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Taxonomy of κ: A review of definitions and estimation approaches targeted to applications

Taxonomy of κ: A review of definitions and estimation approaches targeted to applications

Ktenidou, Olga‐Joan, Cotton, Fabrice, Abrahamson, Norman A. and Anderson, John G. (2014) Taxonomy of κ: A review of definitions and estimation approaches targeted to applications. Seismological Research Letters, 85 (1). pp. 135-146. ISSN 0895-0695 (Print), 1938-2057 (Online) (doi:

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In a way perhaps not dissimilar to stress drop (Atkinson and Beresnev, 1997), the high-frequency attenuation parameter κ (kappa), introduced by Anderson and Hough (1984), is one of the most used yet least understood or agreed-upon parameters in engineering seismology. It describes the deviation at high frequencies between observed Fourier amplitude spectra calculated from seismograms and an ω−2 source model, such as the Brune (1970) model. Almost 30 years after its introduction, κ is used by seismologists and engineers alike and constitutes an important input parameter for several applications. Perhaps because of its importance, it is estimated, physically explained, and used in many different ways. This note aims to illustrate the multiple approaches to its estimation, and to suggest that, in order to reduce ambiguities, the parameter should always be given a notation consistent with its measurement and application to help avoid inconsistencies in its application of κ scaling to ground-motion models.

Hanks (1982) observed that above a given frequency the acceleration spectrum decays sharply. He termed this frequency fmax (e.g., Fig. 1a) and attributed it mainly to local site conditions. Soon after, Anderson and Hough (1984) introduced an alternative parameter to model this decay, which is the one most commonly used today: κ. They measured κ directly from the high‐frequency part of the acceleration Fourier amplitude spectrum of a record. Above a certain frequency (which they named fe but we will call here f1), the overall shape of the spectrum generally decays exponentially with frequency; the decay constant is most easily measured by finding a linear approximation to the spectrum plotted in log–linear space. The slope of the linear approximation is −πκ (e.g., Fig. 1b). In this note we use the notation κr for individual observations of κ, for example, the κ value corresponding to the slope of a particular record; this record may be at any epicentral distance Re≥0. Anderson and Hough (1984) also observed that κr at individual stations increases with distance and concluded that it includes components related both to the local geology of the top few km of crust beneath the station and to the regional structure. They then suggested that the site component of κ (denoted κ0) could be computed by extrapolating the κr values to zero epicentral distance, thus correcting for the regional effect of anelastic Q.

In this note, we discuss the use of κ0 in various engineering seismology applications today and why interest in this parameter has been revived. We briefly discuss its possible physical interpretations, and detail the known approaches to estimate κ0 from seismic records. We group these approaches into families according to basic features, such as the range of frequencies over which κ0 is computed and the trade‐off with path effects. We then discuss the alternative option for estimating κ0 when site‐specific records are not available, based on empirical correlations with VS30. We collect previously published correlations and demonstrate the scatter observed across different studies. Finally, we make suggestions as to how κ0 estimation can be made in a more consistent way with the applications that use it, and how existing correlations can be made more consistent to improve both the inference of κ0 in the absence of site‐specific data and the physical understanding of κ0.

Item Type: Article
Additional Information: Print issue - Volume 85, No. 1 - published in January/February 2014.
Uncontrolled Keywords: High frequency attenuation; kappa; uncertainty
Subjects: T Technology > TA Engineering (General). Civil engineering (General)
Faculty / School / Research Centre / Research Group: Faculty of Engineering & Science > School of Engineering (ENG)
Last Modified: 15 Mar 2018 14:34

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