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U.S. Geological Survey Open-File Report 2010–1296, v. 1.1

In cooperation with Tufts University

Implementation of the Next Generation Attenuation (NGA) Ground-Motion Prediction Equations in Fortran and R

By James Kaklamanos, David M. Boore, Eric M. Thompson, and Kenneth W. Campbell

2010, revised 2011


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This report presents two methods for implementing the earthquake ground-motion prediction equations released in 2008 as part of the Next Generation Attenuation of Ground Motions (NGA-West, or NGA) project coordinated by the Pacific Earthquake Engineering Research Center (PEER). These models were developed for predicting ground-motion parameters for shallow crustal earthquakes in active tectonic regions (such as California). Of the five ground-motion prediction equations (GMPEs) developed during the NGA project, four models are implemented: the GMPEs of Abrahamson and Silva (2008), Boore and Atkinson (2008), Campbell and Bozorgnia (2008), and Chiou and Youngs (2008a); these models are abbreviated as AS08, BA08, CB08, and CY08, respectively. Since site response is widely recognized as an important influence of ground motions, engineering applications typically require that such effects be modeled. The model of Idriss (2008) is not implemented in our programs because it does not explicitly include site response, whereas the other four models include site response and use the same variable to describe the site condition (VS30). We do not intend to discourage the use of the Idriss (2008) model, but we have chosen to implement the other four NGA models in our programs for those users who require ground-motion estimates for various site conditions. We have implemented the NGA models by using two separate programming languages: Fortran and R (R Development Core Team, 2010). Fortran, a compiled programming language, has been used in the scientific community for decades. R is an object-oriented language and environment for statistical computing that is gaining popularity in the statistical and scientific community. Derived from the S language and environment developed at Bell Laboratories, R is an open-source language that is freely available at (last accessed 11 January 2011). In R, the functions for computing the NGA equations can be loaded as an add-on user-contributed code, which is referred to as a “package” in R. The details of the nga package (Kaklamanos and Thompson, 2010) are presented in this report. In addition, differences between the R and Fortran implementations will be discussed later in this report.

The NGA models have established a new baseline for seismic hazard assessments, and they have been incorporated into the most recent national seismic hazard maps published by the U.S. Geological Survey (Petersen and others, 2008). However, many of the new models are significantly more complicated than previous GMPEs and, therefore, require a substantial investment of time to implement and validate. We hope that the scientific and engineering communities find our implementations to be useful in research and practice. Our implementations may be considered as an alternate to the Microsoft Excel spreadsheet implementation available on the PEER NGA project Web site (, last accessed 11 January 2011). The implementations in Fortran and R are more appropriate for performing batch calculations than the implementation in Microsoft Excel. Spreadsheets and Fortran code for some of the individual models also are available on the PEER NGA project Web site; our programs implement the four GMPEs simultaneously. Our programs give the same results as the programs on the PEER NGA Web site, but we offer some additional flexibility of input, additional methods of estimating unknown input parameters, and additional options for output.

Although these programs have been used by the U.S. Geological Survey (USGS), Tufts University, and others, no warranty, expressed or implied, is made by Tufts or the USGS as to the accuracy or functioning of the programs and related material, nor shall the fact of distribution constitute any such warranty, and no responsibility is assumed by Tufts or the USGS in connection therewith.

Last modified December 2, 2011
First posted January 11, 2011

  • This report is available only on the Web.

For additional information:
Contact Information, Earthquake Science Center, Menlo Park Science Center
U.S. Geological Survey
345 Middlefield Road, MS 977
Menlo Park, California 94025

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Suggested citation:

Kaklamanos, J., Boore, D.M., Thompson, E.M., and Campbell, K.W., 2010, revised 2011, Implementation of the Next Generation Attenuation (NGA) ground-motion prediction equations in Fortran and R: U.S. Geological Survey Open-File Report 2010–1296, v. 1.1, 43 p., available at



Estimation of Input Parameters

Implementation in R

Implementation in Fortran

Selecting Between the R and Fortran Implementations


References Cited

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