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7 Quantitative Interpretation Quantitative Interpretation Objectives - To use seismic attributes to derive rock properties with care - Familiar with many different ways of doing quantitative interpretation - Understand data precondition for quantitative interpretation Why do we need quantitative interpretation? - It is tempting to instantly relate mapped seismic attribute patterns to geology without considering the physics (qualitative Interpretation) - It is very easy to derive spurious correlation of attributes and well data. Later there is a need to find physical explanation for seismic attributes - To understand key factors that effect seismic amplitude as it has the potential to directly impact the risk on exploration The Essentials of Amplitude Interpretation Wavelet Shape (phase and polarity) Type of Seismic (full, near, far, intercept, gradient) Interpretation Gas Sand Carbonate High porosity brine sand Igneous over pressure tuning imaging artifact, ?? Reflection Model + Shale Amp. 0 Offset Sand - Basic Rock Properties Two basic rock properties that control the elastic response of isotropic rocks to sound waves - Acoustic Impedance (AI) = Vp* Density - Ratio of compressional to shear waves velocity (Vp/Vs) Compression and Shear Wave Velocity - Vp and Vs relate to rock properties because they can be thought of as the degree to which rock can be changed in its volume versus the degree to which it can be changed in its shape Relationship Velocity to Rock Properties Stress (S) = Force (kg-m/sec2)/ Area (pr2) Strain = Amount of deformation an object experiences compared to its original size and shape (dimensionless) S Relationship Velocity to Rock Properties POISSON RATIO (s) and Vp/Vs Relationship First Order Rock Property Relationship Of Different Elastic Parameters 1. Porosity decrease with depth due to compaction 2. Bulk density is linearly relate to porosity 3. AI is negatively correlated to porosity 4. For a given lithology there is strong relationship between density and velocity 5. For a given porosity density and AI can be lowered (red arrow) by less dense fluid (HC) and more pore space 6. Vp/Vs decreases with depth 7. HC presence lowers Poisson Ratio and AI First Order Rock Property Relationship with Pressure 1. Vp (and Vs) increase with increasing effective pressure (Pe) 2. Over pressure sand tend to have higher Poisson Rations than overpressured gas sands 3. Experimental data show that brine sands generally show increasing poisson ratio with decreasing effective pressure. But it is also possible that there is a slight decrease with decreasing effective pressure Normal Incidence Reflectivity NOTE: - The primary factor in seismic reflectivity is the RC which depends on the contrast of AI at interface - When the seismic is normally incident to the interface (incident angle is 0) the amount of energy reflected is proportional to the RC Non-normal Incidence Reflectivity NOTE: - When the seismic is incident at non-normal angle to the interface (incident angle is < 0) the amount of energy reflected not only depends on AI contrast, but also Poisson Ration contrast (Zoeppritz 1919) Angle of Incident vs transmitted waves Simplification of Zoeppritz Equation Amplitude Changes With Angle Linearization of Zeoppritz Equation NOTE: - To simplify the equation so that variation in amplitude is linear in terms of Sin2q - To represent AVO response in terms of normal incidence amplitude (Ro) and the Gradient (G) (Shuey 1985) - However, Linearization becomes invalid at large angle Processing For Relative Amplitude Objective of AVO Processing: - To remove noise and propagation effects unrelated to primary reflectivity of rock units whilst preserving (as much as possible) the relative amplitude across the prestack gather. Seismic Attributes • Attributes is the quantity of envelop amplitude, instantaneous phase, instantaneous frequency and other measurements derived from seismic data • Attributes can be extracted from any type of data (amplitude, velocity, complex trace, etc.). • Interpreters use attributes in reservoir delineation and reservoir characterization. • Interpreters should understand the physical processes associated with attribute responses. • If you do not understand why attributes are related to reservoir characteristics, use these attributes with caution. Attributes Product of Seismic Inversion Elastic Attribute Parameters Vp: Vs: r: Ip: Is: l: m: Q: s: R0: G: Compressional velocity Shear velocity Density P impedance = acoustic impedance S impedance Lambda, compressibility Mu, rigidity Incidence angle Sigma, Poisson’s ratio Zero offset reflectivity, intercept of elastic impedance curve Gradient of elastic impedance curve Elastic Attributes Vp/Vs Ratio Poisson Ratio Acoustic Impedance Shear Impedance Rho Mu Rho Lambda Lambda Mu Ratio Seismic Attributes Group • amplitude statistics • complex trace statistics • spectral statistics • sequence statistics Statistic calculation of any input data Seismic Attributes Group • amplitude statistics • complex trace statistics • spectral statistics • sequence statistics Complex trace calculation of input amplitude traces Seismic Attributes Group • amplitude statistics • complex trace statistics • spectral statistics • sequence statistics Calculating the characteristic of power spectra of the data in frequency domain Seismic Attributes Group • amplitude statistics • complex trace statistics • spectral statistics • sequence statistics These attributes focus upon energy build-up in a sequence, polarity comparisons, and amplitude threshold analysis. RMS Amplitude • RMS amplitude is calculated as the square root of the average of the squares of the amplitudes found in the analysis window • Because amplitudes are squared before averaging, the RMS computation is very sensitive to extreme amplitude values. Average Absolute Amplitude • For each trace, the absolute values of the amplitudes in the analysis window are added; then the total is divided by the number of samples in the window to yield the mean. • Average absolute amplitude is not nearly as sensitive to extreme amplitudes as is RMS amplitude, which involves squaring of the amplitude values. Maximum Peak Amplitude For each trace, PAL does a parabolic fit through the maximum positive amplitude in the analysis window and the two samples on either side of it. The maximum value along that curve is interpolated and output to the attribute horizon file. Average Peak Amplitude To calculate the average peak amplitude for each trace, all the positive values within the analysis window are added; then the total is divided by the number of positive samples within the window. Maximum Trough Amplitude • For each trace, PAL does a parabolic fit through the maximum negative amplitude in the analysis window and the two samples on either side of it. • The maximum negative value along that curve is interpolated and the absolute value is output to the attribute horizon file Maximum Absolute Amplitude • To calculate the Maximum Absolute Amplitude for each trace, PAL calculates the peak and trough values within the analysis window and determines the largest peak or trough. • AL then does a parabolic fit through the values in this peak or trough and the two samples on either side of it. The maximum value is interpolated and output for that trace. Total Absolute Amplitude For each trace, the sum of all absolute trace amplitudes within the specified window are output to the attribute horizon file. Total Amplitude For each trace, Total Amplitude computes the total amplitude (integration of amplitude) for samples within the horizons. Average Energy For each trace, the squared values of the amplitudes in the analysis window are added. The total is then divided by the number of samples in the window to yield the mean Total Energy For each trace, the squared values of the amplitudes in the analysis window are added. Maximum Trough Amplitude For each trace, PAL does a parabolic fit through the maximum negative amplitude in the analysis window and the two samples on either side of it. The maximum negative value along that curve is interpolated and the absolute value is output to the attribute horizon file. Mean Amplitude For each trace, this process adds the values of the amplitudes in the analysis window and then divides the sum by the number of non-zero sample values. Attribute Sensitivity Summary Of Attribute Applications Quantitative Analysis Methods Linear Regression Principal Component Neural Network Region Growing Classification Discriminate Analysis Cluster Analysis Thresholding Linear Regression Data Analysis Linear Regression Data Analysis Linear Regression Data Analysis Linear Regression Data Analysis Using Rank Correlation Well data and Seismic Attribute Correlation Seismic Section Generated Impedance Section 45 RMS Amplitude extraction from Seismic Amplitude Cube RMS Amplitude extraction from Impedance Cube 46 Linear Regression Data Analysis Linear Regression Data Analysis Seismic Derived Net Pay Map Waveform Classification Supervised Waveform Classification • Use Similarity Values to compare the target wavelets to the reference wavelet. • The darker areas in this display identify wavelets that more closely match the reference wavelet than those wavelets mapped in white. Un-supervised Waveform Classification Quantitative Analysis Result Using Discriminant Analysis Seismic Attributes Seismic Attributes Seismic Attributes Seismic Attributes Seismic Attributes Seismic Attributes Seismic Attributes Seismic Attributes Seismic Attributes Seismic Attributes Convolution Model & Polarity Convention