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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
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