Sliding displacements due to subduction-zone earthquakes

• Empirical relations are not accurate for subduction zone events.
• Even when other parameters are introduced, prediction is poor.
• Existing relations do not incorporate analytical results.
• Incorporating analytical results gives dimensionally consistent expressions.
• New relations give reproducible results for three earthquakes in three regions.

Empirical studies of earthquake ground motions have developed relations between sliding displacement and acceleration ratio and other parameters such as Arias intensity. Computations using strong motion records from the Maule 2010 Chile M = 8.8 earthquake indicate that the published relations do not conform well to the computed displacements, and some tend to be unconservative. Extensions to the empirical equations incorporating Arias intensity are, if anything, less accurate. These results suggest that these empirical relations may not apply to subduction zone events and indicate that further study using records from other recent subduction zone events is appropriate. Examining the analytical solutions for sliding displacements induced by sinusoidal shaking and the definition of Arias intensity leads to an improved normalization for sliding displacements. When this improved normalization is applied to the records from three different earthquakes in different parts of Chile, the results are nearly identical, and the results for the Chi Chi and Northridge earthquakes are very close to those from the Chilean events. Suggestions for practical use of the new normalization relations are provided.