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By Haseeb AhmedM.Phil GeophysicsInstitute of Geology, University of the Punjab AVO Analysis

Amplitude versus offset (AVO) is primarily the variation in seismic reflection amplitude with change in distance between shot point and the receiver

Its another name is AVA (amplitude variation with angle)

AVO analysis is conducted on CMP data

Fig. showing AVO (a) & (b)

Avo iNTRODUCTIONIt can physically explain presence of hydrocarbon in the reservoirs and the thickness, porosity, density, velocity, lithology and fluid content of the reservoir of the rock can be estimated.

The Zoeppritz EquationsZoeppritz derived the amplitudes of the reflected and transmitted waves using the conservation of stress and displacement across the layer boundary

which gives four equations with four unknowns.

Inverting the matrix form of the Zoeppritz equations gives us the exact amplitudes as a function of angle

The Zoeppritz Equations

6The Aki-Richards EquationThe Aki-Richards equation is a linearized approximation to the Zoeppritz equations.

The initial form (Richards and Frasier, 1976) separated the velocity and density terms:

The Aki-Richards EquationWhere;

Wiggins Version of the Aki-Richards EquationA more intuitive, but totally equivalent, form was derived by Wiggins.

He separated the equation into three reflection terms, each weaker than the previous term:

Where ?

Interpreting the Aki-Richards EquationThe first term, A, is a linearized version of the zero offset reflection coefficient and is thus a function of only density and P-wave velocity.

The second term, B, is a gradient multiplied by sin2, and has the biggest effect on amplitude change as a function of offset. It is dependent on changes in P-wave velocity, S-wave velocity, and density.

The third term, C, is called the curvature term and is dependent on changes in P-wave velocity only. It is multiplied by tan2*sin2 and thus contributes very little to the amplitude effects below angles of 30 degrees. (Note: Prove to yourself that tan2*sin2 = tan2 - sin2, since the equation is often written in this form.)

Ostranders Gas Sand ModelOstrander (1984) was one of the first to write about AVO effects in gas sands and proposed a simple two-layer model which encased a low impedance, low Poissons ratio sand, between two higher impedance, higher Poissons ratio shales. (This model is shown in the next slide).

Ostranders model worked well in the Sacramento valley gas fields. However, it represents only one type of AVO anomaly (Class 3) and the others will be discussed in the next section.

* Note : The model consists of a low acoustic impedance and Poissons ratio gas sand encased between two shales.

Synthetic from Ostranders Model

(a) Well log responses for the model.

(b) Synthetic seismic.

Wet and Gas Models

Wet Sand ModelGas Saturated Model

AVO ModelsIn the next two slides, we are going to compute the top and base event responses from Models A and B, using the following values, where the Wet and Gas cases were computed using the Biot-Gassmann equations:

Wet: VP= 2500 m/s, VS= 1250 m/s, = 2.11 g/cc, s = 0.33

Gas: VP= 2000 m/s, VS= 1310 m/s, = 1.95 g/cc, s = 0.12

Shale: VP= 2250 m/s, VS= 1125 m/s, = 2.0 g/cc, s = 0.33

We will consider the AVO effects with and without the third term in the Aki-Richards equation.

AVO Wet Model

These figures show the AVO responses from the (a) top and (b) base of the wet sand. Notice the decrease of amplitude, and also the fact that the two-term approximation is only valid out to 30 degrees.

AVO Gas Model

The above figures show the AVO responses from the (a) top and (b) base of the gas sand. Notice the increase of amplitude, and again the fact that the two-term approximation is only valid out to 30 degrees.

Shueys EquationShuey (1985) rewrote the Aki-Richards equation using VP, , and . Only the gradient is different than in the Aki-Richards expression

This figure shows a comparison between the two forms of the Aki-Richards equation for the gas sand considered earlier.

AVO Effects(a) Gas sandstone case: Note that the effect of Dd and De is to increase the AVO effectsb) Wet sandstone case: Note that the effect of Dd and De is to create apparent AVO decreases.

Class 1Class 2Class 3

Class 1Class 2Class 3Back-Trend AVO

For brine-saturated clastic rocks over a limited depth range in a particular locality, there may be a well-defined relationship between the AVO intercept (A) and the AVO gradient (B). linear A versus B trends, all of which pass through the origin (B = 0 when A = 0).

Thus, in a given time window, non-hydrocarbon-bearing clastic rocks often exhibit a well-defined back- ground trend; deviations from this background are indicative of hydrocarbons or unusual litholo- gies.

Possible Deviation B/w Gas and Brine

Deviations from the background petro- physical trends, as would be caused by hydrocarbons or unusual litholo- gies, cause deviations from the background A versus B trend. This figure shows brine sand-gas sand tie lines for shale over brine-sand reflections falling along a given background trend

General classification

Rutherford and Williams (Geophysics, 1989) for Class I (high impedance) and Class II (small impedance contrast) sands. However, we differ from Rutherford and Williams in that we subdivide their Class III sands (low impedance) into two classes (III and IV).

Amplitude vs angle

Class 1 (Dim out)

Amplitude decreases with increasing angle, and may reverse phase on the far angle stackAmplitude on the full stack is smaller for the hydrocarbon zone than for an equivalent wet saturated zone.

Wavelet character is peak-trough on near angle stackWavelet character may or may not be peak-trough on the far angle stack.

Class 2 (Phase reversal)

There is little indication of the gas sand on the near angle stack.

The gas sand event increases amplitude with increasing angle. This attribute is more pronounced than anticipated because of the amplitude decrease of the shale- upon-shale reflections.

The gas sand event may or may not be evident on the full stack, depending on the far angle amplitude contribution to the stack.

Wavelet character on the stack may or may not be trough-peak for a hydrocarbon charged thin bed.

Class 2 (Phase reversal)

Wavelet character is trough-peak on the far angle stack.

Inferences about lithology are contained in the amplitude variation with incident angle.

AVO alone, unless carefully calibrated, cannot unambiguously distinguish a clean wet sand from a gas sand, because both have similar (increasing ) behavior with offset.

Class 3 (Bright spot)

Hydrocarbon zones are bright on the stack section and on all angle limited stacks.The hydrocarbon reflection amplitude, with respect to the background reflection amplitude, is constant or increases slightly with incident angle range.

Even though the amplitude of the hydrocarbon event can decrease with angle, as suggested for the Class 4 AVO anomalies, the surrounding shale-upon-shale reflections normally decrease in amplitude with angle at a faster rate.

Class 3 (Bright spot)

Wavelet character is trough-peak on all angle stacks. This assumes that the dominant phase of the seismic wavelet is zero and the reservoir is below tuning thickness

Hydrocarbon prediction is possible from the stack section.

Cont

Behavior of the various gas sand classes.

Thank you

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R (All three terms)R (First two terms)Angle (degrees)AmplitudeAVO - Wet Sand (Model A) Top

Sheet1Model ATopBasedeltaavgdelta/avgShaleWet SandGas SandVp =2250250025023750.105225025002000Vs =112512501251187.50.105112512501310rho =22.110.112.0550.05422.111.95Vs/Vp =0.500Rp =0.079Rs =0.079G =-0.079C =0.053inc =0.0872663889radians5degreesAngle(Rad)Angle(Deg)RR - C000.0790.0790.087266388950.0790.0790.1745327778100.0770.0770.2617991667150.0740.0740.3490655556200.0710.0700.4363319444250.0670.0650.5235983333300.0640.0600.6108647222350.0620.0530.6981311111400.0620.0470.7853975450.0660.040

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R (All three terms)R (First two terms)Angle (degrees)AmplitudeAVO - Wet Sand (Model A) Top

Sheet2

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R (All three terms)R (First two terms)Angle (degrees)AmplitudeAVO - Wet Sand (Model A) Base

Sheet1Model ATopBasedeltaavgdelta/avgShaleWet SandGas SandVp =25002250-2502375-0.105225025002000Vs =12501125-1251187.5-0.105112512501310rho =2.112-0.112.055-0.05422.111.95Vs/Vp =0.500Rp =-0.079Rs =-0.079G =0.079C =-0.053inc =0.0872663889radians5degreesAngle(Rad)Angle(Deg)RR - C00-0.079-0.0790.08726638895-0.079-0.0790.174532777810-0.077-0.0770.261799166715-0.074-0.0740.349065555620-0.071-0.0700.436331944425-0.067-0.0650.523598333330-0.064-0.0600.610864722235-0.062-0.0530.698131111140-0.062-0.0470.785397545-0.066-0.040

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R (All three terms)R (First two terms)Angle (degrees)AmplitudeAVO - Wet Sand (Model A) Base

Sheet2

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R (All three terms)R (First two terms)Angle (degrees)AmplitudeAVO - Gas Sand (Model B) Top

Sheet1Model ATopBasedeltaavgdelta/avgShaleWet SandGas SandVp =22502000-2502125-0.118225025002000Vs =112513101851217.50.152112512501310rho =21.95-0.051.975-0.02522.111.95Vs/Vp =0.573Rp =-0.071Rs =0.063G =-0.242C =-0.059inc =0.0872663889radians5degreesAngle(Rad)Angle(Deg)RR - C00-0.071-0.0710.08726638895-0.073-0.0730.174532777810-0.079-0.0790.261799166715-0.088-0.0880.349065555620-0.101-0.1000.436331944425-0.117-0.1150.523598333330-0.137-0.1320.610864722235-0.160-0.1510.698131111140-0.188-0.1710.785397545-0.222-0.192

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R (All three terms)R (First two terms)Angle (degrees)AmplitudeAVO - Gas Sand (Model B) Top

Sheet2

Sheet3

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R (All three terms)R (First two terms)Angle (degrees)AmplitudeAVO - Gas Sand (Model B) Base

Sheet1Model ATopBasedeltaavgdelta/avgShaleWet SandGas SandVp =2000225025021250.118225025002000Vs =13101125-1851217.5-0.152112512501310rho =1.9520.051.9750.02522.111.95Vs/Vp =0.573Rp =0.071Rs =-0.063G =0.242C =0.059inc =0.0872663889radians5degreesAngle(Rad)Angle(Deg)RR - C000.0710.0710.087266388950.0730.0730.1745327778100.0790.0790.2617991667150.0880.0880.3490655556200.1010.1000.4363319444250.1170.1150.5235983333300.1370.1320.6108647222350.1600.1510.6981311111400.1880.1710.7853975450.2220.192

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R (All three terms)R (First two terms)Angle (degrees)AmplitudeAVO - Gas Sand (Model B) Base

Sheet2

Sheet3

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A-R TopShuey TopA-R BaseShuey BaseAngle (degrees)AmplitudeGas Sand ModelAki-Richards vs Shuey

Sheet1Model ATopBasedeltaavgdelta/avgShaleWet SandGas SandVp =22502000-2502125-0.118225025002000Vs =112513101851217.50.152112512501310rho =21.95-0.051.975-0.02522.111.95Vs/Vp =0.5000.6550.573sigma =0.3330.124-0.2090.229Rp =-0.071Rs =0.063Ga-r =-0.242B =0.823Gshuey =-0.227C =-0.059inc =0.0872663889radians5degreesAngle(Rad)Angle(Deg)Ra-rRshueyBase:00-0.071-0.0710.0710.0710.08726638895-0.073-0.0730.0730.0730.174532777810-0.079-0.0780.0790.0780.261799166715-0.088-0.0870.0880.0870.349065555620-0.101-0.0990.1010.0990.436331944425-0.117-0.1140.1170.1140.523598333330-0.137-0.1330.1370.1330.610864722235-0.160-0.1560.1600.1560.698131111140-0.188-0.1820.1880.1820.785397545-0.222-0.2140.2220.214

Sheet1

A-R TopShuey TopA-R BaseShuey BaseAngle (degrees)AmplitudeGas Sand ModelAki-Richards vs Shuey

Sheet2

Sheet3