Contents

7.1 H/V measurements

This tutorial helps you interpreting single station measurements of ambient vibration with the H/V spectral method.

This chapter contains the following sections:

7.1.1 Basic idea

7.1.1.1 Description of the H/V method

The technique originally proposed by Nogoshi and Igarashi (1971), and wide-spread by Nakamura (1989), consists in estimating the ratio between the Fourier amplitude spectra of the horizontal (H) to vertical (V) components of the ambient noise vibrations recorded at one single station.

The computation of the H/V ratio follows different steps (see Figure 1):

record a 3-component ambient noise signal
select of the most stationary time windows (e.g., using an anti-triggering algorithm) in order to avoid transient noise
compute and smoothing of the Fourier amplitude spectra for each time windows
Average the two horizontal component (using a quadractic mean)
compute the H/V ratio for each window
compute the average H/V ratio

Figure 1: Description of the computation of H/V ratio

7.1.1.2 Criteria for reliable H/V curve

Figure 2: Criteria for a reliable H/V curve (after SESAME, D23.12, Guidelines for the implementation of the H/V spectral ratio technique on ambient vibrations)

7.1.2 Physical explanations

The following explanations have been taken from the 'SESAME H/V User Guidelines' ( HV user guidelines ). Please cite this this text as: Guidelines for the implementation of the H/V spectral ratio technique on ambient vibrations - measurements, processing and interpretations. SESAME European research project, deliverable D23.12, 2005.

The interpretation of the H/V spectral ratio is intimately related to the composition of the seismic wavefield responsible for the ambient vibrations, which in turn is dependent both on the sources of theses vibrations, and on the underground structure. It is also related to the effects of the different kinds of seismic waves on the H/V ratio. The present section will briefly summarise, for each of theses issues, the status of knowledge and consensus reached by the SESAME participants at the end of three years of intensive work and exchanges, also benefit from an abundant scientific literature (see Bonnefoy-Claudet et al. (2006) for a comprehensive review).

One must however admit that our knowledge is still very incomplete and partial: we by no means claim everything is known and clear, and much remains to be learnt! You are thus strongly invited to consider this section simply as a snapshot of the views of the SESAME participants, which, tough based on three years of in-depth investigations, will certainly evolve throughout the next decade.

7.1.2.1 Nature of ambient vibration wavefield

Understanding the physical nature and composition of the ambient seismic noise wavefield, especially in urban areas, requires answering two sets of questions, which are not independent of each other:

What is the origin of the ambient vibrations (where and what are the sources)?
What is the nature of the corresponding waves, i.e., body or surface waves? What is the ratio of body of body and surface waves in the seismic noise wavefield? Within surface waves, what is the ratio of Rayleigh and Love waevs? Again, within surface waves, what is the ratio of fundamental mode and higher modes?

While there is a relative concensus on the first question, only few and partial answers were proposed for the second set of questions, for which a lot of experimental and theoretical work still lies ahead.

As known and taught for a long time in Japan, sources of ambient vibrations are usually separated in two main categories: natural and human, which very often - and more particularly within urban areas - correspond to different frequency bands:

At low frequencies (f < 1Hz), the origin of is essentially natural, with a particular emphasis on ocean waves, which emit their maximal energy around 0.2 Hz. These waves can be very easily seen on islands and/or during oceanic storms. Higher frequencies (around 0.5 Hz) are emitted along coastal areas due to the interaction between sea waves and coasts. Some lower frequency waves (f << 0.1 Hz) are also associated with atmospheric forcing, but this frequency range has very little interest for engineering seismology. Higher frequencies (> 1Hz) may also be associated with wind and water flows.
At high frequencies (f > 1Hz), the origin is predominantly related to human activity (traffic, machinery); the sources ares mostly located at the surface of the earth (except some sources like metros), and often exhibit a strong day/night and week/weekend variability.

The 1 Hz limit is only indicative, and may vary from one city to another. Some specific civil engineering works (highways, dams) involving very big engines and/or trucks may also generate low frequency energy. Locally, this limit may be found by analysing the variations of seismic noise amplitude between day end night, and between work and rest days as well.

Energetic low frequency sources are often distant (being located at the closest oceans), and the energy is carried from teh source to the site by surface waves guided in the earth's crust. However, locally, these waves may (and actually often do) interact with the local structure (especially deep basins). their long wavelength induces a significant penetration depth, so that the resulting local wavefield may be more complex: subsurface inhomogeneities, excited by the long crustal surface waves, may act as diffraction poitns and generate local surface waves, and even possibibly body waves. The energy at frequencies between 0.1 and 1 Hz decreases with increasing distance from oceans: extracting information from microseisms is thus easier on islands (such as Japan) than in the heart of continental areas (such as Kazakhstan).

High frequency waves generally correspond to much closer sources, which, most of the time, are located very close to the surface: while the wavefield in the immediate vicinity (less than a few hundred meters) includes both body and surface waves, at longer distances, surface waves become predominant.

Besides this very qualitative information, only very little information is available on the quantitative proportions between body and surface waves, and within the different kinds of surface waves that may exist (Rayleigh/Love waves, fundamental/higher modes). The few available results, reviewed in Bonnefoy-Claudet et al. (2006), report that low frequency microseisms perdominantly consist of fundamental Rayleigh waves, while there is no real consensus for higher frequencies (f > 1Hz). Different approaches were followed to reach these results, including analysis of seismic noise at depth and array analysis to measure the phase velocity.

The very few investigations on the relative proportion of Rayleigh and Love waves all agree on more or less comparable amplitudes, with a slight trend towards a slightly higher energy carried by Love waves (around 60% - 40%).

Table 1: summary (with some simplification however) of the above discussion

	Natural	Human
Name	Microseism	Microtremor
Frequency	0.1 - 0.5 to 1 Hz	0.5 to 1 - 10 Hz
Origin	Ocean	Traffic/Industry/Human activity
Incident wavefield	Surface waves	Surface + body waves
Amplitude variability	Related to oceanic storms	Day/night, week/weekend
Rayleigh/Love issue	Incident wavefield predominantly Rayleigh	Comparable amplitude - slight indication that Love waves carry a little moer energy
Fundamental/Higher issue	Mainly fundamental	Possibility of higher modes at high frequencies (at least fot 2-layer case)
Further comments	Local wavefield may be different from incident wavefield	Some monochromatic waves related to machines and engines. The proximity of sources, as well as the short wavelength, probably limits the quantitative importance of waves generated by diffraction at depth

These results, although partial, do indicate that the seismic noise wavefield is indeed complex, especially at 'high' frequencies where the origin is human activity: when interpreting the H/V ratio, one has therefore to consider the possible contributions to H/V from both surface and body waves, including also higher modes of surface waves.

7.1.2.2 Links between wave type and H/V ratio

H/V and surface waves

H/V and Rayleigh waves

Rayleigh waves are characterised by an elliptical particle motion in the radial plane, and their phase velocity. In horizontally stratified media where velocity varies with depth, both characteristics exhibit frequency dependence. Stratification also gives rise to the existence of distinct Rayleigh waves mode: while the fundamental mode exists at all frequencies, higher modes appear only beyond some cut-off frequencies, the values of which increases with the mode order. The H/V ratio of all modes of Rayleigh waves, which is a measure of the elipticity, exhibits therefore a frequency dependence in stratified media

There exist a rich literature on that topic, a list of which may be found in Kudo (1995), Bard (1998), Stephenson (2003), Malischewsky and Scherbaum (2004) and Bonnefoy-Claudet (2004). The main relevant results may be summarised as follows, considering first simple one layer over half-space structures:

For intermediate to high S-wave impedance contrasts (i.e., larger than about 3), the H/V ellipticity ratios of Rayleigh waves exhibit infinite peaks and/or zeros corresponding to the vanishing of the vertical (respectively horizontal) component, and inversion of rotation sense (from retrograde to prograde, or inversely). For low contrasts, because of the rotation sense does not change with frequency, the elipticity ratio only exhibits maxima at som frequencies and minima at other frequencies with no zeroes or infinities.
Focusing first on the fundamental mode, the vanishing of the vertical component occurs at a frequency Fr which is very close (i.e., less than 5% different) to the fundamental resonance frequency for S waves only if the S-wave impedance contrast exceed a value of 4. For intermediate velocity contrasts (2.6 to 4), the ellipticity peak is still infinite and occurs at a frequency that may be up to 50% higher than the S-wave fudamental resonance frequency. For lower impedance contrast, the infinite peak is replaced by a broad maximum that has only low amplitude (less than 2-3), and occurs at a frequency that may range between 0.5 to 1.5 times the S-wave fundamental resonance frequency.
The ellipticity ratio H/V of the fundamental mode may also exhibit not only a peak at Fr, but also a minimum (zero) at higher frequency Fz, corresponding to the vanishing of the horizontal components, and a second rotation sense inversion (from prograde to retrograde). A few studies have been performed to investigate the variability of the ratio Fz/Fr; while Konno and Ohmachi (1998) report a value of 2 for a limited set velocity profiles, Stephenson (2003) concludes that peak/trough structures with a frequency ratio around 2 witness both a high Poisson ratio in the surface soil, and a high impedance contrast to the substrate. Some other studies for more complex velocity profiles report a dependence of the ratio on the velocity gradient in the soft sediments.
Higher modes exhibit also H/V peaks at higher frequencies corresponding to a vanishing vertical component; some of these peaks, especially for high contrasts structures, coincide with the higher harmonics of S-wave resonance. However, for single layer structures, no case is known, for which all existing Rayleigh wave modes exhibit simultaneously a peak at the same frequency. In other words, for all frequencies for which several modes exist simultaneously (i.e., generally beyond the S-wave fundamental frequency), there always exist one Rayleigh wave mode (often the fundamental one) which may carry some energy on vertical component.
These results may generally be extrapolated to more complex horizontally layered structures involving several layers or velocity gradients; one major difference however concerns the third item and the number of elipticity peaks. Some sites may present a large velocity contrast (i.e., exceeding 2.5) at different depths Zk (however, given the minimum threshold of 2.5, the number of such depths rarely exceeds 2 ...). In such case, the S-wave response will exhibit major amplifications at frequencies Fk corresponding to the fundamental frequencies of the layering located above theses depths with major dicontinuity. In such cases, the available results show that all Rayleigh wave modes existing at frequency Fk do exhibit a commom ellipticity peak (in other words, the vertical component of all existing Rayleigh waev modes vanish at frequencies Fk). In such sites, a H/V curve with several peaks is therefore consistent with the surface waves interpretation. An example of this situation is a shallow very soft layer resting on a thick, stiff unit underlain by very hard bedrock.
No relation could be established between the S-wave amplification at the resonance frequency, and the characteristics of the H/V infinite peak (for instance its width) or maximum amplitude.

H/V and Love waves

Love waves carry energy only on horizontal component. Their influence on the frequency dependence of the H/V ratio can therefore come only from the frequency dependence of the horizontal component. Different studies (see for instance Konno and Ohmachi (1998)), have shown that, at least for high impedance contrast cases, Love waves do strengthen the H/V peak: all surface waves carry their maximum energy for frequencies corresponding to group velocity minima ('Airy pahse'). For high impedance contrast layering, the group velocity minimum of the fundamental Love mode occurs, like the vanishing of the Rayleigh vertical component, at a frequency Fl which is very close to the fundamental S-wave resonance frequency.

Higher modes of Love waves may also have group velocity minima and associated Airy phase at higher frequencies: this may result in other maxima if higher modes carry a significant amount of energy.

H/V and body waves

As site amplifications occuring during actual earthquakes essentially involve incoming body waves, it is obvious that the horizontal and vertical components of body waves are both highly sensitive to site conditions. the main question to adress here is the relation of the H/V ratio and site conditions for body waves; a side question concerns the differecnes or similarities between H/V ratios derived from earthquake recordings and H/V ratios derived from ambient vibration recordings.

When considering, once again, a simple horizontally layered structure with one soft layer over a half-space, and its response to obliquely incident plane waves, a striking result is the fact that, whatever the incident wave type (P or SV or SH), the horizontal components systematically exhibit resonant peaks at the S-wave resonance frequencies (even for P wave incidence), while the vertical component always exhibits resonant peaks at the P-wave resonance frequencies (even for S wave incidence). This result is valid when the impedance contrast is large both for S and P waves, and comes from the conversion from P and SV waves at the bedrock/layer interface, and their relatively small incidence angles within the surface lower velocity layer.

This has very interesting consequences for the fundamental mode, since the S-wave fundamental frequency is always significantly smaller then the P-wave fundamental frequency (ratio equal to the S-P velocity ratio within the surface layer):

As the fundamental frequency is only weakly dependent on subsurface topography - for usual configurations-, this explain why the H/V ratio for a body wavefield should always exhibit peak around the fundamental S-wave frequency, for high impedance contrast sites.
In the case of horizontally stratified media, the H/V ratio should also exhibit peaks at the S-wave harmonics, at least for all peaks that do not coincide with a lower order harmonic of P-wave resonance.
Finally, again for high impedance contrast, horizontally stratified media, the amplitude of the firts H/V peak is also expected to be somewhat correlated with the S wave amplification.

These latter two items constitute the main differences from the surface wave case, wher it is not generally expected to have eithers harmonics, or any correlation between H/V peak amplitude and actual amplification values. The presence or absence of harmonics at least for a large impedance contrast, 1D structure, may thus be a good indicator of the composition of the wavefield.

One should remain very cautious however in interpreting H/V ratios derived from earthquake ercordings beyond the fundamental S frequency, since this ratio is highly influenced by the amplification of the vertical component, which cannot be neglected, especially in sites with pronounced subsurface topography.

H/V and complex wavefields: results from numerical simulation

Since the actual composition of the seismic noise wavefield is mostly unknown, a series of numerical simulations have been performed to investigate the origin of an H/V peak. A wide variety of subsurface structures have been studied (1D, 2D and 3D), but only 'local' sources have been considered (i.e., less than 10km away from the receiver): the 'microseism' case has not yet been investigated (incoming crustal surface waves generated by oceanic waves). These comprehensive analyses are presented and discussed in various reports (SESAME deliverables D12.09 and D17.10, Bonnefoy-Claudet (2004), Bonnefoy-Claudet et al. (2006)), and only the main conclusions are summarised belpw:

For 1D structures, a single H/V peak is obtained only when the predominant noise sources are located within the surface layer and within limited distances from the sites (less than around 20-30 times the layer thickness); the wavefield then consists of a mixture of Rayleigh, Love and body waves. For more distant predominant noise sources (a case not often met in urban sites, but possible in the countryside), and/or deep sources (i.e., located at depth below the interface associated with the main impedance contrast), the wavefield includes a large proportion of body or head waves, especially at high frequencies, and H/V exhibit several peaks associated with fundamental and harmonics of S-wave resonance. In all cases, the frequency of the H/V peak exhibits a very good agreement (within +/- 20% at most) with the actual fundamental S-wave frequency of the layered structure.
For laterally varying structures, the wavefield associated with 'local' noise sources is more complex, since it also includes additional waves diffracted from the lateral heterogeneities. the composition of this diffracted wavefield depends on the location of the site of interest with respect to the lateral heterogeneities: away from them (for instance, in the flat central parts of valleys and basins), it mainly consists of surface waves (fundamental or higher mode depending on the frequency); close to them is also includes a significant portion of body waves. For all the investigated similation cases (all with a large impedance contrast), H/V curves exhibit clear (sharp) peaks in the 'flat' parts (i.e., those with only gentle underground interface slopes), and broader and generally lower maxima at sites with rapidly varying thickness (for instance valley edges).

Additional comment: H/V and surface topography

All the above discussion and results implicitly adressed mainly sedimentary/alluvial sites within valleys or plains, and are therefore valid only for horizontal free surfaces. As frequency dependent site amplification has been repeatedly observed also on top of rocky hills, several attempts have been performed to investigate whether H/V ratios from ambient vibrations also exhibit a peak in the same frequency range. These attempts have generally been successful, but no theoretical interpretation and no numerical simulation have been proposed to explain this apparent success.

7.1.2.3 Consequences for the interpretation of H/V curves

The above mentioned results exhibit a few consistent robust characteristics which have to be kept in mind when interpreting H/V curves ad peak(s):

The results are clear and simple in case of horizontally layered structures with large impedance contrasts (> 4-5).
The results become more and more fuzzy a) for decreasing contrasts and/or b) for increasing underground interfaces slopes.
Theoretical and numerical results are by far more numerous and easier to interpret for local, cultural sources, i.e., essentially, above 1 Hz.
Clear urban situations with non stationary, spatially distributed local sources are generally associated with one single H/V peak.
In the Rayleigh wave interpretation, the H/V peak should be associated with a (local) trough in the Fourier spectra of the vertical component, while Love or body wave interpretations should be associated with a (local) peak in the Fourier spectra of the horizontal component.

This has the following direct practical consequences for H/V investigations:

One should always gather the available geological and geotechnical information, looking in particular for a priori rough estimations of impedance contrasts (keeping in mind that large impedance contrasts are generally associated with either very young unconsolidated deposits, or very hard bedrock), and indications as to the lateral variability of underground structures.
Low-frequency peaks (i.e., < 1Hz) are often less easy a) to detect and b) to interpret than high-frequency peaks. Additional measurements in the vinicity of the site of interest often help to find a consistent H/V peak.
One should never forget to have a look at the original Fourier spectra of the horizontal and vertical components, especially when the H/V maximum is not very clear.

One must also bear in mind that real ambient vibration recordings also include a number of 'spurious' sources (such as wind, or industrial harmonic machinery) which may affect the estimation of the H/V curve, and downgrade the possibility of interpretations: while clear and sharp 'natural' peaks generally remain visible, fuzzy maxima may completely disappear.

1D media

When the available geological information allows the deposit to be considered as horizontally layered with a smooth and flat interface with the underlying berock, at least locally, then the wavefield composition and interpretation of H/V ratio can be seen as follows:

High frequencies (human origin, f > 1 Hz)

If the site is located in an urban environment, the noise sources are essentially local and superficial; the wavefield predominantly consists of surface waves (Rayleigh and Love) with however a slight proportion of body waves. The H/V curve should exhibit one single peak, at a frequency that is within +/- 20% of the S-wave resonant frequency of the site.
If the site is located in the countryside and the predominant sources are distant, the wavefield also includes resonating head waves and the H/V curve may exhibit several peaks corresponding to the various harmonics.

Low frequencies (oceanic origin, f < 1 Hz)

Unless there exist energetic low frequency sources (big trucks or engines) close to the site under consideration, the seismic noise wavefield is most probably caused by oceanic activity. this may be checked through continuous measurements and an analysis of the daily/weekly amplitude variations.

The geological structure certainly does not exist over the all distance between the site and the ocean: therefore the low frequency crustal surface waves carrying the noise energy certainly undergo some conversion (mode conversion: Rayleigh/Love, fundamental/higher) and/or type conversion (surface to body waves) along laterally varying substructures at some distance from the site. For instance, for a deep inland basin, incoming low frequency crustal waves have a penetration depth of at least 1 km, and will be diffracted along basin edges. In such a case, the sources of seismic noise may be seen as a collection of point sources located along the basin/bedrock interface, re-emitting the same energy envelope spectrum as different waves: local surface waves and body waves. The associated H/V ratio should then be somewhat similar to the H/V ratio derived from earthquake recordings, in the low frequency range only of course (if available, site to reference rock spectral ratios should then be also comparable for ambient vibration and earthquake recordings).

Low frequency H/V peaks are associated either with extremely soft soil (e.g., Mexico City clays) with a thickness of several tens of meters, or with 'normal' soil deposits having a very large thickness (several hundred of meters at least). The former case if obviously associasted with a large impedance contrast, while this can occur in the latter case only if the bedrock is very hard (the confining pressure at large depth automatically induces a stiffness increase).

2D/3D structures

We consider here sites under which at least one of the interfaces with significant impedance contrast exhibits steep slopes (i.e., larger than around 10�, this value being however only indicative). Such sites are therefore either 'transition' zones between areas with more or less horizontal layering, or deeply embanked valley and basins having a large thickness to width ratio (typically, larger than 0.2).

Transition zones

If such transition zones are expected from the available geological/geotechnical/geophysical information, it is always recommended that measurements be made on each part of the transition zone, and to have a rather dense measurement mesh (the 'density' being related to the predominant wavelength, i.e., to the frequency: the higher the frequency the smaller the mesh size).

High frequencies (human origin, f > 1Hz, possibily varying from site to site)

Numerical simulations have consistenly shown that, for local surface sources, the H/V curve at such 'transition' sites exhibit broader and lower maxima, which may be hard to identify. Surface waves cannot develop with one single 'pure' mode, nor can resonance of body wave occur.

Low frequencies (oceanic origin, f < 1Hz, possibily varying from site to site)

No simulation is available for incoming crustal surface waves; the local diffraction phenomena already mentioned for this case let us think that the wavefield should include a significant proportion of body waves egnerated at depth; so that the H/V ratio should reflect at least partly the differential amplification between H and V components, and be a more reliable indicator of the site frequency than for high frequency local surface sources. This interpretation is not consensual and should be taken with cautious.

Deeply embanked valley and basins

The presence of such deep structures should be at least guessed from the geological map and a minimum knowledge of the geological history of the area (ancient glacier valleys filled with lacustrine deposits are a typical example of such structures). However, this kind of structure may also be met in the case of buried canyons, which may remain unknown in the absence of detailed geophysical surveys.

When associated with large impedance contrasts, the seismic response of these structures to incoming body waves exhibits a global 2D (or 3D) resonance pattern characterised by similar resonance frequencies at all sites, whatever the local thickness, and mode shapes with both a strong spatial dependence, and a strong polarisation. As a consequence:

Resonance frequencies may be different on the horizontal components (for instance, in a valley, the components parallel and perpendicular to the valley axis).
The amplitude of the corresponding H/V peak may undergo significant variations from site to site, due to the variations in both H and V components (for instance, a given mode may include a node in the perpendicular component at one site, and a node on V component at another site).

Considering the importance of diffraction phenomena of steep interfaces, and the fact that these resonance modes are the eigen-solutions of the wave equation in such structures, it is logical to conclude that such modes will exist whatever the excitation wavefield, provide there is enough energy in the corresponding frequency range. This theoretical consideration is supported by the few numerical simulations performed on such structures (Cornou et al. (2004) - SESAME deliverables D12.09 and D17.10).

Common recommendations for 2D/3D structures

in any case, when other information sources (geology, geophysics,...) suggest a 2D or 3D structure, three kinds of actions/processing are strongly recommended to check these possibilities:

One should never limit one's investigations to one single measurement, but should have a wide and dense spatial coverage, starting with a mesh size comparable with the expected thickness of the softer cover. The mesh size may be reduced in a second step in case of strong lateral discontinuities, indications either faults or very steep underground slopes.
One should also investigate the differences between differently polarised horizontal components (i.e., applying different rotation angles); for instance, along valley edges, clear differences may appear between the perpendicular and parallel components.