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<p>Directional variability in horizontal earthquake ground motions is commonly represented through orientation-independent scalar measures obtained by rotating the two horizontal components and summarizing the resulting response spectra. Such measures are useful, but they are operators applied to an underlying directional response field. This paper examines one component of that field: the directional peak-factor fluctuation, defined as the orientation-dependent modulation that links second-order oscillator response (RMS) to peak spectral response. Using a uniformly processed strong-motion dataset of 2182 horizontal record pairs, directional peak factors are analysed as functions of oscillator period and orientation. After removing the angular median in logarithmic space, the remaining peak-factor fluctuation field is treated as a <InlineEquation ID="IEq1"> <EquationSource Format="TEX">\(\:\pi\:\)</EquationSource> </InlineEquation>-periodic stochastic field on orientation. Its angular structure is characterised using autocorrelation diagnostics, harmonic energy decomposition, effective harmonic dimensionality, and coefficient-space statistics. The results show that the peak-factor fluctuation field is smooth and strongly dependent across angle, with a systematic anticorrelation near orthogonal orientations. Most of its coherent angular structure is captured by the lowest admissible harmonic, while higher harmonics produce residual local corrections. The dominant harmonic has no preferred orientation at the ensemble level, and its coefficient statistics support an approximately isotropic Gaussian representation with a smoothly varying period-dependent scale. The findings provide a reduced-order peak-factor component for future field-based models of horizontal response spectra, complementing the RMS geometry of oscillator response.</p>

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Directional peak factors of strong-motion response spectra: a stochastic field representation on the circle

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  • 发表日期：

    2026年7月29日

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  • Rajesh Rupakhety,
  • Victor Moises Hernández-Aguirre

摘要

Directional variability in horizontal earthquake ground motions is commonly represented through orientation-independent scalar measures obtained by rotating the two horizontal components and summarizing the resulting response spectra. Such measures are useful, but they are operators applied to an underlying directional response field. This paper examines one component of that field: the directional peak-factor fluctuation, defined as the orientation-dependent modulation that links second-order oscillator response (RMS) to peak spectral response. Using a uniformly processed strong-motion dataset of 2182 horizontal record pairs, directional peak factors are analysed as functions of oscillator period and orientation. After removing the angular median in logarithmic space, the remaining peak-factor fluctuation field is treated as a \(\:\pi\:\) -periodic stochastic field on orientation. Its angular structure is characterised using autocorrelation diagnostics, harmonic energy decomposition, effective harmonic dimensionality, and coefficient-space statistics. The results show that the peak-factor fluctuation field is smooth and strongly dependent across angle, with a systematic anticorrelation near orthogonal orientations. Most of its coherent angular structure is captured by the lowest admissible harmonic, while higher harmonics produce residual local corrections. The dominant harmonic has no preferred orientation at the ensemble level, and its coefficient statistics support an approximately isotropic Gaussian representation with a smoothly varying period-dependent scale. The findings provide a reduced-order peak-factor component for future field-based models of horizontal response spectra, complementing the RMS geometry of oscillator response.