15.1 Introduction
15.2 A Short Review on the H/V Theory
15.2.1 The H/V Origins: Body-Wave Based Theories
15.2.2 The Role of the Surface Waves
15.2.3 The Sources’ Role and the Full-Wavefield
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Low-frequencies (below the S-wave resonance frequency, f S ), where ambient-vibration spectral-powers are relatively low; in this range, the shallow layer acts as a high-pass filter, with an effect as more pronounced as sharper the impedance contrast is; both near sources and body waves dominate the wavefield; power spectra and H/V curves are significantly affected by source-free area dimension, V P /V S ratio and impedance-contrast strength at the bottom of the shallow layer;
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High-frequencies (above max{f P , 2f S }, where f P is the P-wave resonance frequency), where surface waves (both Love and Rayleigh, in their fundamental and higher modes) dominate the wavefield; in this range, spectral powers smoothly decrease with frequency as an effect of material damping, which also results in the fact that relatively near sources mostly contribute to ambient vibrations, as more as the frequency increases; H/V curves are almost unaffected by subsoil configuration and source/receiver distances;
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Intermediate frequencies, where the most of the ambient-vibration energy concentrates; in this range, sharp peaks in the horizontal and vertical spectral powers are revealed around its left and right bounds; irrespective of the subsoil structure and source-free area considered, horizontal ground motion is dominated by surface waves, with a varying combination of Love (in the fundamental mode) and Rayleigh waves that depends on the shallow-layer Poisson’s ratio (Love-wave contribution increases with it) and, to a minor extent, on the strength of the impedance contrast; in the vertical component, Rayleigh and other phases play different roles, both depending on the source-free area dimension and of V P and V S profiles.
M2 | |||||
h (m) |
V
S
(m/s) |
ν
|
ρ (g/cm3) |
D
P
|
D
S
|
25 | 200 | 0.333 | 1.9 | 0.001 | 0.001 |
5,000 | 1,000 | 0.333 | 2.5 | 0.001 | 0.001 |
∞ | 2,000 | 0.257 | 2.5 | 0.001 | 0.001 |
M2* | |||||
h (m) |
V
S
(m/s) |
ν
|
ρ (g/cm3) |
D
P
|
D
S
|
25 | 200 | 0.01–0.\( \overline{49} \)
| 1.9 | 0.001 | 0.001 |
5,000 | 228–1,520 | 0.333 | 2.5 | 0.001 | 0.001 |
∞ | 2,000 | 0.257 | 2.5 | 0.001 | 0.001 |
M3 | |||||
h (m) |
V
S
(m/s) |
V
P
(m/s) |
ρ/ρ
4
|
D
P
|
D
S
|
5 | 30 | 500 | 1 | 0.001 | 0.001 |
25 | 100 | 500 | 1 | 0.001 | 0.001 |
50 | 150 | 500 | 1 | 0.001 | 0.001 |
∞ | 500 | 1,500 | 1 | 0.001 | 0.001 |
15.2.4 A Different Point of View: The Diffuse Wavefield
15.2.5 Current Research Branches
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The branch that studies the ambient-vibration wavefield as a whole; in this case, the theory aims to explain the H/V curve as it is measured in field, with all its components in terms of different seismic phases; this theory has to face the problems about the role of body and surface waves as well as about the role of the sources;
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The branch that should be better named “ellipticity theory” or “Rayleigh-wave H/V”; the subject is, in this case, just the Rayleigh ellipticity, both in theory and in experiments; as it chooses, a priori, to take into account the Rayleigh ellipticity only, the relative theory does not need to deal neither with body waves nor with the wavefield sources, while experiments are devoted to extract Rayleigh waves from the recorded signal (e.g., Fäh et al. 2001).
15.3 Comparison Between the DSS and the DFA Models
15.3.1 The DSS Model
15.3.2 The DFA Model
15.3.3 Comparison
15.4 A Mention to the Most Recent Results in H/V Modelling
15.5 Rayleigh Ellipticity Theory
15.5.1 Osculation Points
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if \( {{\overline{\nu}}_1}^{(1)}<{\nu}_1<{{\overline{\nu}}_1}^{(2)} \) the H/V curve has two peaks,
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if \( {{\overline{\nu}}_1}^{(2)}<{\nu}_1<0.5 \) the H/V curve has one peak and one zero-point,