NAME
avaws - module to compute AVO attributes by weighted stack-
ing of NMO-corrected CDP data
SYNOPSIS
avaws [ -Nntap ] [ -Ootap ] [ -vRMS Velocity File ] [
-SShear Velocity File ] [ -rs ] [ -re ] [ -as ] [ -ae ] [
-md ] [ -? ] [ -H ]
DESCRIPTION
avaws computes various AVA (Amplitude Versus Angle) attri-
butes from CDP-sorted, NMO-correct seismic data (see table
below for list of attributes). All of these attributes are
derived as weighted stacks of the CDP data. The weights for
each attribute are derived from a least squares solutions of
a modified form of the linearized approximation of the
Knott-Zoeppritz equations (the "Bortfeld" equation) given by
Aki and Richards (1980), Thomsen (1982), and Thomsen and
Hanson (1985). This equation by assuming that density
varies with Vp according to Gardner's equation (rho =
K*Vp^c, where "^" denotes exponentiation) (Thomsen and Han-
son, 1985).
To compute the weights to be used to create the weighted
stacks, a incident angles are first computed as a function
of time and input velocity functions, one incident angle for
each time sample for each trace in the CDP, using the ray
tracing procedure used in programs AVOIR and ANGST. RMS
velocity input is assumed, but stacking velocities are gen-
erally used. Once the incident angles are known for each
time sample, the seismic data values are combined with the
incident angle information to form the AVA attributes listed
below.
The Vp/Vs ratio is an integral part of the computation of
the stacking weights. Program avaws requires the input of
shear (interval) velocity data. The source of the data is
up to the user, and the data would typically come from
logs. However, since availability of shear logs is more the
exception than the rule, the shear velocities may be derived
by converting the rms (Vp) velocity file to interval and
applying a scalar (such as a constant 0.5 for a constant
Vp/Vs ratio of 2.0). If the file contains multiple records,
however, the number of records MUST be the same as the
number of input CDPs.
All of the attributes listed below are computed and output
by program avaws. The desired attributes can be selected
from the output for further processing and/or display. The
order of the traces is (using "D" to denoted "delta" or
change in):
1. Intercept (B0)
2. Slope (B1)
3. DVp/Vp (change in Vp divided by average Vp)
4. DVs/Vs (change in Vs divided by average Vs)
sity) *
5. DRho/Rho (change in density divided by average den-
5. B1*sign(B0)
6. B1/B0
7. D(Vp/Vs)/(Vp/Vs) **
* The change in density is computed as (2*B0' -
DVp/Vp) and
B0' is the B0 computed from
R=B0+B1*tan^2*theta)+B2*tan^2(theta)*sin^2(theta)
** The change in Vp/Vs is computed as (DVp/Vp - DVs/Vs)
The two-component equation used for DVp/Vp and DVs/Vs compu-
tation is
R= A*DVp/Vp + B*DVs/Vs
with A= 0.5*[1.0+tan^2(theta)+ c - 4*c*K*sin^2(theta)] and
B= -4.0*K*sin^2(theta), where
K = (Vs/Vp)^2, "^" denotes exponentiation, theta is the
angle of incidence, and c is the exponent for the Gardner's
relation rho = const*Vp**c.
The two-component B0 and B1 are the intercept and slope of
the equation
R = B0 * X + B1 * Y, where
X = 1.+((1.+c)^-1)*tan^2(theta)*sin^2(theta) and
Y = sin^2(theta)
Program avaws gets its data and parameters from command line
arguments. These arguments specify the input data and velo-
city files, the output data set, the ray tracing parameters,
and other computation limitations.
Command line arguments
-N ntap
Enter the input data set name immediately after typing
-N. This input file should include the complete path
name if the file resides in a different directory.
Example -n/b/tsp/dummy tells the program to look for
file 'dummy' in directory '/b/tsp'. (Default = stdin)
-O otap
Enter the output data set name immediately after typing
-O. Specify the full path to write the file to a
directory other than the current working directory.
(Default = stdout )
-v RMS velocity file
Enter the name of the file containing the RMS veloci-
ties corresponding to the input data set, one velocity
record for each CDP. This is typically the output from
program VELIN or program VOMIT. (Default = NONE. This
parameter is REQUIRED)
-S S-wave (interval) velocity file
Enter the name of the file containing the S-wave inter-
val velocities corresponding to the input data set, one
velocity record for each CDP. (Default = NONE. This
parameter is REQUIRED).
-rs start record
Enter the sequential number of the record on which to
begin processing. All data prior to this record will
be skipped and not output. (Default = first)
-re end record
Enter the sequential number of the record on which to
end processing. All data following this record will be
skipped and not output. (Default = last)
-as mininum angle
Enter the minimum incident angle, in degrees, to limit
the data values used in the weighted stacks. Data
corresponding to incident angles less than this value
are ignored. (Default = 0 degrees)
-ae maximum angle
Enter the maximum incident angle, in degrees, to limit
the data values used in the weighted stacks. Data
corresponding to incident angles greater than this
value are ignored. (Default = 45 degrees)
-md angle calculation mode
Enter the flag to indicate the type of ray-tracing
solution desired. A value of 0 gives a straight ray
solution; a value of 1 gives a curved ray solution; and
a value of 2 give a perturbed curved ray solution
wherein the smooth curved ray solution is "perturbed"
in accordance with the true input velocity function.
There is NO DEFAULT. This parameter is required.
-? Enter the command line argument '-?' to get online help.
The program terminates after the help screen is printed.
-H Same as -?, except a list of the output traces is also
printed. The program terminates after the help screen is
printed.
SEE ALSO
angst(1)
square(1)
sscale
sscaleu
REFERENCES
Aki, K. and Richards, P.G., 1980, Quantitave Seismology:
Theory and Methods, Freeman, San Francisco.
Castagna, J.P., Batzle, M.L., and Eastwood, R.L., 1985,
Relationships Between Compressional-Wave and Shear-Wave
Velocities In Clastic Silicate Rocks, Geophysics, Vol. 50,
pp 571-581.
Castagna, J.P., Batzle, M.L., and Kan, T.K., 1992, Rock Phy-
sics - The Link Between Rock Properties and AVO Response in
Offset-Dependent Reflectivity - Theory and Practice of AVO
Analysis, J.P. Castagna and M.M. Backus (eds), Society of
Exploration Geophysics.
Castagna, J.P., and Smith,, S.W., 1994, Comparison of AVO
Indicators: A Modeling Study, Geophysics, Vol. 59, pp
1849-1855.
Smith, G.C. and Gidlow, P.M., 1987, Weighted Stacking for
Rock Property Estimation and Detection of Gas, Geophysical
Prospecting, Vol. 35, pp 993-1014.
Thomsen, L.P., 1982, Amplitude Vs. Range Attributes: Interim
Report, Amoco Production Company Research Department Report
T82-E-10.
Thomsen, L.A. and Hanson, K.E., 1985, Linear RDA: S and P,
Amoco Production Company Research Department Report T86-E-
44.
AUTHOR
Richard Crider Houston
COPYRIGHT
copyright 2001, Amoco Production Company
All Rights Reserved
an affiliate of BP America Inc.
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