seismic amplitudes correction
DESCRIPTION
Seismic Amplitudes CorrectionTRANSCRIPT
Amplitude Correction
Seismic amplitude correction has an unachievable, idealized
goal. The correction strives to provide a seismic section in
which the seismic amplitudes accurately portray the values
of the reflection coefficients. Under a more modest goal, but
still rarely achieved goal, the displayed amplitudes are
locally proportional to the reflection coefficients’ values.
The first section reveals why these are difficult goals and the
later sections show examples of amplitude correction
algorithms.
What causes the seismic amplitude problem?
The real world is a messy place. A multitude of phenomena
determines the recorded seismic amplitudes. Figure 1
summarizes many of the phenomena that determine the
recorded amplitudes. The following paragraphs review these
illustrated phenomena.
Figure 1: Factors that alter amplitudes. After (Sheriff,
1975)
Geometric Dilution Through the application of the conservation of total flux
(energy), the further the observation point is from the source,
the weaker the appearance of the source. The more distant
you are from a light bulb, the dimmer it appears. In a
constant-velocity world, the amplitude decreases linearly
with distance as the power decreases with the square of the
distance.
In the world of velocity gradients and directional sources,
the actual geometric fall-off depends upon the velocity
gradient.
Absorption There are different hypotheses for the origin of the
absorption of sound waves in the Earth. Prominent
hypotheses include the role of the movement of fluids in the
pores, the friction of microfractures and scattering. It is
difficult to confirm the relative influence of different
mechanisms because laboratory measurements operate at a
case, “close” means separated by a distance equal to the
characteristic wavelength of the wavefront. A later chapter
explaining the role of wavelets elaborates this point.
AVO The change of the reflection coefficient with offset depends
upon a ratio of six elastic parameters at each interface. (The
elastic parameters are P-wave velocity, S-wave velocity, and
density.) Each interface has a unique amplitude variation
with offset (AVO) as determined by these ratios. The
situation becomes even more complex if the seismic speed
becomes dependent on the angle of propagation (“seismic
anisotropy”) or if the medium is attenuative.
Changes in source strength and coupling
Surface sources, such a vibroseis, have different coupling
characteristics on hard versus compliant material. (With the
vibroseis source, an oscillatory mass is the energy source.)
In the marine case, there may be air-gun “drop out” because
of mechanical problems. Thus, not all air guns in the array
are necessarily in service at all times.
Changes in receiver coupling The geophone’s coupling to the ground depends on the
nature of that ground. With some near-surface conditions,
there may be difficulties in properly placing the geophones.
The receiver coupling can vary significantly within a seismic
recording line. The coupling of a single receiver can change
while the survey is acquired due to wind, rain or temperature
changes.
Source and receiver arrays Even in the ideal case, the source and receiver arrays create
amplitude directivity. This amplitude directivity is termed
the radiation pattern. (This is similar to a television
antenna’s directional sensitivity. A Rabbit-ear antenna, for
example, is often re-oriented in order to strengthen the
received signal.)
What is the appearance of raw shot profiles?
The net effect of the above-listed phenomena creates
recoding time-dependent amplitude decays. The following
figure shows a series of raw shot profiles.
Figure 2: Raw shot profiles. (Yilmaz, Seismic Data
Processing, 1987) p. 44, Figure 1-36. With author’s
permission.)
Yilmaz reference:
(1987) Page 44,
Figure 1-36
Similar to:
(2001) Page 96,
Figure 1.5-3
Raw shot gathers show
amplitude decay.
What are the realistic goals of amplitude correction?
Many migration algorithms assume the input trace
amplitudes are in direct proportion to the reflection
coefficients. Other, amplitude-correcting migration
algorithms assume the trace amplitudes originated from a
transparent Earth, one with only geometric amplitude
effects. In either case, the recorded trace amplitudes violate
either of these assumptions. With the multitude of
phenomena that alter amplitudes, it might be tempting to
give up and do nothing. Geophysicists try to at least partially
correct seismic wave energy loss with application of an
amplitude correction algorithm.
With the above-listed, amplitude-altering phenomena, we do
not know enough about the specific details of these
processes to apply a full inversion, directly solving for the
values of the reflection coefficients. In other words, the task
of inverting each of these phenomena is overwhelming. In
the face of this daunting task, we have goals that are more
modest:
1. Keep the data visible.
2. At the completion of all processing, trace
amplitudes are “representative” of the relative
strengths of the reflection coefficients in
comparison to other nearby amplitudes.
Evidence that we have not met these goals:
1. There are amplitude streaks.
2. There are dim or bright regions.
3. Amplitudes do not tie between different surveys.
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Figure 3 shows seismic data before the application of a
poststack amplitude correction. Figure 4 shows the same
seismic data after the application of a poststack amplitude
correction. This example illustrates the advantages of
keeping the data visible.
Figure 3: Seismic data before the application of a poststack
amplitude correction. (Processed by Hill from data
provided by Parallel Geoscience.)
Figure 4: Seismic data after the application of a poststack
amplitude correction. (Processed by Hill from data
provided by Parallel Geoscience.)
Yilmaz reference:
(1987) Page 51 & 55,
Figure 1-48 & 53
Similar to:
(2001) Page 115 & 116,
Figure 1.5-22 & -23
These figures show
the stacked section
before and after
application of gain
function shows
importance of
keeping data visible.
What are amplitude-correction solutions?
Amplitude-correction solutions can be divided into
deterministic and statistical categories. The deterministic
processes use the understanding of a dominant amplitude-
decay mechanism to invert the amplitudes. The statistical
approach depends upon the statistics in the traces
themselves.
In fact, the division between “deterministic” and “statistical”
is not quite so clean-cut because deterministic methods also
typically use the data to determine an essential theoretical
parameter.
The following provides both deterministic and statistical
amplitude-correction examples.
Deterministic The deterministic amplitude-decay compensation procedure
selects an algorithm and its parameters that best mimics the
decay of seismic amplitudes.
Spherical divergence Spherical divergence correction is a very common
deterministic amplitude process. For the constant-velocity
Earth, the spherical divergence decay is:
(1)
This relationship follows from the inverse-square law for
energy.
In the presence of a vertical velocity gradient, the curved-ray
effects further attenuate the amplitude according to the
following formula.
. (2)
Figure 5 cartoons the reason for the stronger decrease in
amplitude with distance. The total flux of energy between
the two ray-traced curves is constant. In the presence of a
velocity gradient, the separation between the two curved
rays increases at a faster rate than in the constant-velocity,
straight-ray case. Thus, for this 2D case, the decay of the
energy (and, associated amplitude) with distance is more
severe in the case with the vertical velocity gradient.
Figure 5: Geometric spreading decay.
While these formulas are theoretically satisfying, they may
do an inadequate job of matching the decay of real field data
because of the presence of additional decay phenomena. For
this situation, a statistical correction often follows the
application of these deterministic corrections.
Figure 6 and Figure 7 show a shot profile before and after
the application of spherical divergence correction. (Data
before the application of an amplitude correction is often
termed “raw” data.) Because this shot profile contains only
1.1 s of data, the differences in the two figures is modest.
Tim
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s)
X
Tim
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X
ConstantVelocity
IncreasingVelocity
Figure 6: “Raw” shot profile. (Processed by Hill from data
provided by Parallel Geoscience.)
Figure 7: Shot profile after application of spherical
divergence correction. (Processed by Hill from data
provided by Parallel Geoscience.)
The next figure (Figure 8) is another example of shot
profiles before and after spherical divergence correction. In
this case, the comparison is significantly more dramatic.
Figure 8: Shot profile before (left) and after (right)
spherical divergence correction. (Yilmaz, Seismic Data
Analysis, 2001) Page 212, Figure 2.4-36. By author’s
permission.)
Yilmaz references:
(2001) Page 212,
Figure 2.4-36
Raw shot before and after
spherical-divergence
correction.
(1987) Page 44,
Figure 1-36 & 37
Similar to:
(2001) Page 82,
Figure 1.4-1, -2
Raw shot before and after
spherical-divergence
correction.
(1987) Page 58,
Figures 1-58 & 59
(2001) Page 84,
Figure 1.4-4, -.5
Shot profiles before and
after spherical-divergence
correction illustrates the gain
application enhanced the
visibility of the ambient
noise.
Attributes of deterministic gain functions The following are attributes of deterministic gain functions.
Data
independence.
Other than the specification of a
constant proportionality factor
through inspection of the
amplitudes in the data, the
deterministic gain processes are
ignorant of the actual amplitudes
in the data.
Tim
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AfterBefore
xOffsetxOffset
t t
Amplitude
contrast
preserving.
The processes preserve the
amplitude contrasts between
nearby amplitudes.
Noise
susceptibility.
If the noise is stronger than the
signal, the deterministic gain
functions preserve the noise.
Reversibility. Because we define the
deterministic gain functions by a
very small number of parameters,
we can save those parameters and
apply an inverse to the gain at a
subsequent stage in processing.
Follow-up
gain.
Because a deterministic gain
algorithm may fail to meet its goal,
a statistical gain process may
follow.
Smooth. The time dependence of
deterministic gain functions is very
smooth; it does not have
discontinuities.
Streaks. A very straightforward application
of a deterministic gain algorithm,
with an identical gain function
applied to all traces, can result in a
vertically streaked seismic section.
The streaks arise through
systematic, location-dependent
variations in the input trace
amplitudes.
Statistical Observing that there is not a single, dominant amplitude-
determining phenomenon leads to the adoption of statistical
amplitude-correction algorithms. The statistical algorithms
use a simple statistical measure, such as an average, to
determine the gain function. Figure 9 idealizes the statistical
approach with the observed time dependence of the
amplitude decay specifying the gain function.
Figure 9: A statistically designed gain function attempts to
compensate for amplitude loss observed along a trace.
Trace-by-trace statistical gain algorithms As the name implies, “trace-by-trace” statistical gain
algorithms determine trace-dependent gain functions for
each trace from its observed amplitudes. The algorithms then
apply the respective gain functions to each individual trace.
Windowed AGC
An example of a trace-by-trace gain function is the
commonly used, windowed AGC (Automatic Gain Control)
process.
Using Figure 10 as a guide, the following are the steps for a
particular implementation of a windowed AGC operation.
1. Window the trace. User specifies a time
interval, the calculation
“window.”
2. Determine window
“power.”
Calculate the sum of the
absolute values of the
amplitudes in each time
window. Some
practitioners term the sum
of the absolute value of
the trace amplitudes as
the trace’s “power.”
3. Reciprocal of
power.
For each window interval,
calculate the reciprocal of
the calculated power.
4. Interpolate
power’s reciprocal
as expansion
function.
Linearly interpolate the
reciprocal of the
summation of the
absolute value of the trace
amplitudes. This
interpolated value is the
expansion function.
5. Apply gain
function.
For each time sample,
multiply the trace
amplitude by the
expansion function,
creating the gained trace.
Figure 10: Windowed AGC operation.
Figure 11 shows a shot profile after the application of a
trace-by-trace, windowed gain function. Figure 6 shows the
same data set before the application of a gain function and
Figure 7 shows the same input data, but after the application
of a deterministic gain function. Using a short window in the
statistical gain algorithm, the amplitudes are more
homogeneous than in these previous two figures.
Observed
Amplitude
Gain
Function
Data
determines
gain function
t t
Original
Trace
Expansion
Table
Expansion
Function
Gained
Trace
iAmpl
1
t
Figure 11: Shot profile after the application of a windowed
gain function. (Processed by Hill from data provided by
Parallel Geoscience.)
Yilmaz reference:
(2001) Page 87
Figure 1.4-8
Illustrates a time-dependent gain
function applied to one trace.
Notice that the time windows in
the middle display does not
exactly correspond to the upper
and lower illustration. This is
probably an illustration error.
Attributes of windowed AGC:
Not reversible. In practice, the algorithm
discards the applied gain
function immediately after its
application to the data.
Therefore, it is not possible to
remove that gain function at a
later stage in processing. This
is unlike the application of a
velocity-dependent, spherical
divergence correction. It is
possible to remove the
spherical divergence
correction in later processing
because we typically save the
velocity functions through the
entire processing. We could
later remove the applied
windowed AGC if the
algorithm saved its large,
applied-gain file.
Shadow zone. Because the algorithm uses
some window-based statistic,
such as the average of the
absolute value of the
amplitudes, very large
amplitude values may
dominate the determination of
the gain function over a
distance of the size of the
user-specified window. The
presence of these large
amplitudes creates small
values in the gain function
over the length of the window.
The gain function’s small
values diminishes the
amplitudes of adjacent small
values. (SeeFigure 12:
Shadow zone. Figure 12)
Regularizes
amplitudes.
The application of a statistical
gain correction causes the
value of its statistic, such as
the sum of the absolute value
of the amplitudes, to be
approximately the same in all
windows for all traces.
Because of this, all traces in
CMP have equal contributions
in the creation of the stacked
trace, providing maximum
signal-to-noise improvement.
Window length. The smaller the window
length, the greater will be the
degree of trace equalization
homogenization. The larger
the window, the lesser will be
the vote by any one amplitude.
Misleading
around salt.
Typically, there will be large
contrast in trace amplitudes at
the edges of salt, for example.
The salt interface itself will
have high amplitudes and the
region within the salt will
have very low amplitudes.
Through a modification of the
shadow zone effect, these low
amplitudes may dominate in
the determination of the
expansion function, causing
large values of the expansion
function if the majority of the
window is within the salt and
only a small portion outside of
the salt. Figure 13 cartoons
this situation for traces
adjacent to a salt dome. In this
model, the horizontal
reflection coefficients outside
of the salt do not vary
laterally, but after the
application of a windowed
gain, these amplitudes
adjacent to the salt are now
misleadingly larger.
Typically, there will be large
contrast in trace amplitudes at
the edges of salt, for example.
The salt interface itself will
have high amplitudes and the
region within the salt will
have very low amplitudes.
Through a modification of the
shadow zone effect, these low
amplitudes may dominate in
the determination of the
expansion function, causing
large values of the expansion
function if the majority of the
window is within the salt and
only a small portion outside of
the salt. Figure 13 cartoons
this situation for traces
adjacent to a salt dome. In this
model, the horizontal
reflection coefficients outside
of the salt do not vary
laterally, but after the
application of a windowed
gain, these amplitudes
adjacent to the salt are now
misleadingly larger. Similarly,
first arrival amplitudes are
amplifies and arrivals
Tim
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immediately behind first
arrivals are diminished.
Figure 12: Shadow zone. Amplitudes in the vicinity of salt
reflections get boosted.
Figure 13: Amplitude gain adjacent to salt.
The windowed AGC method has many different variations.
For example, the windowed amplitude statistic may be the
sum of the squares of the trace amplitudes or the windowing
function may be tapered.
Yilmaz reference:
(1987) Page 60,
Figure 1-63
Similar to:
(2001) Page 89,
Figure 1.4-11
As we decrease the size of
the window for the gain
function, the degree of
amplitude homogenization
is increased.
Figure 14: Deterministic gain correction. (Displayed by Jim
Reusser, Conoco. Shown by permission of ConocoPhillips.)
shows stacked land seismic data whose processing includes
the application of a deterministic gain correction. The
vertical oval surrounds one of many vertical amplitude
streaks. This is marine data whose onboard log noted
sporadic source problems. The vertical amplitude streaks are
most likely due to malfunctioning air guns in the source
array. As strictly applied, this deterministic amplitude
correction does not correct for the effects of source air gun
malfunctions.
Figure 15 shows the same data after the application of the
windowed AGC gain correction, among other processing
changes. In the quest to improve the data, the processing
geophysicist implemented many variations from the prior
processing represented by Figure 14. Notice the improved
top-to-bottom amplitude visibility and the reduced amount
of vertical amplitude streakiness at numerous lateral
locations. In spite of the increased vertical streaking, it may
very well be that Figure 14 provides the more accurate
representation of the differences in the average value of the
reflection coefficients between the upper and lower halves of
the displayed data. With the improved visibility in the lower
half of Figure 15, it is apparent that the character of the data
in the lower half is quite different from that of the upper
half.
Figure 14: Deterministic gain correction. (Displayed by
Jim Reusser, Conoco. Shown by permission of
ConocoPhillips.)
Figure 15: Windowed AGC gain correction. (Processed by
Jim Reusser, Conoco. Shown by permission of
ConocoPhillips.)
The following series of four figures compare the results of
the application of deterministic versus statistical gain
corrections for land and marine data. In these cases, the
data’s amplitudes clearly did not satisfy the assumptions of
the applied deterministic gain correction.
In the first land data example (Figure 16), there might have
been lateral variability of the source coupling or receiver
coupling. For a more optimal deterministic amplitude
correction process, it would be necessary to address those
variations in addition to the spherical divergence corrections.
Time
Am
plit
ude
Original amplitudes
Windowed gain function
Gained amplitudes
x
t
x
t
Figure 16: Land data after application of deterministic
gain correction. (Processed by Conoco. Shown by
permission of ConocoPhillips.)
Figure 17: Land data after application of statistical gain
correction. (Processed by Conoco. Shown by permission of
ConocoPhillips.)
In the following marine case, there might have been a gun
dropout problem. Thus, the source strength varied from shot
to shot. This variation produced the amplitude steaks visible
in Figure 18. A more successful deterministic approach
would have included a correction for the gun strength
variations in addition to the spherical divergence correction.
Figure 18: Marine data after application of deterministic
gain correction. (Processed by Conoco. Shown by
permission of ConocoPhillips.)
Figure 19: Marine data after application of statistical gain
correction. (Processed by Conoco. Shown by permission of
ConocoPhillips.)
Other processes A large number of seismic processing algorithms alter the
time-dependent gain of a trace. Because some of these
processes alter the amplitudes in a deleterious fashion, it
may be appropriate to follow that process with an
application of a statistical gain process. The following is an
itemization of various processes and the advisability of the
use of a following gain process.
X
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x
t
x
t
Process Alters
gain?
Comments
Acquisition Yes As indicated in Figure 1, all
aspects of acquisition
determine the gain of the
recorded trace.
De-spiking Removal of noise spikes.
Deconvolution Yes Because decay is a function
of frequency, re-balancing
the amplitude spectrum
alters the overall time-
dependent amplitude decay.
A following chapter
explains deconvolution.
Frequency
Filtering
Yes Because amplitude decay is
a function of frequency,
altering the amplitude
spectrum through frequency
filtering alters the overall
time-dependent amplitude
decay. A later chapter
explains frequency filtering.
NMO
Correction
No Alters the times of events on
traces. It effect on the trace
amplitude times is most
dramatic for shallow, far
offset traces. Even as such,
we customarily neglect this
effect on amplitudes.
Statics
Solutions
No In general, trace shifts
applied by statics solutions
are not large. However,
stacked trace amplitudes can
increase with the application
of a proper statics solution.
De-multiple Yes Considering the average
multiple and primary
amplitude over a time
window, such an average
amplitude of multiples has a
slower decay rate than
primaries. This occurs
because the number of
multiples in a time window
increases with time in
comparison to the number
of primaries. With
increasing time, the total
number of independent,
multiples paths increases. In
the general case, the time-
dependent decay of a
window-based amplitude
measure (such as the
average of the absolute
value of the amplitude)
shows slower decay for
multiples than primaries.
After demultiple, we may
wish to gain the remaining
primaries to improve their
visibility or to take out the
effect of geometry (1/r)
amplitude decay.
Stack Yes Because stack improves the
signal-to-noise ratio and
because the signal-to-noise
ratio is time dependent,
stack alters the time
dependent gain. In addition,
necessary trace muting
alters the time-dependent
fold-of-stack and with that,
the time-dependent
amplitudes.
Coherency Yes Post-stack coherency
improvement alters the
signal-to-noise ratio and the
frequency content. Through
that, coherency algorithms
alter the apparent amplitude
decay.
Migration Yes By collapsing diffractions
and moving steep dips to a
shallower portion of the
seismic section, migration
alters the amplitude decay.
Yilmaz reference:
(1987) Page 40,
Figure 1-33,
Record 40
(2001) Page 80,
Figure 1.3-40
Example of noise spikes from
recording system.
Well calibration The availability of well information provides an opportunity
to estimate an appropriate gain function under the criterion
of matching the seismic amplitudes to a synthetic trace
created from the density and velocity logs. This method is
distinctly different from the previous, deterministic methods
because it does not require a theoretical hypothesis of the
origin of the amplitude decay. Instead it uses ground truth to
furnish the criterion for the creation of a gain function that
would tie the synthetic’s amplitude with that of a coincident
trace. This gain function may then be applied to all traces,
under the assumption that the amplitude attenuation is not a
function of lateral position.
Lateral homogeneity is not the only limiting assumption of
the well calibration approach. Density and velocity logs are
measured at frequencies that are much higher than that of
seismic waves recorded at the surface. The log data requires
careful upscaling and blocking to emulate the subsurface
properties sensed by propagating seismic waves.
Display of amplitudes A wiggle-trace display can reveal a dynamic range of up to
20 to 1. The values of the reflection coefficients in the
ground have a much greater variation. This explains the
popularity of color displays that are not limited by a
representation of a lateral trace excursion. However, the
storage requirements on interpretation workstations demand
that we reduce the dynamic range of the amplitudes before
display. The high amplitudes may be clipped and the low
amplitudes may become invisible.
To make informed decisions about trace amplitudes, it is
vital to have a standard of comparison. For this reason, some
prefer the use of the calibrated color bar along with the
expansion. A robust statistic, such as the median of the
amplitudes, may be the basis of the expansion and the
calibrated color bar. With the application of these tools, the
color display may portray the amplitude in terms of the
median of the absolute value of the amplitude for the entire
survey.
Interpreters’ role Raw seismic data are often un-interpretable and flat-out
ugly. Seismic records require processing to be displayed for
meaningful analysis. Here are some issues that the
interpreter should keep in mind:
Be aware of what the processed amplitudes
represent. Are these amplitudes processed with the
goal of being most visually pleasing? Are the
amplitudes balanced to bring out weak (but
important) reflection events or are the amplitudes a
representation of the subsurface reflectivity?
True amplitude processing aims at preserving the
reflection coefficient in the data. Is your data “true
amplitude”? If not, are the seismic processing steps
deterministic and reversible? Does your
interpretation depend upon the successful retrieval
of the true amplitudes through processing?
What were possible amplitude related problems of
the raw data? What processing-tools were
employed to fix these issues?
Be aware of the amplitude correction’s
assumptions. Does your data meet these amplitude
correction’s assumptions?
Does the shallower section introduce
uncompensated amplitude problems? The presence
of salt or gas serves as a couple of examples.
Be caution in interpreting amplitudes close to
strong reflection events such as water bottom or salt
bodies. High amplitude reflections often dominate
statistical amplitude-gaining algorithms and may
cause side effects.
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