GEOPHYSICS, VOL. 49, NO.
`
`IO (OCTOBER
`
`1984); P. 1637-1648, 20 FIGS., 1 TABLE
`
`reflection coefficients
`Plane-wave
`angles of incidence
`
`for gas sands at nonnormal
`
`W. J. Ostrander*
`
`ABSTRACT
`
`The P-wave reflection coefficient at an interface sep-
`arating two media is known to vary with angle of inci-
`dence. The manner in which it varies is strongly affected
`by the relative values of Poisson’s ratio
`in the two
`media. For moderate angles of incidence, the relative
`change in reflection coefficient is particularly significant
`when Poisson’s ratio differs greatly between the two
`media.
`Theory and laboratory measurements indicate that
`high-porosity gas sands tend to exhibit abnormally low
`Poisson’s ratios. Embedding
`these low-velocity gas
`sands into sediments having “normal” Poisson’s ratios
`should result in an increase in reflected P-wave energy
`with angle of incidence. This phenomenon has been ob-
`served on conventional seismic data recorded over
`known gas sands.
`
`INTRODUCTION
`
`During the past decade, the use of “bright spot” type analy-
`sis in petroleum exploration has become increasingly common.
`Oil companies, both large and small, are making use of the fact
`that high-intensity seismic reflections may be indicators of hy-
`drocarbon accumulations, particularly gas. Bright spot ex-
`ploration has significantly increased the recent success ratio for
`wildcat gas wells. Nonetheless, problems still do exist. Many
`seismic amplitude anomalies are not caused by gas accumula-
`tions, or they are caused by gas accumulations which are
`subcommercial. The latter problem is difficult to resolve. How-
`ever, amplitude anomalies caused by nongaseous, abnormally
`high- or low-velocity layers may have distinguishing character-
`istics. This paper proposes a method which potentially may
`distinguish between gas-related amplitude anomalies and
`nongas related anomalies. Notable observations contained
`herein are (I) the somewhat surprising effects of Poisson’s ratio
`on P-wave reflection coefficients and (2) the existence of these
`effects in seismic amplitude anomalies related to gas accumula-
`tions.
`
`BACKGROUND
`
`Poisson’s ratio
`
`Poisson’s ratio, sometimes denoted by the Greek letter small
`sigma (o), is a somewhat neglected elastic constant. It is related
`to other elastic constants by a simple set of equations. In
`particular, Poisson’s ratio for an isotropic elastic material is
`simply related to the P-wave (V,) and S-wave (V,) velocities of
`the material by
`
`CVJV,) - 2
`o = Z[(V,/v,)Z - 1)’
`
`(1)
`
`This equation indicates that Poisson’s ratios may be deter-
`mined dynamically using field or laboratory measurements of
`both VP and I$
`Poisson’s ratio also has a physical definition. If one takes a
`cylindrical rod of an isotropic elastic material and applies a
`small axial compressional force to the ends, the rod will change
`shape. The length of the rod will decrease slightly, while the
`radius of the rod will increase slightly. Poisson’s ratio is defined
`as the ratio of the relative change in radius to the relative
`change in length. Common isotropic materials have Poisson’s
`ratios between 0.0 and 0.5. Incompressible materials such as
`liquids will have Poisson’s ratios of 0.5, while “spongy” materi-
`als might have ratios closer to zero.
`
`Reflection coefficients
`
`In 1940, a classic article was published by Muskat and Meres
`showing the variations in plane-wave reflection and transmis-
`sion coefficients as a function of angle of incidence. Since then,
`several additional articles on the subject have appeared in the
`literature, including those by Koefoed (1955, 1962) and Tooley
`et al. (1965). Using the simplified Zoeppritz equations given by
`Koefoed (1962), one can show that four independent variables
`exist at a single reflecting/refracting interface between two iso-
`tropic media: (1) P-wave velocity ratio between the two bound-
`ing media; (2) density ratio between the two bounding media;
`(3) Poisson’s ratio in the upper medium; and (4) Poisson’s ratio
`
`Presented at 52nd Annual International SEC, Meeting in Dallas, Texas, on October 21, 1982. Manuscript received by the Editor February 1%
`1983; revised manuscript received April 30, 1984.
`*Chevron U.S.A., Inc., 2003 Diamond Boulevard, Concord, CA 94520.
`d‘m 1984 Society of Exploration Geophysicists. All rights reserved.
`
`1637
`
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`
`1636
`
`Ostrander
`
`0.4
`
`0.3
`
`t
`
`t
`
`q=0,=0.3
`
`u;,-0.2
`
`VPZZ”R
`VPI
`
`DR
`
`.!L
`P,
`
`0.
`
`4-
`
`qt0.4
`
`cTpo.1
`
`--_--
`q= 0.3
`
`s,= 0.1
`
`0.
`
`3-
`
`vpz,
`VPI
`
`“R
`
`pz,
`PI
`
`DR
`
`0.
`
`2-
`
`t
`Ly
`;
`kl
`0
`‘: 0.
`0
`F
`v
`!Y -0.
`k!
`oz
`
`0.
`1’
`
`o-
`
`,l L
`
`100
`
`200
`
`300
`
`400
`
`“Rz09D&0
`
`__--
`9
`
`__--
`
`_---
`
`./#
`
`AH
`
`1, ;;.
`
`0
`F
`v
`Y
`
`k
`c*
`
`r
`
`-0.1
`
`-0.2-
`
`-0.2
`
`-0.4
`
`-0
`
`.2-
`
`-0
`
`.3-
`
`-0
`
`.4-
`
`FIG. I. Plot of P-wave reflection coefficient versus angle of
`incidence for constant Poisson’s ratios of 0.2 and 0.3.
`
`FIG. 2. Plot of P-wave reflection coefficient versus angle of
`incidence for a reduction in Poisson’s ratios across an interface.
`
`in the lower medium. These four quantities govern plane-wave
`reflection and transmission at a seismic interface.
`Since Muskat and Meres (1940) had very little information
`on values of Poisson’s ratios for sedimentary rocks, they used a
`constant value of 0.25 in all their calculations, i.e., Poisson’s
`ratio was the same for both media. Results similar to theirs are
`shown in Figure 1 for various velocity and density ratios and
`constant Poisson’s ratios of 0.2 and 0.3. One would conclude
`from these results that angle of incidence has only minor effects
`on P-wave reflection coefficients over propagation angles com-
`monly used in reflection seismology. This is a basic principle
`upon which conventional common-depth-point
`(CDP) reflec-
`tion seismology relies.
`The work of Koefoed (1955) is of particular interest since his
`calculations involved a change in Poisson’s ratio across the
`reflecting interface. He found that by having substantially dif-
`ferent Poisson’s ratios for the two bounding media, large
`changes in P-wave reflection coefl$cients versus angle of inci-
`dence could result. Koifoed showed that under certain circum-
`stances? reflection coefficients could increase substantially with
`increasing angle of incidence. This increase occurs well within
`the critical angle where high-amplitude, wide-angle reflections
`are known to occur.
`Figures 2 and 3 illustrate an extension of Koefoed’s initial
`computations. Figure 2 shows P-wave reflection coefficients
`from an interface, with the incident medium having a higher
`Poisson’s ratio than the underlying medium. The solid curves
`represent a contrast in Poisson’s ratio of 0.4 to 0.1, while the
`dashed curves represent a contrast of 0.3 to 0.1. One may
`
`FIG. 3. Plot of P-wave reflection coefficient versus angle of
`incidence for an increase in Poisson’s ratios across an interface.
`
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`
`Table 1. List of measured Poisson’s ratios for various sedimentary rock
`types*
`
`1639
`
`POD10 ET AL. (1968)
`
`HAMILTON
`
`(1976)
`
`GREGORY
`
`(1976)
`
`DOMENICO
`
`(1976)
`
`DOMENICO
`
`(1977)
`
`GREEN AIVEA SHALE
`
`0.22-0.30
`
`SHALLOW MARINE
`SEUIMENTS
`
`0.45-0.50
`
`CONSOLlllATEO SEDIMENTS
`BRINE SATURATED
`GAS SATURATED
`
`0.20-0.30
`0.02-0.14
`
`SYNTHETIC SANDSTONE
`BRINE SATURATED
`GAS SATURATED
`
`OTTAWA SANDSTONE
`BRINE SATURATE0
`GAS SATURATED
`
`0.41
`0.10
`
`0.40
`0.10
`
`Reflection Coefficients for Gas Sands
`0.45 and 0.50. Gregory (1976) gave results including fluid satu-
`ration effects for many consolidated sedimentary rocks. His
`samples included sandstones, limestones, and chalks ranging in
`porosity from 4 to 41 percent. The work of Domenico (1976,
`1977) is of special interest because it applies to many of our
`shallow gas fields which have related seismic amplitude anoma-
`lies. In both a synthetic high-porosity glass bead and a high-
`porosity Ottawa sandstone mixture, Domenico found marked
`changes in Poisson’s ratios between brine and gas saturations.
`In these unconsolidated 38 percent porosity specimens, the
`replacement of brine with gas reduced Poisson’s ratio from 0.4
`to 0.1. A summary of the foregoing results is shown in Table 1.
`Several conclusions can be drawn from measurements of
`Poisson’s ratios for sedimentary rocks. First, unconsolidated,
`shallow, brine-saturated sediments tend to have very high Pois-
`son’s ratios of 0.40 and greater. Second, Poisson’s ratios tend to
`decrease as porosity decreases and sediments become more
`consolidated. Third, high-porosity brine-saturated sandstones
`tend to have high Poisson’s ratios of 0.30 to 0.40. And fourth,
`gas-saturated high-porosity sandstones tend to have abnor-
`mally low Poisson’s ratios on the order of 0.10.
`The above conclusions result from the fact that the shear
`modulus u of a rock does not change when the fluid saturant is
`changed. However, the bulk modulus k does change signifi-
`cantly (Gassmann, 1951). The bulk modulus of a fluid-saturated
`rock is a function of the bulk moduli of the fluid, the grains, and
`the dry rock framework. The bulk modulus of a brine-saturated
`rock is greater than that of gas-saturated rock because brine is
`significantly stiffer than gas. This results in the P-wave velocity
`(VP) of the brine-saturated rock being considerably higher than
`that of a gas-saturated rock from equation (2). The S-wave
`velocity (V,) defined in equation (3) is only affected by a small
`change in the density p. Since density is reduced by a gas
`saturant, the S-wave velocity is slightly increased with gas
`saturation. Equations (2) and (3) show the relationships among
`these parameters.
`
`conclude from these curves that if Poisson’s ratio decreases
`going into the underlying medium, the reflection coefficient
`decreases algebraically with increasing angle of incidence. This
`means positive reflection coefficients may reverse polarity and
`negative reflection coefficients increase in magnitude (absolute
`value) with increasing angle of incidence.
`Figure 3 shows the opposite situation to that shown in
`Figure 2. Here Poisson’s ratio increases going from the incident
`medium into the underlying medium. In this case, the reflection
`coefficients increase algebraically with increasing angle of inci-
`dence. Negative reflection coefficients may reverse polarity, and
`positive reflection coefficients increase in magnitude with in-
`creasing angle of incidence.
`The foregoing three illustrations point to a strong need for
`more information on Poisson’s ratio for the various rock types
`encountered in seismic exploration. This is particularly impor-
`tant when one considers the long offsets commonly in use today
`and the resulting large angles of incidence. It will become
`evident later that this phenomenon has an important effect on
`bright spot analysis. For additional computations of reflection
`and transmission coefficients, the reader should refer to Koe-
`foed (i962) and Tooiey et ai. (i-965j.
`
`MEASUREMENTS
`
`OF POISSON’S RATIO
`
`In the Handbook of Physical Constants, Birch (1942) lists
`Poisson’s ratios for various materials, including many rock
`types. However, little significance can be placed on these values
`because of the methods and environments of measurement. As
`will become obvious later, any air or gas in cracks or pore
`spaces can severely alter measurement of Poisson’s ratio. Until
`recently, other published measurements for sedimentary rocks
`were quite limited.
`Many comprehensive measurements of Poisson’s ratios for
`sedimentary rocks were reported in the literature during the
`1970s. Hamilton (1976) presented a review of measurements
`made for shallow marine sediments including both sands and
`shales. His results showed that shallow, unconsolidated marine
`sediments to depths of 2 000 ft had Poisson’s ratios between
`
`and
`
`0 1.2
`v,=p
`
`.P,
`
`Analysis of Gassmann’s equation shows that the weaker the
`framework modulus, the greater the differences between brine
`and gas saturations. This explains the dramatic differences
`observed in poorly consolidated rocks such as those analyzed
`by Domenico.
`Depth of burial and differential pressure also influence the
`elastic behavior of rocks. Differential pressure is the difference
`between the overburden pressure and the fluid pressure and is
`generally a monotonic function of depth. As differential pres-
`sure increases, the bulk and shear moduli of a rock increase,
`resulting in greater P- and S-wave velocities. Sediment consoli-
`dation and increased differential pressures tend to decrease
`fluid saturation effects with increased depth of burial.
`Theoretical results also support the large reduction in Pois-
`son’s ratio as gas replaces brine as the saturant in high-porosity
`sandstones. Using the equations of Gassmann (1951), one can
`compute theoretical P-wave and S-wave velocities as a function
`
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`
`1640
`
`Ostrander
`
`7K-
`
`0
`
`50
`% GAS SATURATION
`
`(a)
`
`100
`
`4.5K.
`0
`
`’
`
`’
`
`’
`
`’
`
`’
`50
`
`’
`
`’
`
`’
`
`’
`
`100
`
`% GAS SATURATION
`
`@I
`
`0.0’
`0
`
`’
`
`’
`
`’
`
`’
`
`’
`50
`?‘a GAS SATURATION
`
`’
`
`’
`
`’
`
`’
`
`J
`100
`
`?‘a GAS SATURATION
`
`(a)
`
`Cc)
`
`FIG. 4. Plots of (a) P-wave velocity. (b) S-wave velocity, (c) Poisson’s ratio, and (d) V,/V, ratio as a function of gas saturation.
`
`of percent gas saturation. Poisson’s ratios can then be com-
`puted using equation (1). Theoretical results for a 35 percent
`porosity sandstone buried at 6 000 ft are shown in Figures 4a.
`4b, 4c, and 4d. In Figure 4c, one sees that the major change in
`Poisson’s ratio occurs with less than 10 percent gas saturation.
`From 10 to 100 percent gas saturation, Poisson’s ratio changes
`very little around an average value of 0.09. These characteristic
`gas saturation curves have been supported by laboratory
`measurements (Domenico, 1976,1977; Gregory, 1976).
`
`GAS SAND MODEL
`
`Using the foregoing review of physical parameters, one can
`now devise a hypothetical gas sand model. This model can be
`used to analyze plane-wave reflection coefficients as a function
`of angle of incidence. Calculations can be made for the reflec-
`tions originating from both the top and base of the gas sand.
`Figure 5 shows a three-layer gas sand model with parameters
`which might be typical for a shallow, young geologic section.
`Here, a gas sand with a Poisson’s ratio of 0.1 is embedded in
`shale having a Poisson’s ratio of 0.4. There is a 20 percent
`velocity reduction going into the sand, from 10 000 k/s to 8 000
`ft;s, and a 10 percent density reduction from 2.40 g/cm3 to 2.16
`g/cm3. These parameters result in normal-incidence reflection
`
`-_---_-2_-2
`-------
`---
`-.-z-1
`SHALE
`----r-_rT_z_7z_
`-_
`--
`-
`-
`- _------
`
`$3
`
`=I 0,000
`
`&
`
`-2.40
`
`6,
`
`-0.4
`
`FIG. 5. Three-layer hypothetical gas sand model.
`
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`
`Reflection Coefficients
`
`for Gas Sands
`
`1641
`
`0.4
`
`0.3
`
`t
`
`.
`NO GAS
`IN SAND
`
`a; =0.4
`
`.
`
`. . . . . . . . .
`
`NO GAS
`
`.
`
`u
`,” -0.1 -
`k
`
`DC
`
`-0.2-
`
`-0.3
`
`-
`
`-0.4 c
`
`Frc;. 6. Plot of P-wave reflection coefficients versus angle of
`incidence for three-layer gas sand model.
`
`coefficients of - 0.16 and + 0.16 for the top and base of the gas
`sand, respectively.
`Changes in plane-wave reflection coefficient as a function of
`angle of incidence for several cases are shown in Figure 6. The
`two solid curves are those reflection coefficients resulting from
`the gas sand model parameters shown in Figure 5. The effect of
`transmission and refraction on the base of sand reflection have
`been taken into account. The horizontal axis is the angle of
`incidence referenced to the top of the sand. Because of refrac-
`tion, a 40-degree incident angle at the top of the sand represents
`
`only 31 degrees incident angle at the base of the sand. The top
`of sand reflection coefficient changes from about -0.16
`to
`-0.28 over 40 degrees while the base of sand reflection coef-
`ficient changes from about +0.16 to +0.26. Thus, the ampli-
`tude of the seismic waveform resulting from this complex reflec-
`tion would increase approximately 70 percent over 40 degrees.
`The dotted curves in Figure 6 indicate what the reflection
`coefficients would be if Poisson’s ratio in the sand were changed
`to 0.4. This would simulate the case of a low-velocity brine-
`saturated young sandstone embedded in shale. In this case, one
`sees only a slight decrease in the magnitude of the reflection
`coefficients as the angle of incidence increases.
`
`DATA ANALYSIS
`
`The obvious question at this point is how one can best
`observe and analyze changes in reflection coefficient with angle
`of incidence on today’s conventionally recorded reflection seis-
`mic data. The answer lies in analyzing amplitudes on CDP-
`gathered traces prior to stacking. In this way, one can observe
`changes in reflection amplitude versus shot-to-group offset. As
`shot-to-group offset increases, the angle of incidence increases
`monotonically.
`
`Angles of incidence
`
`There are several ways to estimate angles of incidence from
`the depth to a reflector and the shot-to-group offset. The first
`and most simple is the straight-ray approach where the angle of
`incidence Bi is given by
`
`where X is the shot-to-group otTset and Z is the reflector depth.
`If velocity increases with depth, which is most common, the
`angles computed from equation (4) will always be too small. In
`this situation, a better approach for estimating angles of inci-
`dence is illustrated in Figure 7. If the section interval velocity
`then all ray-
`can be approximated in the form V, = V, + KZ,
`paths are arcs of circles whose centers are V,/K above the
`
`01-
`
`RAY PATH ARC CENTERS
`
`-
`
`0
`
`T
`
`STACKING
`
`CHART DIAGRAM
`
`.S.COP’S.
`
`SHOTS
`
`/ +
`
`OUTPUT
`
`/
`
`m
`
`_
`
`FK. 7. Geometry for estimating angles of incidence for a veloci-
`ty function of the form V, = V, + KZ.
`
`FE. 8. Trace-summing technique to increase S/N ratios.
`
`SUMMING
`
`BOXES
`
`TRACES
`INPUT
`IO
`PER OUTPUT
`TRACE
`
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`
`1642
`
`Oslrander
`
`q v
`
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`
`Reflection Coefficients for Gas Sands
`
`1643
`
`ground surface. Using the resulting geometry, one can derive
`the following relationship:
`
`0, = tan
`
`’
`
`ZX + V’X/K
`- X2/4 > .
`Z2 + 2V,Z/K
`An example calculation for K = 6 000 + 0.62, at a depth (Z) of
`7 000 ft, and an offset (X) of 7 000 ft, gives an angle of incidence
`&Ii) of 34 degrees. Thus, one sees that angles of 30 degrees or
`more are not uncommon in today’s CDP recording and are in
`many cases unmuted during CDP stacking.
`
`(5)
`
`Trace summing-S/N
`
`improvement
`
`traces for amplitude vari-
`In viewing single CDP-gathered
`ations, one major drawback occurs: poor signal-to-noise (S/N)
`ratios. As a means of signal enhancement, trace summing can
`prove most worthwhile. A method of partial trace summing is
`illustrated in Figure 8. Shown in the tigure is a stacking chart
`diagram on the right with an enlargement of the same in the
`upper left. The recording geometry is for 4%trace, single end,
`24-fold CDP coverage with a near otTset of gl0 ft and a far
`offset of 7 155 ft. Here CDP
`traces lie on a vertical line,
`common-offset traces on a horizontal line, and common-shot
`profile traces on the diagonals as shown. In the enlargement,
`individual traces are shown as small circles. To form a partial
`sum trace, all traces fall within boxes which are 5 CDPs by 4
`offsets in dimension and which are summed together forming a
`single output trace. ‘This limited summing will produce a lo-
`fold sum trace, and thus improve the S/N ratio by a factor of
`about 3. Repeating the procedure for groups of 4 offsets will
`produce 12 traces, all with improved S/N ratios. Displaying
`these 12 partially summed traces in increasing average shot-to-
`group offset gives a desirable product for analyzing amplitude
`information. Variations on this type of limited offset summing
`are easily implemented for different recording geometries.
`In the examples which follow, the reader will find that some
`CDP gathers are displayed as individual traces while others
`have been partially summed. The advantages of summing will
`become obvious.
`
`EXAMPLES
`
`Several examples will now be presented which illustrate ap-
`parent changes in reflection amplitude versus angle of inci-
`dence. All of the examples are in areas of well control, so the
`origin of the bright spot or amplitude anomaly is known. In
`two cases, the anomalies are caused by gas. while in the third,
`the seismic amplitude anomaly is caused by a high-velocity
`layer of basalt. Prior to drilling, all of these seismic anomalies
`were thought to be caused by gas-saturated sediments.
`The illustrations presented for each example are (1) a conven-
`tionally stacked section showing the given amplitude anomaly;
`and (2) CDP gathers at locations indicated by vertical dashed
`lines and the letters A, B, and C on the stacked sections. The
`processing flow, prior to the displays shown, employed stan-
`dard techniques. These included spherical divergence correc-
`tion, exponential gain, minimum phase-spiking deconvolution,
`statics, velocity analysis, normal moveout (NMO)
`removal,
`time-invariant band-pass filtering, and single long-gated trace
`equalization. No wavelet processing was done on these data, so
`no implications as to reflector polarity can be made.
`
`SINGLE-FOLD
`
`CDP GATHERS
`
`SP 81
`.., I
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`:::‘::‘:;.i
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`: .
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`1. . . . . . . . . . . ..I..
`.,
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`
`“I:;),):,”
`
`-ll-~‘,,.
`
`1.5
`
`2.0
`
`SP 80
`
`pxiJ
`
`,yqJ::~
`::I:‘..,
`“!‘,,,,,
`,,:,j;r~~;:;.:::.iii:
`“t.:;:,,‘r,,,ij:;~:j:’
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`:,,‘!:<!#I,.’
`.L ..I. ;:L....!:j::.‘I’:
`;;:,,.:,:‘;::;..i!!:;::
`,.,.
`),
`I
`,;,,;,,‘:,‘I,::‘.,!,’
`~,;).I,‘:’
`,,,.,,.,,..,,)),.“.‘.’
`.I).,.
`.,l,,.,l..P*.~,I
`. . . . ..L.........~~.
`..,
`‘~.~I....~..,“rr......
`810’
`7155’
`
`*,I
`
`.,,I.‘,),
`
`lo-FOLD
`
`SUMMED
`
`CDP GATHERS
`
`FIG. 10. CDP gathers for location A on line SV-1.
`
`Line SV-1
`
`Shown in Figure 9 is a 24-fold CDP stacked seismic line over
`a large gas field in the Sacramento Valley. The sand reservoir
`occurs at a depth of about 6 700 ft which corresponds to a
`seismic amplitude anomaly at about 1.75 s. The reservoir is a
`Cretaceous deep-sea fan deposit having a maximum net pay of
`95 ft. The trap is both structural and stratigraphic with the
`reservoir being offset along a fault at about SP 95. The down-
`thrown portion of the reservoir on the left is trapped against the
`fault, while the reservoir pinches out in the upthrown block at
`about SP 75. The velocity and density within the gas sand are
`substantially lower than the encasing shales, giving rise to
`strong seismic reflections at the top and base of the gas sand. A
`flat fluid contact reflection may be present at 1.8 s between SP
`115 and SP 135. The discovery well is located at about SP 86
`with the reservoir limits extending from about SP 75 to SP 130.
`CDP gathers from three locations, A, B, and C, are shown in
`Figures 10, 11, and 12, respectively. Both single-fold and lo-fold
`summed gathers are shown for locations A and B, while only
`the summed gathers are shown for location C. Shot-to-group
`of&et for all gathers increases to the left. These distances change
`on the summed gathers because the summing is done over four
`offsets. At the objective sand, the near-offset corresponds to
`about 5 degrees angle of incidence while the far-offset corre-
`sponds to about 35 degrees.
`A strong amplitude increase with increasing offset is appar-
`ent in the gathers at locations A and B shown in Figures 10 and
`11. The IO-fold summing obviously improves S/N ratios, and
`an amplitude increase by a factor of about three is indicated
`from the near offset to far offset. The gathers at location C,
`shown in Figure 12, show no indication of amplitude increase
`with offset and in fact show a decrease. This possibly indicates
`
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`
`PGS Exhibit 2042
`WesternGeco v. PGS (IPR2015-00313)
`
`

`
`1644
`
`Ostrander
`
`SINGLE-FOLD
`
`CDP GATHERS
`SP 101
`
`lo-FOLD
`
`SUMMED
`
`CDP GATHERS
`
`SP 142
`
`SP 141
`
`SP 140
`
`lo-FOLD
`
`SUMMED
`
`SP 102
`,,;;;-‘.6-
`I,;,
`“lt’t111:;
`tttttttttttt
`Bbcbtttt
`Prr)Pttfffft
`, , I 1 b
`
`-
`
`CDP GATHERS
`SP 101
`
`I/’
`“Wlll~ij
`tttttttt’tt’tt
`mbbuobiii
`~~~rlrfttffr
`,/I,tbI/
`I.9 T9S2’
`
`1012’
`
`FIG. 11. CDP gathers for location B on line SV-1
`
`FIG. 12. CDP gathers for location C on line SV-1.
`
`an absence of gas in the vicinity of location C. This possibility is
`also supported by the presence of a gas-water contact in a well
`which would structurally project in at about SP 120.
`In this example and those which follow, no S-wave velocity
`data were available to model variations in reflection coefficient
`in shot-to-group offset. The P-wave sonic velocities within this
`gas reservoir may also be subject to error. The behavior of the
`observed seismic amplitude in shot-to-group offset is as ex-
`pected from theory and laboratory measurements. However the
`magnitude of the change of amplitude may be influenced by
`
`CDP GATHER LOCATIONS
`cl B
`D A
`1770
`1740
`
`1750
`
`1760
`
`1790
`
`1780
`
`1730
`
`17.20
`
`FIG. 13. Stacked seismic section for line GM- 1.
`
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`
`PGS Exhibit 2042
`WesternGeco v. PGS (IPR2015-00313)
`
`

`
`8-FOLD SUMMED CDP GATHERS
`
`Reflection Coefficients for Gas Sands
`8-FOLD SUMMED CDP GATHERS
`
`1645
`
`1773
`
`1771
`
`1769
`
`1767
`
`1745
`
`1743
`
`1741
`
`1739
`
`FIG. 14. CDP gathers for location A on line GM-l.
`
`FE. 15. CDP gathers for location B on line GM-l.
`
`CDP GATHER LOCATION
`u A
`130
`
`150
`
`140
`I-c--l’
`
`120
`
`110
`
`100
`
`90
`
`80
`
`70
`
`0.0
`
`0.5
`
`180
`
`170
`
`160
`
`0.0
`
`+t
`
`0.5
`
`1.0
`
`1.5
`
`2.0
`
`FIG. 16. Stacked seismic section for line FB-1.
`
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`
`PGS Exhibit 2042
`WesternGeco v. PGS (IPR2015-00313)
`
`

`
`1646
`
`Ostrander
`
`lo-FOLD SUMMED CDP GATHERS
`
`5610’
`
`710
`
`FIG. 17. CDP gathers for location A on line FB-1.
`
`Frc;. 18. Relationship between array attenuation, apparent re-
`flector dip, and normal moveout.
`
`FAR OFFSET
`
`factors to be discussed later. Because one has great difficulty in
`separating out “true”
`reflection amplitudes, the interpreter
`typically must rely on relative changes, concentrating on anom-
`alous behavior of the amplitude.
`
`Line GM-1
`
`Figure 13 shows two gas-related seismic-amplitude anoma-
`lies on line GM-1
`located in the Gulf of Mexico. The first of
`these anomalies is located on the left half of the seismic section
`at about 0.65 s. The second, deeper anomaly is toward the
`middle of the seismic section at about 1.35 s. Summed CDP
`gathers are displayed in Figure 14 for location A on the shallow
`anomaly and in Figure 15 for location B on the deeper anoma-
`ly. In both anomalies, it is quite apparent that reflection amph-
`tude tends to increase with increasing offset. In the case of the
`shallower anomaly at location A, the effect of array attenuation
`and NM0 stretch on the fifth offset trace is obvious.
`
`(1) Reflection coefficient
`(2) Array attenuation
`(3) Event tuning
`(4) Noise
`(5) Spherical spreading
`(6) Emergence angles
`(7) Reflector curvature
`(8) Spherical wavefronts
`(9) Transmission coefficients
`(10) Instrumentation/processing
`(11) Inelastic attenuation
`
`The first of these, the reflection coefficient, is the factor which
`one would like to observe. In actuality, one can only observe
`relative changes in reflection coefficient versus offset. If no other
`factors existed, one could simply observe the CDP gathers with
`a spherical divergence correction applied. However, because of
`the other offset-related amplitude factors listed above, simple
`observation of the reflection coefficient is not always feasible.
`Considered below are some of the other factors in more detail.
`
`Line FB-1
`
`Array attenuation
`
`Shown in Figure 16 is a 24-fold CDP-stacked seismic line
`recorded in a virgin basin in Nevada. Several years, ago, a well
`was drilled on this line at SP 127 (location A) to a depth below
`2.0 s. A seismic amplitude anomaly is indicated on the stacked
`seismic data at this location and at a time of about 1.6 s. Upon
`drilling, the amplitude anomaly was found to originate from a
`high-velocity basaltic interval of about 160 ft in thickness. As
`has happened elsewhere, the apparent bright spot is not due to
`the presence of gas in the sediments.
`The CDP gathers at the well location are shown in Figure 17.
`Here, there is a strong indication of a decrease in reflection
`amplitude with increasing offset or angle of incidence. This
`finding is consistent with a relatively uniform Poisson’s ratio in
`the geologic section. Basalt is not expected to have an anoma-
`lous Poisson’s ratio.
`
`OFFSET AMPLITUDE ANALYSIS
`
`At this point, the reader may wonder what type of amplitude
`balancing is desirable in order to analyze offset-dependent am-
`plitude changes. One must then look at some of the major
`factors which affect the recorded amplitude of a reflection as a
`function of offset. Some of these factors are listed below.
`
`Array attenuation arises because one generally does not have
`a point source and a point receiver. As the dip of the apparent
`reflector becomes large, geophone arrays tend to reduce ampli-
`tudes of reflections. The same is true for shot arrays. This effect
`is greatest for shallow reflectors at long offsets and diminishes
`with greater depths of reflectors and shorter offsets.
`As illustrated in Figure 18, array attenuation is a result of
`NMO. For a flat-lying reflector, one can see that the apparent
`dip of the reflection across a geophone group array comes
`purely from NMO. This dip or slope is simply the derivative of
`the NM0 with respect to offset, dT,/dX. Using the NM0
`equation
`
`one finds that
`
`7; = (T; + X2/Vf,,,s)1'2,
`
`dT
`L = X(7‘;!&
`dX
`
`+ XzVj,,,,)-“*.
`
`(6)
`
`(7)
`
`In equations (6) and (7) 7; is the two-way event arrival time at
`shot-to-group offset X, To is the zero-offset two-way time and
`I$,,, is the root-mean-square (rms) velocity to the reflector.
`Using the above relationship and information about the
`
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`
`PGS Exhibit 2042
`WesternGeco v. PGS (IPR2015-00313)
`
`

`
`Reflection Coefficients
`
`for Gas Sands
`
`1647
`
`VRMS
`
`OFFSET
`
`2K
`
`4K
`
`[FEET]
`6K
`
`8K
`
`EFFECTIVE ARRAY
`q 135 FT.
`LENGTH
`cps
`
`FREQ.=28
`
`8800,/s
`
`9800’1
`
`s
`
`GAS SAND
`
`\
`
`I ATo= T,- T*
`
`FIG. 19. Plot of array attenuation versus two-way traveltime
`and shot-to-group offset.
`
`A& < ATo
`
`recording geometry, one can obtain an array attenuation plot
`similar to the one shown in Figure 19. The recording parame-
`ters corresponding to this figure are for an effective shot and
`group array length of 135 ft. The plot is for a frequency of 28 Hz
`and for the velocity function shown along the vertical axis. The
`contours are in decibels (dB) and include the effects of both shot
`and group arrays. An overlay plot of this type is convenient in
`analyzing amplitudes on