Slide 8 - Rock Physics Ambiguity

Regression-based approach and Litho-Fluidal classes = Involves analyzing relationships between variables to classify facies Crossplot approach = Uses graphical representation of data points to classify facies Bayesian classification and facies-based properties prediction = Utilizes Bayesian techniques to classify facies and predict properties

Cubes of elastic parameters = Represented in 3D models of Acoustic Impedance and Vp/Vs ratio Density variations = Can be retrieved from seismic amplitude responses with some uncertainty

Predicting petrophysical properties using linear regression models = Relies on strong statistical correlations with elastic parameters Petrophysical properties influenced by multiple factors = May be challenging to predict from seismic inversion results due to uncertainty and ambiguity

Bayes' theorem = Combines likelihood function with prior probabilities Prior probability = Beliefs about parameter before observing data Likelihood function = Quantifies evidence provided by observed data Posterior distribution = Updated beliefs about parameters after observing data

Manually defining zones on elastic parameter crossplots = Historical method for addressing rock physics dependencies Subjective perception of seismic and well data = Dependency of zone polygon method on interpreter's perception Gas-saturated sandstones exhibit low Acoustic Impedance and Vp/Vs ratio = Characteristic of gas-saturated sandstones in seismic inversion Classification based on modified polygon may fail to highlight gas saturation intervals = Impact of slight modification on classification results

Prior probability = Represents beliefs about the parameter before observing data Likelihood function = Quantifies evidence provided by observed data Posterior distribution = Updated beliefs about parameters after observing data Bayesian classification = Involves estimating prior and posterior probabilities for classification

Bayesian methods = Updating prior beliefs based on observed data Posterior probabilities = Represent updated understanding of subsurface system Prior distribution = Assigns higher probabilities to certain parameter values Likelihood function and prior probabilities = Influence final posterior probabilities in Bayesian inference

Developing Litho-Fluidal classes of Facies = First step in practical implementation Estimating likelihood functions of facies = Involves using training sets of elastic parameters Estimating prior probabilities of Facies = Based on geological interpretation using well information Estimating posterior probabilities of Facies = Involves seismic volume samples with elastic parameter values

Red polygon on crossplot = Represents conditions for identifying gas-saturated sandstones Classification results from seismic inversion = Depicted on right cross-section panel Defined zone for gas-saturated sandstones = Highly dependent on manually set boundaries Training points remaining same but classification result changing = Illustrates susceptibility of method to boundary modifications

Integrating information from both models probabilistically = Avoids favoring one model over the other or applying arbitrary weights Conditional probability functions for classes L1 and L2 = Describe scenarios for distribution of porosity values given an impedance value Blending predictions with arbitrary weights = Not favored in Bayesian approach, which integrates information from both models Influences on final posterior probabilities in Bayesian inference = Include likelihood function and prior probabilities

Bayesian classification = Method used for estimating conditional probabilities Inversion results = Output of seismic data processing Rock physics models = Models used in quantitative interpretation of seismic data Facies-based approaches = Approaches integrating geological characteristics for property prediction

Simple joint probability distributions of petrophysical properties = Characterize Facies (Litho-Fluidal classes) in Bayesian classification Statistical relationships between elastic parameters and petrophysical properties = May exhibit differences between different facies Two facies characterized by joint distributions of acoustic impedance and porosity = Example used to demonstrate regression models for prediction Regression models of porosity vs. impedance for each facies exhibit slight differences = Shows variation in predictive models for different facies

Posterior probability = Probability of an event occurring after considering new information Prediction uncertainty = Estimation of the uncertainty in predicted values Ill-posed problem = A problem that may not have a unique solution or may not have a solution at all Joint distribution = Distribution representing the probability of two or more events occurring together

Quantitative interpretation of seismic inversion results = Involves analyzing numerical data to understand subsurface properties Conditional probabilities of X given Elastic parameters (EP) = Probabilities of a petrophysical parameter given certain elastic properties Weighting conditional probabilities with class probabilities = Estimating a probability distribution by considering class probabilities Integration of facies-based approaches with probabilistic methods = Combining geological characteristics with statistical methods for property prediction

Porosity values = Petrophysical parameter to be predicted Acoustic impedance = Elastic parameters from seismic inversion EP (Elastic parameters) = Data used for estimating posterior probabilities X (Petrophysical parameter) = Parameter whose conditional probabilities are considered

Porosity = Key factor controlling elastic parameters variations Calcite microfossils (coccoliths) = Primary composition of chalk Fluid saturation = Factor impacting elastic properties in chalk reservoirs Dolomite = Mineral leading to alterations in porosity-acoustic impedance relationship

High porosity in chalk reservoirs = Significant impact when changing fluid saturation Linear regression model between acoustic impedance and porosity = May not capture all factors affecting elastic properties Limited number of elastic parameters retrieved from seismic inversion = Constraint in comprehensive petrophysical characterization Multivariate regressions and neural networks = Techniques that can assist in solving the inverse rock physics problem

Stable mineralogical composition of chalk = Considerable variability in porosity Chalk lacking significant clay minerals or cementing materials = Contributes to stable mineralogical composition Shaly rocks forming a distinct cluster on crossplot = Influence on porosity-acoustic impedance statistical relationship Incorporating information about lithology, mineralogy, and fluid saturation = Mitigates uncertainty in predicting petrophysical properties

Water-saturated chalk reservoirs with high porosity = Risk of misinterpretation during classification Regression line developed for oil saturation cases = Potential misclassification of water-saturated reservoirs Changing dominant mineral from calcite to dolomite = Leads to significant alterations in statistical relationship Nonlinear relationships of petrophysical parameters with elastic properties = Introduces varying degrees of uncertainty into predictions