Improved directional ambient-noise horizontal-to-vertical spectral ratios based on nonparametric mode statistics

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ID: 321659
2026
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Abstract
Summary Seismic ambient-noise horizontal-to-vertical spectral ratios (H/V, HVSR) are widely used to characterise near-surface structure and to identify site resonant frequencies. In this article, we propose a nonparametric statistical descriptor of ambient-noise HVSRs. In single-station practice, HVSR curves are typically represented by the geometric mean of window-wise ratios at each frequency, i.e., by the median of a lognormal model. However, distributions of window ensembles are frequently skewed or multimodal. The lognormal median and symmetric uncertainty bands can then depart from the most probable amplitudes and distort the spread. The lognormal mode can mitigate this bias in near-lognormal cases, but it remains tied to a unimodal parametric form. As a consequence, many workflows rely on strict window selection or rejection to justify lognormal assumption. To address this problem, we present a data-driven, nonparametric alternative that provides a marked improvement when ensembles deviate from lognormality. At each frequency, we estimate the probability density of the log-amplitude distribution using kernel density estimation (KDE), transform it to linear space, and take the mode of the linear-domain density as the representative curve. Uncertainty is quantified by highest-density intervals (HDIs), which naturally accommodate asymmetry and multi-branch distributions. Using an example of a near-lognormal microtremor, we demonstrate that the KDE mode closely tracks the lognormal mode while revealing a systematic upward shift of the commonly used lognormal median. Using a microtremor at a structurally complex site, we observe strongly multimodal amplitude and directional statistics. Both the lognormal-median and lognormal-mode curves fall between competing modes. However, the KDE-based modes and intervals follow the dominant branches and capture multimodal spread. Because the density is inferred directly from window-wise data, the method reduces the need for strong window rejection. We also compare the KDE-mode descriptor with the energy-ratio estimator which averages horizontal and vertical component energies before taking their ratio. Agreement between the energy-ratio estimator and the KDE mode is consistent with a stable single HVSR population, whereas discrepancies help identify frequency bands affected by multimodality, non-stationarity or directional effects. Finally, we extend the same framework to directional HVSR using the horizontal spectral matrix and quantify directional variability through a $\pi $-periodic circular KDE of the axial principal horizontal directions. We show that KDE-based modes, highest-density intervals and directional spread provide robust distribution-aware observational diagnostics that can guide data selection, uncertainty assignment and frequency weighting in site-characterisation and inversion workflows.
Reference Key
openalex_W7169778715 Use this key to autocite in the manuscript while using SciMatic Manuscript Manager or Thesis Manager
Authors Jozef Kristek, Miriam Kristeková, Peter Moczo, Pierre-Yves Bard
Journal geophysical journal international
Year 2026
DOI
10.1093/gji/ggag292
URL
https://doi.org/10.1093/gji/ggag292
Keywords Keywords not found

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