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Conditional Probability Distributions for Ground Motion Parameters

A collection of MATLAB scripts that develops a probability distribution for a ground motion parameter, conditioned on the occurrence of a specified value of another ground motion parameter.

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Version 1.0 - published on 07 Oct 2013

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The ConditionalGMP scripts construct a ground motion parameter probability distribution, conditioned on the occurrence of a specified value of another ground motion parameter.  The conditional distribution may be developed in two ways:

(1)    By consideration of the mean magnitude and rupture distance as found through the magnitude/rupture distance deaggregation from a probabilistic seismic hazard analysis.

(2)    By consideration of all rupture scenarios that contribute to the seismic hazard.

ConditionalGMP includes three MATLAB scripts and a supporting Word document. The ConditionalGMP MATLAB script develops conditional distributions for Arias Intensity conditioned on a value of PGA. This script make use of ground motion prediction MATLAB functions (AS_2008_nga_mod_wCD and AriasIntensity, also attached). The supporting document explains input formats and provides example inputs and outputs.

The provided scripts use a site in downtown Los Angeles as an example. Arias intensity distributions are developed, given the occurrence of the 2% probability of exceedance in 50 years peak ground acceleration (PGA) value. The code can be modified to develop conditional distributions for other ground motion parameters as well. 


Abrahamson, N. and Silva, W. (2008) Summary of the Abrahamson & Silva NGA Ground-Motion Relations. Earthquake Spectra: February 2008, Vol. 24, No. 1, pp. 67-97.

Baker, J. "Ground Motion Prediction Model Scripts." Baker Research Group. (accessed September 1, 2013).

Bradley, B. A. (2010), A generalized conditional intensity measure approach and holistic ground-motion selection. Earthquake Engng. Struct. Dyn., 39: 1321–1342.

Rathje, E. and Saygili, G. (2008). Probabilistic Seismic Hazard Analysis for the Sliding Displacement of Slopes: Scalar and Vector Approaches. J. Geotech. Geoenviron. Eng., 134(6), 804-814.

Travasarou, T., Bray, J. D. and Abrahamson, N. A. (2003), Empirical attenuation relationship for Arias Intensity. Earthquake Engng. Struct. Dyn., 32: 1133–1155. 

Cite this work

Researchers should cite this work as follows:

  • Breanna Peterman; Ellen M. Rathje (2013), "Conditional Probability Distributions for Ground Motion Parameters,"

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