Incorporating correlated variables into GIS-based probabilistic submarine slope stability assessments

First-order, second-moment (FOSM) formulations are useful tools for assessing uncertainty in GIS based submarine slope stability models. In the simplest applications, variables are assumed to be uncorrelated. In some cases, however, correlation among variables may be significant enough to require inclusion. Correlations among variables can be incorporated by creating an empirical covariance matrix and combining it with analytically derived expressions for partial derivatives of the factor of safety equation. Example calculations show that ignoring correlated variables over-predicts the probability of sliding for gentle slopes and underpredicts the probability of sliding for steep slopes, with small differences for moderate slopes. GIS-based application is illustrated using a hypothetical example motivated by an actual deepwater geohazard assessment, showing areas in which the use of uncorrelated rather than correlated variables over-predicts the likelihood of instability.