Probabilistic seismic-hazard analysis (PSHA) is the current tool of the
trade used to estimate the future seismic demands at a site of interest. A modern PSHA
represents a complex framework that combines different models with numerous inputs.
It is important to understand and assess the impact of these inputs on the model
output in a quantitative way. Sensitivity analysis is a valuable tool for quantifying
changes of a model output as inputs are perturbed, identifying critical input parameters,
and obtaining insight about the model behavior. Differential sensitivity analysis
relies on calculating first-order partial derivatives of the model output with respect to
its inputs; however, obtaining the derivatives of complex models can be challenging.
In this study, we show how differential sensitivity analysis of a complex framework
such as PSHA can be carried out using algorithmic/automatic differentiation
(AD). AD has already been successfully applied for sensitivity analyses in various
domains such as oceanography and aerodynamics. First, we demonstrate the feasibility
of the AD methodology by comparing AD-derived sensitivities with analytically
derived sensitivities for a basic case of PSHA using a simple ground-motion prediction
equation. Second, we derive sensitivities via AD for a more complex PSHA study
using a stochastic simulation approach for the prediction of ground motions. The presented
approach is general enough to accommodate more advanced PSHA studies of
greater complexity.