An exploratory analysis of the Joyner-Boore attenuation data

Abstract

Abstract Joyner and Boore (1981) present a set of strong-motion data and from it derive equations for predicting peak horizontal acceleration as a function of moment magnitude and fault distance. In our work, exploratory data analysis procedures are applied to that data set and alternate prediction procedures are derived. Two distinct types of procedure are presented. The first, like Joyner and Boore's, involves a parametric functional form. The second is nonparametric and requires graphical interpolation, but involves much weaker assumptions in its derivation. The stochastic models employed include a specific (random) effect for individual earthquakes. This effectively handles the problem of “weighting” observations and allows investigation of the relative sizes of between and within earthquake variation. The model considered has the form θ ( A i j ) = φ ( M i ) + ψ ( d i j ) + ∈ i + ∈ i j where i is the indexing event, j is the indexing record within event, A is the peak horizontal acceleration, M is moment magnitude, and d is distance. The ∈j and ∈ij are random variables representing between and within earthquake variation. In the parametric case θ, φ, and ψ have special functional forms. In the nonparametric case, they are given as curves.