Stochastic Fluid Substitution

Monte Carlo simulation of Gassmann fluid substitution with uncertainty ranges on all input parameters. Propagates rock and fluid property uncertainties through fluid substitution to generate probabilistic P10/P50/P90 velocity and impedance outcomes. Essential for quantifying seismic response uncertainty.

Rock Physics Gassmann Monte Carlo Uncertainty Probabilistic

Input Parameters

Monte Carlo Settings

More iterations = more accurate distribution

Initial Saturated Rock (Uncertainty Ranges)

m/s
m/s
m/s
m/s
m/s
m/s
Shear modulus unchanged by fluids
g/cm³
g/cm³
g/cm³
fraction
fraction
fraction

Mineral Matrix (Uncertainty Ranges)

GPa
GPa
GPa
g/cm³
g/cm³
g/cm³

Original Fluid (State 1 - Uncertainty Ranges)

GPa
GPa
GPa
g/cm³
g/cm³
g/cm³

Substitution Fluid (State 2 - Uncertainty Ranges)

GPa
GPa
GPa
g/cm³
g/cm³
g/cm³

Scenario Presets

Results

Theory & References

Stochastic Fluid Substitution

Combining Gassmann + Monte Carlo:

Traditional deterministic Gassmann assumes all input parameters are known exactly. In reality, rock and fluid properties have measurement uncertainty and spatial variability.

Stochastic Workflow:

  1. Define uncertainty ranges (min/mean/max) for all inputs
  2. Sample randomly from uniform distributions (Monte Carlo)
  3. Run Gassmann substitution for each realization
  4. Calculate percentiles (P10/P50/P90) of output distributions

Key Outputs:

  • P10: 90% chance actual value exceeds this (optimistic)
  • P50: Median outcome (50% probability)
  • P90: 90% confidence lower bound (conservative)

When to Use Stochastic vs Deterministic

Use Stochastic Gassmann when:

  • Input parameters have significant measurement uncertainty
  • Planning exploration wells (risk quantification)
  • Assessing seismic detectability with uncertainty
  • Building probabilistic AVO models
  • Communicating uncertainty to decision-makers

Use Deterministic Gassmann when:

  • Input parameters are well-constrained (core, logs)
  • Quick "what-if" scenario testing
  • Educational or conceptual modeling
  • Sensitivity studies on individual parameters

Input Uncertainty Ranges:

Define ranges based on:

  • Laboratory measurement precision
  • Log interpretation uncertainty
  • Lateral rock property variability
  • Fluid property variation with P/T

Typical ranges: Vp ±5%, porosity ±0.03, K_fluid ±10%

Applications & Best Practices

Applications:

  • Seismic amplitude uncertainty quantification
  • DHI (Direct Hydrocarbon Indicator) risk assessment
  • AVO anomaly strength prediction with confidence intervals
  • Reservoir monitoring feasibility (4D seismic)
  • Prospect de-risking (chance of seismic detection)

Best Practices:

  • Use 5,000+ iterations for stable percentiles
  • Validate ranges against offset well data
  • Check if outputs follow expected distributions
  • Consider correlations (e.g., Vp-Vs coupling)
  • Combine with AVO modeling for full uncertainty chain

Limitations:

  • Assumes uniform distributions (may be oversimplified)
  • Does not capture spatial correlation
  • Gassmann assumptions still apply