tricky conceptdescribed by the Laplacian

2

d .e point is, the only properties that control the

propagation of waves through time and through space are the elasticity of the

springs and the inertia of the mass.

Some vector calculus can move our springmassspring system to three dimen-

sions and unpackk, m, and2

d into more familiar earth properties:

( ) ( )uF

u u2

$ # #d d d d

t t

m n

t

n= +

+-p

: :D DHere, and are the Lam parameters, representing Hookes elasticity, and

is the density of the medium, representing Newtons inertia. You dont need to

fully comprehend the vector calculus to see the link between wave mechanics,

as described by the displacement terms, and rock properties. I have deliberately

written this equation this way to group all the earth parameters in the square

brackets.ese terms are equal to the squares of P-wave velocityVP and S-wave

velocityVS, which are therefore nothing but simple ratios of tensional ( and

) to inertial properties ().

To sum up, the Lam parameters and density are the coecients that scale the

P-wave and S-wave terms in the wave equation. When rock properties change

throughout space, the travelling waveform reacts accordingly. We have a dir-

ect link between intrinsic properties and extrinsic dynamic behaviours. e

implication is that propagating waves in the earth carry information about the

mediums intrinsic parameters. Rock properties dance upon the crests of travel-

ling waves, and they dance to the tune of seismic rock physics.


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90

If geophysics requires mathematics for its treatment,

it is the earth that is responsible not the geophysicist.

Sir Harold Jereys

is quote was oered as a disclaimer on a course I took at the University of

Calgary in 1988: Dr Ed Krebes Geophysics 551 Seismic Techniques.is excel-

lent course was pivotal in my enlightenment regarding Lams parameters. I

repeat the quote here as it disclaims my seemingly unnecessary obfuscation in

the use of equations that follow.

e basic earth parameters in reection seismology are P-wave velocityVP,

and S-wave velocityVS. However, these extrinsic dynamic quantities are com-

posed of the more intrinsic rock parameters of density and two moduli terms,

lambda () and mu (), introduced by the 18th-century French engineer, math-

ematician, and elastician Gabriel Lam. Lam also formulated the modernversion of Hookes law relating stress to strain as shown here in its most general

tensor form:

)jkkl ik il kl(cij ijkl ij kl jlv f md d nd d nd d f= = + +

Here, ij is the i-th component of stress on thej-th face of an innitesimally

small elastic cube, cijkl is the fourth rank stiness tensor describing the elas-

ticity of material, kl is the strain, and ij is the Kronecker delta. e adage

stress is proportional to strain was rst stated by Hooke in a Latin anagramceiiinosssttuv, whose solution he published in 1678 as Ut tensio, sic vis mean-

ing As the extension [strain], so the force [stress]. Despite being interestingly

reversed and non-physical, Hookes pronouncement is illustrated here with

complete mathematical rigor, and this equation creates the basis for the sci-

ence of materials, including rocks. Interestingly, and most notably, only Lams

moduli and , appear in this equation; not bulk modulus, Youngs modulus,

Poissons ratio, VP, VS, or any other seismically derived attribute.

e methods to extract measurements of rocks and uids from seismic ampli-

tudes are based on the physics used to derive propagation velocity. is deriva-

tion starts with Hookes law and Newtons second law of motion, and yields a

set of partial dierential equations that describe the progression of a seismic

The magic of LamBill Goodway


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91

30$,1)

:4*$4

t."5)&."5*$4

t#"4*$4The methods to extract measurements of

rocks anduids from seismic amplitudes are

based on the physics used to derive propagation velocity.

wave through a medium. It also forms the basis of AVO-based descriptions of

the propagating medium.

e P-wave propagation of a volume dilatation term derived from Hookes

law is:

( )t 22

22

2

2

dti

m n i= +

and the S-wave propagation of the shear displacement term ( )ush#d :

( )( )

t

uu2

2

2shsh

##

2

2 dd dt n=

e vector calculus in these equations says that the particle or volume displace-

ment for a travelling P-wave in the earth is parallel to the propagation direction

(as 0#d i = ), whereas the particle displacement imposed by a passing S-wave

is orthogonal to the travelling wavefront. Consequently, the intuitively simple

Lam moduli of rigidity and incompressibility aord the most fundamental

and orthogonal parameterization in our use of elastic seismic waves, thereby

enabling the best basis from which to extract information about rocks within

the earth.

ese Lam moduli form the foundation for linking manyelds of seismological

investigation at dierent scales. Unfortunately the historical development of

these elds has led to the use of a wide and confusing array of parameters,which are usually complicated functions of the Lam moduli. None of these

are inherent consequences of the wave equation, as the Lam moduli are.is

includes standard AVO attributes such as intercept and gradient or P-wave

and S-wave reectivity that are ambiguous and complex permutations of Lam

moduli and , or Lam impedances and . Many other parameters such as

Poissons ratio and Youngs modulus have arisen due to inappropriate attempts

to merge the static un-bound domain of geomechanics to the dynamic bound

medium of wave propagation in the earth. ese attempts have resulted in theuse of contradictory assumptions, which are completely removed when restat-

ing equations using the magic of Lam moduli.

52 Things Hooke

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