Uncertainty Analysis¶

Site response analysis involves numerous uncertain parameters. PyStrata provides tools for systematic uncertainty quantification using logic trees and Monte Carlo simulation.

Sources of Uncertainty¶

Aleatory Uncertainty (Natural Variability) - Spatial variability in soil properties - Earthquake source characteristics - Ground motion variability

Epistemic Uncertainty (Knowledge Limitations) - Model selection (equivalent linear vs. nonlinear) - Parameter estimation uncertainty - Methodological assumptions

Logic Tree Framework¶

Logic trees provide a structured approach to capture epistemic uncertainties by:

Defining Alternatives: Different models or parameter values
Assigning Weights: Relative confidence in each alternative
Computing Branches: All possible combinations
Aggregating Results: Weighted ensemble statistics

Example Logic Tree Structure

Site Response Method
├── Equivalent Linear (0.7)
│   ├── Darendeli Curves (0.8)
│   └── Zhang Curves (0.2)
└── Frequency Domain (0.3)
    ├── Darendeli Curves (0.8)
    └── Zhang Curves (0.2)

Monte Carlo Simulation¶

For aleatory uncertainties, Monte Carlo simulation generates random realizations:

# Example: Uncertain shear wave velocity
vs_mean = 400  # m/s
vs_std = 50    # m/s

for i in range(1000):
    vs_sample = np.random.normal(vs_mean, vs_std)
    # Run site response analysis
    # Store results

Result Processing¶

Statistical quantities of interest: - Mean: Central tendency - Standard deviation: Variability measure - Percentiles: Confidence intervals - Sensitivity indices: Parameter importance