We define two scalers, S global and Sgradient, this way: Iscaled Gscaled This means that we need to determine a scaling from the real data amplitudes to the model amplitudes. In order to apply Bayes’ Theorem to (I,G) points from a real seismic data set, we need to “calibrate” the real data points.
Gas Probability By this process, we can investigate the sensitivity of the probability distributions to individual parameters. Showing the Effect of Bayes’ Theorem Note the effect on the calculated gas probability This is the result of assuming 10% noise in the VS calculation Last Updated: April 2005 Authors: Dan Hampson, Brian Russell Showing the Effect of Bayes’ Theorem This is an example simulation result, assuming that the wet shale VS and VP are related by Castagna’s equation. When the distributions overlap, the probabilities decrease: Even if we are right on the “Gas” peak, we can only be 60% sure we have gas. How Bayes’ Theorem works in a simple case: This is the calculated probability for (gas, oil, brine). VARIABLE Last Updated: April 2005 Authors: Dan Hampson, Brian Russell How Bayes’ Theorem works in a simple case: Assume we have these distributions: Gas Gaussian) estimated from the stochastic simulation output. P(Fk) represent a priori probabilities and F k is either brine, oil, gas p(I,G|Fk) are suitable distribution densities (eg. The Depth-dependence can often be understood using Rutherford-Williams classification 4īayes’ Theorem Bayes’ Theorem is used to calculate the probability that any new (I,G) point belongs to each of the classes (brine, oil, gas): Last Updated: April 2005 Authors: Dan Hampson, Brian 2000m The Results are Depth Dependent Because the trends are depth-dependent, so are the predicted 1600m Monte-Carlo Analysis By repeating this process many times, we get a probability distribution for each of the 3 sand fluids: This creates 3 points on the I-G cross plot: Using Biot-Gassmann Substitution Starting from the Brine Sand case, the corresponding Oil and Gas Sand models are generated using Biot-Gassmann substitution. Note that these amplitudes include interference from the second interface.Ĭalculating a Single Model Response Using these picks, calculate the Intercept and Gradient for this model: I G 0o 45oĬalculating a Single Model Response On the synthetic traces, pick the event corresponding to the top of the sand layer: Trend Analysis Castagna’s Relationship with % error Trend AnalysisĬalculated from sand trend analysis Trend Analysis Uniform Distribution from petrophysicsĬalculating a Single Model Response From a particular model instance, calculate two synthetic traces at different angles. Practically, this is how we set up the distributions: Shale: Vp Vs Density Sand: Brine Modulus Brine Density Gas Modulus Gas Density Oil Modulus Oil Density Matrix Modulus Matrix density Dry Rock Modulus Porosity Shale Volume Trend Analysis Some of the statistical distributions are determined from well log trend analyses: 5000 4500 4000 3500 3000 2500 2000 1500 1000 500 0 0.4ĭBSB (Km) Last Updated: April 2005 Authors: Dan Hampson, Brian Russellĭetermining Distributions at Selected Locations Assume a Normal distribution. Last Updated: April 2005 Authors: Dan Hampson, Brian Russell
Porosity Shale Volume Water Saturation ThicknessĮach of these has a probability distribution. Oil Density Matrix Modulus Matrix density
The Basic Model The Sand is characterized by: Brine Modulus Brine Density We assume a 3-layer model with shale enclosing a sand (with various fluids).Įach parameter has a probabilit distribution: Monte Carlo Simulation: Creating many synthetics “Conventional” AVO Modeling: Creating 2 pre-stack synthetics IN INSITU SITU=OIL OIL STOCHASTIC AVO MODEL FLUID PROBABILITY MAPS GRADIENT ! INTERCEPT ! BURIAL DEPTH AVO ATTRIBUTE MAPS ISOCHRON MAPS In this talk we present a procedure for analyzing and quantifying AVO uncertainty.Īs a result, we will calculate probability maps for hydrocarbon detection.ĪVO Uncertainty Analysis: The Basic Process But: all AVO attributes contain a great deal of “uncertainty” – there is a wide range of of lithologies which could account account for any AVO response. Overview AVO Analysis is now routinely used for exploration and development. Last Updated: Updated: April 2005 Authors: Dan Hampson, Brian Russell AFI (AVO Fluid Inversion) Uncertainty in AVO: How can we measure it? Dan Hampson, Brian Russell Hampson-Russell Hampson -Russell Software, Calgary