AAPG Bulletin, v. 86, no. 1 (January 2002), pp. 129–144 129
Seismic simulations of
experimental strata
Lincoln Pratson and Wences Gouveia
ABSTRACT
Experimental strata formed in the new Experimental Earthscape
(XES) basin at the St. Anthony Falls Laboratory of the University
of Minnesota offer a realistic model for simulating the seismic response
of natural strata and thus for advancing understanding of
the geologic information that can be extracted from seismic data.
A new method is presented here for using digital photos of the
experimental strata to generate synthetic seismic data at the length
scales and frequencies relevant to oil and gas exploration. In the
method, the digital photos are transformed into models of acoustic
velocity and bulk density, which are then input into algorithms
that generate synthetic seismic data. Three such algorithms are
used to demonstrate the approach: a convolutional algorithm,
which produces the equivalent of ideal, poststack, time-migrated
seismic data; an exploding-reflector algorithm, which produces unmigrated,
poststack seismic data; and a full-wave equation algorithm,
which we use to produce a synthetic version of prestack,
unmigrated, multichannel seismic data. Data generated by the latter
two algorithms are processed to compare their information
content against both the experimental strata and the ideal seismic
data derived from the convolutional algorithm. The qualitative
comparison nicely illustrates the filtering of geologic information
in seismic data and its further degradation by wave-propagation
phenomena, such as diffractions, multiples, and interbed
reverberations.
INTRODUCTION
Seismic reflection data have arguably become the most important
type of data for determining where to drill for oil and gas. As a
result, the generation of synthetic seismic data from stratigraphic
models has become an important means for understanding how to
interpret seismic data and improve data quality through
processing.
The stratigraphic models used for this purpose have tended to
be simple geometric constructs of layered strata, but the use of
Copyright 2002. The American Association of Petroleum Geologists. All rights reserved.
Manuscript received September 7, 1999; revised manuscript received December 12, 2000; final acceptance
March 13, 2001.
AUTHORS
Lincoln Pratson Division of Earth and
Ocean Sciences, Duke University, Durham,
North Carolina, 27708;
lincoln.pratson@duke.edu.
Lincoln F. Pratson is an assistant professor at
Duke University. He holds a B.S. degree in
geology from Trinity University, an M.S.
degree in oceanography from the University
of Rhode Island, and a Ph.D. in geology from
Columbia University. He was a research
scientist at Lamont-Doherty Earth Observatory
of Columbia University and at the Institute of
Arctic and Alpine Research of the University of
Colorado before joining the Division of Earth
and Ocean Sciences at Duke University in
1998. He researches seascape evolution and
strata formation along continental margins
through numerical and experimental modeling
and the analysis of sedimentologic,
stratigraphic, and geophysical data.
Wences Gouveia ExxonMobil Upstream
Research Company, 3319 Mercer Street,
Houston, Texas, 77027-6019;
wences_p_gouveia@email.mobil.comWences P. Gouveia received his B.S. (1986)
and M.S. (1990) degrees in electrical
engineering from the Catholic University of
Rio de Janeiro, Brazil, and his Ph.D. (1996) in
geophysics from the Colorado School of
Mines. He joined Mobil Technology Company
in 1996 where he conducted research in the
fields of seismic waveform and pressure data
inversion, optimization-based geological
modeling, and stratigraphic numerical and
experimental simulations. He is currently a
member of the ExxonMobil Time-Lapse
Seismic research team, where his activities
have special emphasis on the development of
algorithms for quantitative four-dimensional
seismic interpretation.
130 Seismic Simulations of Experimental Strata
more natural and thus complex models has been increasing over
the past decade. These models include computer-generated simulations
of basin strata (Shuster and Aigner, 1994; Courtney and
Syvitski, 1996; Syvitski et al., 1999) and models constructed from
outcrops (e.g., Stafleu and Schlager, 1993; Bracco and Schlager,
1999).
In this article, we introduce experimental strata as another
means for investigating the seismic response of natural strata. To
our knowledge, experimental strata have never been used to generate
synthetic seismic data, apparently because of the very little
experimental work that has been done on the problem of basin
infilling (Paola, 2000). Now, however, a new facility with a novel
subsiding basin floor offers an exceptional opportunity to create
synthetic seismograms from this type of stratigraphic model. The
facility is the Experimental Earthscape (XES) basin at the St. Anthony
Falls Laboratory of the University of Minnesota (Paola,
2000; Heller et al., 2001; also see
http://www1.umn.edu/safl/research/research.html). In contrast to physical models constructed
for examining the seismic response of specific geologic
structures (e.g., Sherlock and Evans, 2001), deposits in the XES
basin form of their own accord under controlled rates of sediment
supply, subsidence, and base-level change. The resulting experimental
strata bear a striking resemblance to natural strata and contain
a variety of stratal patterns and structures encountered in real
basins (Figure 1A). These include normal faults, reverse faults, and
growth faults; facies regressions and transgressions; truncations;
and offlapping and onlapping strata.
The experimental strata can be seismically imaged using transducers.
The overall deposit, however, is so thin ( 1.3 m) that it
would be difficult to resolve the fine-scale stratal patterns and
structures that give the strata the look of a true large-scale basin.
An alternative approach, which we present here, is to compute
synthetic seismograms from digitized photographs of the strata
taken during sectioning (Figure 1). This approach has the added
flexibility that the experimental strata can be rescaled to the size
of actual sedimentary basins, allowing their appearance in seismic
reflection data to be modeled at exploration-scale frequencies.
We demonstrate the approach in this article using part of a
single digitized photograph of experimental strata formed in a prototype
of the XES basin (Figure 1B). The photo is translated into
acoustic property models that are then input into three different
seismic modeling algorithms. These range in sophistication from a
convolution algorithm that produces an ideal poststack, time-migrated
seismic section to an algorithm that numerically solves the
full two-way wave equation to produce an approximation of raw,
multichannel seismic data, which we subsequently process. The
synthetic data produced by these algorithms are qualitatively compared
to the original stratigraphic simulation. The preliminary
analysis elucidates various avenues of research that potentially
could be accelerated by seismic modeling of experimental
stratigraphy.
ACKNOWLEDGEMENTS
Our study was partially supported by grants
to Lincoln F. Pratson from the National Science
Foundation (NSF EAR Grant No. 98-
96392), the Office of Naval Research (ONR
Grant No. N00014-99-1-0044, part of the
STRATAFORM program), and a consortium of
oil companies, including Amoco, Conoco,
Exxon, JAPEX, Mobil, and Texaco. Wences
Gouveia thanks Mobil Oil Co. for supporting
his involvement in the study. We gratefully acknowledge
the help and input of several colleagues.
C. Paola provided the stratigraphic
simulation used in the seismic modeling. R.
Courtney, J. Syvitski, D. O’Grady, and, particularly,
E. Hutton helped at various stages with
the normal-incidence modeling. R. Sarg and S.
Cullick provided constructive criticism during
preparation of the article.
Pratson and Gouveia 131
delta front
coal
sand
growth
faults
point of
maximum
subsidence
delta top
base of
channel
incision
channel
infill
B
A
initial rapid
progradation
aggradation
slow
base-level cycle
rapid
base-level cycle
0
-10
10 20 30 40 50
base level
(cm)
experiment run time (hr)
EQ SC EQ RC EQ
100 mm
Figure 1. (A) Digital photograph
of a dip-oriented cross
section through experimental
strata formed in the XES basin
prototype (cross section location
shown in Figure 2). Sediment
transport was from left to
right. Light tones are quartz
sand, and dark tones are
crushed coal. Base-level history
is shown in the panel at the
bottom of the figure, with slow
and rapid base-level cycles (SC
and RC, respectively) and periods
of equilibrium (EQ)
marked. All other variables
were held constant. (B) Region
used to generate synthetic seismic
data. Note the variety of
stratal patterns and structures
in the experimental strata that
are also found in natural strata.
Figure modified from Paola
(2000).
BACKGROUND: EXPERIMENTAL STRATA
The experimental strata used in this article come from
the first experiment conducted in the XES basin prototype.
This experiment is described in detail by Paola
(2000) and Heller et al. (2001) and so is only summarized
here.
The XES basin prototype is 1.6 m long by 1 m
wide and has up to 0.8 m of accommodation space for
deposition (Figure 2). Spatial and temporal variations
in accommodation space are created by the basin’s subsiding
floor. Underlying the floor are ten hexagonalshaped
subsidence cells arranged in a honeycomb pattern.
At the beginning of an experiment, these cells are
buried beneath a layer of dry, well-sorted commercial
gravel (Figure 2A). The top of the gravel is then covered
with a thin rubber membrane, which forms the
basin floor. The membrane subsides by withdrawing a
small volume of gravel from the bottoms of the underlying
subsidence cells. The subsidence in each cell
is controlled independently to a precision of about 0.1
mm. Hence the subsidence is smooth and continuous
in time and space and can be varied between adjacent
cells to produce slopes in the membrane of up to 60.
In the experiment, water mixed with a 50:50
blend (by volume) of fine (120 lm) quartz and coal
sand was fed from a single source point into one side
of the basin while base level was adjusted from the
other side (Figure 2B). The more buoyant coal sands
(specific gravity of 1.3) were a visibly distinct proxy for
sediments that were finer grained and slower settling
than the quartz sands (specific gravity 2.65) (Figure
1).
Subsidence rates were varied across the basin so as
to produce a simple bowl-shaped geometry centered
over the middle of the basin (Figures 1, 2). The rates
of subsidence and of water and sediment discharge
were held constant throughout the experiment. The
only factor that was varied was base level, the history
of which is shown in Figure 1. This history included a
slow fall and rise of base level, followed hours later by
a rapid fall and rise.
After the experiment was completed, the basin
strata were sliced lengthwise at intervals of 2.5 cm.
Each cross sectional slice was digitally photographed.
The photographic panel shown in Figure 1 is an example
of such a cross section located just off the centerline
through the strata (Figure 2B). Labels on the
photograph identify a range of deposits and structures
in the strata and indicate the relative timing of their
formation with respect to the changes in base level that
occurred during the experiment.
132 Seismic Simulations of Experimental Strata
Gravel Basement
Rubber
Membrane
Experimental
Deposit
Water
Jet
Exhaust Line
shore line
fluvial
plain
A
B
Fig. 1
Figure 2. (A) Schematic, cross sectional diagram of the XES
basin prototype. Subsidence is produced by controlled removal
of gravel through cells underlying the basin floor. Cell tops are
0.4 m wide. (B) Plan view of XES basin prototype. Honeycomb
arrangement of subsidence cells indicated in gray. Direction of
sediment transport indicated by arrows. Position of photographic
panel in Figure 1 indicated by dashed line. Figure modified
from Paola (2000).
BASIC METHOD FOR CREATING ACOUSTIC
MODELS FROM A DIGITAL PHOTO
The method for converting digital photographs of the
experimental strata into acoustic property models for
use in seismic simulations is still evolving. In this article
we present only the simplest and most straightforward
approach. Improvements to the method for achieving
more realistic acoustic models are being investigated
(e.g., Herrick et al., 2000).
Scaling the Stratal Architecture
The time and length scales under which strata formed
in the XES basin prototype are short and narrow in
range compared to the temporal and spatial scales involved
in the filling of natural basins. Heller et al.
(2001), however, demonstrate that the prototype experiment
still provides unequivocal insight into the influence
of subsidence, base level, and sediment supply
on the formation of natural basin strata. Irrespective of
how well the experimental processes scale up to natural
processes, the experimental strata clearly capture
in miniature the sequence stratigraphic architecture of
basin strata, that is, the structures, stratal patterns, and
facies distributions. Therefore, because of the natural,
scale-independent appearance of the experimental
strata, we simply assume that their architecture can be
resized to basin proportions and used to generate synthetic
seismic data at exploration frequencies.
The experimental strata are resized by assuming
an appropriate length scale for the pixels making up
the digital photographs of the strata. In the photo
shown in Figure 1B, which is the example used to generate
synthetic seismic data throughout the article, the
pixels are assumed to be 5 m wide and 1 m tall. These
lengths give the figure the overall dimensions of a 5 km
segment of a continental slope dipping approximately
4, which is a typical gradient (Pratson and Haxby,
1996; O’Grady et al., 2000). Larger or smaller pixel
sizes can be used to depict other scales of interest.
Relating Photo Gray Levels to Bulk Density
The resized digital photograph forms the template for
constructing the acoustic property models. Each photo
pixel has a gray level corresponding to the averaged
reflection of light from a small area in the experimental
strata containing numerous sediment grains that are
too small to be individually resolved. Because the
grains are commonly a mixture of quartz and coal, the
gray levels equate to an average of these two lithologies,
which we in turn equate to a bulk density.
In Figure 1B, photo pixels of the experimental
strata with a gray level of 0 (i.e., black) reflect regions
of pure coal. Because the coal is a proxy for clay, we
have assigned these pixels a bulk density of 1800 kg/
m3, a typical value for uncompacted clay (Middleton
and Wilcock, 1994). Correspondingly, pixels with a
Pratson and Gouveia 133
gray level of 255 (i.e., white) reflect regions of pure
quartz sand. We have assigned these a bulk density of
2055 kg/m3, which is a mean value for uncompacted
fine quartz sand (Middleton and Wilcock, 1994). All
other pixels with intermediate gray levels have been
linearly scaled to lie between these two density bounds
(Figure 3A).
Note that the end-member bulk densities and the
linear scheme for equating them to gray levels in the
digital photo are used here simply for illustrative purposes.
Other densities and more sophisticated, rock
physics–based mapping schemes can be used as well
(e.g., Herrick et al., 2000).
Porosity and Velocity from Bulk Density
Once the digital photo has been transformed into a
matrix of bulk densities, an acoustic velocity model for
the experimental strata is established. A variety of relationships
exist for computing velocity from other
rock properties (Mavko et al., 1998), and the one we
use here is based solely on porosity.
Assuming that quartz is the dominant mineral in
the rock frame (i.e., in both the sand and the clay), a
first-order approximation of porosity can be derived
from bulk density using the standard equation
qbulk (1 )qquartz qwater (1)
where is porosity; qbulk is bulk density; qquartz is the
density of quartz, which is 2650 kg/m3; and qwater is
the density of water, which is taken to be that of seawater,
or 1030 kg/m3.
The porosities obtained from equation 1 are then
used to calculate acoustic velocities at each photo
pixel, V, via the following relationship established by
Hamilton (1980):
V a a a 2 (2) 0 1 2
where the constants a0, a1, and a2 are, respectively,
1782, 833, and 522. The resulting velocities, which
range from 1400 (seawater) to 1532 m/s, are shown in
Figure 3B.
SEISMIC DATA SIMULATION
The acoustic property models developed from the
methodology described previously can be input into
seismic modeling algorithms to simulate how the rescaled
experimental strata would appear in seismic reflection
data. An important use for this type of modeling
is in constraining the information contained in
real seismic reflection data of natural sedimentary
strata. Such constraints are established by using the
models in a series of sensitivity tests.
Amplitude
Time (s)
-0.4 0 0.4
0
0.05
0.1
0.15
0.2
0.25
D
0
Reflectivity
0 1250 2500 3750 5000
Distance (m)
0.5
1.0
1.5
2.0
Time (s)
-0.0025 0.0 0.0025
C
0 1250 2500 3750 5000
0
500
1000
1500
Distance (m)
Depth (m)
1800 1850 1900 1950 2000
Bulk Density (kg/m 3 )
A
0 1250 2500 3750 5000
0
500
1000
1500
Distance (m)
Depth (m)
Velocity (m/s)
1400 1433 1466 1499 1532
B
Figure 3. Physical properties modeled from the gray levels of photographic pixels in Figure 1B: (A) bulk density; (B) compressional
or acoustic wave velocity; and (C) vertical incidence reflection coefficients. (D) Seismic wavelet or seismic source used with the physical
property models to create synthetic seismic data. Wavelet has a frequency range of 0–60 Hz and a peak frequency of 18 Hz.
134 Seismic Simulations of Experimental Strata
Several types of sensitivity tests can be conducted
using the methodology described in previous sections,
and these tests involve three variables: the set of acoustic
property models, the seismic source wavelet, and
the seismic modeling algorithm. One sensitivity test
would be to explore how changes in the acoustic properties
of strata affect seismic data. In this test, a range
of acoustic property models would be used along with
a single seismic source as input into a single seismic
modeling algorithm. A second test would be to investigate
how the seismic source affects data resolution.
In such a test, the acoustic property models and the
seismic modeling algorithm would remain unchanged,
whereas the form/frequency content of the seismic
source is varied.
The third type of sensitivity test is the one we conducted
for this article. In this test, a single set of acoustic
property models (Figure 3A–C) is used with a single
seismic source (Figure 3) as input to seismic modeling
algorithms of varying sophistication. The three algorithms
used here are (1) a convolution model, (2) an
exploding-reflector model, and (3) a full-wave equation
model. This sequence of algorithms progressively
increases the realism of the modeling of seismic-wave
propagation through the strata, which in turn increases
the realism of the resulting seismic section.
Convolutional Model
The convolutional seismic model convolves a seismic
wavelet with a time series of reflection coefficients,
which are calculated as follows. The bulk density and
velocity modeled for each photo pixel are multiplied
to give an acoustic impedance, I. The impedances for
each vertical column of pixels are then used to compute
a depth series of reflection coefficients via equation
3 (Clay and Medwin, 1977),
I(x,z dz) I(x,z)
R(x,z) (3)
I(x,z dz) I(x,z)
where R is the reflection coefficient of the strata at a
horizontal position x and a depth z. The term dz is the
change in depth corresponding to the height of one
pixel in the digital photo, so the reflection coefficients
approximate a first-order difference of the acoustic impedances.
These reflection coefficients are then converted
from the depth to the time domain using the
model velocities.
Note that the convolutional model is one dimensional.
It assumes that the seismic source is propagating
vertically downward through the strata. This, in fact,
is the ultimate imaging objective of seismic data processing.
Therefore, the convolutional simulation is theoretically
the best data that can be obtained using the
seismic source. In the lingo of seismic processing, it is
an ideal version of poststack, time-migrated, zero-offset
data.
The synthetic seismic section shown in Figure 4A
was generated using a Ricker wavelet (Sheriff and Geldart,
1995) with a dominant frequency of 18 Hz (Figure
3D), which is characteristic of frequencies used in
exploration. The wavelet was convolved with the reflectivities
shown in Figure 3C using a version of the
convolutional model developed by Courtney and Syvitski
(1996). This version can simulate the added effect
of the attenuation of seismic energy as it propagates
through the subsurface. The phenomenon, which
is called intrinsic attenuation (Aki and Richards, 1980),
is due to the dissipation of seismic-wave energy into
heat through particle motion. The rate of dissipation is
frequency dependent, with higher frequencies attenuating
more rapidly than lower frequencies. The
frequency-dependent rate is quantified by the so-called
quality, or Q, factor. In this article, the Q factor was
derived from the porosity model via empirical correlations
published by Hamilton (1980).
The result when attenuation is modeled is shown
in Figure 4B. Because high frequencies are attenuated
most rapidly, the deeper half of the synthetic seismic
section has a noticeably lower frequency content than
the nonattenuated synthetic section shown in Figure
4A. This result demonstrates the degradation of seismic
resolution with depth of penetration.
Exploding-Reflector Model
As discussed in previous sections, the convolutional
model simulates perfectly imaged seismic data in
which all seismic events are correctly positioned in
time and space. In actual data, seismic events are commonly
compromised by wave-propagation phenomena,
such as diffractions, interference patterns, and
misplaced events caused by heterogeneities in the velocity
of the strata as the seismic waves propagate
through them.
These phenomena can be simulated using the
exploding-reflector model introduced by Loewenthal
et al. (1985). This model uses a wave equation–based
methodology to simulate unmigrated zero-offset seismic
sections, that is, sections in which seismic events
have not yet been properly positioned in space and
Pratson and Gouveia 135
0
0.5
1.0
1.5
2.0
Time (s)
0 500 1000 1500 2000 2500 3000 3500 4000 4500 5000
Distance (m)
0
0.5
1.0
1.5
2.0
Time (s)
0 500 1000 1500 2000 2500 3000 3500 4000 4500 5000
Distance (m)
A
B
Figure 4. Synthetic seismic
data of Figure 1B produced by
convolutional model: (A) nonattenuated
data and (B) attenuated
data. Note that these synthetic
data are ideal versions of
poststack, time-migrated, zerooffset
seismic data.
time. In the model, every reflectivity is treated as a
seismic source, the strength of which is made proportional
to the magnitude of the reflectivity. The sources
are simultaneously detonated, generating a wavefield
that propagates upward at speeds and directions that
are governed by the velocity structure of the geologic
model.
The results generated by the exploding-reflector
model for the experimental strata are shown in Figure
5. The wavelet used in simulating the data is the same
136 Seismic Simulations of Experimental Strata
Figure 5. Synthetic seismic
data of Figure 1B produced by
exploding-reflector model.
These synthetic data, which
contain diffractions, approximate
poststack, unmigrated
seismic data.
0
0.5
1.0
1.5
2.0
Time (s)
0 500 1000 1500 2000 2500 3000 3500 4000 4500 5000
Distance (m)
as that used in the convolutional simulation (Figure
4A). An obvious difference in the exploding-reflector
simulation is that it contains a large number of diffractions
(Figure 5). These are caused by the scattering of
the acoustic wavefield where it encountered sharp
boundaries in the geologic model.
A direct comparison of the convolutional simulation
with the exploding-reflector simulation requires
that the latter first be migrated. In practice, migration
is accomplished using a velocity model constructed
from the seismic data. To do this, however, the data
must be multichannel seismic data, that is, data containing
reflections from the strata recorded at different
offsets between the seismic source and receiver. This
type of data is not simulated by the exploding-reflector
model, and a different, more sophisticated algorithm is
needed.
Full-Wave Equation Modeling
The simulation of multichannel seismic data involves
modeling the full seismic experiment. In the simulation,
a source generates a seismic wavefield that is
transmitted through the acoustic properties models.
An array of receivers then records direct waves and
reflections from this field.
The propagation of the wavefield is simulated by
numerically solving the acoustic wave equation. The
solution was obtained in this article using the algorithm
developed by Fei and Larner (1995). The inputs to the
algorithm included the density and acoustic velocity
models shown in Figure 3A and B. They also included
the seismic acquisition geometry. We modeled 201 receivers
arranged symmetrically about a single source
(i.e., a split-spread configuration). The source signature
was nearly identical with the wavelet used in the previous
modeling exercises (i.e., Figure 3D). The receivers
were spaced 5 m apart, with the middle receiver
being located at the source. Following each simulated
seismic shot, the entire source-receiver configuration
was moved laterally across the model surface a distance
of 10 m. Using this procedure, 300 synthetic shot gathers
were generated of the experimental strata, examples
of which are shown in Figure 6.
Like the exploding-reflector data (Figure 5), the
full-wave equation data (Figure 6) must be processed
Pratson and Gouveia 137
0
0.5
1.0
1.5
2.0
Time (s)
1 3 5 7
Shot Point Figure 6. Shot gathers of synthetic
seismic data of Figure 1B
produced by full-wave equation
model. These synthetic data approximate
prestack, unmigrated,
multichannel seismic data.
before they are compared to the convolutional data
(Figure 4). In this case, however, the processing entails
more than migration. This is because in addition to
spatial mispositioning of seismic events, the full-wave
equation data include several other wave-propagation
phenomena not accounted for in the other synthetic
seismic data sets, such as geometrical spreading of the
source energy, refractions, multiples, and interbed
reverberations.
As a result, the full-wave equation simulation is an
approximation of true prestack multichannel seismic
data. Because it is more realistic, it offers the opportunity
to evaluate the effectiveness of standard seismic
processing techniques.
SEISMIC DATA PROCESSING
The confidence and ease with which seismic reflection
data can be interpreted depend not only on the physical
makeup of the strata and the way the data were
acquired but also on how well the data are processed.
Limitations of seismic processing algorithms and errors
in the estimation of parameters required by these algorithms
introduce artifacts that compromise the
stratigraphic information available in the final processed
seismic section.
As noted in previous sections, the explodingreflector
and full-wave equation simulations provide
opportunities to investigate such limitations. Specifically,
a migration procedure is required for correctly
positioning seismic events in both simulations. In the
case of the full-wave equation simulation, additional
processing is required to precondition the data for
migration.
In this article, we process the synthetic seismic
data using routines from Seismic Unix (Stockwell,
1997), the public-domain seismic processing library
developed at the Colorado School of Mines (available
at
http://www.cwp.mines.edu/cwpcodes). We
first outline the preprocessing of the full-wave equation
simulation and the development of a velocity
model from these data. We then briefly discuss use of
the velocity model in migrating not only the full-wave
equation simulation but also the exploding-reflector
simulation.
Prestack Processing
Prestack processing of the shot gathers generated using
the full-wave equation model was accomplished
using a standard seismic processing sequence (Figure
7). The sequence consisted of (1) muting the data, (2)
converting the shot gathers into common midpoint
138 Seismic Simulations of Experimental Strata
Good?
Band-Pass Filtering
Automatic Gain Control
Time Migration
Velocity Analysis
CMP Stacking
Dip Moveout
Spiking Deconvolution
Prestack Seismic Data Geometry/Mute/CMP Sorting
Migrated Data
yes no
Prestack Seismic Data
Figure 7. Seismic processing flow applied to synthetic prestack
data (i.e., full-wave equation data, Figure 6) and synthetic
poststack data (i.e., exploding-reflector data [Figure 5] and processed
full-wave equation data).
gathers, (3) deconvolving the data, (4) correcting the
data for dip-dependent normal moveout, (5) conducting
velocity analysis, and (6) stacking the data.
The purpose of this type of processing flow is twofold.
First, it enhances the frequency content of the
data via deconvolution. Second, it yields an estimate of
the velocity field within the strata, which is obtained
via the velocity analysis of the dip-moveout–corrected
data. This velocity model is used to migrate the wavebased
simulations.
Poststack Processing
The migration of the poststack, wave-based simulations
could be accomplished using the original velocity
model constructed for the experimental strata (Figure
3B). This would yield little practical insight, however,
for strata velocities are never completely known when
migrating real seismic data.
Instead, we migrate both the exploding-reflector
and full-wave equation simulations using the same velocity
model derived from the prestack processing of the
full-wave equation simulation. In this way, the migrated
version of the exploding-reflector simulation (Figure
8A) provides a measure of how well the true velocity
structure of the strata (i.e., Figure 3C) was reconstructed
from the synthetic multichannel seismic data.
Correspondingly, the migrated version of the full-wave
equation simulation (Figure 8B) provides a measure of
the success of the prestack processing algorithms in removing
other wave-propagation phenomena not reproduced
by the exploding-reflector model.
The migrations are accomplished using a timemigration
algorithm (Yilmaz, 1987). The algorithm
moves mispositioned reflections in an updip direction
toward their true subsurface locations, collapsing distortions
such as diffractions. Band-passing filtering and
gain functions are then applied to the migrated data to
visually enhance coherent reflections.
Migrated sections of the processed simulations are
shown in Figure 8. In both, stratal geometries are now
seen more clearly. The amount of improvement can be
determined by directly comparing the processed simulations
to the ideal migrated section represented by
the convolutional simulation (Figure 4A).
ANALYSIS OF RESULTS
We now present a general analysis of the three synthetic
seismic data sets, that is, the convolutional simulation,
the exploding-reflector simulation, and the fullwave
equation simulation, in a comparison with the
experimental strata and with each other. The comparison,
which is qualitative, aims to portray graphically
the type of information that is lost when strata are seismically
imaged. It also offers an example of how features
that would be present in ideal seismic data
(i.e., the convolutional simulation) become obscured
by wave-propagation phenomena and by limitations
inherent to seismic processing algorithms. We begin
the comparison with an examination of the frequency
content of the data sets. We then assess their information
content from the standpoint of stratigraphic
interpretation.
Frequency Content
A fundamental difference among the synthetic seismic
data sets is the detail to which they resolve the bedding
boundaries in the experimental strata. Visual comparison
of Figures 4A, 5, and 6 shows that the convolutional
simulation provides the highest resolution image
of bedding boundaries in the experimental strata,
whereas the full-wave equation simulation provides
the lowest.
This difference in resolution is better characterized
by frequency spectra from the simulations. Figure 9
shows the normalized amplitude spectra of the middle
trace from the preprocessed and postprocessed synthetic
seismic data sets. Also shown in this figure are
Pratson and Gouveia 139
0
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1.5
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Time (s)
1500 1750 2000 2250 2500 2750 3000 3250
Distance (m)
A
0
0.5
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1.5
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1500 1750 2000 2250 2500 2750 3000 3250
Distance (m)
B
Figure 8. Time-migrated versions
of (A) exploding-reflector
data (Figure 5) and (B) fullwave
equation data (Figure 6).
the normalized amplitude spectra for the inputs used
to generate the data, that is, the seismic source (Figure
9A) and the modeled reflectivities (Figure 9B), the latter
being from the center column in the experimental
strata.
The spectrum for the seismic wavelet (i.e., the
seismic source, Figure 8B) shows that it is a welldefined,
composite cycle made up of frequencies from
0 to 60 Hz and having a peak frequency of about 18
Hz. In contrast, the spectrum of the reflectivity data
(Figure 9B) exhibits a somewhat white-noise spectrum,
indicating that the bedding boundaries in the experimental
strata are essentially random within the region
shown in Figure 1B.
140 Seismic Simulations of Experimental Strata
Figure 9. Normalized amplitude spectra showing frequency content of the (A) synthetic seismic wavelet and the central trace from
(B) the reflectivity model, (C) convolutional data, (D) unmigrated exploding-reflector data, (E) time-migrated exploding-reflector data,
(F) zero-offset, unprocessed full-wave equation data, and (G) zero-offset, processed full-wave equation data. Shaded regions in (D) and
(E) are the spectrum in (C).
The relative contributions of both these inputs to
the synthetic seismic data are clearest in the spectrum
from the convolutional simulation (Figure 9C), which
is simply the reflectivity data after they have been
band-passed filtered by the seismic source.
Similar but more irregular spectra are produced by
the unmigrated and migrated versions of the exploding-
reflector simulation (Figure 9D, E, respectively).
The slightly lower frequency content of the simulation
relative to the convolutional simulation is due to the
fact that wave-based seismic algorithms capture the
natural attenuation of some frequencies in the wavefield
that results from wave propagation (these attenuated
waves are the so-called evanescent waves [Gazdag
and Squazzero, 1984]). Note, however, that this
phenomenon does not significantly diminish the frequency
content of the exploding-reflector simulation,
which still approaches that of the convolutional simulation
(Figure 9C).
The frequency spectrum from the full-wave equation
simulation is shown in Figure 9F and G. In addition
to a lower frequency content caused by interbed
reverberations and evanescent waves, frequency
notches are present toward the lower end of the spectrum.
Such artifacts are common in marine seismic
data. They are caused by wavefield reverberations
(ghosts) between the sea surface and the source, which
is towed below the surface (Yilmaz, 1987). In the
simulation, the source was positioned 1 m below sea
level, which was taken to be the top of the digital
photo. In principle, such frequency notches can be attenuated
by more elaborate seismic processing.
Worth emphasizing is that the frequency degradation
in both the exploding-reflector and full-wave
equation simulations is only due to wave-propagation
phenomena. Frequency loss due to frictional dissipation
of seismic energy is not explicitly modeled in either
simulation. Finally, note that some of the highfrequency
content lost in the full-wave equation
simulation is partially recovered by the deconvolution
step in the seismic processing. This step leads to the
slightly broader band spectrum for the processed version
of the full-wave equation simulation when compared
to the unprocessed version (compare Figure 9G
vs. 9F).
Stratigraphic Content
Although the normalized amplitude spectra indicate
the vertical resolution inherent in the synthetic seismic
Pratson and Gouveia 141
data sets, the spectra provide no information on the
lateral resolution of the data. Of particular importance
are the clarity of onlap, downlap, and truncation of
seismic reflection horizons, as well as reflector continuity.
These patterns, which are best discerned by eye,
are used to subdivide seismic images of strata into sequences
and systems tracts. Thus, the level to which
the patterns can be visually identified and mapped determines
the detail, quality, and, ultimately, correctness
of any seismic interpretation.
The region of the experimental strata used in generating
the synthetic seismic data sets is too narrow to
be able to interpret surfaces of onlap or downlap. It
does, however, contain facies transitions between shale
(i.e., coal) and sand, as well as three growth faults (Figure
1B) that are analogous to sand-trapping growth
faults common in the Gulf of Mexico and west Africa
(Emery, 1980).
Figure 10 shows the level to which these features
are resolved in the synthetic seismic data. In the figure,
the digital image of the experimental strata is overlain
by segments of the convolutional simulation (Figure
10A), the exploding-reflector simulation (Figure 10B),
and the full-wave equation simulation (Figure 10C).
This direct comparison nicely illustrates two consequences
of seismically imaging strata. The first is obvious
and expected but worth noting. Seismic reflection
horizons do not correspond to bedding but to
bedding boundaries. As a result, the relatively thick,
nearly horizontal sand layer that stands out so clearly
in the experimental strata simply appears as two reflections
in the synthetic seismic data sets, a reflection
at the top of the layer and one at the bottom (Figure
10). Also illustrated by Figure 10 is the filtering effect
of the seismic source on the strata. This was discussed
previously in terms of the frequency content of the
synthetic seismic data, but the impact of the filtering
effect on the lateral resolution of the strata can now be
clearly seen.
As already noted, the highest resolution seismic
image is provided by the convolutional simulation
(Figure 10A). In these data, details of the strata layering
and growth faults are lost as individual beds are
lumped together into single seismic events with amplitudes
that are based on averaged bed reflectivities.
Despite the information loss, however, important patterns
for interpreting the data are still retained. For
example, truncated seismic horizons clearly define the
fault footwalls (Figure 10A), and changes in reflector
continuity from distinct to diffuse seismically delineate
the facies transitions from sand to shale (e.g., between
1750 and 2000 m at 1 and 1.25 s, respectively,
in Figure 10A).
Such patterns are not as well retained in the
exploding-reflector and full-wave equation simulations.
For example, the number of seismic horizons and
the clarity of these horizons are significantly reduced
in the time-migrated output from the explodingreflector
model (Figure 10B). Most sand-shale transitions
can still be seen, but the footwalls of the lower
two growth faults would be hard to identify without
the underlying photo of the experimental strata. Resolution
of these faults is even lower in the processed
version of the full-wave equation simulation (Figure
10C). Because of the lower resolution of this data set,
the sand-shale transitions can no longer be confidently
delineated.
DISCUSSION
The cause for the lower quality of the wavepropagation–
based seismograms is their inclusion of
such wave-propagation phenomena as diffractions,
multiples, and reverberations. In theory, the effects of
these phenomena on data quality should have been removed
by the seismic processing algorithms. In reality,
however, not all effects were removed. Although the
processing scheme employed here can be classified as
preliminary, even more extensive processing would not
achieve perfect results. This is partly because of limitations
to the degree to which certain propagation
events can be corrected for and also because errors undoubtedly
exist in the information supplied to the processing
algorithms.
One of the greatest sources of error would be the
velocity model used in migrating the explodingreflector
and full-wave equation simulations. As discussed
in previous sections, this velocity model was
not the true velocity model assigned to the experimental
strata (Figure 3B). Instead, it was constructed
from the full-wave equation simulation in the same
way that velocity models are derived from real seismic
data, that is, through velocity analysis. The velocities
in this model are averages of the correct velocities and
are prone to errors due to the velocity estimation process.
As a consequence, both resolution and accurate
positioning of seismic horizons are compromised. Velocity
inaccuracies certainly contributed to the degraded
resolution of the growth faults and facies transitions
in the wave-propagation–based seismograms
(Figure 10B, C).
142 Seismic Simulations of Experimental Strata
Figure 10. Comparison in
which sections of synthetic seismic
data (SS) are overlain onto
the digital photo (DP) of the experimental
strata (Figure 1B),
the depth dimension of which
has been converted to time using
the velocity model:
(A) normal-incidence seismogram;
(B) time-migrated,
exploding-reflector seismogram;
and (C) poststack, timemigrated,
synthetic multichannel
seismogram.
0
0.5
1.0
1.5
2.0
Time (s)
1500 1750 2000 2250 2500 2750 3000 3250
Distance (m)
0.5
1.0
1.5
2.0
Time (s)
1500 1750 2000 2250 2500 2750 3000 3250
Distance (m)
0
0.5
1.0
1.5
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Time (s)
1500 1750 2000 2250 2500 2750 3000 3250
Distance (m)
0
A
B
C
DP SS DP SS DP SS DP
Growth
Faults
Facies
Transition
The impact of such seismic artifacts on image quality
and the effectiveness of standard processing algorithms
in removing these artifacts have been studied in
great detail (Yilmaz, 1987). Now, however, synthetic
seismograms of experimental strata offer seismic interpreters
a realistic and known context in which to assess
Pratson and Gouveia 143
the effect of these artifacts on the specific features they
are trying to interpret.
Other uses for synthetic seismic modeling of experimental
strata exist as well. One example is in
teaching seismic sequence stratigraphy. Interpretations
of the synthetic seismic data can be checked against
the experimental strata, which are completely known.
Another use is in advancing understanding of the
physical significance of seismic attributes (Taner et al.,
1994). Attributes computed from the synthetic seismic
data can be thoroughly evaluated for relationships
with the physical properties assigned to the experimental
strata. A third use is in the inversion of seismic
data for direct estimates of physical properties. Synthetic
seismic data generated from the experimental
strata provide realistic scenarios for testing the new inversion
algorithms and establishing their likelihood of
success in field applications.
CONCLUSIONS
1. Experimental strata formed in the new XES basin
approximate the appearance and complexity of natural
strata and thus provide an excellent model for
generating synthetic seismograms to investigate the
stratigraphic content of seismic data.
2. Digital photos of the experimental strata can be
transformed into physical property models that
then can be used to generate synthetic seismic data
of the strata at basin scales and exploration
frequencies.
3. By generating synthetic seismic data of varying degrees
of realism, the impact of different factors that
affect seismic data quality can be isolated. These
factors include the frequency content of the seismic
source, which dictates the level to which vertical
stratal variations can be resolved; reverberations of
seismic waves, which also degrade resolution; and
lateral variations in strata velocities, which, if not
properly accounted for, may distort the imaging of
seismic horizons.
4. Like synthetic seismic modeling of computergenerated
strata and outcrops, synthetic seismic
modeling of experimental strata offers a realistic
and known context in which to understand the
seismic response of natural strata. Significant advantages
of experimental strata include its range
of analogs for structural and stratigraphic traps
and its complete documentation in three dimensions.
The latter offers a basis for eventually generating
realistic three-dimensional synthetic seismic
data.
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