The 2008 Next Generation Attenuation (NGA-West1) ground motion prediction equations (GMPEs) did not include directivity; it was implemented as a post-facto correction without guidance for its application. The NGA-West2 GMPEs may be developed including the effects of directivity. Four directivity models (DMs) have been developed based on data from the NGA- West2 database and based on numerical simulations of large strike-slip and reverse-slip earthquake. All DMs avoid the use of normalized fault dimension, enabling them to scale up to the largest earthquakes sensibly. Models by Shahi and Baker, Spudich and Chiou, and by Rowshandel are explicitly “narrow-band” (in which the effect of directivity is maximum at a specific period which is a function of earthquake magnitude). The model by Bayless and Somerville is the only model in this report that predicts directivity for fault-normal and fault- parallel motions as well as azimuthally averaged motion. Functional forms and preliminary coefficients of the DMs are presented in this report, but the final coefficients should be produced by including the directivity functional forms ab initio in the development of a GMPE. Also shown is a comparison of maps of the directivity amplification from the various DMs applied to a set of test rupture geometries. This comparison suggests that the directivity model predictions are strongly influenced by effects of their assumptions, and more than one model should be used for site-specific studies of directivity from ruptures dipping less than about 65°.
Bayless and Somerville present an improved version of the classic Somerville et al. [Seismol. Res. Let. 1997] model, which retains that model's computational simplicity but updates the model with new data and a better functional form. Major changes include rupture-length denormalization, a modified dependence on site azimuth, use of azimuth tapers to obviate the need for an excluded zone, and extension of the algorithm to allow directivity calculations for complicated, noncontiguous rupture zones. A set of coefficients is presented that is adequate for simulating directivity for several different GMPEs.
The directivity model of Rowshandel presented in this report is a major modification of the earlier models developed by the author. Specifically, in comparison with the earlier versions, several major improvements are made: (i) Rupture length de-normalization is used, (ii) in the new model the direction of rupture and the direction of slip both contribute to directivity, and (iii) Unlike the older model, the model presented here is a “narrow-band” model. Many analyses have been performed to assess and quantify the potential impact of the model on the uncertainty term in GMPEs. A few test results based on earthquakes in the NGA-W2 database are also presented.
The Shahi and Baker model is specifically aimed at predicting the characteristics of impulsive ground motions often found at short (< 10 km) distances from fault ruptures (i.e., Lucerne station in the 1992 Landers earthquake). Because the presence of a directivity pulse amplifies spectral acceleration in a narrow band of periods close to the pulse period, their model consists of a wide-band spectral shape plus a superposed narrow-band spectral shape that is multiplied by a logistic variable which is 1 if the pulse is present and zero otherwise. The Shahi and Baker model is the narrowest of the narrow-band models in this report.
Spudich and Chiou present a modified version of the Spudich and Chiou [Earthquake Spectra 2008] directivity model. This new model retains the use of Isochrone Directivity Parameter IDP as the predictor. However, the new model has the following differences: (1) It is iv a “narrow-band” model, and (2) the predictor IDP is “centered” by subtracting from it the average IDP computed over a “racetrack” of constant RRup or RJB . Coefficients of a preliminary model are given.
Chiou and Spudich introduce a new directivity predictor, the Direct Point Parameter (DPP), although they do not present empirically derived coefficients, so it does not presently constitute a 'model.' The DPP, like the IDP, is based on isochrone theory but has a stronger theoretical underpinning, as it is based on a special point on a rupture (called the “direct point”) that is more closely correlated with directivity than the IDP “closest point,” (point on the fault closest to the site where ground motions are to be evaluated). Because it does not depend on closest point, it is less likely a user’s site will unknowingly be on the high or low side of a discontinuity in the predictor.
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