The origin ofSH-wave resonance frequencies in sedimentary layers

Abstract

SUMMARY Resonance frequencies are often analysed in geo-engineering studies to evaluate seismic risk and microzonation in urban areas. The Nakamura technique constitutes a popular approach that computes the spectral ratio of horizontal-to-vertical ground motion in ambient noise recordings to reveal the existence of any site resonance frequencies. Its theoretical basis remains however unclear with some authors arguing that the method de-emphasizes any Rayleigh-wave contributions and that the resonance frequencies are solely caused by vertically incident SH waves. Other authors explain the same resonance frequencies by the ellipticity of the fundamental Rayleigh wave. Recent numerical simulations reveal that the magnitude of the peak frequency is proportional to the relative portion of Love waves present. This study demonstrates that Love waves alone can be responsible for any observed resonance frequencies in sedimentary layers. Yet sharp SH-wave resonance frequencies are only excited by a source in the bedrock. These resonance frequencies are caused by inhomogeneous waves excited by the bedrock source that tunnel through the high-velocity bedrock to emerge in the low-velocity sediments with a very reduced range of slownesses. The resulting SH waves are then free to interfere constructively thereby creating the observed resonance frequencies. This general trigger mechanism leads to resonances that are almost offset independent. The resulting resonance frequencies map onto points of maximum curvature in the Lovewave phase–velocity dispersion curves at or just beyond the critical horizontal slowness. They can be analysed with the quarter-wavelength law if a large velocity contrast exists between the unconsolidated sediments and the bedrock. A minor modification of the quarter-wavelength law provides more accurate predictions, also for smaller velocity contrasts. Multisource simulations show that site amplification factors as determined by horizontalover-vertical (H/V) spectral ratios would not only depend on the relative portion of Love waves in the total wavefield but also on the depth distribution and the relative strength of the SH sources inside the bedrock compared with those in the sediments. An accurate interpretation of site amplification factors by means of H/V peak frequencies would thus require in-depth knowledge of the causes and origins of the local microseismic noise field.