NAME
attin - compute AVO attributes from cdp gathers
SYNOPSIS
attin [ -Nntap ] [ -Ootap ] [ -vRMS Velocity File ] [
-SShear Velocity File ] [ -rs ] [ -re ] [ -as ] [ -ae ] [ -c
] [ -at ] [ -md ] [ -M ] [ -E ] [ -D ] [ -rc ] [ -sa ] [ -?
] [ -h ]
DESCRIPTION
attin computes various AVA (Amplitude Versus Angle) attri-
butes from either CDP (X-T or X-Z) gathers or from angle-
dependent gathers (angle-T domain) created by program ANGST.
All of the attributes are derived through least squares
inversion of the trace amplitudes with basis functions
defined by various forms of the linearized approximation of
the Knott-Zoeppritz P-wave reflectivity equation attributed
to Aki and Richards.
One form is a 3-term equation generally considered the stan-
dard form for the linear equation describing amplitude vari-
ation with incident angle and frequently called the "Shuey"
equation. This equation is defined below. The 3rd coeffi-
cient is expected to be very noisy.
A second form of the basis function is a 2-term equation
formed from a Shuey-like equation by replacing the change in
density by the Gardner's equation equivalence in terms of
change in Vp (Thomsen and Hanson, 1985) and recombining
terms. This equation is valid for all angles of incidence
and is defined below.
A third form is the 3-term Aki and Richards equation
(defined below), which gives the P-wave reflectivity as a
function of incident angle in terms of the fractional varia-
tions in rock properties Vp, Vs, and density. From the
solution of this equation, other properties, such as frac-
tional change in bulk and shear moduli, can be computed (see
definitions below). These coefficients are expected to be
noisy.
Yet another form for the basis function is a 2-term equation
formed from the Aki-Richards equation by using the Gardner
relation to fold the fractional change in density term into
the fractional change in velocity term, giving a 2-term
equation for fractional change in Vp and Vs. This equation
is more stable than the 3-term equation, although the Vs
term is still expected to be noisy.
Althought a Vp/Vs ratio is not needed for inversion of the
standard form of the reflectivity equation (first two forms
described above), it is an integral part of the inversion
according to the basis function forms defined by the Aki-
Richards equation (last two forms described above). The
program permits the input of (interval) shear velocities,
which may be derived from any reasonable source. A simple
method for creating the shear function is to convert the RMS
function to an interval function and scale by an appropriate
amount. **NOTE**: If no shear wave velocity is available
the user may exclude the file and the module will enable
Castagna's Mudrock relationship. The input shear function,
like the input RMS function, may contain a single record or
multiple records. If the file contains multiple records,
however, the number of records MUST be the same as the
number of input gathers.
Note: when running inside XIKP the 0 connector is for the
input data, the 1 connector is for the output data, the 3
connector is for the RMS P-velocity, and the 4 connector is
for the S-interval velocity.
All of the attributes listed below are computed and output
by program attin. 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):
Trace Number Attribute
1. Intercept (B0) from 2-term equation below
2. Slope (B1) from 2-term equation below
3. DVp/Vp from 2-term equation below
4. DVs/Vs from 2-term equation below
5. DRho/Rho from 3-term equation below
6. DVp/Vp from 3-term equation below
7. DVs/Vs from 3-term equation below
8. Coefficient of determination (r^2) for the
B0', B1', and B2' solution.
9. B0' from 3-term equation below
10. B1' from 3-term equation below
11. B2' from 3-term equation below
12. Fractional change in shear modulus
13. Fractional change in bulk modulus
The two-
term equation used for DVp/Vp and DVs/Vs computation 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, Vp and Vs are the average P and S velocities
at the interface, "^" denotes exponentiation, theta is the
angle of incidence, and c is the exponent for the Gardner's
relation rho = const*Vp**c. Note: By setting c = 0, the A
term is reduced to 0.5*[1.0 + tan^2(theta)].
The two-component B0 and B1 are the intercept and slope of
the equation
R = A + D, where
A = B0(1.0+(1/(1.+c)*tan^2(theta)*sin^2(theta)) and
D = B1*sin^2(theta)
Note: By setting c = 0, A is reduced to a constant.
The three-component equation used for B0', B1', and B2' com-
putation is
R= B0' + B1'*sin^2(theta) + B2'*sin^2(theta)*tan^2(theta)
with B0 = 0.5*[DVp/Vp + Drho/rho],
B1 = 0.5*(DVp/Vp -K*[2*DVs/Vs + Drho/rho]), or
B2 = 0.5*DVp/Vp
The three-component equation used for DVp/Vp, DVs/Vs, and
Drho/rho computation is
R= [1 + tan^2(theta)]DVp/Vp - K*sin^2(theta)DVs/Vs +
[1-K*sin^(theta)]Drho/rho
The fraction change in shear and bulk moduli (G and K,
respectively) can be computed from the fractional changes in
DVp/Vp, DVs/Vs, and Drho/rho as
DG/G = (2*DVs/Vs + Drho/rho) and
DK/K = (2*DVp/Vp + Drho/rho - 4/3*K*DVs/Vs)/(1 - 4/3 K)
Note than equivalent expressions for DG/G and DK/K are given
by
DG/G = (B2 - B1)/(2/K)
DK/K = (3B0+B1+2B2)/(2/(3-K))
Program attin gets its data and parameters from command line
arguments. These arguments specify the input data and velo-
city files, the output data set, and other computation limi-
tations.
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).
Note: when running inside XIKP the 0 connector is for
the input data, the 1 connector is for the output data,
the 3 connector is for the RMS P-velocity, and the 4
connector is for the S-interval velocity.
-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 ). Note: when running inside XIKP the
0 connector is for the input data, the 1 connector is
for the output data, the 3 connector is for the RMS P-
velocity, and the 4 connector is for the S-interval
velocity.
-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 IF INPUT IS X-T DOMAIN, ignored
otherwise). Note: when running inside XIKP the 0 con-
nector is for the input data, the 1 connector is for
the output data, the 3 connector is for the RMS P-
velocity, and the 4 connector is for the S-interval
velocity. This file is assumed to be in the same
domain as the gathers. DO NOT INPUT X-Z gathers AND
X-T velocities!
-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 = Castagna's
Mudrock relationship). If the user does not use an
input file for this, then Castagna's Mudrock relation-
ship is enabled. Note: when running inside XIKP the 0
connector is for the input data, the 1 connector is for
the output data, the 3 connector is for the RMS P-
velocity, and the 4 connector is for the S-interval
velocity.
-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)
-c Gardner's Exponent
Enter the value to be used for exponent for Gardners
equation. The value may be set to 0.0 and the default
only applies if the parameter is not coded on the com-
mand line. (Default = 0.25, if the parameter is not
coded)
-at angle-T Domain flag
If this flag is present, the input data are assumed to
be in the angle-T domain and ray tracing will be used
to define the incident angle field for the regression
procedure. (Default = X-T, if -at is not present the
input data is assumed to be X-T domain.)
-M Input data is in Metric Units (Default). This flag is
ignored if Shear interval velocity is supplied.
-E Input data is in English Units. This flag is ignored
if Shear interval velocity is supplied.
-md Ray tracing mode
Enter the flag indicating the type of ray-tracing solu-
tion desired. A value of 0 gives a straight ray solu-
tion. A value of 1 gives a curved ray solution. A
value of 2 gives a perturbed curved ray solution
wherein the smooth curved ray solution is "perturbed"
in accordance with the input velocity function. This
parameter is ignored if the -xt flat is not present.
Otherwise, the default is 1 (curved ray).
-rc Minimum number of points in inversion
Enter the minimum number of amplitude values to use in
the least square solutions. Technically, this number
should be on the order of 20 to ensure valid solutions.
However, as few as 3 may be used but is not recom-
mended.
-sa Flag to turn off averaging of incident angles
Supply this flag to tell the program to NOT average
angles across each interface. The default is to aver-
age the angles.
-? 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.
Simmons, James L., and Backus, Milo M., 1994, AVO inversion
and direct hydrocarbon detection, SEG Abstracts.
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, Leon, 1992, Weak Anisotropic Reflections in
Offset-Dependent Reflectivity - Theory and Practice of AVO
Analysis, J.P. Castagna and M.M. Backus (eds), Society of
Exploration Geophysics.
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
Minor command line change (9-96) by James Gridley. Unit
flag and Castagna Mudrock line made 10-96 by James Gridley.
COPYRIGHT
copyright 2001, Amoco Production Company
All Rights Reserved
an affiliate of BP America Inc.
Man(1) output converted with
man2html