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AVO

AVOA performs Amplitude-versus-Offset (AVO) analysis by extracting AVO attribute stacks. This analysis can give indications of lithology and pore content. Two methods to compute the attributes are supported: Linear regression, and Geostack. Eleven different attribute types can be created.

Input data must be CMP or common-bin sorted gathers with NMO applied. Coherent and random noise will degrade the AVO analysis. Noise can be reduced on the CMP gathers by angle and offset-mixed super-gathers as well as offset-consistent amplitude corrections. The attribute analysis is done across iso-time samples or gated time intervals.

The program AVOA computes the various attributes to facilitate amplitude-versus-offset studies. For each common reflection point, an amplitude-versus-incident-angle curve can be plotted, but it is difficult to draw any useful information from this kind of curve because noise always exists. However, under the assumption of a small change in elastic parameters, it has been proven that the reflection coefficient varies linearly with the square of the sine of the incident angle (Shuey, 1985).

This module will also accept angle of incidence gathers from module XAVA. The center angle for each angle group that is stored in DIST header word is used to compare with the min/max angles specified in this module. Center angles outside of this range will be rejected.

Linear regression (least squares) analysis is used to get a best-fit straight line of amplitude verses square sine of the incident angle. A sample from each trace in the gather is used in the best-fit line analysis. The Intercept (P) and the Gradient (G) are taken from the straight-line equation:

Y = G * X + P
The intercept (P) of the line from the best-fit analysis is called the pseudo P-wave reflection coefficient at zero-offset. The gradient, G, indicates the variation of the amplitude with offset. The gradient can be plotted as gradient stack section (Denham, 1985). By combining the intercept, P, and the gradient, G, other attribute sections, such as pseudo S-wave section, pseudo Poisson's ratio section, hydrocarbon-indicator section and fluid factor section, can be obtained. Each attribute represents a different aspect of the offset dependent reflectivity. A combination of all the attributes is recommended for a comprehensive AVO study.

When using the normal linear regression best-fit straight-line technique, a correlation coefficient and a randomness statistic section can be built. You can also set a minimum threshold correlation coefficient to reject best-fit analysis at samples that don't meet the threshold. The correlation coefficient and randomness sections can later be used to weight the other attribute stacks.

The Geostack option is uses a weighted stacking technique. It outputs the P-Wave velocity reflectivity (Rp) into the intercept (P) field and the S-Wave velocity reflectivity (Rs) into the gradient (G) field. It also outputs the sum of the Rp for the trace window as the correlation coefficient and the sum of the Rs as the statistics. This option computes the Gradient from the P and S wave reflectivity series as:

G = Rp - 2 * Rs
Even though the Gradient is not output when using this option, it is used to compute the remaining attributes.

The AVO attribute analysis is done across same-time sample values or within stack polarity defined gates. A common problem with AVO attributes stacks is residual NMO on the CMP gathers because of imperfect velocity analysis. To compensate, amplitudes may be selected within polarity gates, thereby relieving the requirement of exact NMO application. Polarity gates are computed using a stack of the CMP gather. The amplitudes in the gate are used to compute a maximum value. The maximum value for each trace in the gather is used in the best-fit analysis. The output values are blocked as constant values over each polarity gate.



RMS and interval velocities are needed to compute the sine square of the incidence angle. They are also used in computing the fluid factor section. The RMS velocities can be provided either as a spreadsheet matrix or in a VIP file. The velocity function should be smoothed before the attributes are computed to reduce noise. An option is included to perform smoothing. If the velocities are coming from a VIP file, then it is recommended to smooth the velocities in the VIP program and not in AVOA.

The AVO attribute analysis may be performed in time gates. Two methods for time gates are included: spatial varying or non-spatial varying. The non-spatial varying method asks for a start and end time for performing the analysis. These times are used across the entire survey. The spatial varying method asks for a times file that was previously built. This module only uses the first start and end time at an analysis location within the file. If the file contains additional start and end at a location, they will be ignored. Header values TIM1 and TIM2 may also be used to center a time window about a horizon.

The user can specify the mud rock line slope and intercept used for the Fluid Factor stack trace. Castagna defines the typical mud-line slope to be 1.16 and the intercept to be 1360. However, experience has shown that this value varies by geology. The Vs/Vp equation is:

Vs/Vp = (1./mud slope) - (mud intercept/mud slope)/Vp
This is then used to compute the fluid factor:

For the Least-Squares option:
FF = (8/5)*P-mud slope*(Vs/Vp) *(0.5*(P-G)) from Castagna, 1993.
For the GeoStack option:
FF = P-mud slope*(Vs/Vp)*S from Castagna, 1993.
where: P=P-wave trace, G=Gradient trace, S=S-wave trace.
A specific request was to allow more flexibility in the Poisson's Ration stack trace. You can now define a weighted Poisson's Ratio to be:

PR = a * P + b * G
The user can specify the weights in the menu. If you choose to do the default Poisson's Ratio then this equation is used:

PR = (P+G)*4/3
AVO attribute sections built by this module include:

1. Pseudo P-wave (Intercept) stack (P):

This is the intercept in the amplitude versus the square of the sine of the incidence angle. The pseudo P-wave section displays the zero-offset P-wave velocity reflectivity series. Conventional CMP stack smears the amplitudes at different incident angles. The pseudo P-wave section is a better representation to the zero-offset reflection coefficient than the CMP stack section. Therefore, it is more suitable for P-wave impedance inversion. The interpretation of a P-wave stack is similar to that of a conventional CMP stack.

If the Geostack option is used, then this value is the P-wave velocity reflectivity series. The algorithm requires a shear velocity, which is computed from the P velocity using Castagnas mud rock equation. A valid mud rock line slope and intercept should be entered into the menu.

2. Gradient (Slope) stack (G) for least squares method:

Pseudo S-wave stack for geo-stack method:

This is the gradient (slope) in the amplitude versus the square of the sine of the incident angle. A large positive gradient indicates that the amplitude increases with offset. It may indicate the existence of gas sand.

If the Geostack option is used, then this value is the S-wave velocity reflectivity series. The algorithm requires a shear velocity, which is computed from the P velocity using Castagnas mud rock equation. A valid Mud rock line slope and intercept should be entered into the menu.

3. Restricted gradient stack (sign(P) * G):

This stack is the sign of the pseudo P-wave times the gradient section. The restricted gradient stack will show a positive anomaly when the absolute amplitude increases with offset. Plotting only the positive quantities can enhance the indications of the potential presence of gas.

4. Pseudo Poisson's-ratio stack ((P+G)*4/3):

This stack is four thirds of the pseudo P-wave section plus the gradient section. This is approximately the Poisson's ratio under the assumption that P-wave travels 1.732 times faster than S-wave. The Poisson's ratio stack has a similar appearance to that of a stacked seismic section. High Poisson's ratio is suggestive of gas sand in a sand-shale sequence.

5. Pseudo S-wave stack (1/2)*(P-G)

The pseudo S-wave section displays the zero-offset S-wave velocity reflectivity series but with the P-wave travel time

6. Potential Hydrocarbon-indicator stack (P*G):

This is the product of the pseudo P-wave section and the gradient section. The potential hydrocarbon-indicator stack is similar to the restricted gradient stack in interpretation; a large positive anomaly often indicates the presence of gas in a sand-shale sequence.

7. Restricted P-wave stack (P*Sign(G)):

This is the sign of the gradient times the pseudo P-wave section. This section displays an anomaly when the absolute amplitude increases with offset.

8. Correlation coefficient or Intercept weights:

When the AVO computation method is 'least squares' then this section displays the correlation coefficient of the least squares fit. The correlation coefficient has an absolute value range of 0.0 to 1.0, with 1.0 indicating a perfect fit of the points to a least squares straight line. If the computation method is geo-stack, then this section displays the intercept weights.

9. Statistics or Gradient weights:

When the AVO computation is 'least squares' then this section displays the randomness statistics. Large absolute values of the statistic (greater than 3) indicate that the data does not trend in a straight line so a straight line fit is not appropriate. If the computation method is geo-stack, then this section displays the gradient weights.

10. Fluid factor:

The fluid factor is computed using Castagna's mud rock equation. Gardner's relationship is used to determine the density. A deviation of the intercept and gradient from a regional trend will show up as a fluid factor anomaly.

11. (Far - Near) * Far

A new option in this module is to output a (Far Near) * Far (FNXF) amplitude trace. The near value is the amplitude on the nearest offset in the CMP that still has a valid (non-zero) sample. The far value is the amplitude on the farthest offset in the CMP that still has a valid (non-zero) sample.

The following attributes are available:

Option Description                       Equation
------------------------------                      --------------
1      P-wave stack (Intercept)       P
2      Gradient stack (Slope)           G
3      Restricted gradient stack       Sign(P) * G
4      Pseudo Poisson's-ratio stack (P+G)*4/3
5      Pseudo S-wave stack            (P-G)/2
6      Potential Hydrocarbon stcak  P*G
7      Restricted P-wave stack        P*Sign(G)
8      Correlation coefficient or Intercept weights
9      Statistics or Gradient weights
10     Fluid factor
11     (Far-Near)*Far


AVOA outputs the AVO stacks side-by-side. The corresponding option number will be placed in the location of offset (DIST) in the header. Module EXTRACT or SELECT can be used to separate the different attribute stacks.

References

Goodway, B., Chen, T., Downton, J., Improved AVO fluid detection and lithology discrimination using Lame petrophysical parameters from P and S inversions.

Denham, L., Palmeria, R. and Farrel, R., 1985, The zero-offset stack: Presented at the 55th SEG annual International meeting, Washington, D.C.

Shuey, R. T., 1985, A simplification of the Zoepritz equations: Geophysics, 50,609-614.

Castagna, J.P., Batzle, M.L., and Eastwood R.L., 1985, Relationships between compressional-wave and shear-wave velocities in clastic silicate rocks.

Smith, G.C., and Gidlow, P.M., 1987, Weighted stacking for rock property estimation and detection of gas: Geophysical Prospecting, 35, 993-1014.

Castagna, J.P., and Backus M.M., 1993, Offset-Dependent Reflectivity - Theory and Practice of AVO Analysis. Investigations in Geophysics No. 8.

Todd, C., 1986, Isolation, display, and interpretation of offset dependent phenomena in seismic reflection data using offset depth ratio partial stacks: M.S. thesis, University of Texas at Austin

Jan L. Fatti, George C. Smith, Peter J. Vail, Peter J. Strauss, and Philip R. Levitt, 1994, Detection of gas in sandstone reservoirs using AVO analysis: A 3-D case history using the Geostack Technique.

Fred Hilterman, 2001, Seismic Amplitude Interpretation, 2001 SEG Short Course Notes

Input Channels

Seismic input
Required
Connect from other process only
GCI data type
VIP velocity database
Optional
Connect from disk file only
SEGY data type
GCI data type
Output Channels

Attribute stacks
Required
Connect to other process only
GCI data type
Parameters

Attribute stack output options:

Options: P-wave (Intercept), Gradient stack (Slope), Restricted gradient, Pseudo Poisson's-ratio, Pseudo S-wave, Potential Hydrocarbon, Restricted P-wave, Correlation coefficient, Statistics, Fluid factor, (Far-Near)*Far
Method for AVO amplitude fit:

The AVO analysis can be computed at each sample or within polarity gates. The polarity gate is determined by a stack of the CMP gather traces. The gate being samples within the same polarity cycle. The amplitude used for each trace is the maximum found using interpolation. The amplitudes are blocked as constant values within the gate times.

Options: At each sample, Polarity gate
Method for AVO attribute computations:

The best-fit line computation is performed using a least squares linear fit or the weighted stacking Geostack method.

Options: Least squares linear fit, Geostack
Least squares method:

Method for AVO attribute computation: = least squares.

Options: Least Squares, Robust Least Squares
Minimum acceptable correlation coefficient:

Method for AVO attribute computation: = least squares. When using the least squares linear fit method, a minimum correlation coefficient can be specified. The correlation coefficient is a statistical measurement of the fit of the data to the best-fit straight line. The correlation coefficient can range from 0.0 to 1.0, with 0.0 being a poor fit and 1.0 being a good fit. Computed correlation coefficients that fall below this minimum value will result in the attributes at that sample being zeroed. A value of 0.0 results in no editing of the attribute values. A value of 0.5 will result in strong editing of the attribute values.

Maximum incident angle (deg.):

The maximum angle for a linear fit of an AVO curve of reflection amplitude versus sin(theta)**2 is 25 degrees (Shuey, 1985). However, AVOA renders this as a parameter at the user's discretion. AVOA will mute the data that has an angle of incidence greater than this maximum angle.

Minimum incident angle (deg.):

Seismic data at less than 3 degrees tends to be noisy and of poor quality. AVOA renders this as a parameter at the user's discretion. AVOA will mute the data that has an angle of incidence that is less than this minimum angle.

Space variant start and end times?

The user may select space variant or non-spatial variant start and stop times. The space variant times are entered through a window file or a spreadsheet. The non-spatial variant times are constant throughout the survey.

Start time(ms.)

Space variant start and stop times? = No. Enter the start time in milliseconds. The attribute stack computations will start at this time.

End time (ms.)

Space variant start and stop times? = No. Enter the end time in milliseconds. The attribute stack computations will end at this time.

Start and stop times

Space variant start and stop times? = Yes. This parameter appears if space variant start and stop times are selected. The user can select a windows file or use the spreadsheet to enter start and stop times. Only one start and stop time is allowed by CMP location. If the file contains additional times per CMP location, they will be ignored.

Matrix Type: WINDOWS2
Header to add to start time

The user may have previously selected a start and stop time and placed them into the trace header. These header values may be retrieved and used as a bulk shift of the start and stop times.

Options: NONE, TIM1, TIM2
Header to add to end time

The user may have previously selected a start and stop time and placed them into the trace header. These header values may be retrieved and used as a bulk shift of the start and stop times.

Options: NONE, TIM1, TIM2
RMS velocities:

This parameter specifies the velocity functions to use for the survey. The user may select a VIP file that was previously built or may enter the time-velocity pairs in a spreadsheet. The velocities enter should be the RMS velocities. The module will compute the interval velocities from the RMS velocities.

Matrix Type: RMSVEL
Velocity smoothing filter length(ms):

A time domain running average filter can be applied to smooth the velocity function. If the velocities are in a VIP file then smoothing should be applied in the VIP program, but it can be applied here. The filter length should be entered in milli-seconds.

Mudrock line slope (Geostack and fluid factor only)

Enter the mudrock line slope to be used in the fluid factor computation. The fluid factor is computed from the mudrock line trend from Castagna(1993) and Hilterman (2001). This value is used for the fluid factor trace only.

Vs/Vp = 1. mud slope-(mud intercept/mud slope)/Vp
dF = dVp/Vpa - mud slope(Vs/Vp)(dVs/Vsa)
Mudrock line intercept (Geostack and fluid factor only)

Enter the mudrock line intercept to be used in the fluid factor computation. The fluid factor is computed from the mudrock line trend from Castagna(1993) and Hilterman (2001). This value is used for the fluid factor trace only.

Vs/Vp = 1./mud slope - (mud intercept/mud slope)/Vp
dF = dVp/Vpa - mud slope(Vs/Vp)(dVs/Vsa)
Weighted Poisson's Ratio? (Poisson's Ratio only)

Select 'YES' to compute a weighted Poisson's Ratio:

PR = a * P + b * G.
The weight parameters will appear below. If you select 'NO' then the normal Poisson's Ratio is computed:

4/3 * (P + G).
This parameter is used for the Poisson's Ratio trace only.

P-Wave weight

Enter the scalar (a) to apply to the P-Wave (P) in the equation:

PR = a * P + b * G.
Gradient weight

Enter the scalar (b) to apply to the Gradient (G) in the equation:

PR = a * P + b * G.