6b. avo theory

AVO TheoryHilfan Khairy

UTP

Rock physics and AVO-Universiti Teknologi PETRONAS

Dr. Hilfan Khairy

6b. Amplitude Versus Offset (AVO)

Seismic reflection amplitude with change in distance between shot-point and receiver.

It can be converted into amplitude change with angle


Dr. Hilfan Khairy

AVO or Amplitude Versus Offset is one of seismic attribute that usually used for lithology and fluid prediction

AVO was firstly introduced by Ostrander in 1982 and 1984. He utilized AVO to analyst gas-sand in seismic anomaly

AVO method successfully identified gas fluid from lithology effect such as: 1. Low impedance gas-sand2. Coal3. Carbonate 4. etc.


Dr. Hilfan Khairy

When seismic wave arrives at the media boundary, it will convert into several types of seismic wave. The amplitude variation is

dependent on Poisson ratio, wave velocity and density of medium


Dr. Hilfan Khairy

The how seismic wave are reflected or transmitted is described by ZOEPPRITZ EQUATION

1 1 2 2 1

1 1 2 2 1

1 1 1 1 2 2 2 2 1 1

1 1 1 1 1 2 2 2 2 2

cos sin cos sin cos

sin cos sin cos sin

cos 2 sin 2 cos 2 sin 2 cos 2

sin 2 cos 2 sin 2 cos 2

pp ps pp ps p

pp ps pp ps p

pp ps pp ps p

pp ps pp ps

R R R

R R R

R Z R W Z W R Z

R W R W W W R

1 1 1

ii i i i i i i

i

sin 2

βγ = ; Z =ρ α ; W =ρ β ; i=1,2

α

: P wave velocity

: S wave velocity

ρ : Density

p W

6b.1 Zoeppritz equation

Karl Bernhard Zoeppritz(1881-1908: 26 years old)


Dr. Hilfan Khairy

Zoeppritz equation did not give direct solution how those equation relate to petrophysics parameter. Aki-Richard simplified it in three elements in term of P-wave velocity, S-wave velocity and density as follow:


Dr. Hilfan Khairy

The Aki-Richard equation can be re-arranged as:

2

2 2 2 2

2 2

1 1 14 2 sin tan sin

2 2 2R

If the ratio of / or Vs/Vp = ½ and ignoring third term of 2 2tan sin

22 sinp p sR R R R

1

2pR

1

2sR

(*)

Q1: 1. Proof equation (*)!2. Determine range of degree when

! 2 2tan sin

Gradient=GIntercept=Rp

2p sR R


Dr. Hilfan Khairy

6b.2 Shuey approximation

Shuey simplified Zoeppritz equation in term of P wave velocity (Vp), density () and poisson ratio ()

2 2 2

2sin tan sin

1p p oR R R A

1 2

2

2 1

1 2

2 11

oA B B

B


Dr. Hilfan Khairy

29sin

4p pR R R

Gradient=GIntercept=Rp 9

4pR

(*) Q2:Proof it!or

Hiltermann approximation =1/3 ; Ao=-1 ; third term 0

2 29cos sin

4pR R First term dominant in near offset

Second term dominant in far offset

4( )

9pG R


Dr. Hilfan Khairy

Shuey and Aki-Richard have almost the same amplitude for the incident angle less than 30o

Shuey

Aki-Richard


Dr. Hilfan Khairy

(Source: Hampson-Russel training manual)


Dr. Hilfan Khairy

6b.3 Smith/Gidlow approximation

2

2 2

2

1 12 4 sin tan

2 2R

Rearrange Aki-Richard equation:

Ignoring density factor by using Gardner equation 1/4a 1

4

R a b

22 2

2

5 1 1sin tan

8 2 2a

22

24 sinb

Q3:Proof it!

This R() is also called as “fluid-factor stack”


Dr. Hilfan Khairy

Most of poisson ratio of the reservoir rocks are in between 0.1 – 0.3 which indicate that Vp/Vs ratio has monotonic increasing with poisson ratio. Thus Vp/Vs .

Smith and Gidlow (1987) introducing “pseudo poisson ratio reflectivity “as:

p s

p s

V V

V V

Q4: Proof it!

Recalling “mudrock line” of Castagnaequation that note all water-bearing clastic silicates should lie close to this line

1.16 1.36Vp Vs


Dr. Hilfan Khairy

It is defined a “fluid factor” parameter

1.16

p p

p pobserved mudrock

p

p observed

V VF

V V

VF

V

Thus if the fluid factor F=0 means that it is non-prospective zone reservoir and if F0 it is prospective zone

Background trend (shale/brine sand): F 0Shale/Gas sand: F < 0 (negative)Gas sand/Brine sand : F > 0 (positive)


Dr. Hilfan Khairy

Ideal gas indicator

(Smith and Sutherland, Geophysics 1996)


Dr. Hilfan Khairy

6b.4 Equating Aki-Richard (AR) with Smith-Gidlow (SG)

2sinpR R G 1

2pR

1

2sR

2p sG R R

recalling Gardner equation 1/4a 1

4

1.6 pR

and

3

5pR G

Q5: Proof it!

Pseudo poisson ratio reflectivity

pR G

0.58

1.252 0.58p

F

F R G

Fluid factor

assume /=1/2


Dr. Hilfan Khairy

Summary of Approximation to Aki-Richards

pX aR bG


Dr. Hilfan Khairy

Example:

Calculate the fluid factor from data measurement below and determine type of fluid.

1

2

Vp1(m/s)

Vs1(m/s)

Rho1(g/cc)

Vp2(m/s)

Vs2(m/s)

Rho2(g/cc)

2000 1420 2.2 2800 1800 2.5

2020 1425 2.1 2810 1910 2.52

1850 1430 1.98 2780 1850 2.6

1930 1400 2.1 2650 1880 2.49

1980 1450 2 2770 1930 2.45


Dr. Hilfan Khairy

Vp Vs Rho Vp Vs Rho Rp Rs G F

800 380 0.3 2400 1610 2.35 0.230496 0.181842 -0.13319 0.211333

790 485 0.42 2415 1667.5 2.31 0.25447 0.236336 -0.2182 0.192039

930 420 0.62 2315 1640 2.29 0.336235 0.26342 -0.1906 0.310416

720 480 0.39 2290 1640 2.295 0.242173 0.231309 -0.22045 0.175342

790 480 0.45 2375 1690 2.225 0.267439 0.243135 -0.21883 0.207912

F > 00.58

1.252 0.58p

F

F R G

Gas sand/Brine sand


Dr. Hilfan Khairy

Pufff…!


Dr. Hilfan Khairy

P-wave (a) and S-wave (b) velocity reflectivity for gas detection (Smith and Gidlow, 1987)

(a) (b)


Dr. Hilfan Khairy

Pseudo poisson ratio reflectivity (a) and fluid factor (b) reflectivity for gas detection (Smith and Gidlow, 1987)

(a) (b)


Dr. Hilfan Khairy

The first term in AVO equation (Rp) represent for zero offset and the second term (G)depend on poisson ratio. Thus any significant change in poissonratio will generate the changes in AVO response, particularly in far offset.


Dr. Hilfan Khairy

Scenario of an AVO in response of AI and poisson ratio


Dr. Hilfan Khairy

ACOUSTIC IMPEDANCE

POISSON’S RATIO

RELATIVEAMPLITUDE

ABSOLUTE AMPLITUDE

AVO RESPONSE SUMMARY


Dr. Hilfan Khairy

6b.5 Transformation from offset into angle

Zoeppritz and Shuey equation havedependency with the angle. Thusany seismic record has to beconverted from the offset into theangle before using Shuey/Zoeppritzequation.

tan2

X

Z Z = depth

X = offset

2

oVtZ

V= velocity (RMS or average)to=total zero-offset traveltime


Dr. Hilfan Khairy

Thus transformation offset-angle function is 1tano

X

Vt

In the constant angle, the amplitude is gained from the longer offset on the AVO gather as the time increase

(*)


Dr. Hilfan Khairy

Previous transformation function is dedicated for single layer case. For multilayer cases, we need to extend the parameter as follow. Defined ray parameter (P)

int

sinP

V

to

t

X

t=+Px

x

t

t2=to2 +x2/v2

P=t/x

22 2

o

rms

xt t

V 2

rms

XP

tV

int

2sin

rms

xV

tV

Finally we obtain

Vint= velocity intervalVrms=root mean square velocity

(**)


Dr. Hilfan Khairy

Q7: By considering the Figure above, please verified that equation (**) will turn back into (*) for single layer case

X

S R

ZVto/2Vt/2

6b. avo theory

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