Uncertainty in AVO: How can we measure it? Dan Hampson, Brian Russell Hampson-Russell Software, Calgary Maurizio Cardamone ENI E&P Division, Milan, Italy

Overview AVO Analysis is now routinely used for exploration and development. But: all AVO attributes contain a great deal of “uncertainty” – there is a wide range of lithologies which could account for any AVO response. In this talk we present a procedure for analyzing and quantifying AVO uncertainty. As a result, we will calculate probability maps for hydrocarbon detection.

AVO Uncertainty Analysis: The basic process STOCHASTIC AVO MODEL G I GRADIENT INTERCEPT BURIAL DEPTH CALIBRATED: FLUID PROBABILITY MAPS PBRI POIL PGAS AVO ATTRIBUTE MAPS ISOCHRON

“Conventional” AVO Modelling : Creating 2 pre-stack synthetics GO IB GB IN SITU = OIL FRM = BRINE Let us go one step back into the “conventional” flow of a typical AVO study. It is quite a complex piece of technology, which is not yet well classified as it is data processing, modelling or interpretation. Most probably it is a mixture of the three ingredients, with many different recipes available on the market. On one side we have anyway the modelling - whenever a well is available - to provide the AVO analyst with a synthetic pre-stack CDP gather for assessment of the AVO behaviour and comparison with real CDP’s. This starts with a set of well logs, preferably including a good quality S sonic measurement, even though this kind of a log can be quite effectively modelled from other logs. It is common practice to start from this set of the so-called insitu and model different fluids, different saturation ratios, different porosity. This is normally carried out using the Biot-Gassmann equation. Then you measure the modelled AVO responses and you can assess the sensitivity of AVO to the different petrphysical conditions, mainly to the different fluids (gas, oil, brine).

Monte Carlo Simulation: Creating many synthetics I-G DENSITY FUNCTIONS BRINE OIL GAS GRADIENT OCCURRENCE

The basic model Shale Sand Shale We assume a 3-layer model with shale enclosing a sand (with various fluids). Sand Shale

The basic model Vp1, Vs1, r1 Vp2, Vs2, r2 The Shales are characterized by: P-wave velocity S-wave velocity Density Vp1, Vs1, r1 Vp2, Vs2, r2

The basic model Vp1, Vs1, r1 Vp2, Vs2, r2 Each parameter has a probability distribution: Vp1, Vs1, r1 Vp2, Vs2, r2

The basic model Shale Sand Shale The Sand is characterized by: Brine Modulus Brine Density Gas Modulus Gas Density Oil Modulus Oil Density Matrix Modulus Matrix density Porosity Shale Volume Water Saturation Thickness Shale Sand Shale Each of these has a probability distribution.

Trend Analysis Sand (Brine) Velocity Some of the statistical distributions are determined from well log trend analyses: Sand (Brine) Velocity

Determining distributions at selected locations. Assume a Normal distribution. Get the Mean and Standard Deviation from the trend curves for each depth:

Trend Analysis: Other Distributions Shale Velocity Sand Density Shale Density Sand Porosity

Practically, this is how we set up the distributions: Shale: Vp Trend Analysis Vs Castagna’s Relationship with % error Density Trend Analysis Sand: Brine Modulus Brine Density Gas Modulus Gas Density Oil Modulus Constants for the area Oil Density Matrix Modulus Matrix density Dry Rock Modulus Calculated from sand trend analysis Porosity Trend Analysis Shale Volume Uniform Distribution from petrophysics Water Saturation Uniform Distribution from petrophysics Thickness Uniform Distribution

Calculating a single model response Note that a wavelet is assumed known. From a particular model instance, calculate two synthetic traces at different angles. 0o 45o Top Shale Sand Base Shale

Calculating a single model response Note that these amplitudes include interference from the second interface. On the synthetic traces, pick the event corresponding to the top of the sand layer: 0o 45o Top Shale P2 Sand P1 Base Shale

Calculating a single model response Using these picks, calculate the Intercept and Gradient for this model: I = P1 G = (P2-P1)/sin2(45) 0o 45o Top Shale P2 Sand P1 Base Shale

Using Biot-Gassman substitution Starting from the Brine Sand case, the corresponding Oil and Gas Sand models are generated using Biot-Gassmann substitution. This creates 3 points on the I-G cross plot: BRINE GAS KGAS GAS OIL KOIL OIL G I

Brine Oil Gas Monte-Carlo Analysis By repeating this process many times, we get a probability distribution for each of the 3 sand fluids: G Brine Oil Gas I

The results are depth-dependent Because the trends are depth-dependent, so are the predicted distributions: @ 1000m @ 1200m @ 1400m @ 1600m @ 1800m @ 2000m

The Depth-dependence can often be understood using Rutherford-Williams classification Sand Burial Depth Impedance Shale 1 2 3 4 5 6 Class 1 Class 2 Class 3

Bayes’ Theorem Bayes’ Theorem is used to calculate the probability that any new (I,G) point belongs to each of the classes (brine, oil, gas): where: P(Fk) represent a priori probabilities and Fk is either brine, oil, gas; p(I,G|Fk) are suitable distribution densities (eg. Gaussian) estimated from the stochastic simulation output.

How Bayes’ Theorem works in a simple case: Assume we have these distributions: VARIABLE OCCURRENCE Gas Oil Brine

How Bayes’ Theorem works in a simple case: This is the calculated probability for (gas, oil, brine). VARIABLE OCCURRENCE 100% 50%

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. VARIABLE OCCURRENCE 100% 50%

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.

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. This is the result of assuming 10% noise in the Vs calculation

Showing the effect of Bayes’ theorem Note the effect on the calculated gas probability 1.0 0.5 0.0 Gas Probability By this process, we can investigate the sensitivity of the probability distributions to individual parameters.

Example probability calculations Oil Brine Gas

Real Data Calibration In order to apply Bayes’ Theorem to (I,G) points from a real seismic data set, we need to “calibrate” the real data points. This means that we need to determine a scaling from the real data amplitudes to the model amplitudes. We define two scalers, Sglobal and Sgradient, this way: Iscaled = Sglobal *Ireal Gscaled = Sglobal * Sgradient * Greal One way to determine these scalers is by manually fitting multiple known regions to the model data.

Fitting 6 known zones to the model 1 4 2 3 5 6

Real data example – West Africa This example shows a real project from West Africa, performed by one of the authors (Cardamone). There are 7 productive oil wells which produce from a shallow formation. The seismic data consists of 2 common angle stacks. The object is to perform Monte Carlo analysis using trends from the productive wells, calibrate to the known data points, and evaluate potential drilling locations on a second deeper formation.

One Line from the 3-D volume Near Angle Stack 0-20 degrees Far Angle Stack 20-40 degrees

One Line from the 3-D volume Near Angle Stack 0-20 degrees Shallow producing zone Deeper target zone Far Angle Stack 20-40 degrees

AVO Anomaly Near Angle Stack 0-20 degrees Far Angle Stack

Amplitude slices extracted from shallow producing zone Near Angle Stack 0-20 degrees +189 -3500 Far Angle Stack 20-40 degrees

Trend analysis Sand and Shale trends Sand velocity DENSITY Sand density VELOCITY BURIAL DEPTH (m) VELOCITY Shale velocity Shale density BURIAL DEPTH (m) DENSITY

Monte Carlo simulations at 6 burial depths -1400 -1600 -1800 -2000 -2200 -2400

Near Angle amplitude map showing defined zones Wet Zone 1 Well 6 Well 3 Well 5 Well 7 Well 1 Well 2 Wet Zone 2 Well 4

Calibration Results at defined locations Wet Zone 1 Well 2 Wet Zone 2 Well 5

Calibration Results at defined locations Well 6 Well 3 Well 4 Well 1

Using Bayes’ theorem at producing zone: oil Near Angle Amplitudes 1.0 .80 .60 Probability of Oil .30

Using Bayes’ theorem at producing zone: gas Near Angle Amplitudes 1.0 .80 .60 Probability of Gas .30

Near angle amplitudes of second event Using Bayes’ theorem at target horizon Near angle amplitudes of second event 1.0 .80 .60 Probability of oil on second event .30

Verifying selected locations at target horizon

Summary By representing lithologic parameters as probability distributions we can calculate the range of expected AVO responses. This allows us to investigate the uncertainty in AVO predictions. Using Bayes’ theorem we can produce probability maps for different potential pore fluids. But: The results depend critically on calibration between the real and model data. And: The calculated probabilities depend on the reliability of all the underlying probability distributions.