Physics-based numerical modeling for seismic risk mitigation

Mathematical and numerical modeling can be used to better understand the physics of earthquakes, improve the design of site-specific structures and facilities, and enhance seismic risk maps. The reliability of existing tools for earthquake and ground-motion prediction, i.e. Ground Motion Prediction Equations (GMPEs), which are based on empirical relations involving earthquake magnitude, source-to-site distance, fault mechanisms, and soil properties, has recently been brought into question.

Physics-based numerical simulations of earthquake ground motion are often advocated as an alternative to GMPEs, as they can provide synthetic ground motion time histories compatible with a more or less detailed model of the seismic source process, of the propagation path, and of the local site response. By numerically simulating a number of realistic earthquake scenarios, it is then possible to obtain reliable estimates of the severity of seismic events and their possible effects on large urban areas -especially important in cases where we have few historical data- and establish collapse-prevention procedures for strategic structures located in the proximity of a fault.

In the perspective of improving tools for seismic hazard identification, a research activity is currently carried on at the Laboratory for Modeling and Scientific Computing (MOX) in the Department of Mathematics in collaboration with the Department of Civil and Environmental Engineering at the Politecnico di Milano. The aim is to develop a certified computer code to run effectively numerical simulations of seismic wave propagation in large-scale models within high-performance computing architectures, and then to use it to produce preliminary sets of physics-based earthquake ground shaking scenarios within large urban areas.

This fruitful collaboration is at the basis of SPEED (, a certified open-source code for the prediction of near-fault ground motion and the seismic response of three-dimensional structures. The code has been tested in a number of realistic seismic events, including the earthquakes in L’Aquila, Italy (2009), Chile (2010), Christchurch in New Zealand (2011), and Northern Italy (2012).


The financial support of Munich RE, MIUR, Indam-GNCS, Fondazione Cariplo, Regione Lombardia and Swissnuclear is acknowledged.


P. F. Antonietti, I. Mazzieri, A. Quarteroni, and F. Rapetti. Non-conforming high order approximations of the elastodynamics equation. Comput. Methods Appl. Mech. Engrg., 209-212:212–238, 2012.

I. Mazzieri, M. Stupazzini, R. Guidotti, and C. Smerzini. SPEED: Spectral elements in elastodynamics with discontinuous Galerkin: a non-conforming approach for 3d multi-scale problems. International Journal for Numerical Methods in Engineering, 95(12):991–1010, 2013.

R. Paolucci, I. Mazzieri, C. Smerzini, and M. Stupazzini. Physics-based earthquake ground shaking scenarios in large urban areas. In Perspectives on European Earthquake Engineering and Seismology, Geotechnical, Geological and Earthquake Engineering, volume 34. Springer, 2014.

R. Paolucci, I. Mazzieri, and C. Smerzini. Anatomy of strong ground motion: near-source records and three-dimensional physics-based numerical simulations of the Mw 6.0 2012 May 29 Po Plain earthquake, Italy.Geophysical Journal International, 203(3):2001–2020, 2015.

P. F. Antonietti, C. Marcati, I. Mazzieri, and A. Quarteroni. High order discontinuous Galerkin methods on simplicial elements for the elastodynamics equation. Numerical Algorithms, 71(1):181–206, 2016.

A. Ferroni, P. F. Antonietti, I. Mazzieri, and A. Quarteroni. Dispersion-dissipation analysis of 3-d continuous and discontinuous spectral element methods for the elastodynamics equation. Geophysical Journal International, 211(3):1554–1574, 2017

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