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`GEOPHYSICS, VOL. 57, NO.
`
`1 (JANUARY 1992); P. 161—170, 10 FIGS., 2 TABLES.
`
`Marine PSSP reflections with a bottom velocity
`transition zone
`
`N. W. Kim* and A. J. Seriffi
`
` ABSTRACT
`
`Marine shear-wave reflection methods using the
`conventional data acquisition system (i.e., source and
`receiver in water) rely on two mode conversions at the
`water bottom to produce shear reflections such as
`PSSP. Some theoretical considerations and the results
`of a marine check shot survey conducted in the Gulf of
`Mexico demonstrate that the difficulty in observing
`PSSP events is attributable to weak P-S and S-P
`conversion at the bottom in regions with very low
`shear velocity (a few hundred ft/s or less) sediments at
`the bottom. For a simple water bottom with a low
`shear-wave velocity, water over a uniform half space,
`the PS conversion factor is proportional to VS, and the
`SP conversion factor is proportional to V3, where Vs
`is the bottom shear velocity. For V, ~ 1500 ft/s their
`product gives PSSP reflections that can be comparable
`in amplitude to typical PPPP events. For Vx S 500
`ft/s, the PSSP events should be about 30 dB weaker
`and probably not visible. For typical Gulf of Mexico
`sediments with a shear velocity transition Zone several
`tens of feet thick at the bottom, the situation is even
`worse, since the velocities start near zero and may not
`reach 500 ft/s. This condition is common in many areas
`of recent sedimentations.
`
`
`
`
`INTRODUCTION
`
`It is well known that the generation and propagation of
`shear waves in a fluid is not possible. Consequently, a
`marine shear-wave reflection method using a seismic source
`and receiver that are both situated in water must use mode
`conversion at, for example. the water bottom. A proposed
`method involves bottom P-to—S conversion for the P—wave
`incident in water and S—to-P conversion at the bottom for the
`reflected S wave incident in the solid.
`
`Theoretical investigations (e.g., Tatham and Stoffa, 1976)
`suggested that such marine PSSP reflections should be
`comparable in amplitude to normal P-wave reflections for
`models in which the water bottom has a P-wave velocity
`
`greater than or equal to that of water. and a Vp/VS ratio on
`the order of three or less. Thus, we searched for these events
`on data from conventional marine P-wave reflection sur-
`veys. Our first search was inconclusive, but some data were
`published in the open literature for a hard water bottom area,
`oflshore western Florida (Tatham and Goolsbee, 1984), and
`detailed studies on the arrival times and expected wavelet
`shapes of these arrivals prompted us to consider searching
`further for experimental observations of PSSP events. These
`detailed studies for regions like the Gulf of Mexico, where
`the shear velocities of the young sedimentary section were
`probably well below water P velocity,
`indicated that the
`shear legs of the PSSP paths would be nearly vertical at
`normal P-P survey source—receiver olfsets and that conse—
`quently the PSSP reflection times would vary almost linearly
`with offset and may be diflicult to recognize if one uses the
`usual hyperbolic moveout velocity scan programs. More-
`over, in water shallower than several hundred feet, the P
`legs of the PSSP reflection would be very long and nearly
`horizontal at normal P-P reflection offsets. In this case, a
`number of multiple reflections in the water would arrive at
`times near that of the first arrival from a given reflector,
`producing a complicated wavelet shape that rapidly ap-
`proached that of a P wave trapped in the water.
`In spite of some encouraging results from our attempts to
`correct for those phenomena, we were not able to identify
`PSSP events on data from any of the low shear velocity sites
`studied. In attempting to understand the problem, we have
`been forced to examine more critically the question ofP to S
`and S to P mode conversion efficiency of actual ocean
`bottoms. In this paper, we report some theoretical investi-
`gations and the results of an experimental measurement of
`PS conversion at one site in the Gulf of Mexico.
`
`Manuscript received by the Editor April 8, 1991; revised manuscript received August 19, 1991.
`*Shell Olfshore lnc., P.O. Box 61933, New Orleans, LA 70161.
`iDeceased May 23, 1991; retired from Shell Development Co., Houston.
`© 1992 Society of Exploration Geophysicists. All rights reserved.
`
`WesternGeco Ex. 1009, pg. 1
`
`WesternGeco Ex. 1009, pg. 1
`
`

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`162
`
`Kim and Seriff
`
`THEORETICAL CONSIDERATIONS
`
`Mode conversion at a simple bottom
`
`The general transmission and reflection properties ofplane
`body waves at a plane interface between elastic solids are
`well known. We are interested in a special case: the fluid—
`solid interface encountered in an actual marine environment.
`A better understanding of the relative importance of the
`difi'erent elastic parameters of this interface in determining
`mode conversion amplitudes should be valuable in the
`assessment of the PSSP reflection method.
`For such a study, we first consider a simple water bottom
`consisting of water overlying a homogeneous solid half—
`space. The elastic parameters in this model, shown in Figure
`l, are the P-wave velocity (VP). S—wave velocity (V5), and
`density (p). The water and solid are denoted by subscripts l
`and 2, respectively. Mode conversions for the incident P
`wave in water and the incident S wave in the solid are
`depicted in the figure. The elastic parameter dependence of
`the corresponding conversion coefl‘icients, Tm and TSP, will
`be examined below. We define the conversion coefficient as
`the ratio of the particle displacement amplitude of the
`transmitted (converted) wave to that of the incident wave; its
`magnitude can be evaluated from the solutions of the Zoep-
`pritz amplitude equations (Cerveny and Ravindra, 1971;
`Waters, 1981) for plane-wave reflection and transmission at
`a plane elastic interface.
`the
`In much of the water-covered area of the world,
`bottom materials consist of poorly consolidated clastic sed-
`iments. The shear velocity (Hamilton, 1976) for such sedi-
`ments is observed to be much smaller than the P-wave
`
`velocity of water. Consequently, using V52 < VP], we can
`greatly simplify the functional expressions for Tm and Txp
`given by Cerveny and Ravindra (1971) and obtain the ap-
`proximate expressions:
`
`Tps == FVSZ ,
`
`Tip = GVEZ,
`
`where
`
`—4p1 sin 61
`F : ————-—-———f——-————
`prpl/cos 61,, + p2 sz/cos 62p
`
`(1)
`
`(2)
`
`(3)
`
`
`
`TPS
`
`1. Raypaths configuration and terminology for the
`FIG.
`simple water—solid interface. The transmission coefl‘icients
`Tpx and TSP are the ratios of transmitted—to-incident particle
`displacement amplitudes. Vp, V5, and p denote P-wave
`veloc1ty, S-wave velocity, and density, respectively.
`
`—4(p1/V,,1) tan 91,,
`G =—— (4)
`Pl Vpl/COS 91,; + p2 sz/cos 92,,
`
`sin 91,,
`sin 92,,
`V
`pl
`
`(5)
`
`=
`
`sz
`
`.
`
`It is noted that the expressions for F and G are indepen-
`dent of the shear velocity;
`they are a function of the
`incidence angle (81p) and the remaining elastic parameters,
`i.e., VP], sz, p1. and p2. Since these parameters (e.g.,
`Hamilton, 1976) have been found to be fairly independent of
`V52, we recognize a simple (and useful) relationship for the
`conversion coefficients in this environment of very low VS as
`a function of the shear velocity, i.e.,
`
`T
`p5 0‘ V52
`
`5:2
`
`T
`
`oc V32.
`
`(13)
`
`(2a)
`
`Conversion efficiency
`
`A field configuration for marine PSSP reflection surveying
`in the environment described above is shown in Figure 2.
`The PSSP reflection is subjected to the two mode conver-
`sions at the water bottom. Thus, We may define the bottom
`conversion efiiciency, Em,” for the PSSP reflection to be
`the product 0f the two conversion coefficients, i.e.,
`
`Epssp Z Tps ' Tsp'
`
`From equations (la) and (2a), we can write
`
`Em ac V32.
`
`(6)
`
`(7)
`
`This result indicates that for the case of a simple water
`bottom the amplitude of PSSP reflections for constant 91,, is
`proportional to the third power of the shear velocity at the
`bottom. In practice, E‘mp at a fixed source—receiver offset
`also varies as V532. This strong dependence on V52 may be
`better appreciated if one considers an illustration, e.g., two
`cases in which the bottom materials have different shear
`velocities while other elastic parameters are essentially the
`same. Taking V52 to be 500 ft/s in the first case and 1600 ft/s
`in the second, we expect that for identical deep reflectors the
`PSSP reflection amplitude for V52 = 500 ft/s would be
`reduced by a factor of (500/1600)3 = 0.03 (Le. -30 dB)
`relative to that for Vfl : 1600 ft/s. (It should be pointed out
`
`
`
`WATER
`
`P
`
`/ ~ \
`\\
`,
`\
`P-s CONVERSIONf\
`
`SOLID
`
`P
`
`s-P CONVERSION
`
`/_ \l
`I
`‘11
`I \—
`I
`
`t
`
`/
`
`‘
`
`
`
`FIG. 2. Field geometry for marine PSSP reflections for
`low-velocity sediments.
`
`WesternGeco Ex. 1009, pg. 2
`
`WesternGeco Ex. 1009, pg. 2
`
`

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`Marine PSSP Reflections
`
`163
`
`that the P—wave reflection levels for both cases would be
`practically the same.)
`
`Mode conversion with V, transition zones
`
`In many real marine environments, the materials immedi-
`ately underlying the water consist of poorly consolidated
`sediments. Due to the nature of the sedimentation process,
`the elastic properties of the first few hundred feet of bottom
`materials cannot be described by the simple elastic half
`space of the previous section. For the frequencies of interest
`in seismic exploration for hydrocarbons (10 S f S 100 Hz),
`the bottom V, varies drastically with depth in distances on
`the order of a wavelength.
`Some published data (Hamilton, 1976) on water bottom
`shear-wave velocity in marine environments suggest that the
`poorly consolidated bottom sediments in some areas consist
`of a transition zone in which V3 may be much less than 500
`ft/s (in fact, near zero) at the water bottom and increase
`rapidly with depth, reaching velocities even greater than 500
`ft/s in a few tens of feet. For the frequencies ofinterest, such
`
`a transition zone may be several wavelengths long. We have
`made theoretical analyses and numerical model studies of
`the mode conversion from such transition zones and have
`concluded that their conversion efficiency at frequencies in
`the 10 to 100 Hz range is extremely low, perhaps less than
`that for a simple bottom with Vs = 500 ft/s. Moreover, the
`converted wave trains produced are quite complicated; the
`strongest single conversion is apparently associated with the
`shear velocity at (and very close to) the water bottom.
`
`Some numerical computations
`
`the conversion coeffi-
`We now examine in more detail
`cients as a function of angle, first for the simple water—solid
`interface, referred to as Model A, then for a possibly realistic
`transition zone. The parameters of Model A are given in
`Table 1.
`
`Table 1. Elastic parameters for Model A.
`
`Vp (ft/s)
`
`
`Vs (ft/s)
`
`p (g/cm3)
`
`1
`0
`5000
`Water
`
`Solid 2 5500 1500
`
`
`
`
`
`
`
`
`
`(”NW 5000
`
`0
`
`l.
`
`5500 1500 2.!
`
`
`
`
`
`
`
`
`
`
`
`um
`
`llllnIlllllllll
`
` AMPLITUDE
`
`
`
`
`
`
`
`
`o
`20
`
`o
`
`20
`
`40
`
`60
`
`80 90
`
`
`40
`60
`so 90
`
`GlplDEGREE)
`
`a IPlDEGREE)
`
`FIG. 3. Conversion coefficients T s and T3}, for plane waves
`at the water-solid interface of Model A. The conversion
`efficrency (Tm - T51) is also shown.
`
`FIG. 4. The effect of bottom density on the conversion
`efficiency Epw = Tps - Tsp for the simple bottom of Model A.
`The model parameters shown on the graph are velocities, in
`ft/s, and densities in g/cm3.
`
`WesternGeco Ex. 1009, pg. 3
`
`WesternGeco Ex. 1009, pg. 3
`
`

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`164
`
`Kim and Seriff
`
`Numerical computations for TN and T5,, for Model A were
`performed with the use of a computer program based on the
`Zoeppritz solutions. In Figure 3, these conversion coeffi—
`cients and their product Em“, (i.e., the bottom conversion
`efficiency for PSSP) are plotted as a function of the P-wave
`angle of incidence 6”,. In the ensuing sections, we examine
`fuIther the sensitivity ofT
`and E
`to some of the
`1:5 1 T51) 1
`pm:
`elastic parameters.
`
`1) Effect of Density: To display the efl‘ect of density of the
`water bottom materials, we computed the conversion
`efficiency for two values of the density of the bottom,
`1.4 and 2.0 g/cm3, holding the other parameters the
`same as in Model A. The computed curves, shown in
`Figure 4, demonstrate no significant dependence on
`density.
`2) Effect of Shear Velocity: To examine the elfect of V52
`on Tps’ TSP, and the conversion efliciency, TN T”, we
`have computed their values for various values of the
`shear velocity (with the other parameters the same as in
`Model A). The computed values ofTTSP, Tm, and Ems”
`for 01p of 40 and 80 degrees are plotted against V_Y in
`
`Figure 5. These are roughly the angles at which the two
`local maxima in Epssp occur. In each plot, the slope
`based upon the theoretical approximations [i.e., equa—
`tions (1), (2), and (7)] is indicated by a dashed line. The
`good agreement between the exact solution (indicated
`by the solid lines joining the computed points) and the
`approximation reaflirms the simple third power depen-
`dence on V32 discussed earlier,
`3) Conversion Efliciency for Various V32: Realizing the
`wide range of the shear velocities (i.e., competent rock
`to poorly consolidated sediments) which may be en-
`countered at real water bottoms, we computed the
`PSSP bottom conversion for sz ranging from 500 to
`3000 NS. The computed curves are shown in Figure 6.
`All other elastic parameters were kept the same as
`those in Model A.
`
`Due to the V32 dependence of the conversion efliciency,
`the absolute levels of the curves plotted in Figure 6 vary over
`a range of 50 dB. For V52— 500 ft/s, the absolute value of the
`first maximum of Epssp (at 91p~— 40 degrees)1s very small, on
`the order of 0.001, and Hamilton’s data suggest that even
`
`”HIM-11: _
`
`
`
`
`3000
`
`
`
`.001
`
`
`
`
`500 1000
`
`3000
`
`500 1000
`
`3000
`
`510 1000
`
`Vs (ft/sec)
`
`Vs (ll/soc)
`
`V, (fl/sec)
`
`1'
`TSP, and EI;”sip versus V2 are
`FIG. 5 The elfect of the bottom shear velocity (V52) on the conversion coeflicients. Plots ofT
`shownIn three separate graphs The other parameters are those of Model A. In each graph, points calculated om Zoeppritz’ s
`equations for two angles of 1nc1dence 9”,, are shown and connected by solid lines The angles chosen, 40 and 80 degrees, are
`near the local maxima of E
`pup The dashed lines indicate the slopes of the approximate expressions given in equations (1), (2)
`and (3)
`
`WesternGeco Ex. 1009, pg. 4
`
`WesternGeco Ex. 1009, pg. 4
`
`

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`Marine PSSP Reflections
`
`165
`
`lower values will be encountered in real sediments. For
`conversion efficiencies less than or equal
`to 0.001,
`the
`detection of PSSP reflections in the earth is probably impos-
`sible with conventional data acquisition and processing
`techniques. For V52 = 1500 ft/s conversion efficiencies of
`0.03 are reached at 01p 2 40 degrees, and the PSSP reflec-
`tions could be comparable to competing PPPP events.
`
`Synthetic seismograms with and without a transition zone
`
`To examine the elTect on PSSP conversion efliciency of a
`V5 transition Zone we have generated synthetic seismograms
`
`TPs'Ts?
`
`
`
`o
`
`20
`
`40
`
`60
`
`elploeckeel
`
`for models with and without a shear—wave velocity transition
`zone. The seismograms were computed using an exact
`frequency-wavenumber domain program designed by J. H.
`Rosenbaum (1971) for models consisting of plane parallel
`elastic layers. These seismograms are displayed with identi-
`cal display gains in Figures 7c and 7b, respectively.
`The earth model used for the calculation in Figure 7c, with
`a transition Zone, is shown in Figure 7a. The transition Zone
`is 100 ft thick and simulates a constant P velocity with a
`linear increase in shear velocity and density with depth. The
`shear velocity increases from 500 to 1500 ft/s, and the
`density from 1.4 to 2.0 g/cm3. The “linear increase” is
`approximated by 23 layers in the 100 ft interval. The shear-
`wave reflection coefficients between these layers are less
`than 0.04. The 100 ft transition zone overlies a 3000 ft
`homogeneous layer resting on a half-space with mechanical
`properties chosen to produce normal
`incidence P- and
`S—wave reflection coeflicients of 0.1 at the interface with the
`layer. For the simple bottom case represented in Figure 7b,
`the 100 ft transition zone is replaced by 100 ft of material
`with the same properties as the 3000 ft layer. The most
`important of these is the 1500 ft/s shear velocity. The source
`and receivers in both models are at 30 ft below the water
`surface. Pressure sources and pressure sensitive detectors
`are used.
`The two synthetic seismograms of Figure 7 show several
`similar events that are associated primarily with contrasts in
`P velocity and density. The primary reflection PPPP is
`marked, and its first multiple from the water surface is
`obvious on both records. The moderate differences in appar-
`ent arrival times and amplitudes between these events on the
`two records are due to the density transition from 1.4 to 2.0
`g/cm3 in the model used for Figure 7c. The first arrivals on
`both records, which are due to direct P-waves and P-wave
`refractions at or near the water bottom, are fairly similar.
`The striking differences between the two seismograms of
`Figure 7 involve events that have undergone a mode con—
`version at or near the water bottom. For the case of the
`simple bottom (Figure 7b),
`the PSSP reflection and the
`PSSP-PSPP complex due to simultaneous arrival times are
`clearly visible. At the same gain, the seismogram of Figure
`7c, with the transition Zone, shows no sign of the PSSP and
`only a very weak PPSP-PSPP complex. Figure 7c contains
`an inset showing the PSSP region of the seismogram at a 20
`times greater gain (26 dB). The PSSP event is visible at this
`gain. From the conversion efficiency relation of equation (3),
`we would expect an amplitude difference of (500/1500)3 or 29
`dB for the events converted precisely at the water bottom in
`the two cases.
`From the high gain insert in Figure 7c, we see that the
`PSSP event for the case with the transition zone is more
`complicated than that for the simple bottom, as seen in
`Figure 7b. Indeed, conversions occur at each interface of the
`thin layers making up the 100 ft transition zone. Reflections
`involving conversions below the water bottom arrive earlier
`than the event with both conversions at the water bottom.
`For the thin layer transition zone model used here,
`the
`largest PS and SP conversion coefficients occur at the water
`bottom. For a gradual transition Zone, it is useful to consider
`the elfect of the entire zone upon the various frequency
`components of the seismic signal. On the records of Figure 7,
`
`WesternGeco Ex. 1009, pg. 5
`
`VP
`
`5000
`
`5500 lVARYlNG)
`
`0
`
`FIG. 6. The effect of the bottom shear velocity (V52) on the
`PSSP conversion efficiency for the simple bottom case. E up
`is plotted against 01,, for five different values of V52. The
`model parameters are shown on the figure. Velocities are in
`ft/s and densities (p) in g/cm3. VP is 5000 ft/s and 5500 ft/s for
`the water layer and the bottom, respectively. The correv
`sponding densities are l g/cm3 and 2 g/cm3.
`
`WesternGeco Ex. 1009, pg. 5
`
`

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`Vp
`5000
`
`V;
`0
`
`P
`1
`
`H
`100
`=100
`
`_.
`
`5500 500-1500 1.4-2 5 09"11351
`
`166
`
`Kim and Seriff
`
`the peak frequencies appear to be about 40 Hz, consistent
`with source and receiver ghosting, and the shear wave-
`lengths are not long compared to the 100 ft transition zone.
`For example, at 500 ft/s, the wavelength at 40 Hz is only 12.5
`ft. Our theoretical and numerical calculations ofthese effects
`give the same qualitative result as that seen in Figure 7. For
`exploration seismic frequencies and typical pulse shapes, a
`realistic transition zone of the magnitude used in Figure 7
`dramatically reduces the PS-SP conversion efficiency of the
`water bottom complex,
`
`In other words, the important parameters in PSSP reflec—
`tions are V5. at the water-solid interface, and the thickness
`and VS gradient of the transition zone. We have not found
`this information readily available or easy to acquire in actual
`marine areas. For this reason, we undertook the experimen-
`tal work to be presented in the next sections to gain some
`insight into the problem of mode conversion efiiciency at an
`actual sea floor.
`
`EXPERIMENTAL RESULTS—PS CHECK SHOT SURVEY
`
`Remarks
`
`Field experiment
`
`Some of the results presented in the preceding sections
`demonstrate that the most critical parameter alfecting PSSP
`reflections is the shear-wave velocity at the water bottom, at
`least for low velocity sediments. In an area where the water
`bottom must be regarded as a transition zone in VS, the
`PSSP reflections will consist of two contributions; one from
`the simple water-solid interface and another from the Vs
`transition zone. The first contribution, though quite small,
`may still play the most important role ifthe transition zone is
`thick in comparison to the seismic wavelengths ofinterest.
`
`Having realized the shear-velocity sensitivity ofthe water-
`bottom mode conversion, we conducted a field experiment
`at a well site 40 miles 01f the Texas coast in the Gulf of
`Mexico. The experiment could be described as a marine
`walkaway check-shot well survey. The general experiment
`configuration is depicted in Figure 8a. Specifically,
`the
`outgoing signals from individual dynamite shots (1 to 2 lb for
`oflset distancesx < 1500 ft, 5 lb forx > 1500 ft) at variousx
`(590 to 4164 ft) from the well were recorded with a three-
`component geophone clamped at a depth of 4121 ft in the
`
`NO TRAN5|T5ION
`
`100i? TRANSITION
`
`2000
`
`4000
`
`6000
`
`'12000
`
`4000
`
`6000 H
`
`SEC
`
`3000 5500
`
`1500
`
`2
`
`-
`Rp-
`
`.
`
`0.1
`
`SOURCE 81 RECEIVER‘
`A130 F1
`
`(a)
`
`
`
`(b)
`
`2
`
`3
`
`a
`
`5
`
`FIG. 7. Synthetic seismograms demonstrating the efl°ect ofa sea--bottom transition zone on the amplitude of PSSP reflections.
`Seismograms with and without a transition zone are shownin (b) and (c), reSBpectively. The model with the transition zone is
`shown as (a). Velocities (Vp and V) are given in ft/s and densities (p)1n g/cm. His the layer thicknessin feet. The half—space
`at the bottom18 descnbed by the reflection coefiicients (RP and R) at its top. For the model without a transition zone, the entire
`100 ft earth layeris given the propenies ofthe 3000 ft layer. For (c), the intervalin the dashed windows18 shown at two gains
`
`WesternGeco Ex. 1009, pg. 6
`
`WesternGeco Ex. 1009, pg. 6
`
`

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`Marine PSSP Reflections
`
`167
`
`well. A shallow charge depth of about 3 ft was chosen to
`allow immediate venting of the gas produced by the explo-
`sion in the water,
`thus minimizing the efiect of bubble
`oscillation. The water depth at the well site was 132 ft.
`The three-component traces recorded in the experiment
`are displayed in Figure 8b. The trace on the left of each
`group of three adjacent traces is the vertical»component
`recording for the shot made at the x-distance indicated (in
`feet) at the top of the figure. To compensate roughly for the
`effects of shot amplitude variations and increasing x—dis—
`tances, we adjusted the fixed gains of the vertical traces
`displayed so that the maximum amplitudes of these traces
`are all equal. The same fixed gain factors were then used to
`adjust the amplitude levels of the corresponding horizontal
`components,
`thus preserving the true amplitude relation
`among the three components. These normalized traces are
`displayed at two difierent levels in Figure 8b; the upper
`portion (0.5—1.5 5) shows the direct arrivals and the lower
`portion (0.5—3.5 s, magnified 20 times in amplitude) shows
`the later arrivals. For the display of Figure 8, the field data
`were filtered with a 30 Hz low-pass filter to suppress
`
`high-frequency noises generated on the drilling platform. For
`several shots, residual bubble pulses can be clearly seen on
`the low-gain traces of Figure 8.
`
`Modeling
`
`To aid in the interpretation of the field data, synthetic
`seismograms simulating the field experiment configuration
`were generated using Rosenbaum’s program and are shown
`in Figure 9c. In the calculation, shots were placed at a depth
`0f3 ft in the 132 ft water layer. The shots were at various
`distances from the well, which contained a single horizontal—
`component velocity detector at 4121 ft.
`For the elastic model used in these calculations (see
`Figure 9b), P—wave interval velocities below 930 ft depth
`were obtained by “blocking” the available P—wave sonic log
`data. The shallow interval was filled with a linear velocity
`trend (in ft/s) V12 = 5500 + 0.4Z. Here the depth Z is in feet.
`Due to the unavailability of any shear-velocity information,
`the shear interval velocities were calculated assuming Vp/
`3 : 2.5 forZ > 1000 ft and a linear trend V, = 1500 + 1.1Z
`
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`FIG. 8. (a) Field experiment configuration. (b) Three-component well data for shots ranging in x from 590 ft to 4164 ft. A vertical
`component and two horizontal component traces are shown for each x-distance indicated at the top of the record. Each trace
`[5 shown at a low fixed gain in the upper part of the figure (0.5 to 1.5 s) at a 26 dB higher fixed gain in the lower portion of the
`figure (0.5 to 3.5 s). The gains of the vertical component traces are adjusted so that the maximum amplitudes displayed on these
`traces are equal, but the relative gains of the three traces for each x-distance are the same.
`
`WesternGeco Ex. 1009, pg. 7
`
`WesternGeco Ex. 1009, pg. 7
`
`

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`168
`
`Kim and Seriff
`
`for the shallow zone. Densities of 1 g/cm3 for liquid and 2
`g/cm3 for solid were used. P-wave reflectivities RCp at
`various interfaces below the water bottom (shown in Figure
`9b) range up to 0.05. Due to the constant Vp/VS forZ > 1000
`ft, the assumed reflectivities RC5 for S waves are identical to
`those for P waves below 1000 ft. No effects of inelastic
`attenuation were included in the model.
`In the model seismogram representing the in-line, horizon-
`tal well geophone traces, three different types of events are
`clearly observed: PP (direct P arrival), PS (water bottom
`conversion), and PPS (P-to-S conversion at some depth ZPS
`below the water bottom). These paths are indicated in Figure
`9a.
`
`PP and PS are easily identifiable in the seismogram.
`However,
`there are numerous PPS events appearing be-
`tween PP and PS. The arrival times at x = 0 for PPS events
`
`of a few interfaces possessing RCA = 0.05 are arrowed in the
`figure. For each of these indicated times, the conversion
`
`the
`that
`It should be pointed out
`depth Zps is given.
`relatively quiet zone between the conversion depths of 1060
`and 132 ft is entirely due to the assumed absence of signifi-
`cant VS contrasts in this interval. Any significant contrasts in
`the shallow zone would produce PPS events and these events
`would arrive before the PS. The strong PS arrival seen in the
`figure results from the high shear velocity,V =1500 ft/s,
`assumed to exist at the water bottom. The amplitude of the PS
`arrival will be significantly reduced if V5 values much lower
`than 1500 ft/s are used in the model.
`In such cases, an
`unequivocal identification of the weak PS event in the presence
`of the interfering PPS arrivals may become diflicult.
`
`Data analysis and interpretation
`
`The data presented in Figure 8 are clearly more difficult to
`interpret than the simple model seismogram of Figure 9. The
`PP first arrival is evident on the real data, but it is followed
`
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`FIG. 9. Model and synthetic seismogram for simulation of the check shot survey: (a) Geometry of the model showing paths for
`PP PS, and PPS arrivals at the well geophone from a source in the water. (b) P and S velocity models. (c) Synthetic
`seismograms for the in--line horizontal--component velocity detector at 4121 ft and sources at the X--distances shown.
`
`WesternGeco Ex. 1009, pg. 8
`
`WesternGeco Ex. 1009, pg. 8
`
`

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`Marine PSSP Reflections
`
`169
`
`by a gradually decaying signal in which no unique arrivals
`stand out clearly over a large range of x-distances. Certainly,
`no PS—like signal comparable in amplitude to the PP arrival
`stands out. In fact, the observed signal amplitudes at the
`times appropriate for a PS event are 20 to 30 dB below the
`PP amplitudes. (We expect the PS event to arrive at a time
`between two and four times as great as the PP time, i.e.,
`between about 1.5 and 3.0 s.) A careful study of Figure 8
`does suggest, however, that certain shear arrivals probably
`are present. Identification of these events and a detailed
`analysis of their amplitudes can provide at least an upper
`limit estimate of the PS conversion efficiency at, or very
`near. the water bottom. Three shear-like events displaying
`some lateral continuity and coherency are picked and
`marked PPS, event A, and event B in Figure 8b.
`Several clues were used to aid in the identification of the
`putative shear events: (1) the relative polarity of the hori-
`zontal and vertical components of motion,
`(2) the arrival
`time and moveout with x, and (3)
`the variation of the
`horizontal component amplitude with x. Since the direct
`P-wave arrivals appear in phase among the three compo-
`nents, SV shear-like events traveling downward to the
`receiver should display opposite polarity between the verti-
`cal component and the two in—phase horizontal components.
`The picked events satisfy this criterion. Of course,
`this
`polarity convention for shear-like events holds also for
`P-waves reflected below the observation depth. Therefore,
`the other criteria must be considered.
`For example. the moveouts associated with the events A
`and B (Vms 2 2500 ft/s) and PPS (V,.,m 2 3400 ft/s) are much
`larger than those expected for P-wave reflections from below
`the detector (V,.,m = 6000 ft/s). Thus, one can conclude that
`these events are probably shear-wave arrivals, not P-wave
`reflections.
`
`Distinguishing between PS and PPS events is more dif-
`ficult. however, particularly where the ratio of VI) to V, is
`quite uncertain. Nevertheless, according to the t~x relation
`computed from the model, the event marked PPS in Figure
`8 appears to have the stepout and To (zero offset time) of a
`subbottom converted shear wave from a conversion depth in
`the vicinity of 1300 ft. Changing Vp/VS in the model by as
`much as :05 would not materially alter this conclusion.
`Similarly, the moveouts and To values of the events marked
`A and B correspond, within the uncertainties, with the
`values expected for the PS event. Of course, they cannot
`both be this event; in fact, both could be PPS events with
`conversion depths within the first few hundred feet below
`the bottom.
`
`In addition to the we relation, the amplitude information of
`these events may be used to ascertain their identity. The
`amplitude levels of the horizontal components for these
`three events (PPS, A, B) together with the vertical and
`horizontal components of the PP event were measured from
`selected traces (excluding shots with severe bubble oscilla-
`tions). These amplitudes, normalized to the vertical PP at
`x = 0, are plotted as individual points in Figure 10.
`Theoretical amplitude curves for the PP, PPS, and PS
`events were taken from the calculations shown in Figure 9,
`modified to include absorption with a loss term of the form
`(“fl/8'68, where a is independent of frequency. To compare
`these computed responses wi