NAME
opstr - create inverse optical stack from the Tp scan data
and the original input X-T data
SYNOPSIS
opstr [ -Nntap ] [ -N2ntap2 ] [ -Ootap ] [ -mfmutefile ] [
-rsnrst ] [ -renred ] [ -v1v1 ] [ -t1t1 ] [ -v2v2 ] [ -t2t2
] [ -v3v3 ] [ -t3t3 ] [ -v4v4 ] [ -t4t4 ] [ -rho ] [ -fl ] [
-fh ] [ -? ]
DESCRIPTION
opstr (OPtical STack Reverse) creates optical stack inverse
transform from the Tp scans of opstf and the original input
data using the optical stacking process described by E. de
Bazalaire in the February, 1988 issue of Geophysics. This
program is one of six programs in a suite of programs for
creating, processing, and/or analyzing optical stack
results. The other programs in the suite, and their func-
tions, are:
opstf - create forward Tp scans and semblance panels
opstk - Extracts the stack and the velocity field from the
optical stack panels.
opstd - Demultiplexes the OPSTF output to create separate
optical stack and semblance panels for analysis.
opstcv - Resamples semblance panels created by program OPSTF
from constant Tp traces to constant (stacking) velocity
traces for analysis.
XOS - Provides graphical analysis of optical stack or
semblance panels created by OPSTF.
Command line arguments
-N ntap
Enter the input data set name or file immediately after
typing -N unless the input is from a pipe in which case
the -N entry must be omitted. The input to the Optical
Stack procedure opstr is the output from opstf
(currently requires SIS/USP format) and the original
data input to opstf.
-N2 ntap2
Enter the name of the original input data. You cannot
pipe into this except from inside IKP where the connec-
tor on this process box is "3". The program will run
if this input is not provided, but the inverse
transform will be far from optimal.
-O otap
Enter the output data set name or file immediately
after typing -O. This output file is not required when
piping the output to another process. The output data
set also requires the full path name (see above). The
output from program OPSTR will be in X-T space like the
original data.
-mf mutefile
Enter the name of the file containing the mute func-
tions (in xsd pick file format). If no muting accord-
ing to picked functions is desired leave this off the
command line. An optional velocity mute is provided
for below. Default: None.
-v1 -t1 -v2 -t2 [-v3 -t3 -v4 -t4] v1 t1 v2 t2 [v3 t3 v4 t4]
These four entries define a trapezoidal mute zone for
the tp scan records. Each mute corner is defined by a
velocity and a time. If only the first two corners are
defined the mute zone is extended to the bottom of the
record.
-rs nrst
Enter start record number. Default value is the first
record.
-re nred
Enter end record number. Default value is last record.
-rho Enter the "-rho" parameter to apply a linear ramp in
the frequency domain. This sometimes is helpful in
reducing noise in the transform. Default: No.
-fl Enter the minimum frequency at which the rho filter
will be applied. Use of this parameter helps to reduce
low-frequency noise in the transform. This parameter
is ignored if the "-rho" parameter is not entered.
Default: DC.
-fh Enter the maximum frequency at which the rho filter
will be applied. Use of this parameter helps to reduce
high-frequency noise in the transform. This parameter
is ignored if the "-rho" parameter is not entered.
Default: Nyquist.
-? Enter the command line argument '-?' to get online
help. The program terminates after the help screen is
printed.
DISCUSSION
The optical stack procedure of de Bazelaire (1988) is a
fast and efficient method for automatically extracting
stacked data and stacking velocities from CDP-sorted seismic
data. The stacked data and velocity information are
extracted from panels containing sums (stacks) of the CDP
data which, when viewed graphically, are not dissimilar to
the spectra computed for conventional velocity analysis. In
either the conventional case or the optical stack case, the
CDP data are summed along various hyperbolas. The optical
stack technique differs from the conventional velocity
analysis technique both in the definition of and application
of corrections for normal moveout. It is these differences
which allow the method to be faster and more efficient than
the conventional technique.
The optical stack technique is based upon a reformulation of
the normal moveout equation in terms of geometrical optics,
from which the name optical stack is derived. In this for-
mulation, the conventional (Dix) equation
T**2 = T0**2 + (X/V)**2 (1)
(where T is the two-way travel time for offset X, T0 is
the zero- offset time, and V is the velocity at time T0, and
the notation **2 means square) is rewritten as (the optical
stack equation)
(T + Tr )**2 = Tp**2 + (X/V0)**2 (2)
where Tr is a delay time of the apex of the hyperbola rela-
tive to T0 (i.e, the time difference between the "true" sub-
surface reflection point and its image in the constant velo-
city medium), Tp is the total zero-offset time, (T0 + Tr),
V0 is the velocity of the input or recording/observing
medium, and the notation "**2" means squared. Fermat's
Principle from geometrical optics theory is invoked to
stipulate that ray paths described by these equations are
equivalent, as long as stigmatism (focusing) exists.
Since the ray paths described by the equations (1) and (2)
above are equivalent, the normal moveout hyperbola for the
two points must be the same. By equating the derivatives of
the Dix equation and the optical stack equation at any
zero-offset time T0, the relation between V, the Dix stack-
ing (RMS) velocity, and V0, the initial velocity, is found
to be approximately
V = V0 * sqrt(Tp/T0), (3)
where sqrt signifies square root. This approximation breaks
down for small T0, but since there is typically little (spa-
tial) sampling of the data where the equation breaks down,
the approximation is generally valid.
Operations
NMO correction and Tp scan panel creation.
Both the Dix (Equation 1) and optical stack (Equation 2)
equations describe a family of hyperbolas. In the case of
Dix's equation, the hyperbolas vary as a function of both V
and T0. In the case of the optical stack equation, the
hyperbolas vary as a function of Tp only, since the velocity
V0 is constant. To correct for hyperbolic moveout using
Dix's equation, compute-intensive time-variant interpolation
techniques must be employed. To correct for hyperbolic
moveout using the optical stack equation, only a static
shift of the trace is required. To see that this is true,
we make the substitution
Tr = Tp - T0
in Equation 2 to find
(T - T0 + Tp)**2 = Tp**2 + (X/V0)**2.
Since T - T0 is just the moveout, dT, it is easy to see that
for each X the movout is constant (a static shift), given by
dT = sqrt(Tp**2 + (X/V0)**2) - Tp.
To create a Tp scan trace, all traces in the CDP are shifted
according to the above equation and stacked. A panel of Tp
scan traces is formed by repeating this shifting and summing
procedure for the number of Tp's you define. The full set
of Tp panels is created by repeating this entire procedure
for all CDP gathers input.
Moveout correction by static shift is not as computationally
intensive as time-variant interpolation, so is faster to
apply. It also does not result in stretching of the far
offset traces, since all samples on a trace are shifted by
the same amount. Additionally, with the optical stack
equation it is a simple matter to correct for inverted
(upward curvature) hyperbolas, which can occur for large
velocity contrasts at a concave (synclinal) interface.
Note that for such an hyperbola, Tr becomes negative.
The inverse is obtained by running the above equations back-
wards.
REFERENCES
de Bazelarie, E., 1988, Normal moveout revisited: Inhomo-
geneous media and curved interfaces, Geophysics, Vol. 53,
143-157.
Arnold, Richard H. and Semaan, Mars E., 1990, Implementation
of the Optical Stack Method, SEG Expanded Abstracts, Vol II,
San Francisco.
BUGS
unknown
SEE ALSO
opstf, opstk, opstd, opstcv
AUTHOR
Richard Crider, ES&S
COPYRIGHT
copyright 2001, Amoco Production Company
All Rights Reserved
an affiliate of BP America Inc.
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