`Ex. PGS 2002
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`EX. PGS 2002
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`

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`RESERVOIR SEISMOLOGY
`
`GEOPHYSICS IN NONTECHNICAL LANGUAGE
`
`:
`
`MAMDOUH R. G ADALLAH
`
`pennWell Books
`
`PENNWELL PUBLISHING COMPANY
`TULSA, OKLAHOMA
`
`Ex. PGS 2002
`
`

`

`Copyright © 1994 by
`PennWell Publishing Company
`1421 South Sheridan/P.O. Box 1260
`Tulsa, Oklahoma 74101
`
`library of Congress Cataloging-in-Publication Data
`
`Gadallah, Mamdouh R.
`Reservoir seismology : geophysics in nontechnical language /
`Mamdouh R. G adallah
`p. cm.
`Includes bibliographical references and index.
`ISBN 0-87814-411-0
`1. Seismic prospecting.
`TN269.8.G33 1994
`622U592—dc20
`
`I. Title.
`
`93-39214
`CIP
`
`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
`and recording, without the prior written permission of the
`publisher.
`
`Printed in the United States of America
`
`1 2 3 4 5 98 97 96 95 94
`
`Ex. PGS 2002
`
`

`

`C H A P T E R 5
`
`SEISMIC DATA PROCESSING
`
`INTRODUCTION
`It is very important for the interpreter to be aware of all the problems
`encountered in seismic data processing. The geophysicist must know and
`understand the particulars of each processing step. In addition, a high
`level of experience is required for quality control at each step to ensure
`its validity before proceeding to the next step. Engineers and geologists,
`however, in order to have a better appreciation for the applications and
`limitations of seismic methods, should at least understand the physical
`meanings of the terms.
`The final interpretation is only as good as the quality of the process­
`ing of the seismic data. Special attention and care should be given to the
`stratigraphic applications of seismic data in areas of subtle traps and of
`rapid lithology and facies changes.
`The process of converting field recordings into a meaningful seis­
`mic section involves many steps of data manipulation. Before a CMP
`gather is corrected for normal moveout and stacked, the data should be
`corrected for near-surface time delays. These adjustments are called the
`static corrections, or simply statics.
`In addition, various deconvolution and filter tests are done, then pa­
`rameters are designed to enhance signal-to-noise ratio and increase ver­
`tical resolution. Finally, we want to convert our seismic reflections into
`a picture representing the true subsurface geology. This is accomplished
`by the process called migration.
`There is no unique processing sequence or cookbook routine to
`follow in processing the data. Each geologic setting stands on its own.
`Extensive testing must be done to study the problems involved and to
`design the optimum parameters for each step of the data-processing flow.
`It is important to have a good idea about the regional geology of
`the basin and specific problems in the area where the seismic data was
`acquired.
`
`43
`
`Ex. PGS 2002
`
`

`

`SEISMIC DATA PROCESSING 57
`
`FIGURE 5-13. Deconvolution comparison (Reprinted from O. Yilmaz,
`Seismic Data Processing, 1987, courtesy of the Society of Exploration
`Geophysicists.)
`
`DECONVOLVED
`
`Sis;
`
`NO DECONVOLUTION
`
`is an inverse filter, and it is used to retrieve the shape of the original
`seismic pulse by attenuating the undesirable signals.
`
`NORMAL M OVEOUT
`Normal moveout (NMO) is the procedure that removes the time shift due
`to the offset between the source and the receiver and corrects all traces
`
`Ex. PGS 2002
`
`

`

`58 CHAPTER FIVE
`
`to zero offset; that is, with the source and receiver at the same surface
`point, which is at the mid-point between the actual source and receiver.
`
`NORMAL MOVEOUT FOR A NONDIPPING HORIZON
`Figure 5-14 shows a simple case of normal moveout geometry for a sin­
`gle, horizontal reflector. At a given midpoint M, the travel time along the
`ray path SDG is /Or), where x is the offset from source to receiver posi­
`tion. If Vis the velocity of the medium above the reflecting horizon, / (0)
`is twice the travel time along the vertical path MD.
`/Or) = SDG
`define /(0) = 2MD
`/0r)2= /(0)2 + x^/i? which is the equation of a hyperbola
`
`NORMAL MOVEOUT IN MULTIPLE HORIZONTAL REFLECTORS
`Consider a medium consisting of horizontal velocity layers, as seen in
`Figure 5-15. Each layer has a certain thickness that can be defined in
`
`FIGURE 5-14. Normal moveout for flat reflector
`
`S
`
`X
`M
`
`G
`
`SI MPLE CASE OF NORMAL MOVEOUT G EOME TRY FOR A S I N G LE HORIZONL
`RE FLEC TOR. AT A GIV EN MIDPOINT M T H E TRAVEL TIME ALONG RAYPATH
`SDG I S t ( x )
`
`X I S O F F S E T FROM S O UR C E TO RECEIVER P OS T I ON .
`V I S VELOCITY O F T H E MEDIUM ABOVE T HE REFLECTING INTERFACE.
`t ( 0 ) I S TWICE TH E TRAVEL TIME ALONG V ERTICAL PATH MD.
`
`t(x)2« t(o)2+ x2/v 2
`
`EQUATION O F A HYPERB OLA
`
`Ex. PGS 2002
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`

`

`FIGURE 5-15. NMO in horizontally-stratified earth
`
`SEISMIC DATA PROCESSING 59
`
`X / 2
`
`X / 2
`
`R
`
`vo\^
`
`V1
`
`V2
`
`Vn-1
`Vn
`
`\
`\
`
`/
`/
`
`/
`
`tC>
`
`t 1
`
`t2
`
`tn-1
`Tn
`
`X
`
`v/
`
`\ /
`
`•
`Vrms - ( v°2* to + V1** t1 + V2** t2 +
`to + t1 + t 2 +.
`t n
`
`+ Vn2* tn °"5
`
`(1)
`
`t(x) - t(0): X2/Vrms2
`
`(2)
`
`terms of two-way zero offset time. The layers have interval velocities V#,
`Vx, V2, . . . Vn, where n is the number of layers.
`A study of this relationship was done by Dix (1955), and Taner and
`Koehler (1969) have derived the relationship between RMS velocity and
`interval velocities, as indicated in Eq. (1) of Figure 5-15.
`The normal moveout equation for the multi-layer case is given in Eq.
`(2). This is similar to the NMO equation for a single horizontal layer
`except for the velocity, which is the RMS velocity.
`
`VELOCITY A NALYSIS
`Acoustic well logs provide direct measurement of formation velocity as a
`function of depth. Seismic data, on the other hand, provides an indirect
`measurement of the velocity. By using both types of information, the
`explorationist can derive a large number of different types of velocity,
`such as interval, apparent, average, RMS, instantaneous, phase, NMO,
`stacking, migration, and so forth.
`The basic objective is to measure "true" interval velocities; this is
`often difficult, or even impossible, with the data available. The potential
`of seismic data as an exploration tool depends significantly on the use of
`velocity information by the geologist, geophysicist, and the engineer.
`
`Ex. PGS 2002
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`

`

`60 CHAPTER FIVE
`
`Velocity may be the most under-utilized tool available. It is an ex­
`tremely powerful tool if its role is understood and if its applications are
`utilized and implemented.
`
`VELOCITY TE RMINOLOGY
`Velocity, in seismic work, is simply the rate of travel of a seismic wave
`through a medium with respect to time. However, as we have seen, there
`are several kinds of velocity. Velocity may be defined by the type of seis­
`mic wave motion or by the method used to determine it. Before going into
`the specifics of velocity analysis, we must understand the terms. Figure
`5-16 illustrates a simple layered-earth model. Assume that the seismic
`energy is initiated at the surface at time t0 and passes through different
`reflectors at depths hx, h2, and ^3, which have velocities of V[, V2, and Vz,
`respectively. Within hx there some reflectors at times tv /2, /3, and /4.
`
`1. Interval velocity: the velocity measured between two reflectors.
`— ^1/(^4 — ^o)
`
`FIGURE 5—16. Velocity terminology
`
`hi
`
`h2
`
`h3
`
`to
`
`t1
`
`t 3
`14
`
`to
`
`te
`
`V1
`
`V2
`
`V3
`
`INTERVAL VELOCITY
`
`V1 - h1/(t4-t0)
`
`AVERAGE VELOCITY
`
`Vavg,3 - d/(t6-tO)
`
`RMS VELOCITY
`
`MIGRATION VELOCITY
`
`WELL SURVEY VELOCITY
`
`SHEAR VELOCITY
`
`Ex. PGS 2002
`
`

`

`C H A P T E R 9
`
`AMPLITUDE VERSUS
`OFFSET ANALYSIS
`
`INTRODUCTION
`The amplitude of a reflected seismic signal normally decreases with the
`increase of the distance between source and receiver. This decrease is
`related to the dependence of reflectivity on the angle at which the seis­
`mic wave strikes the interface, spreading, absorption, near surface effects,
`multiples, geophone planting, geophone arrays and instrumentation.
`In certain depositional environments, the amplitude variation can
`also be an important clue to the lithology or to the presence of hydrocar­
`bons. An increase in amplitude with increased offset, resulting in a "bright
`spot" on the section, may indicate a gas sand reservoir. A decrease in
`amplitude with offset may indicate a carbonate reservoir. However, these
`amplitude anomalies are masked in the common midpoint stack (CMP),
`as every trace of the stack section represents an over-all average of off­
`sets in the common midpoint gather.
`
`AMPLITUDE VERSUS O FFSET METHODOLOGY
`Amplitude versus offset analysis is designed to retrieve the variation in
`amplitude with angle of incidence by conducting the analysis on the nor­
`mal moveout corrected gathers be/ore stack.
`
`REFLECTION COEFFICIENT
`The amplitude of a seismic reflection is related to three rock properties.
`1. Vp - compressional wave velocity
`2. Vs = shear wave velocity
`3. p = density
`
`1 7 9
`
`Ex. PGS 2002
`
`

`

`1 8 0 CHAPTER N INE
`
`The interpretation of a stacked seismic section is restricted to the
`zero-offset model. Accordingly, an incident plane wavefront of amplitude
`A0 on a horizontal interface will produce a reflected plane wavefront of an
`amplitude of Av The ratio of Al to A0 is defined as the re/lection coefficient
`(R) of this interface, and it is expressed by the following relation:
`^ - ( p , y 2- p , K ) / { p 2y2 + p , K )
`
`POISSON'S RATIO
`Poisson's Ratio is defined as the ratio of transverse strain to longitudinal
`strain of a material under stress. For example, if a piece of rubber is
`squeezed it is shortened, but it also becomes wider as the volume re­
`mains approximately constant. The ratio of the change in width to the
`change in length is the Poisson's ratio of that material. In seismic appli­
`cations, it is the ratio between the velocities of P and S waves:
`
`or -
`
`(Sheriff, 1973)
`
`For liquids, V vanishes, and a is 0.5.
`
`REVIEW OF AVO DEVELOPMENT
`THE ZOEPPRITZ EQUATION
`Zoeppritz derived a relationship governing the reflection and transmission
`coefficients for plane waves as a function of angle of incidence and six
`parameters, three on each side of the reflecting interface. These are Vp,
`Vs, and density. The equation is complex, and its solution is laborious.
`
`SHUEY'S SIMPLIFICATION
`Shuey in 1985 simplified the Zoeppritz equation to the following:
`
`= P0 A0P0 + kcrI(l - cr} sin2 6 + A VpjVp{\zri 6 - sin2 #)/2
`
`where P(d) = the compressional wave coefficient
`A0 = t h e normal, gradual decrease in amplitude with offset
`= is the amplitude at normal incidence (0 = 0 )
`(at normal incidence, amplitude and reflection coefficient
`are the same)
`The first term on the right side of the equation, J?0, gives the reflec­
`tivity at normal incidence (0 = 0).
`
`Ex. PGS 2002
`
`

`

`AMPLITUDE VERSUS OFFSE T ANAL YSIS
`
`1 8 1
`
`The second term characterizes R(0) at an intermediate angle. The
`coefficient of the second term is a combination of elastic properties that
`can be determined by analyzing the offset dependence of event amplitude.
`If the amplitude of the event is normalized to its value for normal
`incidence, then:
`
`A = A0
`
`i/(i- c r )2][A<7/je0]
`A0 specifies the normal, gradual decrease of amplitude with offset. Its
`value is small enough that the main information conveyed is in the sec­
`ond term, in which A a is the contrast in Poisson's ratio at the reflecting
`interface.
`
`Where
`
`HILTERMAN'S MODIFICATION OF SHUEY'S EQUATION
`Hilterman modified Shuey's equation and established a linear relationship
`between incident angle and reflection coefficient.
`R{6) = R0 cos2 6 + 2.25Acr sin2 6
`= reflection coefficient at normal incidence
`= {PzV„ ~ P^p)/{P2^P 2 + P^p)
`ACT = a2 - cr 1
`6 = angle of incidence
`This approximation for amplitude behavior with angle of incidence
`is valid if 6 < 30°, Rc(d) < 0.15, and Vp^2Vs.
`For plane waves only, by using linear regression, it is possible to get
`estimates of
`from normal moveout corrected CDP gathers. Essential­
`ly, the following are known or can be estimated:
`R(x,t) = R{6), the seismic trace amplitude
`6 (x,t) = angle of incidence as a function of offset and time
`For each CDP, J?0 and A a can be computed for each time sample.
`The result is two seismic sections, one called the normal incidence sec­
`tion and the other the delta sigma, or Poisson's ratio, section.
`If R(Q) is normalized by dividing by cos20, the following equation
`is obtained:
`
`R{d)/cos2 6 = R0 + 2.25Acrtan2 6
`
`Which is a linear equation of the form
`y{ = b + mx;
`
`Ex. PGS 2002
`
`

`

`1 8 2 CHAPTER NINE
`
`CONCEPTS AN D INTERPRETATION O F AVO
`Refer to Figure 9-1. For a given interface, acoustic and elastic properties
`are given. Both the Zoeppritz and Shuey equations are applied to obtain
`a relationship between reflection coefficient and incident angle (in de­
`grees) .
`The two equations give the same results up to 10° angle of inci­
`dence, and they do not differ significantly up to 45°. One can see the
`increase of reflection coefficient (amplitude) with the increase of angle of
`incidence or offset.
`
`FIGURE 9-1. Typical concept
`
`LAYER 1
`
`P-
`
`VELOCITY - 12.000.00 ft/amc
`
`DENSITY" 1.96 grn/oc
`
`POtSSON*S RATIO - 0.40
`
`P- WUVE VELOCITY -10,000.00 «/®ec
`
`DENSTTY- 2.20 grn/oc
`
`P0tS30N*3 RATIO - 0L2O
`
`LAYER 2
`
`ANGLE OF INODENT (DEGREES)
`
`Ex. PGS 2002
`
`

`

`AMPLITUDE VERSUS O FFSET ANALYSIS
`
`1 8 3
`
`Figure 9—2 i s the reflection coefficient versus angle of incidence for
`a typical Gulf Coast gas sand. The reflection coefficients are the troughs
`and have negative signs, since the plane wavefront is passing from high
`velocity and density to lower velocity and density. Notice the decrease of
`Poisson's ratio and the increase in absolute amplitude with angle of inci­
`dence. Figure 9—3 shows little change of reflection coefficient with the
`angle of incidence. Shuey's curve shows a slightly smaller value of reflec­
`tion coefficient than Zoeppritz for the same angle of incidence between
`
`FIGURE 9-2. Gulf Coast gas sand
`
`LWER 1
`
`p- VWVE VELOCITY - 0400.00 ft/MC
`
`DENSITY- 1.06 gm/cc
`
`POiSSON"S RATIO * O.10
`
`R
`p -0 10 ZOEPPRITZ
`L
`E
`
`P- \A*Vfc VELOCITY -
`DENSITY — 2 .16 fpn/cc
`
`POISSON'S RATIO - 0.40
`
`7570.00 n/mmc.
`
`LAYER 2
`
`SMUEY
`
`ANGLE OF INaDENT (DEGREES)
`
`Ex. PGS 2002
`
`

`

`1 8 4 CHAPTER NIN E
`
`FIGURE 9-3. Little change—possible brine sand
`
`1
`
`p- vmwe velocity - .1100000 tt/Mc,
`DENSITY" 2.15 vn/cc
`POtSSON*8 FVCIIO » 0-28
`
`p- vmtE VELOCITY - 9000.00 n/ttc
`
`DENSITY- 2.20gm/oc
`
`P0330N*3 RATIO - 0.20
`
`LAYER 2
`
`(10-40°). Otherwise, the two curves are essentially identical and may in­
`dicate brine (salt water) sands.
`Figure 9-4 illustrates a decrease of amplitude with increase of an­
`gle of incidence or offset. This is a typical dim spot as observed in car­
`bonate rocks. The curve was derived from the modeling of the Austin
`Chalk formation in the Texas Gulf Coast.
`Notice the departure of the curves from the two methods of com­
`puting the angle of incidence. Yet, both show the same trend of the re­
`lationship between reflection coefficient and the angle of incidence.
`
`Ex. PGS 2002
`
`

`

`AMPLITUDE VERSUS OFFS ET ANALYSIS 185
`
`FIGURE 9-4. Dim spot in carbonate rock—Austin chalk
`
`LATER 1
`
`POiSSOWS RATIO » 0.4O
`
`P- VNHVE VE LOCITY - 8000.00 ft/we
`DENSITY- 2.16 gm/oc
`
`P~
`
`VELOCITY - 113GCXOO ft/MC
`
`DENSITY- 2J2 gm/oc
`
`POtSSON*S RATIO - 0 30
`
`LAYER 2
`
`Figure 9-5 shows a slight decrease of amplitude with the angle of
`incidence, and the trends of the two curves match up to 30° of angle of
`incidence. The Shuey curve suggests it is consistent for all angles, while
`the Zoeppritz curve suggests an increase in amplitude. Above 30°, the
`calculations will be sensitive due to the NMO stretch on far offsets with­
`in the CMP gather.
`Figure 9-6 shows a decrease of amplitude with increase of angle of
`incidence, which suggests a dim spot anomaly. The two curves have the
`
`Ex. PGS 2002
`
`

`

`186 CHAPTER NINE
`
`FIGURE 9-5. Little chang
`
`shale to sand
`
`UWER 1
`
`P- y*T VELOCITY -
`
`11000.00 ft/
`
`DENSITY" 2.1 gm/cc
`
`POWSON'S RATO - o^«
`ZOEPPRITZ
`
`0 .15
`
`P- WHVE VELOCTTY - 0000.00 «/
`
`DENSITY- 2_20 am/cc
`potssoN*s RATIO - OJM
`
`LAYER 2
`
`SHUEY
`
`0.10 -
`
`R
`E
`F
`L
`E
`C
`T
`I
`O
`N
`C
`0
`E
`F
`F
`1
`C
`I
`E
`N
`T
`
`0 05
`
`5
`
`—r~
`10
`
`—I—
`—f—
`25
`AO
`15
`Z5
`20
`35
`20
`ANGLE OF MODENT (DEGREES)
`
`—I—
`40
`
`—I
`45
`
`same trend, even though the Zoeppritz curve may show higher reflection
`coefficient values above 35° angle of incidence.
`Zoeppritz equations are the complete solution, which relates the
`change in amplitude with the angle of incidence. The other approximations
`such as Shuey's are acceptable to a certain extent for most lithologies.
`Other approximations are suitable for some localized and specific areas.
`
`GEOPHONE ARRAY CO RRECTION
`The data will be handled, for the most part, in the data reduction and
`setting up the lines geometry, as we discussed briefly in Chapter 5. A
`
`Ex. PGS 2002
`
`

`

`AMPLITUDE VE RSUS OFFSET AN ALYSIS
`
`1 8 7
`
`FIGURE 9-6. Decreased amplitude with increased angle—dim spot,
`(carbonate)
`
`P- WAVE VELOCITY - OOOO.OO It/
`
`DENSITY* 2.20 gm/oc
`
`POiSSOWS RATIO - 0J2fi
`
`LATER I
`
`P- VWWE VELOCTTY -
`
`11000.00 ft/
`
`DENSITY- 2.1 gm/cc
`
`0.15 •,
`
`R
`E
`F
`L
`E
`C
`T
`I
`O
`N
`C
`0
`E
`F
`F
`1
`C
`I
`E
`N
`T 0.05
`
`0.10 -
`
`POtSSON*3 RATIO- O_20
`zoeppRrrz
`
`LAYER 2
`
`SHUEY
`
`—r
`5
`
`-Tr­io
`
`-i—
`1—
`~i
`—r-
`—r~ 20
`35
`30
`25
`15
`(DEGREES)
`ANGLE OF MODENT
`
`—I—
`40
`
`—1
`45
`
`geophone array correction must be applied to compensate for the time
`differential within the array from the first to the last geophone in the
`pattern.
`Figure 9-7 and Figure 9-8 show the theory and a synthetic exam­
`ple to illustrate the need to correct for the geophone array spread. Fig­
`ure 9-8 shows 12 geophones planted in line on the ground over 220 feet.
`Observing from left to right on the first reflector, the time differential
`between geophone 1 and geophone 12 is about 10 ms. The individual
`geophone signals are summed together in one trace on the extreme right.
`
`Ex. PGS 2002
`
`

`

`1 8 8 CHAPTER N INE
`
`FIGURE 9-7. Geophone array correction
`
`T I M E D I F F E R E N C E
`
`S O U R C E
`
`SURFACE
`
`CONSTANT VELO CITY ME DUIM (V)
`
`REFLECTOR
`
`TIME DIFF.- (OFFSET X ARRAY LENGTH)/ TRAVEL TIME X VEL. SEQ.
`
`FIGURE 9-8. Array of 12 geophones (After Fouquet, courtesy of
`Seismograph Service Corporation)
`
`1- 100
`
`0.000
`(X 100
`Q. 200
`a 3oo
`0- 400
`a soo
`A BOO
`0» TOO
`a. 000
`a. 9oo
`1. ooo
`i. 200
`1.30O
`1. 400
`1. soo
`1. GOO
`1- TOO
`1. 0OO
`1.90O
`a. ooo
`2. LOO
`2.200
`Zm 300
`2- -400
`2. SOO
`2. GOO
`2- 700
`2. 800
`2. SOO
`3. OOO
`
`i ^ •£
`
`1
`
`"f T T
`~r -r -r
`
`"5: t t
`
`-f
`
`-r
`
`Ex. PGS 2002
`
`

`

`AMPLITUDE V ERSUS OFFSET AN ALYSIS
`
`1 8 9
`
`Each trace has the same high-frequency component but the summed
`trace, recorded as the array response, lacks some of the high frequencies
`because of the time shift from geophone to geophone within the array.
`The differential time within the array from the first geophone to the
`last geophone decreases with depth, as the angle of incidence decreases
`with depth. It is critical to maintain the high-frequency component up
`shallow, especially if the data is recorded for shallow targets.
`
`DATA PROCESSING FLOW CHART
`Figure 9-9 illustrates the flow of data processing designed to preserve
`and enhance the true amplitude of each trace within the CMP.
`Scaling is a critical step, and it should be done in a surface-consis­
`tent manner. Figure 9-10 shows the scale factor display, which is used
`
`FIGURE 9-9. Recommended AVO processing flowchart
`
`DEMULTIPLEX / EDIT / GEOMETRY
`
`GEOPHONE ARRAY CORRECTION
`X
`SPHERICAL DIVERGENCE
`T
`DECONVOLUTION - CMP SORT
`r
`VELOCITY ANALYSIS
`
`NMO / STATIC CORRECTION
`
`SURFACE CONSISTENT SCALING
`
`COMPUTE RESIDUAL STATICS
`
`EDIT ST ATICS
`
`PLOT S TATICS
`
`COMPUTE SURFACE CONSISTENT SCALING
`X
`APPLY SCALING TO CORRECTED GATHER
`SUPER GATHERS
`QUADRATIC FIT
`OF THE EVEN T
`OF INTERE ST
`
`COMPUTE ANGLES
`OF INCI DENCE
`
`NEAR T RACE S TACK
`
`FAR TR ACE ST ACK
`
`PLOT CUR VE
`
`GRADIENT
`
`CONSTANT
`ANGLE ST ACK
`
`DIFFERENCE / RATIO
`
`Ex. PGS 2002
`
`

`

`1 9 0 CHAPTER NINE
`
`FIGURE 9-1 0. Surface consistent scaling display (courtesy of
`Seismograph Service Corporation)
`
`for editing and modifying to derive the scale factor for each source and
`receiver on the line. It is used as a quality control display; the final surface-
`consistent scaling is achieved when all the bars on the display are approx­
`imately equal in hight.
`Figure 9-11 illustrates an AVO stack with all the offsets in the CMP
`gather. The amplitude anomaly at the event between 1.600-1.700 seconds
`at CMP 305-337 represents a bright spot. It stands out in the section and
`is normally a direct indicator of gas sand reservoirs.
`Figure 9-12 is the same line. A range of the near traces in every
`CMP gather corrected for NMO are stacked to form this line. The bright
`spot anomaly has disappeared.
`Figure 9-13 is the stack generated from a set of far offset traces in
`every CMP gather stacked. The bright spot stands out.
`Figure 9-14 is the differential amplitude between far trace and near
`trace amplitudes. One can see that the bright spot is still anomalous on
`the section.
`From this discussion, an increase in the amplitude of a seismic
`event with the increase of distance from the source to receiver (related
`to increased angle of incidence) represents a geological marker. In this
`case, the bright spot is associated with a gas sand reservoir.
`
`Ex. PGS 2002
`
`

`

`AMPLITUDE VERSUS OF FSET ANALY SIS 191
`
`FIGURE 9-11. AVO stack (courtesy of Seismograph Service
`Corporation)
`
`2 7 2 2 2 2 2 2 2 2 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3
`9 9 9 9 9 9 9 9 9 9 0 0 0 0 0 0 0 0 0 0 1 1 1
`I 1 1 1 I I 1 2 2 2 2 2 2 2 2 2 2 3 3 3 3 3 3 3 3 3 3 4
`0 I 2 3 4 5 6 P 8 9 0 I 2 3 4 5 6 7 0 9 0 1 2 3 4 5 & 7 8 9 0 I 2 3 4 5 6 P 9 9 0 1 2 3 4 5 6 7 8 9 0
`
`0. ooo
`
`O. 100
`a 200
`O. 300
`a *00
`O. 500
`o. GOO
`a 700
`O. BOO
`0. 900
`1. 000
`1. too
`1. 200
`1. 300
`1. 400
`1. 500
`1.600
`1. TOO
`1. 800
`1. 900
`2. OOO
`2. lOO
`2. 200
`2.300
`2. 400
`2. 500
`
`0. 000
`0. LOO
`a. 200
`a 300
`O. 400
`0.500
`a GOO
`a TOO
`0. 800
`a 900
`1. 000
`1. 100
`1. 200
`1. 300
`1. 400
`1. 500
`1.600
`1. 700
`1. 800
`1. 900
`2.000
`2. LOO
`2.200
`2. 300
`2. 400
`2.500
`
`Figure 9-15 is a display of the amplitude versus offset, or angle of
`incidence, run of CMP gathers 310, 314, 318 from Figure 9-11. Notice the
`time slices between 1.600-1.700 seconds. One can see the increase of the
`amplitude as the offset increases on all three, but it is most pronounced
`on CMP 318. A curve of RMS or maximum amplitude can be plotted to
`define this anomaly.
`
`Ex. PGS 2002
`
`

`

`1 9 2 CHAPTER NINE
`
`FIGURE 9-12. Near traces stack (courtesy of Seismograph Service
`Corporation)
`
`3."5 3333333333333333333333333333333333333332222222222
`4 3 3 3 3 3 3 3 3 3 3 2 2 2 2 2 2 2 2 2 2 1 1 I I 1 t I I I 1 0 0 0 0 0 0 0 0 0 0 9 9 9 9 9 9 9 9 9 9
`0 9 0 7 6 5 4 3 2 1 0 9 6 7 6 5 4 3 2 1 0 9 8 7 6 5 4 3 2 l 0 9 8 7 6 5 4 3 2 l 0 9 8 7 6 5 4 _ j 2 1 0
`
`1.700
`
`FIGURE 9-13. Far traces stack (courtesy of Seismograph Service
`Corporation)
`
`3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 2 2 2 2 2 2 2 2 2 2
`4 3 3 3 3 3 3 3 3 3 3 2 2 2 2 2 2 2 2 2 2 1 1 I I 1 I I 1 1 1 0 0 0 0 0 0 0 0 0 0 9 9 9 9 9 9 9 9 9 9
`0 9 8 7 6 5 4 3 2 1 0 9 0 7 6 5 4 3 2 1 0 9 9 7 6 5 4 3 2 1 0 9 0 7 6 5 4 3 2 1 0 9 8 7 6 5 4 3 2 1 0
`
`2.400
`
`2.500
`
`2- 400
`
`2. SOO
`
`Ex. PGS 2002
`
`

`

`AMPLITUDE VERSUS OFFSET A NALYSIS
`
`1 9 3
`
`FIGURE 9-14. Difference stack (courtesy of Seismograph Service
`Corporation)
`
`1.500
`
`1. GOO
`
`1. TOO
`
`1. 0OO
`
`1.900
`
`2. OOO
`
`2. lOO
`
`1. SOO
`
`1. GOO
`
`1.700
`1-80O
`
`1.900
`
`2. OOO
`
`2- lOO
`
`2. SOO
`
`CONSTANT-ANGLE STACK
`As we reviewed in the AVO analysis, AVO provides the interpreter with
`tools to observe and measure variation in the amplitude with either off­
`set or angle of incidence. We discussed how observation of the change
`of amplitude with offset can be done on a corrected NMO gather or CMP.
`To observe how amplitude varies with reflection angle, however, it
`is convenient to transform traces recorded at fixed offset to traces char­
`acterized by a fixed (or a limited range) of angle of incidence. The dis­
`tinction between fixed offset traces or fixed angle traces is illustrated in
`Figure 9-16.
`In the constant angle stack gather, each angle trace is generated by
`a partial stacking of traces in an NMO corrected CMP gather. The extent
`of partial stacking is by an angle range width or window beam. The an­
`notated angle represents the central angle of the range.
`Figure 9—17 i s a computer printout of a common midpoint, normal
`moveout corrected, gather. The near trace is trace 1 at the left, and the
`far trace is trace 22 at the right. The data has a 4 ms sampling rate, and
`a total of 450 samples scanned for this illustration.
`Every trace has a sample range from 54—450, and for each sample
`the angle of incidence was computed; a window beam of 5 degrees range
`
`Ex. PGS 2002
`
`

`

`z m
`
`•H m
`> "D
`X
`o
`
`<o
`
`0 —*
`(D C/5 <
`0 c
`s~\ 0
`0
`D O
`ro
`a
`5" 0
`0 -*
`Zt. 3 O (0 a 0
`V < 0 </» Q Q
`0 a>
`a
`0 C
`O V 0 3!
`< 3
`CO CD >
`"0 3"
`<Ji
`•d
`1
`Q
`V
`(Q
`70 0 m
`3 c
`CD co" 0
`CO -n
`
`CD
`H*
`CO
`
`CO H*
`
`CO »•* o
`
`Oi
`
`•spuooss III SUI]X
`
`05
`
`-J
`
`o
`+
`H
`to
`o 05
`CO
`
`H-> « <0 t-1
`
`w
`O
`+
`H
`
`#>•
`
`o if"
`+
`W
`c& 05 a M o
`
`>3
`
`o
`o
`+
`
`o
`
`o o o o o PJ
`
`E
`
`spuooss hi auiij,
`
`WINDOW: 1600-1700m*
`
`RMS AMPUTUDE
`
`MAXIMUM AMPLITUDE
`WINDOW: 1600-1700ml
`
`Ex. PGS 2002
`
`

`

`AMPLITUDE VERSUS OFF SET A NALYSIS
`
`1 9 5
`
`FIGURE 9-1 6. Constant offset and constant angle (courtesy of
`Seismograph Service Corporation)
`
`UYFX # 4
`
`1000 r_
`
`2000 -
`
`3000 -
`
`4000 -
`
`6000 -
`
`7000
`
`LAYER 4 S
`
`WV B B S
`
`8000
`-
`
`LAYER | 9
`
`9000
`
`-
`
`LA.YE* | LO
`
`U«R 10 I jN
`
`UTD 11 am
`
`LAYER 4 B
`
`LAYER 4 0
`
`LAYER 4 tO
`
`10000
`
`UYEK f
`1
`
` It
`1
`
`1
`
`•
`
`i
`
`LAYER g kl
`.
`1
`
`.
`
`LAYER 4 II
`1
`,
`
`.
`
`1
`
`RAY PATHS WITH C ONSTANT
`ANGLE OF INCIDENCE. THESE RAY
`PATHS ILLUSTRATE THE REQUIRED
`RECORDING GEOMETRY FOR
`ENERGY COMING FROM A
`PARTICULAR REFLECTION ANGLE.
`INSTEAD OF USING SUCH
`RECORDING GEOMETRY IN THE
`FIELD, A SIMPLE TRANSFORMATION
`CAN BE APPLIED TO THE CMP
`GATHER, AFTER NMO CORRECTION,
`TO FORM ANGLE TRACES.
`
`Ex. PGS 2002
`
`

`

`1 9 6 CHAPTER NINE
`
`FIGURE 9-17. Computer printout, angle of incidence (courtesy of
`Seismograph Service Corporation)
`
`m *• 70 »i
`« « I T f t l V I
`M M »• T O
`ki r«
`»? n ir
`m it ftft
`M
`45 41
`M »| ftft »r
`« H Vft M
`» 41 4* 44
`IT 40 41 It
`H M 4? 44
`fl t| M
`• 5 ft w ia
`51 57 mO »!
`
`II R I 7* 77 t r
`
`14 17 41 4 1 4* 17 »t r\ n
`4) 57 49 4t 44 44 74 »• ?l
`71 74 74 77 77
`7 2 74 71 77 7 7
`11 54 49 41 4* 44 70 7S f|
`X »J 11 41 41 14 70 70 7(
`71 74 75 7ft 7ft
`41 55 M IO 41 41 4« 14 H
`,71 71 75 2* 7ft
`IO 54 57 ftO 4/ l« 44 44 ft
`71 75 7* 7ft 7ft
`71 71 74 74 7ft
`44 51 54 54 41 41 44 44 71
`*4 12 44 54 Al 4] ftO ft• 70
`70 ft 74 75 75
`»» 12 51 4>» 10 42 47 47 IO
`70 72 7% 75 75
`»7 11 5* 17 ftft KZ ftl 47 70
`70 7t 71 75 71
`II 7| 71 7* 7*
`*4 50 44 57 VI II 4V 47 *4
`
`41 47 51 54 41 54 ftl 45 40 40 Ti 71 7*
`•I 47 IO 11 14 54 44 ft* 47 17 70 7t 74
`• t 44 14 41 4ft II ft! 4ft ft7 ft7 70 71 74
`41 4ft 14 11 15 54 1% 44 ftV ft?
`70 72 74
`41 45 4ft »1 45 41 44 44 47 ft7 70 71 74
`
`IO 5« 14 ft«
`10 44 14 4*
`5? 54 54 14
`17 S« }• ftO
`1* 4ft 50 ftO
`17 50 5« 54
`1* 14 50 54
`5ft 14 40 44
`54 17 17 54
`5ft 41 57 50
`55 57 5F 50
`15 17 17 50
`15 4ft 44 Ml
`55 1ft 4ft 17
`
`54 H 1ft 1T
`14 II II 47
`14 11 51 17
`14 45 51 II
`14 11 55 5ft
`11 11 55 11
`
`M M M H
`
`11 44 14 II
`11 44 14 11
`11 14 14 14
`12 51 51 11
`12 11 41 11
`11 11 51 14
`
`57 ftj ftl ft7
`57 ftl II Ift
`51 II IB ft*
`5ft ftl II I*
`
`5ft II ft1 ftft
`
`15 ftl II ft*
`51 II ftl ftl
`55 ftl ftl ftl
`14 ftl ftl
`1* ftl ftl ftl
`5 4 ftO 10 14
`
`1.4
`
`47 ft4 71 7ft
`ftft ftO 71 74
`ftft ftft 71 71
`ft* 14 71 71
`ftft ft* 71 71
`ftft 44 71 71
`44 10 71 71
`•4 ftft 7 1 7k
`*5 ftO 71 7>
`14 40 70 71
`ftft 47 TO 72
`ftft *7 70 71
`44 ft7 70 71
`41 ft7 l» 71
`ftl ftft 14 71
`II ftft 14 71
`ftl ftft ftft 71
`
`11 10 IO ftft
`
`11 ftO ftO ftft
`57 ftO IO ftl
`51 54 14 ftl
`52 54 54 ft*
`51 54 14 ft?
`51 50 10 ftl
`51 50 10 ftl
`
`71 71 71 71
`
`»> 17 41 44 47 IO 47 17 *1 ftl ftl ftl
`70 70 71 71 71
`12 14 44 ftft 47 IO 17 17 ftl ftl ftft ft7
`7 70 70 7» 7l 72
`12 1ft ftO 41 ftft % 4 17 17 ft| ftl ftft ft
`12 1* ftO ftl
`4ft 44 1ft 5ft ftO ftO ftft ftl 14 ftft 71 71 72
`»f 5ft #4 ftl
`ift ftft i* 1* ftO ftO *1 *4 44 |4 70 70 71
`11 11 14 42 45 40 1ft 1ft ftp »0 II Ift ftft ftft 70 70 71
`
`70 70 71 71 77
`
`15 10 ftl ftft *7 55 14 14 1* II II IO ftO ftft 14 TO
`4 II 10
`0 II 17 1* In 1ft 10 ftl
`44 ft7 1ft 1ft 10 1ft *2 *4 IO *0 *4 *0 70
`11 17 21 l» 1ft 10 *1 4ft 47 44 1ft 10 10 42 45 l» *7 14 44 TO
`11 I* 24 If 14 17 40 4ft *4 5ft 5ft 5« 50 41 Ift 47 47 *0 10 14
`11 17 24 | If 11 57 ftO ft) ftft 51 51 57 57 41 44 47 *7 IO 4<l 4ft
`12 17 25 p| 11 17 40 41 4* 11 51 17 17 41 4ft 44 44 10 II 44
`
`41 II 41
`41 41 42
`41 41 42
`IO IO 12
`10 IO II
`
`• CMP GATHER, NMO APPLIED
`• 22 TRACES (FOLD)
`• 4 MS SAMPLE RATE
`• TRACE 1 TO LEFT, TRACE 22 TO RIGHT
`• ANGLES LISTED FOR EVERY SAMPLE AND FOR EVERY TRACE
`
`Ex. PGS 2002
`
`

`

`AMPLITUDE VERSUS OFFSET ANALYSIS 1 9 7
`
`FIGURE 9 -18. Constant angle stacks (courtesy of Seismograph Service
`Corporation)
`
`1.000 -
`
`t I
`
`\ 2 3 2 1
`
`369?!.a 1470
`
`I
`
`I
`
`I ? 2 2 J
`
`n 6 9 7 5 f l 1 ^ 0
`
`I
`
`1
`
`I 2 2 2 3
`
`was chosen. All the partial traces with an angle from 1 to 5 degrees were
`used and stacked. The annotation was at the midpoint of this beam, or 3
`degrees; the second beam will be 4 to 8 degrees, then all partial traces
`in the gather having an angle of incidence within this range will be
`stacked and annotated 6 degrees, and so on.
`Figure 9-18 illustrates this approach; it was done on three common
`midpoint, normal moveout corrected, gathers. The constant angle range
`is from 2° to 30°. A bar graph representing the amplitude variation with
`the angle of incidence is plotted below each set of constant angle stack
`gathers. As we can see, the amplitude at the same window of investiga­
`tion (1.6 to 1.7 seconds) increases with increased angle of incidence.
`
`AVO ATTRIBUTES A ND DISPLAYS
`A number of other parameters can be displayed on sections in a manner
`similar to the conventional stack, such as a near-trace stack, which con­
`sists of short trace distances selected from each CMP gather, corrected
`for NMO, and stacked together. Likewise, a far-trace stack with selected
`far offset distance range can be stacked together to form a far-trace stack.
`
`Ex. PGS 2002
`
`

`

`1 9 8 CHAPTER NINE
`
`The observed variation (increase) of amplitude can be easily seen as the
`far trace offset stack section shows a pronounced increase in the ampli­
`tude. Also, the amplitude ratio between the near-and far-trace stacks can
`be displayed, as well as the gradient normal incidence amplitude.
`These attributes are shown in Figures 9-19, 9-20, 9-21 and 9—22.
`Color displays may be used for easier interpretation.
`Other useful displays that can be created include:
`
`• Amplitude versus sin20.
`• P-wave reflection.
`• Gradient of amplitude versus sin20.
`• Mimic of shear wave stack can be generated by assuming that the S-
`wave velocity is half of the P-wave velocity. The travel time of the sec­
`tion is governed by the P-wave velocity.
`• Poisson's Ratio stack, using the same assumption that the shear wave
`velocity is half the P-wave velocity.
`
`All these are shown in Figures 9-23 and 9-24.
`
`PROCESSING DON'TS
`Certain data processing operations, although possible, must be avoided
`in order to preserve the amplitude versus offset relation:
`Multichannel operations such as:
`
`• Mixing traces will remove the significance of true amplitude.
`• Trace-to-trace scaling with small windows.
`• F-K operations.
`• Deconvolution derived from trace summation.
`
`ADVANTAGES OF AVO
`AVO is a proven tool in the verification of direct indicators, such as bright
`spots in gas sands and dim spots in carbonate reservoirs, and any relat­
`ed amplitude anomalies. An AVO analysis using NMO-corrected CMP is
`a two-dimensional analysis, whereas a stacked trace is a one-dimensional
`analysis. The amplitude variation with the angle of incidence is another