avo prim attr

AVO Primary Attributes (AVO_PRIM_ATTR)

Abstract

Primary AVO attributes are estimated from prestack P-wave reflection angle gathers.

Prestack moveout-corrected P-wave data are input. The input data must be common anglegathers. This process is robust in the presence of noisy data outliers (e.g., anomalous amplitudes).Additional AVO quality control (QC) attributes can be generated consisting of the modeled AVOand residual noise traces.

For incident angles up to 30 degrees, use the 2 term fitting options in this SFM, to estimate theintercept and gradient or P-wave impedance contrast and Pseudo shear-impedance attributes.

For incident angles greater than 30 degrees, use the 3 term fitting option in this SFM, whichestimates P-wave AVO attributes from Common Angle Gathers, using Pan and Gardner's quadraticapproximation.

These primary quadratic AVO attributes may be converted to contrasts in elastic parameters, orimpedances.

NOTICECopyright protection as an unpublished work is claimed by WesternGeco. The work wascreated in 2013. Should publication of the work occur, the following notice shall apply. "©2013 Westerngeco". This work contains valuable tradesecrets; disclosure without written

authorization is prohibited.

AVO_PRIM_ATTR 1July 2013 - WesternGeco

Contents

1.0 Technical Discussion

1.1 Introduction

1.2 Seismic Characteristics

1.3 Theoretical Background

1.3.1 Shuey’s Approximation

1.3.2 Gidlow Approximation

1.3.3 Pan and Gardner Approximation

1.3.4 Azimuthal AVO: Ruger Approximation

1.4 Operation Mode

1.4.1 SHUEY_2_TERM

1.4.2 GIDLOW

1.4.3 QUAD_3_TERM

1.4.4 RUGER

1.4.5 RUGER_HIGHER

1.5 Line Fitting Mode

1.6 QC Output Mode

1.7 Example Setups

2.0 References

3.0 Additional Reading

4.0 Inputs and Outputs

4.1 Inputs

4.2 Outputs

5.0 Literal Summary

5.1 Inputs

5.1.1 STANDARD_INPUT Port

5.2 Outputs

5.2.1 STANDARD_OUTPUT Port

6.0 Parameter Set Summary


AVO Primary Attributes

7.0 Setup Parameters

7.1 Units

7.2 General

7.3 Shuey 2 Term

7.4 Gidlow

7.5 Quad 3 Term

7.6 Ruger

7.7 Ruger Higher

7.8 Standard Fit

7.9 Robust Fit Control

7.10 Ruger Axes

Attachment A


AVO Primary Attributes

1.0 Technical Discussion

1.1 Introduction

The AVO Primary Attributes (AVO_PRIM_ATTR) Seismic Function Module (SFM) estimatesprimary Amplitude Variation with Offset (AVO) attributes from common angle gathers using alinear or quadratic fit. the linear fit is valid up to an incident angle of approximately 30 degrees.If good quality data is available for larger angles then the quadratic fit may be used to extractadditional information.

For a linear fit, the primary attributes may be intercept and gradient of the line fitted to the reflectioncoefficient vs sin2( ) (the 2–term Shuey equation) or the P-wave and S-wave reflection coefficientsbased on the 2–term Smith and Gidlow equation. For the quadratic fit, the primary AVO attributesare the three fitting parameters from the 3–term Pan and Gardner equation. In either case theparameter fitting may be done using conventional least-squares, or robust fitting may by used tominimize the effects of spurious noise on the data.

The input common angle gathers have to be generated with the Decompose CIP/CMP Gathersinto Common Incidence Angle Traces for AVO (AVO_ANGLE_DECOMP) SFM, using the STACKoutput port. The common angle gathers may be either sampled linearly in the sine of the incidenceangles, or even linearly in the squared sine.

The linear or quadratic primary attributes can be used to compute additional secondary attributesusing the Compute Secondary AVO Attributes from Primary Attributes (AVO_SECN_ATTR) SFMas shown in Figure 1.


1.0 Technical DiscussionAVO Primary Attributes

Typical AVO flow generating primary and secondary AVO attributesFigure 1.

1.2 Seismic Characteristics

The bright spot methodology actually involves three different scenarios about the amplitudevariation with offset or incident angle.

1. The dim spot scenario, in which a large positive amplitude reduces to a smaller positiveamplitude with offset.

2. The phase reversal scenario, in which a small positive amplitude changes to a small negativeamplitude with offset.

3. The bright spot scenario, in which a negative amplitude increases to a larger negative amplitudewith offset.

The interpretation of bright spot reflections has been most successful for interpreting lithologyand making estimates of layer thickness. Interpretation of phase reversal reflections is extremelydifficult, for their tendency to disappear on a conventional stack. The dim spot method ofinterpretation is normally associated with large acoustic impedances.

Several different attributes describe the amplitude variation with offset or incident angle. Moststraightforward is the parameterization of the amplitude variation with incident angle using (1)the normal incidence P-wave reflection coefficient and (2) the gradient of a linear fit of amplitudeversus the squared sine of the incident angle. The normal incidence P-wave reflection coefficient,in this case, is given by the intercept of the fitted line with the amplitude axis, hence this attributeis usually called the intercept. See Figure 2.



Linear fit of AVO curve of reflection amplitude versus the squared sine of theincident angle.

Figure 2.

For reflection angle less than 30 degrees, the amplitude of a P-wave reflected from a planar

interface between two elastic media varies linearly with sin2( ). In the linear fit, P is the interceptand G is the gradient (or slope).

Alternatively, normal incidence reflection coefficients can be estimated for both wave types(P-waves and S-waves).

Both quantities, either intercept and gradient, or P-wave and S-wave reflection coefficient, candirectly be estimated from common angle gathers. These gathers should contain at least 5 tracesto avoid erratic estimates of the gradient.

The normal incidence P-wave reflection coefficient is also lithologically useful, because it is basedon velocities and densities on opposite sides of a reflecting boundary, while the gradient ofamplitude versus squared sine of incident angle is not. A far better parameter is the sum of thegradient and the normal incidence P-wave reflection coefficient, which is related to the Poisson’sratio on opposite sides of the reflector. It is convenient to refer to it as the Poisson’s reflectivity.

Poisson’s reflectivity is a secondary attribute, to be computed from intercept and gradient asdelivered by AVO_PRIM_ATTR using AVO_SECN_ATTR.



Other secondary attributes are related to the product of intercept and gradient and can becomputed using AVO_SECN_ATTR.

1.3 Theoretical Background

Reflection coefficients (reflectivities) derived for the exact Zoeppritz equations(blue) and the 3- and 2-term approximations of Pan-Gardner (red), Gidlow (green)and Shuey (purple) .

Figure 3.

Layer 2Layer 1

3.002.50Vp

1.451.60Vs

2.302.20Density



2.071.56Vp:Vs ratio

0.350.15Poisson's ratio

4.845.66P-wave modulus

20.7013.75S-wave modulus

In Omega, there are three methods to approximate the Zoeppritz equations:

1. Shuey, for angles of 30 degrees or less.

2. Gidlow, for angles of 30 degrees or less.

3. Pan and Gardner, for 30 degrees or more.

1.3.1 Shuey’s Approximation

When SHUEY_2_TERM is selected, intercept and gradient primary attributes are computed usinga least-squares linear fit of amplitude versus squared sine of incidence angle.

Aki and Richards (1980) developed a three-term approximation involving density,compressional-wave velocity and shear-wave velocity. This equation was later written in termsof reflection coefficients by Shuey (1985), as shown in Equation 1.

(1)

where

Average angle at the reflector. For a slowly varying velocity field,

this is approximately equal to the incident angle.

=

the incident angle =

the refracted angle =

Reflectivity of reflected P-waves as a function of angle of incidence =

Average of P-wave velocity (Vp) above and below the interface = Average of S-wave velocity (Vs) above and below the interface = Average of density above and below the interface = Difference in above and below the interface = Difference in above and below the interface = Difference in above and below the interface = Vp / Vs =



Shuey then simplifies Equation 1 further, to just two terms (in Equation 2), by making theassumptions that the Vp:Vs ratio be set equal to 2:1 and that angles of incidence in excess of30 degrees can be discarded.

(2)

where

P-wave reflectivity at normal incidence = R pp (0)

Shear wave reflectivity at normal incidence = R ss (0)

Gradient = GIntercept = P

This first AVO option, is a linear approximation, which may, in theory, be used

to invert the amplitude information to provide rock elastic parameters. P and G can be extractedfrom the data when the data is input in the form of common incident angle gathers per CMP(created with AVO_ANGLE_DECOMP) using the STACK output port. AVO_PRIM_ATTR is thenrun and outputs P (which is equal to Rp) and G as data samples setting the AVO_TRC_TYPEtrace header literal equal to 1 for P and setting the AVO_TRC_TYPE trace header literal equalto 2 for G. The attributes P and G are known as the primary AVO attributes of the linearapproximation.

From the P and G primary attributes, secondary AVO attributes can be generated withAVO_SECN_ATTR. P is lithologically useful because it is based on velocities and densities onopposite sides of a reflecting boundary.

The sum of P and G, which is related to Poisson’s ratio, contains information from both sides ofa reflector. The secondary AVO attribute P + G is known as Poisson’s Reflectivity, and is generatedusing AVO_SECN_ATTR.

1.3.2 Gidlow Approximation

When GIDLOW is selected, zero-offset P-wave and S-wave impedance contrasts are estimatedby a least-squares fit using Equation 3, following Gidlow, Smith, and Vail (1992).



(3)

where

Angle of incidence at reflector. See Average angle = Reflectivity of reflected P-waves as a function of angle of incidence =

The Gidlow acoustic impedance contrast, which is related to the normal

incidence P-wave reflectivity by the equation.

=

The Gidlow shear impedance contrast, which can be related to the S-wave

reflectivity by the equation

=

Vp / Vs =

1.3.3 Pan and Gardner Approximation

As can be seen from Figure 3, when angles are greater than 30 degrees, the observed variationof amplitude with incident angle is closer to a parabola. This case is catered for using theapproximation which consists of three separate terms in the form of a parabola, and was developedby Pan and Gardner in 1987.

The Pan and Gardner (1987) re-parameterization of the Aki and Richards approximation is shownin Equation 4.

(4)

where

Average of the P-wave incidence and transmission angle above and belowthe interface. See Average angle

=

Reflectivity of reflected P-waves as a function of the average angle ofincidence and transmission above and below the interface

=

= a

= b

= c

Average of P-wave velocity (Vp) above and below the interface = Average of S-wave velocity (Vs) above and below the interface = Average of density above and below the interface = Difference in above and below the interface =



Difference in above and below the interface = Difference in above and below the interface = Vp / Vs =

To get a band limited reflectivity for density combine b and c

For the P-wave velocity reflectivity combine all three parameters

The S-wave velocity reflectivity requires also the Vp/Vs ratio

Alternatively, the output traces can be combined to produce P-wave and S-wave reflectivities,where parameter a already is the P-wave reflectivity, and the S-wave reflectivity finally is

.

A range of secondary quadratic AVO attributes with direct geophysical meaning, including theabove, can be obtained by using AVO_SECN_ATTR after AVO_PRIM_ATTR.

1.3.4 Azimuthal AVO: Ruger Approximation

In some situations amplitudes vary not only with offset but also with azimuth. This can happenwhen vertical fracture systems are present. As a result both the P and S-waves velocities canchange with respect to the fracture strike and the rock is said to be azimuthally anisotropic. Thusit is possible to extract information on fractures by performing an azimuthal and offset dependentAVO inversion. Clearly, this method can only be applied to wide azimuth data.

Appropriate AVO expressions were developed by Ruger (1997,2000). This has two forms, whichwe will refer to as ‘normal’ and ‘higher order’. These can be selected using the ‘RUGER’ and‘RUGER_HIGHER’ options.

The normal form of Ruger’s approximation is similar to Shuey’s two term approximation but thegradient term now changes with azimuth.

(5)

where



the zero-incidence reflectivity term = a

the azimuthally isotropic gradient term = biso

the azimuthally anisotropic gradient term = bani

the azimuth from the maximum absolute AVO gradient (i.e., the maximumabsolute value of (bani + biso ))

=

The and are anisotropy parameters similar to those defined by Thomsen (1986) but for anHTI anisotropic medium (see Ruger, 1997, for more details).

The biso and bani parameters define an ellipse whose major axis corresponds to the azimuth max

, where the absolute value of ( biso+ bani) is maximum.

The ‘higher order’ form of Ruger’s approximation is

(6)

where

the higher order isotropic term = ciso

higher order anisotropic term = c4ani

higher order anisotropic term = c2ani

The azimuth definition for RUGER_HIGHER is the same as for RUGER. It is measured from themaximum AVO gradient given by biso and bani. The AVO curvature terms (ciso, c4ani, and c2ani) makethe azimuthal AVO surface more complex and larger amplitudes are possible at other azimuths,particularly at large incidence angles, .

The is another anisotropy parameter defined by Thomsen (see Ruger, 1997, for more details).

1.4 Operation Mode

Depending on the parameter options selected, the primary AVO attribute traces have differentAVO_TRACE_TYPE trace header literal values. A list of all AVO attributes is referred to inAttachment A.

The Operation Mode determines the AVO primary attribute traces that are generated and usedby AVO_SECN_ATTR to create AVO secondary attribute traces.



1.4.1 SHUEY_2_TERM

The SHUEY_2_TERM option uses Shuey’s two-term equation to produce P and G, where P isthe AVO intercept and G is the AVO gradient. See 1.3.1 Shuey’s Approximation.

In a run, when SHUEY_2_TERM is selected, these traces are output.

AVO_TRC_TYPETRACE TYPE

1Intercept

2Gradient

101Standard Deviation of Intercept

202Standard Deviation of Gradient

1.4.2 GIDLOW

The GIDLOW option uses the Gidlow et al.(1992) equation to produce and , where

relates to the P-wave impedance contrast or zero-offset reflectivity, see Equation 3, and is

a scaled-version of the S-wave impedance contrast or zero-offset reflectivity. See 1.3.2 GidlowApproximation

In a run, when GIDLOW is selected, these traces are output.


10Gidlow acoustic impedance contrast

21Gidlow shear impedance contrast

1010Standard Deviation of Gidlow acoustic impedancecontrast

2121Standard Deviation of Gidlow shear impedance contrast



1.4.3 QUAD_3_TERM

The QUAD_3_TERM option uses the Pan and Gardner equation to produce the 3 quadratic termsa, b and c. In a run, when QUAD_3_TERM is selected, these traces are output.


4Pan-Gardner Constant term a

5Pan-Gardner Linear term b

6Pan-Gardner Quadratic term c

404Standard Deviation of Pan-GardnerConstant term a

505Standard Deviation of Pan-GardnerLinear term b

606Standard Deviation of Pan-GardnerQuadratic term c

1.4.4 RUGER

The RUGER option uses the Ruger equation to produce the 4 azimuthal terms a, biso , bani , and

max . In a run, when RUGER is selected, these traces are output.

AVO_TRC_TYPEDESCRIPTIONTRACE TYPE

31Ruger Zero-incidence reflectivity terma

32Ruger Azimuthally isotropic gradient termbiso

33Ruger Azimuthally anisotropic gradientterm

bani

37Ruger Azimuth of Maximum AVOGradient term ( max )



3131Standard Deviation of RugerZero-incidence reflectivity term

sd_a

3232Standard Deviation of Ruger Azimuthallyisotropic gradient term

sd_biso

3333Standard Deviation of Ruger Azimuthallyanisotropic gradient term

sd_bani

3737Standard Deviation of Ruger Azimuth (

max)sd_

1.4.5 RUGER_HIGHER

The RUGER_HIGHER option uses the Ruger high order equation to produce the azimuthal termsa, biso , bani, ciso , c2ani, c4ani and max . In a run, when RUGER_HIGHER is selected, these tracesare output.

AVO_TRC_TYPEDESCRIPTIONTRACE TYPE

31Ruger Zero-incidence reflectivity terma

32Ruger Azimuthally isotropic gradient termbiso


bani

34Ruger Azimuthally isotropic gradient termciso


c2ani


c4ani

37Ruger Azimuth of Maximum AVOGradient term ( max )

3131Standard Deviation of RugerZero-incidence reflectivity term

sd_a




sd_biso


sd_bani


sd_ciso


sd_c2ani


sd_c4ani

3737Standard Deviation of Ruger Azimuth (

max)sd_

1.5 Line Fitting Mode

The AVO primary attributes (e.g., intercept and gradient) are obtained by linear regression, orstraight-line fit, of the amplitude versus sine-squared angle. Similarly, for three term fitting, a leastsquares fit of the parabola is made. The LINE_FIT selection determines whether standard linearfitting (STANDARD_FIT option) or robust linear fitting (ROBUST_FIT option) is employed.

The standard linear regression mode (STANDARD_FIT option) applies a least-squares fit to thedata. This is generally acceptable when the noise in the data is randomly distributed (Gaussian).However, the standard least-squares fit is not robust in the presence of data outliers caused bynoise contamination from ground roll, multiples, etc.

The robust linear fitting (ROBUST_FIT option) follows the approach of Walden (1991) usingM-estimates (maximum-likelihood). The robust fitting is slower than the standard least-squaresfitting. The robust estimation method limits the damage done by outlying amplitudes.

NOTE that only the STANDARD_FIT option is available for the azimuthal Ruger options.

AVO_PRIM_ATTR will output zero values for each of the attributes at samples where there arenot enough points to fit a line or where the distribution of points does not allow an unambiguousline to be defined. The following table shows the minimum number of live points required

Minimum number of pointsORDERMETHOD



32–TERMSTANDARD_FIT

33–TERMSTANDARD_FIT

52–TERMROBUST_FIT

63–TERMROBUST_FIT

4RUGERSTANDARD_FIT

7RUGER_HIGHERSTANDARD_FIT

The regression line is the line of best fit for the data and is a reasonably good model for a givenset of data. For 2 term fitting, to measure how well the regression line fits the data, the linearcorrelation coefficient is used. This is a number between -1 and +1 that tells the strength of theamplitude versus angle relationship. It takes on a value of +1 when the data lies on a perfect linewith positive gradient and -1 for a negative gradient. The value holds independent of the magnitudeof the AVO gradient. A linear correlation coefficient near zero indicates that there is no linearcorrelation between the amplitudes and angles. Since Pearson’s (linear) correlation coefficientis greatly affected by the presence of outliers, a robust linear correlation coefficient is calculatedfrom the goodness-of-fit measure, based on the weighted sum of the residuals.

The standard linear regression mode (STANDARD_FIT option) applies a least-squares fit to thedata. This is acceptable when the noise in the data is randomly distributed (Gaussian). However,the standard least-squares fit is not robust in the presence of data outliers caused by noisecontamination such as ground roll or multiples. In such circumstances, it is necessary to use therobust estimation method which limits the damage done by outlying amplitudes.

The robust linear fitting (ROBUST_FIT option) follows the approach of Walden (1991) usingM-estimates (maximum-likelihood). The robust fitting is slower than the standard least-squaresfitting.

The LINE_FIT selection of ROBUST_FIT option is done in two steps. In the first step, an initialfit is performed using medians following Walden’s method. The data is divided into segmentswith the same number of traces. The median angle and amplitude are calculated in each segment,forming median points. A line or parabola is then fitted through the points to form the initial fit.

In the second step, a decision is made as to which amplitude values are considered as outliers.Outliers are weighted down or eliminated from the following least-squares fit. The decision isbased on the distance from the data point to the initial fitted line.

For 3 term and Ruger fitting, the coefficient of determination is a statistic that is used to determinehow well a regression fits. It is similar to the linear correlation coefficient that is used when doinga 2 term fit.



The definition of the “coefficient of determination” statistic varies in the literature. The one usedhere is equation 15.2.13 from Numerical Recipes.

AVO_TRC_TYPETRACE TYPEORDERMETHOD

9004Standard Linear Correlation Coefficient2–TERMSTANDARD_FIT

9004Standard Coefficient of Determination3–TERMSTANDARD_FIT

9004Standard Coefficient of DeterminationRUGERSTANDARD_FIT

9004Standard Coefficient of DeterminationRUGER_HIGHERSTANDARD_FIT

9005Robust Linear Correlation Coefficient2–TERMROBUST_FIT

9005Robust Coefficient of Determination3–TERMROBUST_FIT

The Z runs statistic trace with AVO_TRC_TYPE 9003 is output with 2–term and 3–term fitting.The purpose of the Z runs statistic is to find out if there are situations that can be considered asa 'model breakdown'. A model breakdown occurs when there is no model that appropriately fitsthe given input data. In AVO inversion, this happens when the input data ( the AVO curve for onesample time) and the inverted/modeled curve are grossly inconsistent.

Mathematically, the Z runs statistic looks at the residuals from the AVO curve fit, i.e. the modelednoise. Long runs of the same sign in the residuals, positive or negative, indicate inconsistenciesbetween model and data. A minimum number of data points is required for the Z runs statistic tobe meaningful. Appendix D in Walden (1991) states 20 as the minimum number of data pointsrequired.

The usefulness of the Z runs statistic is still controversial and under discussion, so it should beused with care.

1.6 QC Output Mode

For QC purposes it may be useful to output signal and noise traces. To do this, the QC_MODEparameter is set equal to the YES option. The signal trace is computed from the intercept andgradient or the a,b,c AVO primary attribute traces, and the angle values of the input trace. Thenoise trace is the difference between the signal trace and the original input trace. These tracepairs are ideal input to the Quantified Quality Attributes of Seismic Data (DATA_QUALITY_ATTR)SFM to produce signal to noise related quality indicators.

When the QC_MODE parameter is equal to the YES option, the following traces are output inaddition to those described above:




9001Signal

9002Noise

1.7 Example Setups

The Gidlow 2-term option is shown in Example 1, the Shuey 2-term option in Example 2, and thePan-Gardner 3-term option in Example 3.

Example 1 shows the setup for AVO_ANGLE_DECOMP which precedes AVO_PRIM_ATTR. InAVO_PRIM_ATTR, the mode is equal to GIDLOW. The QC_MODE parameter is equal to YES,which generates signal and noise traces. The LINE_FIT selection indicates a standardleast-squares fit is used for linear regression.

Example 1

$AVO_ANGLE_DECOMP[STACK4]*UNITS

*GENERALVEL_FILE_NAME = 'vel_2d'

*ANGLE_RANGEMIN_ANGLE = 3MAX_ANGLE = 43NUM_ANGLE_BANDS = 20ANGLE_BANDWIDTH = 6

*STACKEND_TAPER_LEN = 0

*QC_DIP_AZIMDIP_ANGLE_QC = 20

/****************************************************************************/[STACK4]$AVO_PRIM_ATTR*UNITS

*GENERALOPERATION_MODE = 'GIDLOW'QC_MODE = 'YES'LINE_FIT = 'STANDARD_FIT'

*ROBUST_CONTROL

The SHUEY_2_TERM option is selected and the QC_MODE parameter is equal to the NO optionin Example 2. These selections generate intercept and gradient primary AVO attribute output



traces, standard deviation traces, a linear correlations coefficient trace and a statistical Z trace.The LINE_FIT selection is for the ROBUST_FIT option.

Example 2

$AVO_PRIM_ATTR*UNITS

*GENERALOPERATION_MODE = 'SHUEY_2_TERM'QC_MODE = 'NO'LINE_FIT = 'ROBUST_FIT'

*ROBUST_CONTROL

In Example 3, the QUAD_3_TERM option is selected and the QC_MODE parameter is equal tothe NO option. There are three output traces corresponding to the Pan and Gardner a, b, and cterms, three standard deviation traces, a coefficient of determination trace and a statistical Ztrace. The LINE_FIT selection is for the ROBUST_FIT option.

Example 3

$AVO_PRIM_ATTR*UNITS

*GENERALOPERATION_MODE = 'QUAD_3_TERM'QC_MODE = 'NO'LINE_FIT = 'ROBUST_FIT'

*ROBUST_CONTROL



2.0 References

Aki, K., and Richards, P., 1980, Quantitative Seismology - Theory and Methods: W. H. Freeman.

Gidlow, P.M., Smith, G.C., Vail, P.J., 1992, Hydrocarbon detection using fluid factor traces: Acase history: Joint SEG/EAEG Summer Research Workshop, Technical Program and Abstracts,78-89.

Pan, N. D., and Gardner, G.H.F., 1987, The basic equations of plane elastic wave reflection andscattering applied to AVO analysis. Annual Progress Review 19, Seismic Acoustic Laboratory,University of Houston.

Ruger, A., 1998, Variation of P-wave reflectivity with offset and azimuth in anisotropic media:GEOPHYSICS, Soc. of Expl. Geophys., 63, 935–947.

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

Thomsen, L., 1986, Weak elastic anisotropy : GEOPHYSICS, Soc. of Expl. Geophys., 51,1954-1966.

Walden, A.T., 1991, Making AVO sections more robust: Geophysical Prospecting, 39, 915-942.


2.0 ReferencesAVO Primary Attributes

3.0 Additional Reading

Draper, N., and Smith, H., 1998, Applied regression analysis - 3rd ed: Wiley.

Fatti, J., Smith, G., Vail, P., Strauss, P., and Levitt, P., 1994, Detection of gas in sandstonereservoirs using AVO analysis: A 3-D seismic case history using the Geostack technique:Geophysics, 59, 1362-1376.

Press, W., Flannery, B., Teukolsky, S., and Vetterling, W., 1989, Numerical Recipes - The art ofscientific computing: Cambridge University Press.

Ruger, A., 1997, P-wave reflection coefficients for transversely isotropic models with vertical andhorizontal axis of symmetry: GEOPHYSICS, Soc. of Expl. Geophys., 62, 713-722.

Ruger, A., 2000, Variation of P-wave reflectivity with offset and azimuth in anisotropic media,Applied seismic anisotropy: theory, background, and field studies, 20: Soc. of Expl. Geophys.,277-289.

Verm, R., and Hilterman, F., 1995, Lithology color-coded seismic sections: The calibration ofAVO crossplotting to rock properties: The Leading Edge, 14, 847-853.


3.0 Additional ReadingAVO Primary Attributes

4.0 Inputs and Outputs

4.1 Inputs

STANDARD_INPUTStandard Input (Required)The input data must be prestack seismic data after angle decomposition (AVO_ANGLE_DECOMP)using the STACK output port. The data must contain the reflection angles in theAVO_CENTRAL_ANGLE trace header literal. Data must be sorted by gather and sub-sorted bytrace.

4.2 Outputs

STANDARD_OUTPUTStandard Output (Required)The possible output traces are as shown in the table with the corresponding AVO_TRC_TYPEtrace header literal values.

AVO_TRC_TYPETRACE TYPEDESCRIPTION

1intercept or P-wave reflection coefficient

2gradient or S-wave reflection coefficient

4aPan-Gardner constant term

5bPan-Gardner linear term

6cPan-Gardner quadratic term

10Gidlow acoustic impedance contrast

21Gidlow shear impedance contrast

31aRuger Zero-incidence reflectivity term

32bisoRuger Azimuthally isotropic gradient term

33baniRuger Azimuthally anisotropic gradient term

34cisoRuger Azimuthally isotropic gradient term

35c2aniRuger Azimuthally anisotropic gradient term


4.0 Inputs and OutputsAVO Primary Attributes

36c4aniRuger Azimuthally anisotropic gradient term

37Ruger Azimuth of Maximum AVO Gradient term ( max )

101standard deviation of intercept

202standard deviation of gradient

404sd_astandard deviation of Pan-Gardner a term

505sd_bstandard deviation of Pan-Gardner b term

606sd_cstandard deviation of Pan-Gardner c term

1010standard deviation of Gidlow acoustic impedance contrast

2121Standard Deviation of Gidlow shear impedance contrast

3131sd_aStandard Deviation of Ruger Zero-incidence reflectivity term

3232sd_bisoStandard Deviation of Ruger Azimuthally isotropic gradient

term

3333sd_baniStandard Deviation of Ruger Azimuthally anisotropic gradient

term

3434sd_cisoStandard Deviation of Ruger Azimuthally isotropic gradient

term

3535sd_c2aniStandard Deviation of Ruger Azimuthally anisotropic gradient

term

3636sd_c4aniStandard Deviation of Ruger Azimuthally anisotropic gradient

term

3737sd_Standard Deviation of Ruger Azimuth ( max)

9001signal

9002noise

9003statistical Z



9004standard linear correlation coefficient or standard coefficientof determination

9005robust linear correlation coefficient or robust coefficient ofdetermination

See Attachment A for a complete list of the output trace types.



5.0 Literal Summary

5.1 Inputs

5.1.1 STANDARD_INPUT Port

Identification Header

DESCRIPTIONLITERAL

Data Set DescriptionDATA_DESCEarliest TIME_SHIFT_ALIGNMENTEARLIEST_TIMEMaximum Gather MultiplicityMAX_GATHER_MULTMaximum Reflection TimeMAX_REFLECT_TIMEData Trace Number MaximumMAX_TRACE_NUMSampling IntervalSAMP_INTSort Direction (Array)SORT_DIRECTIONSort Literal (Array)SORT_LITERAL

Trace Header

DESCRIPTIONLITERAL

3–D Azimuth3D_AZIMUTHCentral AngleAVO_CENTRAL_ANGLELength of the Trace in SamplesLTRSAMMute TimeMUTE_TIMEInside Mute TimeMUTE_TIME_INSIDEStackwordSTACK_WORDTime Shift for First Sample AlignmentTIME_SHIFT_ALIGNMENTX Coordinate at Detector LocationXCORD_DETECTX Coordinate at Source LocationXCORD_SOURCEY Coordinate at Detector LocationYCORD_DETECTY Coordinate at Source LocationYCORD_SOURCE

NOTES

FIRST_LIVE_SAMPLE and LAST_LIVE_SAMPLE are not expected as input trace headers, butif present they MUST be the equivalent values of the MUTE_TIME and MUTE_TIME_INSIDEliterals.


5.0 Literal SummaryAVO Primary Attributes

5.2 Outputs

5.2.1 STANDARD_OUTPUT Port

Identification Header

DESCRIPTIONLITERAL

Data Set DescriptionDATA_DESCEarliest TIME_SHIFT_ALIGNMENTEARLIEST_TIMEMaximum Gather MultiplicityMAX_GATHER_MULTMaximum Reflection TimeMAX_REFLECT_TIMESort Direction (array)SORT_DIRECTIONSort Literal (Array)SORT_LITERAL

Trace Header

DESCRIPTIONLITERAL

Amplitude Versus Offset Trace TypeAVO_TRC_TYPEMute TimeMUTE_TIMEInside Mute TimeMUTE_TIME_INSIDEX Coordinate at Average Centroid LocationXCORD_CENTROIDY Coordinate at Average Centroid LocationYCORD_CENTROID


5.0 Literal SummaryAVO Primary Attributes

6.0 Parameter Set Summary

StatusParameter Set TitleParameter Set NameParameter TitleGeophysical Language

RequiredUnitsUNITSUnits of TimeUNITS_TIME

RequiredGeneralGENERALQC Output ModeQC_MODEMinimum number of data samples for fitMIN_POINTS

OptionalShuey 2 TermSHUEY_2_TERMOperation ModeOPERATION_MODE

RequiredGidlowGIDLOWOperation ModeOPERATION_MODE

RequiredQuad 3 TermQUAD_3_TERMOperation ModeOPERATION_MODE

RequiredRugerRUGEROperation ModeOPERATION_MODE

RequiredRuger HigherRUGER_HIGHEROperation ModeOPERATION_MODE

RequiredStandard FitSTANDARD_FITSTANDARD_FITSTANDARD_FIT

RequiredRobust Fit ControlROBUST_CONTROLOverlapOVERLAPScale FactorSCALE_FACTOR

RequiredRuger AxesRUGER_AXESRuger axes testRUGER_AXES


6.0 Parameter Set SummaryAVO Primary Attributes

7.0 Setup Parameters

UNITS7.1 Units(Status: Required, Type: standard)

General InformationThis parameter set specifies the units of measurement. These units of measurement are utilizedfor values specified in other parameters in this SFM.

PARAMETERS:

UNITS_TIMEUnits of Time

This parameter defines the units of time to use when specifying time parameters.

NoOptional:optionType:NoTrace-varying:NoMulti-valued:

Options:Milliseconds'MILLISECONDS'Milliseconds'MS'Microseconds'MICROSECONDS'Microseconds'US'Nanoseconds'NANOSECONDS'Nanoseconds'NS'Seconds'SECONDS''MILLISECONDS'Default:


7.0 Setup ParametersAVO Primary Attributes

GENERAL7.2 General(Status: Required, Type: standard)

General InformationThis parameter set is required and is used to set some general parameters.

PARAMETERS:

QC_MODEQC Output Mode

This parameter determines whether QC traces are output. Two output traces per angle gatherare created when this is used.

For the YES option, signal and noise traces are output for each input trace.

The signal trace is computed from the intercept and gradient, or the a,b and c parameters, withrespect to the angle values of the input trace, while the noise trace is the difference betweenthe signal trace and the original input trace. These trace pairs are ideal input to theDATA_QUALITY_ATTR SFM to produce signal-to-noise related quality indicators.

Reference 1.6 QC Output Mode.

NoOptional:optionType:NoTrace-varying:NoMulti-valued:

Options:Standard output mode of primary attribute and statistical traces'NO'QC output mode of signal and noise traces'YES''NO'Default:



MIN_POINTSMinimum number of data samples for fit

This parameter can be used to increase the minimum limit of the number of points required forthe fitting of the line or curve through the data. A value of COMPUTED will result in thisparameter defaulting to the minimum possible value for the method selected. If a value belowthis minimum possible value is selected for this parameter, it will be increased back to theminimum possible value, otherwise the given value will be taken.

NoOptional:integerType:NoTrace-varying:NoMulti-valued:param()>0Constraint:COMPUTEDDefault:



SHUEY_2_TERM7.3 Shuey 2 Term(Status: Optional, Type: standard)

PARAMETERS:

OPERATION_MODEOperation Mode

The Shuey two-term equation is used to produce the primary AVO intercept (P) and the primaryAVO gradient (G).

NoOptional:stringType:NoTrace-varying:NoMulti-valued:check(param() = "SHUEY_2_TERM","Method isSHUEY_2_TERM for this parameter")

Constraint:

SHUEY_2_TERMDefault:



GIDLOW7.4 Gidlow(Status: Required, Type: standard)

PARAMETERS:


The Gidlow equation is used to produce , the Gidlow acoustic impedance contrast, and ,

the Gidlow shear impedance contrast, see Equation 3

NoOptional:stringType:NoTrace-varying:NoMulti-valued:check(param() = "GIDLOW","Method is GIDLOW for thisparameter")

Constraint:

GIDLOWDefault:



QUAD_3_TERM7.5 Quad 3 Term(Status: Required, Type: standard)

PARAMETERS:


The Pan and Gardner equation is used to produce a, b and c, where a, b and c are combinationsof the P-wave velocity, the S-wave velocity and the density.

NoOptional:stringType:NoTrace-varying:NoMulti-valued:check(param() = "QUAD_3_TERM","Method isQUAD_3_TERM for this parameter")

Constraint:

QUAD_3_TERMDefault:



RUGER7.6 Ruger(Status: Required, Type: standard)

PARAMETERS:


The normal form of Ruger's approximation is used to produce 4 terms, a, biso, bani and .

NoOptional:stringType:NoTrace-varying:NoMulti-valued:check(param() = "RUGER","Method is RUGER for thisparameter")

Constraint:

RUGERDefault:



RUGER_HIGHER7.7 Ruger Higher(Status: Required, Type: standard)

PARAMETERS:


The higher order form of Ruger's approximation is used to produce 7 terms, a, biso, bani, ciso,

c4ani, c2ani and

NoOptional:stringType:NoTrace-varying:NoMulti-valued:check(param() = "RUGER_HIGHER","Method isRUGER_HIGHER for this parameter")

Constraint:

RUGER_HIGHERDefault:



STANDARD_FIT7.8 Standard Fit(Status: Required, Type: standard)

General InformationThis parameter set is used when the LINE_FIT selection is for the STANDARD_FIT option.

PARAMETERS:

STANDARD_FITSTANDARD_FIT

Linear regression is a standard least-squares fit.

NoOptional:stringType:NoTrace-varying:NoMulti-valued:check(param() = "STANDARD_FIT","Option isSTANDARD_FIT when this parameter is selected")

Constraint:

STANDARD_FITDefault:



ROBUST_CONTROL7.9 Robust Fit Control(Status: Required, Type: standard)

General InformationThis parameter set is used when the LINE_FIT selection is for the ROBUST_FIT option.

The robust fit is done in two steps. In step one, the data is divided into two segments (or threefor the three-term case), each with the same number of traces. A median point is found for eachsegment and a line or parabola is fitted through them to form the initial fit. In step two, amplitudevalues are found which do not conform to the initial fit. These amplitude outliers are then eitherweighted or eliminated from the least-squares fit. See 1.5 Line Fitting Mode.

PARAMETERS:

OVERLAPOverlap

This parameter defines the overlap in the number of traces between the segments in the firststep of the robust-fitting process. For a value of 0, every trace falls into only one segment. Fora value of 3, three traces are shared by adjacent segments. An OVERLAP parameter valuegreater than 0 should be specified if non-random noise contaminates more than 50% of anysegment.

NoOptional:integerType:NoTrace-varying:NoMulti-valued:param() >= 0Constraint:0Default:



SCALE_FACTORScale Factor

This parameter specifies the scale factor of a term which defines the maximum distance betweena data point and the initial robust fit. If a data point is greater than this distance from the initialfit, it is considered an outlier. The default of 2.1 is appropriate for random noise. For lowervalues such as from 1.0 to 1.5, more data points are identified as outliers, and thus eliminatedfrom the least-squares fit.

NoOptional:numberType:NoTrace-varying:NoMulti-valued:param() > 0.1 and param() < 5.0Constraint:2.1Default:



RUGER_AXES7.10 Ruger Axes(Status: Required, Type: standard)

PARAMETERS:

RUGER_AXESRuger axes test

Temporary parameter to allow sign convention for Ruger axes to be tested.

YesOptional:optionType:NoTrace-varying:NoMulti-valued:

Options:Ba same sign as Bi'SAME_SIGN'Ba opposite sign to Bi'OPPOSITE_SIGN'SAME_SIGNDefault:



Attachment A: AVO_TRC_TYPE Definitions

This attachment provides associated numbers and definitions for the AVO_TRC_TYPE traceheader literal.

Click here to view the attachment.


Attachment AAVO Primary Attributes

avo prim attr

Documents

offset avo attributes

primary avo attributesare

azimuthal avo

quadratic fit

input common angle gathers

input data

robust fitting

ruger approximation1