# Preprocessing of seismic amplitudes
William S. Harlan
(Presented at a 1994 SEG Annual Meeting
workshop on seismic amplitude preservation.)
We cannot process seismic data without
changing seismic amplitudes, but we can
determine whether processing affects an
interpretation of amplitudes. If we adjust
amplitudes in an invertible way (e.g., as a
simple function of time, position, frequency,
wavenumber, or dip), then we have lost no
information that cannot be reconstructed.
Moreover, if we understand how a particular
wave phenomenon affects amplitudes, then we
can remove these effects from the data to
simplify the expression of more useful
information. Variations in reflectivity
versus angles of incidence (RVA) are very
informative, while transmission and
propagation effects are usually distracting.
To examine seismic amplitudes visually, we
must reduce the dynamic range. Dynamic gain
ideally removes only amplitude information
that an interpreter can take for granted,
without seeing it visually displayed. Gain
over time corrects only partly for the
geometric divergence of wavefronts. Ray
modeling of this divergence should improve
upon a constant-velocity correction; however,
absorption and incoherent scattering weaken
amplitudes over time even more, and these
effects are less easily modeled.
A constant-Q model of absorption
(Kjartansson, 1981) assumes individual
frequencies decay exponentially in time.
Integration over a finite bandwidth produces
a decay dominated by a reciprocal power of
time, with lesser exponential terms. J.
Claerbout (1985) has noted that this effect,
plus geometric divergence, explains why a
second power of time balances very well the
forty seismic profiles published by O. Yilmaz
(1988). (Multiples, surface-noise, and the
near field appear poorly balanced.) Dynamic
gain can use a single analytic function to
rescale all traces, with one or two
parameters dependent upon the data.
Trace balancing should be handled separately
from dynamic gain. We observe variations in
source strengths, receiver receptivities, and
near-surface impedances by their distortion
of reflections. Surface-consistent trace
balancing uses few degrees of freedom and yet
removes most source and near-surface effects
(ignoring radiation patterns). The
constraint is so rigid that a change in the
statistic of trace strength, such as norms or
percentiles, appears not to change results.
Marine cables also require offset-dependent
balancing, which more easily distort RVA
information. Since the correction is
stationary over time, and should be the same
for all sources, the adjustment is easily
inverted if necessary. Rapid changes in
cable receptivity over offset can be
decoupled and corrected independently of
smoother changes, just as we decouple short
and long-period static corrections.
Multi-trace processing of midpoint gathers
requires increasing attention. For example,
multiple suppression by generalized Radon
transform weakens incoherent energy at far
offsets. These linear filters suppress a
larger range of dips at the far offset than
at the near offset. Later statistical
interpretations must acknowledge that the
signal-tonoise ratio changes with offset.
Dip filters affect incoherent noise consis
tently over offset, but leave multiple energy
at the near offsets. Multidimensional
filters should use least-squares
implementations (such as f -x) that invert
only recorded, unmuted offsets. Discrete
approximations of continuous analytic
transforms (such as f -k filters) assume
unrecorded offsets to be zero or to wrap
around, and produce fatal edge effects.
As preprocessing mixes information from more
traces, we must anticipate methods of
amplitude interpretation. Many displays of
RVA at tributes accentuate anomalous
gradients with angle and de-emphasize
background trends, such as a consistent
weakening with angle. For example, fluid
factor analysis and a geogain function
(Gidlow et al., 1992) can remove background
trends in the RVA gradients of waterfilled
sands to emphasize the RVA of gassy
reflections with anomalous Vs/Vp contrasts.
Such an adjustment can depend on seismic
rather than assumed rock properties.
Preceding processes might be able to adjust
amplitudes with offset and not affect the
final displays.
Imaging inverts and removes only the effects
of wave propagation that carry no useful
interpretive information. For example, we do
not want DMO (dip moveout or prestack partial
migration) actually to convert
constant-offset sections into zero-offset
sections because RVA information must remain.
DMO is often derived as prestack acoustic
imaging in time, minus the effects of NMO and
poststack migration. Unfortunately, we
frequently refine and change our definition
of full imaging.
Within Conoco, "full imaging" often avoids
any separation of DMO from other imaging
steps. A prestack cascaded migration by R.H.
Stolt estimates reflectivities as a function
of depth and reflection angle. A prestack
depth migration by D.P. Wang includes
amplitude adjustments for variations in
aperture and velocity perturbations.
DMO still retains a useful role as
preprocessing rather than as partial imaging.
If we are working toward time displays of
RVA, we apply DMO with linear space-time
operators on constant-offset sections (mis
named "Kirchhoff"). The kinematics of DMO
remain the same. Rather than derive
amplitude obliquity factors according to Born
imaging, we choose amplitude scaling that can
easily be reversed. Very simply, this
constant-offset DMO should not affect the
amplitude of an a unaliased monochromatic
plane wave. The dip of the monochromatic
plane wave changes, but not the amplitude.
(Constant-velocity DMO is easy to adjust, but
not DMO with depth-variable velocities or
anisotropy.) Later programs can readjust
amplitudes as a function of dip and frequency
if necessary, or perform truer imaging. An
implementation with antialiasing (Hale, 1991)
may weaken high frequencies at high dips but
should preserve unaliased frequencies at
consistent strength.
Transmission effects that are not
surface-consistent, such as defocusing by
velocity anomalies, can greatly obscure RVA
displays. A separate expanded abstract
(Harlan, 1994) explains how to model and
remove transmission perturbations of
amplitudes.
Some RVA displays require partial stacking
with variable folds of stack. If later
processes are unaware of the fold of stack,
then renormalization is crucial. The power
ratio of coherent signal to incoherent noise
ideally increases as the square root of stack
fold. If we normalize for ideal signal, then
less coherent energy will be weakened as the
fold increases. Such statistical assumptions
must be consciously made, and changed when
appropriate.
The customers of a seismic processing shop
naturally prefer reproducible processing
sequences that allow consistent comparisons
between many seismic sections. Such
sequences often rely upon statistical am
plitude balancing programs that highlight
anomalous changes in amplitude with offset
and de-emphasize consistent background
changes in amplitude with angle. For
example, amplitudes may be scaled locally ac
cording to some statistic of neighboring
samples. The original changes in amplitudes
over offset are not recoverable. Statistical
balancing often provides the best default
correction of unusual amplitude distortions
but also hides problems which reduce
confidence in the results.
We learn more by adjusting amplitudes with
one restrictive physical model at a time.
Model parameters derived from the data should
be diagnostic of the seriousness of each
physical effect. Restrictive models minimize
the accidental misinterpretation and removal
of useful amplitude information.
Just as important, but ignored by this
discussion, is phase preservation. Amplitude
cannot be considered independently of phase
and other spectral properties. Similar
principles should apply: use restrictive
models, allow invertible adjustments, and
document the behavior.
* REFERENCES *
Claerbout, J. F., 1985, Imaging the Earth's interior: Blackwell Scien-
tific Publications.
Gidlow, P., Smith, G., and Vail, P., 1992, Hydrocarbon detection using
fluid factor traces: a case history: Joint SEG/EAEG summer re-
search workshop, How Useful is Amplitude-Versus-Offset Analysis?,
Technical Program and Abstracts, 78-89.
Hale, D., 1991, A nonaliased integral method for dip moveout: Geo-
physics, 56, no. 6, 795-805.
Harlan, W. S., 1994, Tomographic correction of transmission distortions
in reflected seismic amplitudes: 64th Annual Internat. Mtg., Soc.
Expl. Geophys., Expanded Abstracts, SI2.2.
Kjartansson, E., 1981, Constant Q - wave propagation and attenuation
in Toksoz, M. N., and Johnston, D. H., Eds., Seismic wave attenua-
tion:: Soc. Expl. Geophys., 448-459.
Yilmaz, O., 1988, Seismic data processing: Soc. Expl. Geophys., Tulsa.