HRS AVO_Attribute_Volumes.pdf

CE7/R2 Last Updated: August 2005 Author: Feby Hapsari 1

AVO Attribute Volumes AVO Attribute Volumes


IntroductionIntroduction

The AVO Attribute Volume process (formerly known as the Gradient Stack) allows us to analyze gathers to determine either the zero-offset and gradient components of the amplitude or the zero-offset P-wave and S-wave reflection coefficients at each time sample.

These results are derived from two formulations of the Aki-Richards approximation to the Zoeppritz equations.

The output of AVO Attribute Volume will be stored in SEGY files, but is typically viewed in a single output window.


Possible AttributesPossible Attributes

For each field and reservoir, not all AVO attributes will give the same results, some may be more robust than others. Modeling and comparing all available AVO attributes is useful in determining the best AVO input for reservoir modeling and simulation.

Following are a number of different possibilities of getting AVO attributes:

Offset or angle-limited stacksElastic Impedance inversionIntercept and GradientExtraction of RP and RS reflectivityInversion of RP and RS to give ZP and ZSLambda-Mu-Rho analysis of ZP and ZS


Types of AVO Attributes Analysis in HRSTypes of AVO Attributes Analysis in HRS

Using AVO program in HRS Software, there are four types of analysis for AVO Attributes:

1. The traditional A/B (Intercept/Gradient) approach2. The three term A/B/C (Intercept/Gradient/Curvature) approach3. The Rp/Rs approach, which is the Geostack method described by Fatti et al.4. The Vp/Vs analysis

Every approach will create some useful attributes that were calculated internally in the software. Theory for each type of analysis is given briefly on next slides.

The following pages have more details on how to create and combine various AVO attributes using HRS software.


Types of AVO Attributes Analysis in HRSTypes of AVO Attributes Analysis in HRS

A description of the relevant AVO equations is accessible from the Help > AVO Equations menu.


A/B (Intercept/Gradient) AnalysisA/B (Intercept/Gradient) Analysis

In this traditional A/B (Intercept/Gradient) approach, the amplitude of any pre-stack data sample can be written as:

R(x,t) = A(t) + B(t)*sin²θ(x,t), where: A(t) is the ideal zero-offset (intercept) traceB(t) is the gradient trace for this gatherθ(x,t) is the P-wave angle of incidence at this sample

This A/B approach will give following attributes:1. Intercept (A)2. Gradient (B)3. Product (A*B)4. Intercept (A) * sign (Gradient (B))5. Gradient (B) * sign (Intercept (A))6. Scaled Poisson’s Ratio Change (aA+bB)7. Scaled S-wave Reflectivity (aA-bB)8. Polarization Angle Difference9. Polarization Magnitude 10. Polarization Coefficient Squared See next slide for more explanation11. Polarization Product 12. Weighted Polarization Product


A/B (Intercept/Gradient) AnalysisA/B (Intercept/Gradient) Analysis

Explanations of Polarization Attributes:

1. Polarization Angle Difference: The calculated angle minus the Background Angle.

2. Polarization Magnitude: The length of the Polarization Vector.

3. Polarization Coefficient Squared: The squared normalized correlation coefficient from the Polarization Vector calculation.

4. Polarization Product: The product of the Polarization Angle times the Polarization Magnitude.

5. Weighted Polarization Product: The product of the Polarization Angle times the Polarization Magnitude times the Polarization Coefficient Squared.


A/B/C (Intercept/Gradient/Curvature) AnalysisA/B/C (Intercept/Gradient/Curvature) Analysis

In the three term A/B/C (Intercept/Gradient/Curvature) approach, the amplitude of any pre-stack data sample can be written as:R(x,t) = A(t) + B(t)*sin²θ(x,t) + C(t)*tan2θ(x,t)sin2(x,t)where: A(t) is the ideal zero-offset (intercept) trace

B(t) is the gradient trace for this gatherC(t) is the curvature termθ(x,t) is the P-wave angle of incidence at this sample

This A/B/C approach will give following attributes:1. Intercept (A) 9. Delta Vp(2*C)2. Gradient (B) 10. Delta Rho(s*(A-C))3. Curvature (C) 11. Delta Vs(1+0.25k)*C-(0.25k)*B-A4. Product (A*B) 12. Polarization Angle Difference5. Intercept (A) * sign (Gradient (B)) 13. Polarization Magnitude6. Gradient (B) * sign (Intercept (A)) 14. Polarization Coefficient Squared7. Scaled Poisson’s Ratio Change (aA+bB) 15. Polarization Product8. Scaled S-wave Reflectivity (aA-bB) 16. Weighted Polarization Product


Rp/RsRp/Rs AnalysisAnalysis

The Rp/Rs approach is the Geostack method described by Fatti et al. (Geophysics, Vol.59,1994), which describes the amplitude of any pre-stack data sample as:

R(x,t) = Rp(t)*a(x,t) + Rs(t)*b(x,t)

where: Rp(t) is the zero-offset P-wave reflectivity Rs(t) is the zero-offset S-wave reflectivity

a(x,t) and b(x,t) are functions of the P-wave angle of incidence at this sample

This Rp/Rs approach will give following attributes:1. Fluid Factor (Vp/Vs=2) 2. aRp + bRs3. aRp – bRs4. Rp5. Rs


Vp/Vs AnalysisVp/Vs Analysis

This Vp/Vs approach will give following attributes:1. Vp2. Vs3. Vp/Vs4. Vs/Vp5. Poisson’s Ratio

The Vp/Vs analysis allows us to display various combinations of the P-wave and S-wave velocities. These velocities are only the input velocities that are used for the AVO Attribute calculation. They are designed to give you a fast method of creating the SEGY velocity volumes from the velocity function that you use in the AVO Attribute calculation.


Creating AVO Attribute in HRSCreating AVO Attribute in HRS

To start creating AVO Attributes in HRS, in the window containing seismic gather, click AVO Attribute > AVO Attribute Volume. A Volume Range Specification window will appear. Specify velocity information from either a well log or a table, and also the Type of Analysis desired.


A/B (Intercept/Gradient) AttributesA/B (Intercept/Gradient) Attributes

Remember that for each field and reservoir, not all AVO attributes will give the same results, some may be more robust than others. Modeling and comparing all available AVO attributes is useful in determining the best AVO input for reservoir modeling and simulation.

We can check and select various combinations of these attributes in the Color Data Volume. Below are attributes calculated when choosing type of analysis A/B.


A/B/C (Intercept/Gradient/Curvature) AttributesA/B/C (Intercept/Gradient/Curvature) Attributes

Calculated Attributes when choosing type of analysis A/B/C.


Rp/RsRp/Rs AttributesAttributes

Calculated Attributes when choosing type of analysis Rp/Rs.


Vp/Vs AttributesVp/Vs Attributes

Calculated Attributes when choosing type of analysis Vp/Vs.


Making AVO Attributes VolumeMaking AVO Attributes Volume

When we calculate the AVO attributes of gathers, AVO determines the values for A(t), B(t), C(t), Rp(t) and Rs(t) and stored the output in two SEGY files. Other attributes in the software are internally calculated and are not output in SEGY files.

Wanting to bring AVO attributes from HRS to other software suite requires a bit different way. The simple way to make AVO attribute volume of desired attribute is by using Process > Utility > Copy, and choose the desirable attribute as input volume.


Making AVO Attributes VolumeMaking AVO Attributes Volume

In the Seismic Window Data menu and seismic.dir of the project, see that the volume and SEGY files of desired attributes have now been created.

We can now move these files to other software suite. For reference to move SEGY data, see the Moving_Data pdf file.


Other Attribute VolumesOther Attribute Volumes

If you have two seismic volumes in the same window, the software will create “on-the-fly” (internally calculated) attributes. This, for example, is the sum, difference, multiplication, etc of the available seismic volumes.

Attribute volumes for these on-the-fly attributes could not be created using the option Process > Utility > Copy. It has to be done using the Trace Math option. After that, the data can be moved to other software suite. See next slide for details.



There are two seismic volumes in the same window. Looking at the Color Data Volume, we have on-the-fly attributes, for example the sum, difference, and multiplication of the seismic volumes.



To create attribute volume of these on-the-fly attributes, do the Trace Math option, and select the desired process.



Check in Seismic Window Data Menu and in seismic.dir of your project, the volume of the on-the-fly attributes is now existing.

HRS AVO_Attribute_Volumes.pdf

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