The domain of existence of prograde Rayleigh-wave particle motion for simple models

Malischewsky, Peter G.; Scherbaum, Frank; Lomnitz, Cinna; Tuan, Tran Thanh; Wuttke, Frank; Shamir, G.

doi:10.1016/j.wavemoti.2007.11.004

Cited by 41 publications

(37 citation statements)

References 10 publications

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“…It is worth noting that, as remarked by Nakamura (2000) this large peak appears at a frequency slightly different (1.9) from the actual value of f 0 (2 Hz). Such a difference has been discussed by Malischewsky and Scherbaum (2004) on the basis of theoretical arguments and has been attributed to the properties of Rayleigh waves ellipticity (for a more general discussion about Rayleigh waves particle motion in simple subsoil configurations, see Malischewsky et al 2008).…”

Section: Comparison Of Theoretical Hvsr Deduced From Approximate and mentioning

confidence: 99%

Alternative interpretations of horizontal to vertical spectral ratios of ambient vibrations: new insights from theoretical modeling

Albarello

Lunedei

2009

Bull Earthquake Eng

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Different positions exist about the physical interpretation of horizontal to vertical spectral ratios (HVSR) deduced from ambient vibrations. Two of them are considered here: one is based on the hypothesis that HVSR are mainly conditioned by body waves approaching vertically the free surface, the other one assumes that they are determined by surface waves (Rayleigh and Love, with relevant upper modes) only. These interpretations can be seen as useful approximations of the actual physical process, whose reliability should be checked case-by-case. To this purpose, a general model has been here developed where ambient vibrations are assumed to be the complete wave field generated by a random distribution of independent harmonic point sources acting at the surface of a flat stratified visco-elastic Earth. Performances of the approximate interpretations and complete wave field models have been evaluated by considering a simple theoretical subsoil configuration and an experimental setting where measured HVSR values were available. These analyses indicate that, at least as concerns the subsoil configurations here considered, the surface-waves approximation seems to produce reliable results for frequencies larger than the fundamental resonance frequency of the sedimentary layer. On the other hand, the body waves interpretation provides better results around the resonance frequency. It has been also demonstrated that the HVSR curve is sensitive to the presence of a source-free area around the receiver and that most energetic contribution of the body waves component comes from such local sources. This dependence from the sources distribution implies that, due to possible variations in human activities in the area where ambient vibrations are carried on, significant variations are expected to affect the experimental HVSR curve. Such variations, anyway, only weakly affect the location of HVSR maximum that confirms to be a robust indicator (in the range of 10%) of the local fundamental resonance frequency.

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Section: Comparison Of Theoretical Hvsr Deduced From Approximate and mentioning

confidence: 99%

Alternative interpretations of horizontal to vertical spectral ratios of ambient vibrations: new insights from theoretical modeling

Albarello

Lunedei

2009

Bull Earthquake Eng

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“…These questions turn out to be surprisingly challenging theoretically even for very simple model and they have only rarely been addressed in the literature (e.g. Malischewsky & Scherbaum 2004; Malischewsky et al . 2008 and Haghshenas et al .…”

Section: Introductionmentioning

confidence: 99%

On the relationship of peaks and troughs of the ellipticity (H/V) of Rayleigh waves and the transmission response of single layer over half-space models

Tuan¹,

Scherbaum²,

Malischewsky³

2010

Geophysical Journal International

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SUMMARY One of the key challenges in the context of local site effect studies is the determination of frequencies where the shakeability of the ground is enhanced. In this context, the H/V technique has become increasingly popular and peak frequencies of H/V spectral ratio are sometimes interpreted as resonance frequencies of the transmission response. In the present study, assuming that Rayleigh surface wave is dominant in H/V spectral ratio, we analyse theoretically under which conditions this may be justified and when not. We focus on ‘layer over half‐space’ models which, although seemingly simple, capture many aspects of local site effects in real sedimentary structures. Our starting point is the ellipticity of Rayleigh waves. We use the exact formula of the H/V‐ratio presented by Malischewsky & Scherbaum (2004) to investigate the main characteristics of peak and trough frequencies. We present a simple formula illustrating if and where H/V‐ratio curves have sharp peaks in dependence of model parameters. In addition, we have constructed a map, which demonstrates the relation between the H/V‐peak frequency and the peak frequency of the transmission response in the domain of the layer's Poisson ratio and the impedance contrast. Finally, we have derived maps showing the relationship between the H/V‐peak and trough frequency and key parameters of the model such as impedance contrast. These maps are seen as diagnostic tools, which can help to guide the interpretation of H/V spectral ratio diagrams in the context of site effect studies.

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“…It is worth highlighting a few studies that look at contradictions to this assumption. First, prograde motion of the fundamental mode has been modeled (Mooney and Bolt, 1966;Tanimoto and Rivera, 2005;Malischewsky et al, 2008); however, these studies observed prograde motion at frequencies much lower than our investigation (0.1-0.3 Hz). Second, De Nil (2005) reports that higher modes can transition from prograde motion to retrograde motion at the surface at high frequencies, typically greater than 50 Hz.…”

Section: Discussionmentioning

confidence: 55%

“…Fundamental mode displacements at the free surface propagate almost exclusively in retrograde motion (Aki and Richards, 1980); however, for a few rare cases, there is a potential for prograde motion at frequencies ranging from 0.1 to 0.3 Hz in earth models (Mooney and Bolt, 1966;Tanimoto and Rivera, 2005;Malischewsky et al, 2008). The higher mode Rayleigh waves propagate in either retrograde or prograde motions (Jones et al, 1963); however, it has been found that higher modes commonly propagate in prograde motion below 50 Hz (De Nil, 2005).…”

Section: Introductionmentioning

confidence: 99%

Isolating retrograde and prograde Rayleigh-wave modes using a polarity mute

et al. 2016

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Estimates of S-wave velocity with depth from Rayleighwave dispersion data are limited by the accuracy of fundamental and/or higher mode signal identification. In many scenarios, the fundamental mode propagates in retrograde motion, whereas higher modes propagate in prograde motion. This difference in particle motion (or polarity) can be used by joint analysis of vertical and horizontal inline recordings. We have developed a novel method that isolates modes by separating prograde and retrograde motions; we call this a polarity mute. Applying this polarity mute prior to traditional multichannel analysis of surface wave (MASW) analysis improves phase velocity estimation for fundamental and higher mode dispersion. This approach, in turn, should lead to improvement of S-wave velocity estimates with depth. With two simple models and a field example, we have highlighted the complexity of the Rayleigh-wave particle motions and determined improved MASW dispersion images using the polarity mute. Our results show that we can separate prograde and retrograde signals to independently process fundamental and higher mode signals, in turn allowing us to identify lower frequency dispersion when compared with single component data. These examples demonstrate that the polarity mute approach can improve estimates of S-wave velocities with depth.

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The domain of existence of prograde Rayleigh-wave particle motion for simple models

Cited by 41 publications

References 10 publications

Alternative interpretations of horizontal to vertical spectral ratios of ambient vibrations: new insights from theoretical modeling

Alternative interpretations of horizontal to vertical spectral ratios of ambient vibrations: new insights from theoretical modeling

On the relationship of peaks and troughs of the ellipticity (H/V) of Rayleigh waves and the transmission response of single layer over half-space models

Isolating retrograde and prograde Rayleigh-wave modes using a polarity mute

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