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AVO analysis and Impedance InversionOkey Ileka

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AVO Analysis

• Introduction• AVO Pre-processing• AVO modeling• AVO parameters• AVO crossplot analysis• AVO attributes• Some application of AVO• Probabilistic AVO analysis

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Impedance Inversion

• Post stack 1D Impedance Inversion• Far-offset elastic Impedance• Lambda-mu-rho estimation• P to S elastic Inversion• Anisotropic elastic Impedance• Interpretation of Rock physics template

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Introduction

• AVO is the amplitude variation with offset

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Introduction

Castagna lecture notes

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Introduction

Castagna lecture notes

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Simplified Shuey (1985) Form of the Richards and Frazier (1976)

Approximation

⎟⎟⎠

⎞⎜⎜⎝

⎛ Δ+

Δ≈

ρρ

p

p

VV

A21

θθ 2sin)( BAR +≈

pRA = sp RRB 2−≈

s

s

p

s

p

p

p

s

VV

VV

VV

VVB Δ

−Δ

+Δ

−≈ 2

2

2

2

4212

ρρ

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Third Order Approximation

θθθθ 222 tansinsin)( CBAR ++≈

⎟⎟⎠

⎞⎜⎜⎝

⎛ Δ+

Δ=

ρρ

p

p

VV

A21

p

p

VV

CΔ

≈21

ρρΔ

≈−21CA

Castagna lecture note

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Hiltermann Approximation

θσθθ sin25.2cos)(48476 G

AR Δ+≈ 22

BAG +=

Castagna lecture note

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AVO preprocessing

Castagna lecture notes

11Castagna lecture note

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Factors that amplitudes

• Earth effects• Acquisition related effects• Noise

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Earth effects

• Spherical divergence• Absorption• Transmission losses• Interbed multiples• Converted phases• Tunning effect• Anisotropy• structure

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Acquisition-related effects and noise

• Acquisition-related effects• Source reciever arrays• Reciever sensitivity

• Noise• Source generated noise• Coherent or random noise

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AVO Pre-processing

• Spiking deconvolution and wavelet processing

• Spherical divergence correction• Surface consistent amplitude balancing• Multiple removal• NMO correction• DMO correction• Pre-stack migration

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AVO preprocesing

Castagna lecture notes

17Castagna lecture notes

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AVO modeling

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Physical Interpretation

(Russel, 1999)

θθ 2sin)( BAR +≈

Castagna lecture notes

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AVO parameters

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Castagna lecture notes

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AVO crossplot

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From Simm et al., 2000

Castagna lecture notes

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AVO attributes

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AVO Indicators/Attributes• Intercept• Gradient• Near and far stacks• Curvature• CDP stack• Change in Poisson’s ratio• Fluid Factor

• Intercept minus Gradient• Intercept plus Gradient• Intercept times Gradient• Rp-Rs• P and S wave velocity

contrast• Density Contrast• Amoco Indicator F(F-N)• Lamba-mu-rho

Castagna lecture notes

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Calculated AVO Attributes

A = interceptB = gradient

RC (θ) = A + B (sin²θ)r² = correlationA × B(A + B)/2 ~ Rp - Rs(A – B)/2 ~ Rs

NI = normal interceptPR = Poisson reflectivity RC (θ) = NI(cos²θ) + PR(sin²θ)

r² = correlationNI × PR

A = interceptB = gradientC = curvature RC (θ) = A + B (sin²θ) + C (sin²θ)(tan²θ)r² = correlationA × B(A + B)/2 ~ Rp - Rs(A – B)/2 ~ Rs

Shuey 2 Term

Shuey 3 Term

Verm-HiltermanA – C

Roden, 2005Castagna lecture notes

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Some application of AVO

• Residual gas saturation (converted waves)

• Flat spot analysis

• Overpressure detection

• Density estimation

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Probabilistic AVO analysis

• In probabilistic AVO analysis the AVO parameters and attributes are assigned probability density function (PDF) or cumulative density function (CDF)

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Impedance Inversion

• The goal of geophysical inversion is to estimate model parameter from observed data

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Impedance Inversion

• Post stack 1D Impedance Inversion• Far-offset elastic Impedance• Lambda-mu-rho estimation• P to S elastic Inversion• Anisotropic elastic Impedance• Interpretation of Rock physics template

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Poststack 1D impedance Inversion

• Inversion of near stack traces

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Acoustic Impedance Inversion

Near Near Angle StackAngle Stack

Sonic,DensitySonic,DensityLogsLogs HorizonsHorizons

WaveletWavelet AI EarthAI EarthModelModel

BandlimitedBandlimitedInversionInversion

TrendTrendModelModel

MergedMergedAIAI

tietie tietie

Sena, 1997Castagna lecture note

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Far offset elastic Impedance

• Inversion of far offset traces

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The Elastic Impedance

E = Vpα Vs

β ργ

α = 1/cos2θ β = -8(Vs/Vp)2sin2θ

γ = 1 + β/2

Sena, 1997Castagna lecture notes

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Elastic Impedance InversionFar Far

Angle StackAngle StackSonic,Shear SonicSonic,Shear Sonicand Density Logsand Density Logs HorizonsHorizons

WaveletWavelet EI EarthEI EarthModelModel

BandlimitedBandlimitedInversionInversion

TrendTrendModelModel

MergedMergedEIEI

tietie tietie

Sena, 1997Castagna lecture note

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Lambda Rho estimation

Hilterman’s lecture note

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P –to- S elastic Inversion

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Reflection Coefficients: Angle vs. Offset

σσ

σ

σ

Stewart and Gasier lecture note

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P-S Reflection Coefficient(Aki & Richards, 1980)

Rps

Relative S-velocity changeRelative density change

First Order

Stewart and Gasier lecture note

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Anisotropic elastic Inversion

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Anisotropy

Hilterman course notes

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Anisotropic Inversion

Hilterman course notes

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Interpretation of Rock Physics Template

• The rock physics template is based on a compiled catalog or atlas of RPT’scalculated by a rock physics expert.

• The seismic interpreter can interpret elastic inversion results without in-depth knowledge about rock physics theory

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• Thank you