Sensitivity of Probabilistic Seismic Hazard Obtained by Algorithmic Differentiation

Wednesday, 17 December 2014
Christian Molkenthin1, Frank Scherbaum1, Andreas Griewank2, Nicolas Martin Kuehn3, Peter Stafford4 and Hernan Leövey2, (1)University of Potsdam, Institute of Earth and Environmental Science, Potsdam, Germany, (2)Humboldt University of Berlin, Department of Mathematics, Berlin, Germany, (3)University of California, Pacific Earthquake Engineering Research Center, Berkeley, CA, United States, (4)Imperial College London, Department of Civil and Environmental Engineering, London, United Kingdom
Probabilistic seismic hazard analysis (PSHA) is the current tool of the trade to assess seismogenic threat at a site of interest. A modern PSHA represents a complex framework which combines different models with several 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 in 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 Differentiation (AD). AD has been successfully applied for sensitivity analyses in various domains such as meteorology or aerodynamics. First we demonstrate the feasibility of the AD methodology by comparing AD derived sensitivities to analytically derived sensitivities for a basic case of PSHA using a simple ground-motion prediction equation. In a second step, we derive sensitivities via AD for a more complex PSHA study using a ground motion attenuation relation based on a stochastic method to simulate strong motion. The presented approach is general enough to accommodate more advanced PSHA studies of higher complexity.