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Seismic Methods and Applications:

A Guide for the Detection of Geologic Structures, Earthquake Zones and Hazards, Resource Exploration, and Geotechnical Engineering

Andreas Stark

BrownWalker Press Boca Raton

Seismic Methods and Applications: A Guide for the Detection of Geologic Structures, Earthquake Zones and Hazards, Resource Exploration, and Geotechnical Engineering

Copyright © 2008 Andreas Stark. All rights reserved. No Part of this book may be reproduced, stored in a retrieval system, or transcribed in any form or by any means, electronic or mechanical including photocopying or recording, without the prior permission of the author.

BrownWalker Press Boca Raton, Florida – USA 2008 ISBN-10: 1-1599-441-X (hardcover) ISBN-13: 978-1-59942-441-5 (hardcover) ISBN-10: 1-1599-442-8 (ebook) ISBN-13: 978-159942-442-2 (ebook) www.brownwalker.com Library of Congress Cataloging-in-Publication Data Stark, Andreas, 1946Seismic methods and applications: a guide for the detection of geologic structures, earthquake zones and hazards, resource exploration, and geotechnical engineering / Andreas Stark. -- 1st ed. p. cm. ISBN-13: 978-1-59942-441-5 (hardcover : alk. paper) ISBN-10: 1-59942-441-X (hardcover : alk. paper) ISBN-13: 978-1-59942-443-9 (pbk. : alk. paper) ISBN-10: 1-59942-443-6 (pbk. : alk. paper) 1. Seismic prospecting--Methodology. I. Title. TN269.8.S72 2008 622'.1592--dc22 2008003217

This book is dedicated to my wife Regina

Contents

Introduction Acknowledgements

ix xi PART ONE:

Chapter 1 Chapter 2 Chapter 3 Chapter 4

THE PHYSICS 1

Waves and Sound Optics and Spectra Electromagnetic Waves Electrical Circuits

3 29 59 72

PART TWO: GEOPHONES AND INSTRUMENTATION Chapter 5 Chapter 6

Geophones and Arrays Seismic Instrumentation and Sources PART THREE: SEISMIC FIELD DESIGN

Chapter 7

95 97 147

185

Seismic Field Design: 2D-3D-4D

187

PART FOUR: ROCKS, PHYSICS AND WELL LOGS 233 Chapter 8 Chapter 9

Rocks and Rock Physics Well Logs

235 246

PART FIVE: THE SEISMIC METHOD 271 Chapter 10 Chapter 11 Chapter 12 Chapter 13 Chapter 14 Chapter 15

Seismic Waves and Velocities Seismic Refraction and the Near Surface Seismic Processing - Pre-Stack Seismic Processing - Post-Stack Acoustic Inversions and AVO Amplitudes, Resolution, Shear Waves and Anisotropy

273 292 304 353 387 427

LEEE Contents

PART SIX: SEISMIC INTERPRETATION AND GEOLOGY Chapter 16 Chapter 17

Seismic Interpretation Seismic Attributes

PART SEVEN: PROBABILITY, STATISTICS AND MAPPING Chapter 18

Statistics, Mapping and Contouring Principles

457 459 479 491 493

References and Bibliography

551

Index

571

Introduction

This book has been written for those who need a solid understanding of the seismic method without the in-depth mathematical treatment that is normally required. It is laid out in a format that allows one to naturally progress from the underlying physical principles to the actual seismic method. The mathematics needed for the topics is kept as simple as possible. High school physics and mathematics are all that are required. The book starts out with the elementary treatment of sound waves, light waves, optics, spectra and electromagnetic wave principles. It will then progress into the principles of electrical circuits and geophone design, geophone arrays and recording instrumentation design and behavior, before treating the seismic shooting method itself. In this way we lay a solid foundation for the understanding of the processes at work, which are waves and their behavior, instruments and their behavior and the subsequent recording, processing and interpretation principles of the geophysical waveforms. The book essentially consist of seven divisions: 1. 2. 3. 4. 5. 6. 7.

Basic physics Geophones and instrumentation Seismic field design Rocks, rock physics and well logs The seismic method Seismic interpretation and geology Probability, statistics and mapping

Many geoscientists believe that formalism aids in the understanding of the subject matter, therefore texts treating this topic are usually too advanced, too mathematical and too specialized, and they also make the assumption that many of the underlying Physics concepts have already been mastered. On the other hand they can treat the subject in such a simplified manner that there is absolutely no understanding or even a foundation. I believe that when one starts out learning this subject this same formalism prevents many students from understanding the concepts and therefore drives them away from this science.

N

Introduction

Audience This book is aimed at those who are first or second year technical school or university students who need to learn about the seismic method. This book can be used for teaching a one or two semester course. As geoscientists we rely greatly on our technicians and technologists. It is therefore important that they have a solid understanding of what we do and what we expect them to know. Another group who might find this book very useful are seismic field personal such as observers and party managers, geological and geophysical technicians, geologists, engineers and financial people who need a more in depth understanding of the subject without having to learn the advanced mathematical treatment. I trust this book fills the gap that has existed for so long. Andreas Stark Calgary, Alberta, Canada November, 2007

Acknowledgements

First of all I would like to thank my wife Regina who has been my inspiration throughout our life together. Without her encouragement I would never have started my thesis and have written this book. She has been my emotional support and my best reviewer and critic through all my struggles in trying to create this book and all of my course materials. I thank her for her unwavering support and for putting up with me over the years. I would also like to thank my thesis advisor at Rushmore University, Professor Donald Mitchell for all his enthusiasm, direction and helpful advice and comments for improvement. I trust that his suggestions for additions and changes have made this a better book that will now have appeal to a much broader audience. I would also like to thank my Rushmore University editor Ms. Laurel Barley for her efforts and dedication in trying to understand the science and to help me write in proper English without the use of technical jargon for as much as possible. I have used the public domain provided seismic data and the SU software, also known as SeismicUn*x, from the Center for Wave Phenomena at the Colorado school of Mines, to create the processing examples. The mathematical pictures and graphs were created in Mathematica© from Wolfram Research. All maps and interpretation examples were created in WinPICS© from Divestco Inc. and in Surfer© from Golden Software Inc. The stacked seismic data is from public domain data that was provided with previous versions of WinPICS©, such as the Stratton data set from the Texas Bureau of Economic Geology. The inversion pictures were created with the Hampson Russell HR© software. All log data is public domain. All photo’s of field examples and equipment are my own and were taken many years ago. The material and structure of the book evolved from over seventeen years of teaching this material at the technical school level and through giving private industry courses, so I like to thank all my students for their feedback and suggestions. The large list of references given on the last few pages all had some part in the final development of this book and should be used for more in-depth information. The responsibility for any errors in this book resides solely with the author. The reader is encouraged to report any errors of fact or of typographical nature to: [email protected]

PART - ONE

THE PHYSICS

Chapter

Waves and Sound



"

Seismic Methods and Applications

To be able to understand the procedures and the principles behind the seismic method, it is necessary to understand some of the basic principles of waves. The first three chapters will provide the basics of waves, optics and electromagnetic waves respectively. We will then combine the different aspects to give the student a clear understanding of the basic seismic wave principles. We will now start with a short introduction to the concept of vector and then treat the laws that are fundamental to it all: the laws of motion. Remember that we induce motion into the subsurface to create waves that will travel through the various geologic layers. They will be altered by the responses of these layers and these altered waves will be recorded at the surface.

SCALARS AND VECTORS Definitions Scalars Scalars are measurable quantities that have only magnitude and sign. Some examples of scalar quantities are length, mass, volume, area, etc. All conventional algebraic rules can be applied to perform mathematical operations on these quantities. It is assumed that the student is already familiar with the handling of scalar quantities.

Vectors Vectors are measurable quantities that have both magnitude and direction with respect to a reference plane. An example of a vector quantity is shown in figure 1.1 in which the magnitude of the gravitational force experienced by the body is indicated by the length of the segment joining the center of the body with the arrowhead and the direction of the force is indicated by the way the arrow points with respect to an arbitrary set of coordinates x, x¢ and y, y¢.

Fig. 1.1

Vector quantity

Addition of Vectors Vectors in general do not obey ordinary algebraic rules, therefore a set of mathematical operations suitable for vector operations must be developed. For instance if we want to represent the sum of two vectors, we may write R = A + B , which means that the resultant is equal to the vectorial sum of vector A and vector B . The resultant will also be a vector quantity. With reference to figure 1.2 the sum of two vectors may be stated as follows: Starting at any arbitrary point and using any convenient scale draw a vector A1 equal and parallel to A and pointing in the same direction. At the head of vector

Waves and Sound

#

A1 start the tail of vector B1 and draw it equal and parallel to B and in the same direction. Then to find the sum of vectors A and B draw a vector from the origin or tail of A1 to the end or head of B 1 . This vector R is the sum of A and B as is shown. The order in which the sum is performed is irrelevant as long as the same origin is used and the original direction and magnitude of the vectors have not been changed.

Fig. 1.2 Vector addition

If the addition of more than two vectors is required then neither the triangle nor the parallelogram method is suitable. We then have to apply the polygon method.

Definition of the Polygon Method is as Follows Again starting from some arbitrary origin we redraw the vectors in sequence and place them from head to tail. The sum of these vectors is a single vector drawn from the origin to the head of the last vector in order to form a closed polygon, as is shown in figure 1.3.

Fig. 1.3

Vector summing by polygon

$

Seismic Methods and Applications

Subtraction of Vectors By using the same rules as those for addition, vectors can be subtracted by employing the following relation:

c h

R = A – B = A + -B When the sign of a vector is changed from plus to minus (or vice versa) its magnitude remains the same although its direction is reversed. Figure 1.4 below shows the diagrammatic sum and subtraction of two given vectors.

Fig. 1.4 Vector subtraction

Resolution of Vectors Since a single vector R is formed by adding together any number of vectors, any vector can be split into any number of components. A useful method is to split a vector into its rectangular components which will then permit the use of the Cartesian coordinate system and the application of the rules of the rectangular triangle. Referring to figure 1.5 below we notice that vector A forms a right-angled triangle with the horizontal projection of A , the vector A x and the vertical segment that joins the arrow heads of A and A x . Of course this vertical segment A y is the projection of A on the y-axis. By using the properties of right angles we can establish the following relationship:

Fig. 1.5 A vector’s rectangular components

R| A || |S A || || A TA

Waves and Sound

x

y

= A * cos(q ) Þ cos(q ) = = A * sin(q ) Þ sin(q ) =

%

Ax A Ay

A sin(q ) = = tan(q ) cos(q ) x = A * cos(q ) Another very useful relationship can be obtained by using the Pythagorean 2

= A * sin(q )

2

A x + A y or, solving for A x and A y

theorem A = 2

y

Ax =

2

2

A - A y and

2

A y = A - A x . These properties of vectors are fundamental in the study of physics and they should be thoroughly understood since they will be used extensively in this and subsequent sections.

Multiplication and Division of a Vector by a Scalar When a vector is multiplied by a positive scalar, the result is still a vector. The new vector points in the same direction as the old one, but its magnitude is the product of the scalar and the magnitude of the old vector. Therefore, any vector quantity can be expressed mathematically as its absolute magnitude A , which is always a positive scalar multiplied by an unit vector u pointing in the same direction as A . Thus we have A = |A| ◊ u . | A| in this expression is also called the modulus of vector u . When a vector is multiplied by the value –1, the result is a vector of the same absolute magnitude but pointing in the opposite direction. The division of a vector 1 by a scalar a is equivalent to multiplication by the scalar . The result of this a operation is always a vector quantity.

General When we say that an object is at rest, we mean that it is at rest with respect to a reference frame such as the earth or the walls of a room. When we speak of the motion of a car or a train, we mean the relative motion of the object with respect to the earth or some other frame of reference. The frame of reference usually takes the form of a set of coordinates such as North–South–East–West. The definition of motion is the distance the body travels along a straight line in equal time intervals. The speed of a body is defined as the distance traveled divided by the elapsed time: i.e. speed = distance/time s If symbols are substituted we get: v = t When numbers are substituted for symbols, they must be accompanied by their proper units; therefore in the equation above we would have units of m/sec, ft/sec,

&

Seismic Methods and Applications

etc. If both speed and direction of a body are specified we use the term velocity, which is defined as follows: the velocity of a body which is in uniform motion in a straight line is the displacement divided by the time during which this

s t The arrows above the symbols are used because both velocity and displacement are vector quantities. If the displacement is not uniform in relation to time, the displacement occurred or in symbols v =

equation must be modified to accommodate the variations; thus V avge ( s - s1 ) = 2 , where V avge is the average velocity over the interval  s2 - s1  and is ( t2 - t1 ) defined as the vector displacement divided by the time difference t2 - t1  . The equation can be written in a more compact form by replacing  s2 - s1  and t2 - t1  with the Greek letter D (delta). This is usually referred to as the increment of the variable which it precedes. Hence we can Ds , where D s represents an write V avge = Dt average displacement interval and not the actual path s1 to s2, unless the path itself follows a straight line. However, if s1 and s2 move toward a fixed point P on the curve, then D s coincides more with the actual path along Ds the curve. The limit which the ratio can Dt reach, if it converges on P, is the value referred Fig. 1.6a Average and instantaneous velocity to as the instantaneous velocity.

f t + Dt  - f t  ds Ds = lim = = f ¢ t  . This is equal to D ® t 0 dt Dt Dt the value of the tangent at that point and can be found by letting the independent variable Dt approach 0 as a limit. The limit can be defined as that constant value which is approached by a sequence of values of the average velocity, also called the derivative with respect to t. Figure 1.6a shows the Representation of Average and Instantaneous Velocity vinstantaneous = lim

Dt ® 0

NEWTON’S LAWS OF MOTION In 1687 Sir Isaac Newton (1643–1727) published for the first time the three fundamental laws of mechanics, which marked a new era in physics. The three laws can be stated as follows: 1. A body remains at rest or in uniform motion in a straight line as long as no net force acts on it (conditions of equilibrium–Galileo’s principle of inertia).

Waves and Sound

'

2. If a net force acts on a body, the body will be accelerated. The magnitude of the acceleration is proportional to the magnitude of the force and the direction of the acceleration is in the direction of the force. (action principle – fundamental law of dynamics) 3. When one body exerts a force on a second body, the latter exerts a force equal in magnitude and opposite in direction on the first body. Another way of stating this law is: (to every action there is an equal and opposite reaction – reaction principle) These laws are fundamental to the sections that follow. They are important in seismic exploration as we induce forces into the earth and therefore we create reactive forces. It is the interaction of these forces that we will need to understand.

Newton’s First Law Newton’s first law is often referred to as the law of inertia because of the reluctance of a body to change its state of rest or motion. When a body is said to be in equilibrium this does not mean that there are no forces acting on it; what is meant is that the resultant of all the vector forces acting on the body are equal to 0, or expressed as vectors R = A + B + C + D + K = 0 where R is the resultant of the vectors A , B , C , D etc. Sometimes it is more convenient to express these vector quantities in a 3-dimensional coordinate system with mutually perpendicular coordinates x, y and z, thus splitting R into its three components: R x = Ax + B x + C x + Dx + L = 0 Ry = Ay + By + C y + Dy + L = 0

R z = A z + B z + C z + Dz + L = 0 If any of these three equations gives a resultant other than zero, then the body will be accelerated in accordance with Newton’s second law.

Newton’s Second Law A body is said to be accelerated when its velocity varies with respect to time. The average acceleration is given by the change in velocity divided by the time in Dv Instantaneous which the change takes place - or in symbols: a avge = Dt acceleration is found by taking the limit of the ratio Dv/Dt in the same manner as dv we defined instantaneous velocity: i.e. a instantaneous = , or dt f t + Dt  - f t  dv d 2s Dv & lim a = lim v = = = = 2 Dt ® 0 Dt Dt ® 0 dt Dt dt We are now able to write Newton’s second law in the form of an equation: F = k × a , where F is the magnitude and direction of the force and k is a

 Seismic Methods and Applications

constant scalar quantity, the value of which depends on the system of units used and the properties of the body. Thus it follows that k = U * M, where U is the system of units used and M represents the properties of the body. M is the symbol of mass, which is the quantitative measurement of inertia in a body. If the SI system is used then U = 1, and M is expressed in kilograms (kg), and acceleration is measured in meters per second2 (m/sec2 ). Hence the equation can be written in terms of the SI units: Fig. 1.6b Average and instantaneous –2 –2 acceleration F = k ◊ a = kg m sec = N = kg m s , where N is the symbol for Newton.

Newton’s Third Law The last law states that a single isolated force is a physical impossibility. Each force is always met by another equal in magnitude and exerted in the opposite direction. These forces are known as action and reaction. A typical example is found in seismic work, either with Vibroseis® or the older gas exploding Dinoseis®, where a force F is impressed into the ground. The reaction of the ground to the force from the seismic source is countered by a force acting on the truck which is sitting over it. This is often called the reaction mass. This is pointed out in the following diagram.

Force

Force

Fig. 1.7 Vibrating force and reacting force indicated by the arrows

VIBRATIONS AND WAVES Vibrations of strings and tuning forks can be described by a simple experiment as a function of time and amplitude. Let’s consider the vibration of a single point. In

Waves and Sound 

figure 1.8, we see a circle and a point H. If we let this point H travel at a constant speed around the circle, starting from point H0, we can determine the position of H at any time by measuring the angle HOH0, or j. The distance that the point H deviates from point H0 is measured by the point P along the axis DE and it is called the Amplitude. If we now continue this process and continually measure the angle and the position of the point P as it moves up and down, then we can create a graph that displays the vibration as a function of Fig. 1.8 Harmonic circular amplitude and time as shown below in figure 1.9. motion By the time we have completed one revolution around the circle, or moved point P from O to D, to O, to E and back to O, we have completed one wave form called l. The circle has been divided into twelve equal arcs of equal time intervals, i.e. constant rotation to demonstrate this. Note that this all happens in place and there is no lateral movement.

Fig. 1.9

Simple harmonic motion

These vibrations are called SIMPLE HARMONIC MOTIONS. In the next picture, figure 1.10 we have marked 13 points, or twelve equal intervals on a string. This indicates a traveling transverse harmonic vibration.

Fig. 1.10

Transverse harmonic motion

The first point started vibrating upwards from H0, the leading edge of the wave train, and returns back to its original state after T seconds. The second point is a



Seismic Methods and Applications

1 l removed from point one. It will start vibrating when point one 12 1 has vibrated for T sec., as that is the time needed to go from the first point to 12 1 1 the second point, a distance of l. The second particle is then T - T sec in 12 12 vibration. The phase difference between particle one and particle two is therefore 1 ö æ çè T - T ÷ø 11 12 = . With the aid of the circle we see that the vector or radius A has T 12 11 traveled the arc H0QH, or ´ 360 ° = 330°, and particle two is therefore at 12 position 2¢. This procedure is followed for all the remaining particles. It can be seen that one vibration of particle one has created one peak and one trough, and is currently at the particle 13 position. The remaining part of the string is still at rest. distance of

Note: If we have one point that vibrates in place, it is in a different position at different times, we get figure 1.9. If we have vibrations of several different points at the same moment in time, we get figure 1.10. In figure 1.11 we have indicated the traveling LONGITUDINAL HARMONIC VIBRATION.

Fig. 1.11 Longitudinal harmonic motion

Again, as in the previous example for transverse waves, the first longitudinal particle starts moving, in this case to the right as indicated. The process is exactly the same as for the transverse motion, except that the particles in this case move in the direction of propagation. The bottom part indicates the particle displacement, and the top part shows the resulting waveform.

Periodic Motion When the resultant force acting on a body is not constant but repeats itself at regular time intervals T (period), the body is said to move with periodic or harmonic motion; i.e., if a body at time t is found in a given position, provided its motion is periodic, it will return to the same position after a time t + T.

Waves and Sound 13

An example of “quasi” periodic motion is the oscillation of a weight attached to a spring or the oscillation of a pendulum. The words quasi periodic are used since the amplitude of successive oscillations decreases because of frictional forces acting on both systems. These types of oscillations are often called aperiodic. Harmonic motion can be plotted on Cartesian coordinates to give an idea of how the amplitude varies as a function of time, as was demonstrated above. The figure 1.12 below shows a fairly complex harmonic motion in (a) and the simplest one in (b), which is also called a sine or cosine curve because it can be described by the sine and cosine functions.

Fig. 1.12 Complex harmonic motion (a) and simple harmonic motion (b)

At this stage, it is also worth mentioning that any complex periodic or aperiodic event can be described by the combination of sine or cosine functions. As already mentioned, periodic motion can be represented by sine or cosine functions. For this purpose, the reference circle can be used to explain how two functions can describe periodic motion.

Fig. 1.13

Vector reference circle and x and y coordinates

14 Seismic Methods and Applications

Vector A rotates at a uniform constant velocity denoted by the Greek letter w (omega). Now, suppose that the vector at each complete revolution per unit of time returns to position a. The angular position of this vector at subsequent time t is given by angle f such that f = w t + f. Therefore, the position of the vector in terms of x and y coordinates is given by x = A cos(w t + f) y = A sin(w t + f) f in the equations is called the phase angle and is defined as the fractional part of a period through which the independent variable (t, in our case) has advanced from our arbitrary origin. By plotting the various values of sine and cosine as a function of the angular position on Cartesian coordinates, we obtain two simple harmonic functions. Although the shape of these two functions is the same, the phase of the cosine function is displaced by p /2 with respect to the sine function if both are plotted on the same axis. The constant circular velocity is written as w =

2p A , or w = 2pf A . T

ELASTICITY AND HOOKE’S LAW A body or mass which is elastic possesses the property of recovering its original form when a distorting or constraining force is applied. Perhaps one of the most descriptive examples of this is a coil spring, but the characteristic is also found in seemingly rigid matter such as ROCK or METAL. Because fluids and gasses are not elastic, the transverse waves will not propagate through fluids and gases. Remember this when we discuss AVO and Rock Physics in later chapters. Robert Hooke (English scientist and mathematician, 1635–1703) discovered that elastic displacement in many materials is directly proportional to the force exerted upon them. In other words, the recovering force is proportional to the distorting or constraining force. This relationship can be expressed mathematically as: F = –k x , where F is the elastic force exerted by the deformed body and x is the displacement. The constant of proportionality k (also called stiffness of the material) has the dimensions of force per unit. This is illustrated in figure 1.14. When an object obeying Hooke’s law is displaced from its equilibrium position and released, the subsequent motion is periodic. This property can be used to explain the transfer of mechanical energy from one point to another in an elastic medium. This phenomenon is called mechanical wave propagation, and is the basis of seismic exploration.

Waves and Sound 15

Fig. 1.14

Hooke’s elastic forces

WAVE ENERGY Although energy can take many forms in nature, waves are perhaps the most important since in wave form energy can be transferred from place to place. Some waves, such as heat, light and acoustic or sound waves, are discernible by human senses while others, such as ultrasonic waves, radio waves, etc. are not. A physical example of how waves are propagated is given by throwing a pebble into a pool. Where the pebble breaks the surface of the water a series of ripples begins to spread outward in the form of concentric circles. If a floating object encounters these ripples, it tends to move up and down in synchrony with the peaks and troughs of the ripples that were created. Wave energy can be divided into two broad classes, viz. mechanical and electromagnetic; the former can propagate in a medium only, whereas the latter is able to also propagate in a vacuum. Mechanical waves can be generated by applying a force or a set of forces simultaneously at a point in a medium. Then, according to Newton’s second law, the equilibrium of particles at that point is disrupted and as a result they receive acceleration in the direction of the applied force(s). The accelerated particles collide with neighboring particles delivering energy to them and then return toward their original equilibrium location but, owing to inertia (Newton’s first law), each particle overshoots. The motion of the particles is then reversed by forces drawing them toward equilibrium, but again they overshoot, and so on.