Apr. 29, 2024
Measurement & Analysis Instruments
R&S®Essentials | Spectrum analyzers fundamentals
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Author: Paul Denisowski, Test & measurement expert
Spectrum analyzers are frequency-domain instruments, showing power versus frequency. This is also the most fundamental measurement on a spectrum analyzer: a plot of power versus frequency.
Most spectrum analyzers automate certain power versus frequency type measurements, like AM modulation depth or third order intercept. These measurements could be done manually but automating them increases efficiency and accuracy. Other measurements like occupied bandwidth or adjacent channel leakage ratio, would be difficult or impossible to manually measure.
There are four essential parameters needed to operate a spectrum analyzer. These four parameters are
These settings are used when making almost any kind of spectrum measurements.
Center and span define the frequency range to be measured by setting the stop and start frequencies.
As an example, to measure power between 840 MHz and 860 MHz. These values could be entered into a spectrum analyzer as start and stop frequencies, but center and span are used more commonly. The names are self-explanatory: center is the frequency in the middle of the display, and span is the width of the display. The range 840 MHz to 860 MHz is the same as a center of 850 MHz and a span of 20 MHz. Most often the center frequency of the signal of interest is known, and by using span it’s easier to zoom in and zoom out by just increasing or decreasing the span.
The experimental data for surface wave analysis are time histories of ground motion (seismic records) measured at a fixed number of points on the ground surface.
In this section, we distinguish between active and passive surface wave measurements because their classical acquisition procedures are very different. As previously mentioned, active and passive measurements may both be applied to gather information over a wide wavelength range. We recommend such complementary data acquisition if the target depth is greater than about 20–25 m and only light active sources are used. While it may be possible to obtain VS profiles down to 30 m using a sledgehammer, we find this only to be possible at stiff sites. At soft sites, the depth of profiling with a sledgehammer will more than likely be limited to 15–20 m.
Datasets can be collected using a wide variety of array geometries. For active-source prospecting, the usual choice is to have the receivers placed in-line with the seismic source. For passive tests, 2D arrays of sensors deployed on the ground surface are recommended, as the ambient vibration wavefield might propagate from any direction. While passive tests are frequently conducted also with linear arrays, we caution analysts and end-users that 2D arrays are much preferred for passive measurements and far superior for developing robust VS profiles. In a dispersive medium, knowledge of the direction of passive energy propagation and the true velocity of its propagation are mutually dependent; one cannot be calculated without knowledge of the other. As the direction of propagation cannot be determined using a linear array, the true phase velocity cannot be verified. Additional information regarding passive recordings with linear arrays is provided in Appendix 9.
2.1
Active prospectingThe most common acquisition layout is composed of evenly-spaced vertical receivers aligned with the seismic source. This layout is often referred to as the MASW (Multichannel Analysis of Surface Waves) method and is described below. Another common (and older) active surface wave technique is the spectral analysis of surface waves (SASW) method, which uses only 2 sensors.
2.1.1
Equipmentthe energy provided by the seismic source must provide an adequate signal-to-noise ratio over the required frequency band, given the target investigation depth. As the wavelength is a function of both frequency and phase velocity of the site, it is necessary to make preliminary hypothesis about the expected velocity range to define the required frequency band of the source. Indeed, at a soft site lower frequencies will be necessary to achieve the same investigation depth than at a stiff one. Furthermore, in the presence of a sharp velocity contrast at shallow depths, the amplitudes of low frequency (long wavelength) surface waves are strongly reduced and difficult to measure irrespective of the seismic source.
Vertically operated shakers or vertical impact sources are typically used for surface wave testing. The former provide an accurate control on the frequency band and very high signal-to-noise ratio in the optimal frequency band of operation of the vibrator. Nevertheless, these sources are expensive and not easily manageable. Impact sources (Fig. 4) are much cheaper and enable efficient data acquisition as impact sources provide energy over a wide frequency band.
Fig. 4Example of vertical impact sources. Left 5 kg sledgehammer, Right weight drop
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Weight-drop systems and vertically accelerated masses are able to generate high signal-to-noise ratios and allow longer wavelengths to be gathered and investigation depths to reach several tens of meters.
Explosive sources also provide high S/N data over a broad frequency band, with the caution that if they are placed in a borehole the amount of surface wave energy could be limited.
The cheapest and most common source is a sledgehammer striking on a metal plate or directly on the ground surface. The weight of the sledgehammer should be at least 5 kg; the 8 kg sledgehammer is the most common choice. However, its limited energy in the low frequency band (typically limited to f > 8–10 Hz) makes the sledgehammer a useful source only for relatively small array lengths (see Sect. 2.1.2), which limits the investigation depths to a few (e.g. typically 1 or 2) tens of meters at most. For example, a sledgehammer is typically not an adequate source for imaging down to 30 m depth at a soft sediment site. If a single source is not able to provide enough energy over the whole required frequency band, acquisitions with different sources have to be planned. In fact this may be the preferred approach in many investigations, where a small hammer source is used to obtain high frequency/small wavelength dispersion data and a portable weight drop is used to obtain the lower frequency/long wavelength dispersion data. As with any active seismic survey, the signal-to-noise ratio can be improved by stacking the records from several shots.
vertical geophones are typically used for the acquisition of Rayleigh wave data (Fig. 5). The natural frequency of the geophones must be adequate to sample the expected frequency band of surface waves without distortions due to sensor response. To some extent, geophones can be used below their natural frequency; however, it should be remembered that the sensor response is non-linear and each geophone goes through a 180° phase shift at its resonant frequency, thus some phase distortions can occur below the resonant frequency if the geophones are not perfectly matched. However, the use of multiple receivers produces a mitigation of errors induced by phase distortions, potentially extending the usable frequency band to about half of the natural frequency of the geophones. Nevertheless, this extension has to be carefully checked by relative calibration of the sensors and/or inspection of the data in the frequency domain. Generally for shallow targets (e.g. 30 m), 4.5 Hz natural frequency geophones are adequate. It is unlikely that higher frequency geophones (e.g. 10–14 Hz) will be reliable for profiling to depths greater than about 10–15 m. Certain types of accelerometers may also be used as a viable alternative to geophones in active data acquisition as they provide a flat response at low frequency, even if they are typically less sensitive.
Fig. 5Examples of 4.5 Hz geophones. Left horizontal geophone with a spike pressed in soil. Right vertical geophone mounted on tripods for a good contact on stiff surfaces
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Usual care needs to be adopted in deploying the receivers to guarantee adequate coupling with the ground. When possible, receivers should be coupled to the ground with spikes and thick grass should be removed from beneath the sensor. When testing on hard surfaces, sensors can be coupled to the ground using a base plate. Care should be taken ensure the sensors are level and to avoid placement of sensors directly over utilities whenever possible. Furthermore, when testing in inclement weather receivers must be protected against rain drops.
different apparatuses may be used for digitization of analog output from the geophones and recording of signals. The most common choice is the use of multichannel seismographs, which are specifically designed for seismic acquisition. Nevertheless it has to be considered that they are typically conceived for other geophysical surveys (e.g. seismic reflection/refraction surveys) and may have some limitation on the usable frequency band, as typically declared in their specification sheets. It is necessary to check that these limitations do not affect the collection of surface wave data, especially with reference to the low frequency limit.
An adequate triggering system, such as a contact closure or hammer switch, is absolutely necessary if seismic data are stacked during acquisition to improve the signal to noise ratio or for some single station procedures. However, if stacking is not applied in the field, the accuracy of the triggering system is typically not a critical issue for surface wave methods as incremental travel time (phase differences) are analysed rather than arrival time.
2.1.2
Acquisition layoutThe acquisition layout is based on a linear array of receivers with the shot position in-line with the receivers. The geometry is then defined by the array length L, the receiver spacing ΔX, and the source offset (Fig. 6). Receiver spacing is typically kept constant along the array, even if other arrangements are possible to optimize the acquisition of high and low frequency bands.
Fig. 6Geometry for active acquisition. L—array length, ΔX—receiver spacing
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the array length (L in Fig. 6) should be adequate for a reliable sampling of long wavelengths, which are associated to the propagation of low frequency components, and an adequate resolution in the wavenumber domain. If a frequency–wavenumber (f–k) transform is applied to the data during processing, the maximum array length controls the wavenumber resolution: the longer the array, the higher the wavenumber resolution and the smaller the minimum observable wavenumber (hence the longer the observable wavelength). Other advanced processing algorithms are not limited by this link between array length and maximum wavelength (see Sects. 3.1.1, 3.2.3), as the result also depends on the characteristics of the records. Moreover, relating maximum wavelength to maximum resolved depth is not trivial, as the result depends strongly on the velocity structure of the site.
The usual rule of thumb is to have the array length at least equal to the maximum desired wavelength, which corresponds to more or less twice the desired investigation depth. With a more conservative approach, it is suggested an array length longer than two or three times the desired maximum investigation depth. Meaning, an array length of 60–90 m is preferred when trying to profile down to 30 m depth.
Care should be taken when lateral variations might be expected at the site because they may more easily affect long arrays.
the spacing between adjacent receivers (ΔX in Fig. 6) should be adequate to reliably sample short wavelengths, which are associated with the propagation of high frequency waves that are necessary for constraining the solution close to the ground surface (inter-receiver distance on the order of at most a few meters with usual active sources). Signals with wavelength less than 2 × ΔX will be spatially aliased (Shannon–Nyquist sampling theorem, see Fig. 7). Aliasing may prevent the correct identification of dispersion curves at high frequencies, particularly when higher modes are excited. It is therefore preferable to design the array according to the minimum wavelength expected in the signal, which mainly depends on the chosen seismic source and on the velocity structure of the site. Suggested values of receiver spacing for near-surface characterization range from 0.5 to 4 m.
Fig. 7Influence of receiver spacing on aliased energy: numerical experiments (without attenuation). Geophone spread from 11 to 200 m, spaced by a 1 m (190 receivers), b 10 m (19 receivers), c 20 m (10 receivers). Black curves indicate the limit from where shorter wavelengths (i.e. higher frequencies) are aliased
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The desired number of receivers would be dictated by the ratio between array length and receiver spacing. Often the number of receivers is dictated by the available equipment and it constrains the trade-off between receiver spacing and array length.
Surface wave methods may be implemented with a minimum number of receivers as low as two (the two-station procedure of the SASW Spectral Analysis of Surface Wave method). In this case, the spacing between receivers is incrementally increased during the survey. Such implementations are however prone to mode misinterpretation and, therefore, require effective mode analytical routines.
The experimental uncertainties on the dispersion image depend on the number of receivers. Theoretically, in the absence of intrinsic material damping, the higher the number of receivers the cleaner the dispersion image. However, high frequencies are rapidly damped-out with increasing distance from the source (i.e. far-field effects) and this loss of high frequency data can cause a loss of clarity in the dispersion image if too many receivers are used. The dispersion curve accuracy may also be influenced by the number of receivers (a higher number of receivers will make phase distortion at few receivers negligible).
It is recommended that a minimum of 24 receivers be used to guarantee an adequate space sampling of the wavefield. It is not unusual to acquire MASW data using 48 receivers, which provides the flexibility of utilizing both a small receiver spacing to constrain shallow velocity structure and a long receiver array to image to greater depth. If only 12 geophones are available then multiple acquisitions with different source and/or array position may be used to build a single seismic record. Adequate procedures should be implemented to check possible phase distortions and consequences of lateral variations.
Theoretically, a single source position at a certain distance from the first receiver of the array would be sufficient to obtain broad-band dispersion data. However, in reality, the source offset (Fig. 6) should be selected as a compromise between the need to avoid near field effects (see Sect. 1.2.4), which requires a large offset, and the opportunity to preserve high frequency components, which are heavily attenuated with distance (i.e. far-field effects).
Near field effects may cause a distortion in phase velocity estimation for low frequency components, and bias phase velocity to lower values. Several studies in the past have provided indications on this issue but no general consensus has been reached for a rule to avoid near field effects in multi-station analysis of surface waves. It is suggested to adopt values three to five times the receiver spacing, provided that the source is capable to guarantee a good signal-to-noise ratio for the furthest receivers.
At a minimum, we would suggest performing two end shots on the two sides of the array (see Fig. 6) (forward- and reverse-shot). In a layered media only subject to surface wave energy the dispersion curve is independent of the relative position of source and receivers and the dispersion curves obtained from forward and reverse shots are equal. When lateral variations are present in the subsurface, the analysis of the forward and reverse shot generally provides different experimental dispersion curves due to the different energy distribution over frequency from one side to the other and to the influence of attenuation which may give a predominant weight to the structure close to the source. This may be a useful indicator of the compliance of the 1D site condition with the hypothesis of horizontally layered medium, which is at the base of the surface wave analysis procedures (see Sect. 3.3.1).
It might be useful to repeat the acquisition with multiple forward and reverse source offsets and different source types. The abundance of data may help to assess data quality and quantify dispersion uncertainty (see Sect. 3.4). In particular, data with different shot positions are extremely relevant to assess the influence of near-field effects on the estimated experimental dispersion curve (see Sect. 3.3.2). At sites that are challenging to characterize, dispersion curves extracted from multiple source locations may also be necessary to develop a dispersion curve over a sufficient frequency/wavelength band.
Two shots close to each end-receiver and one, or more, mid-array shots (e.g. center shot) may also be useful for refraction analysis in order to constrain P-wave velocities, potentially locate the ground water table, and detect strong lateral variations along the array.
Stacking of multiple shots increases the signal-to-noise ratio and hence improves the phase velocity estimation. A classical vertical stacking in the time domain can be used only if the trigger system has sufficient accuracy that phase cancellation associated with trigger error is not an issue. However, the non-perfect repeatability of the source may still lead to some phase cancellation, particularly for the higher modes. Stacking in the f–k domain is hence suggested.
Characterization of shallow sediments (expected average shear wave velocity around 300 m/s) with the desired investigation depth of 30 m, in an accessible field with medium traffic (about 10 cars/min) 200 m away:
Minimum array length = 1.5 × desired maximum wavelength ≈ 3 × desired investigation depth = 3 × 30 m = 90 m,
Source : accelerated weight drop (sledgehammer would require significant stacking),
Receiver Spacing = ½ × expected minimum wavelength = ½ × minimum expected velocity/maximum expected frequency = ½ × 270/50 ≈ 2 m,
Number of receivers = (array length/receiver spacing) + 1 = 46. Rounded to 48.
Source positions: shots on both sides at 2, 5, 10 and 20 m (if space available) + one shot in the middle.
2.1.3
Recording parametersSampling rate affects the retrieved frequency band. Nyquist criterion dictates that the sampling frequency (inverse of the sampling interval) should be at least equal to twice the maximum frequency of the propagating signal. For surface wave analysis at geo-engineering scales, a sampling interval of 2 ms (sampling frequency of 500 Hz) is adequate in most situations. Higher sampling frequencies (e.g. 2–4 kHz) should be used for picking of P-wave first arrivals to be used for seismic refraction analysis. The latter may provide useful information for the interpretation (e.g. the position of the water table) and would not be accurate enough with 2 ms of sampling interval. The position of the water table helps to define the a priori parameters on P-wave velocity or Poisson’s ratio of the layers in the inverse problem solution (see Sect. 4.2.4).
It must be long enough to record the whole surface wave train. Usually 2 s is sufficient for most arrays, but it is suggested to use longer windows when testing on soft sediments (formations with low seismic velocity). It is good practice to visually check the seismic record during data acquisition to ensure sufficient record length (Fig. 8). Since surface wave analysis is performed in the frequency domain, depending on the analytical routine utilized it may be a good practice to use a pre-trigger time (e.g. 0.1–0.2 s) in the acquisition to simplify the application of filtering techniques aimed at mitigating leakage during signal processing.
Fig. 8Example of different time windows with a pre-trigger time of 0.2 s (data from Mirandola site, InterPACIFIC project)
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2.1.4
Summary of suggested acquisition parameters for active prospectingTable 1 gives a summary of typical data acquisition parameters used for MASW surveys, and their implication on the results. Of course, these parameters depend on the objective of the survey and the specificities of the site, and are to be adapted at each case study.
Table 1 Suggested parameters for MASW surveysFull size table
2.1.5
Signal quality controlSignal quality should be always carefully checked.
At least the following basic visual quality control is always required on-site during the acquisition:
All sensors are correctly recording and correctly coupled to the ground (similar waveforms on receivers close to each other),
The time window contains the whole surface wave train, if possible with sufficient pre-trigger,
The overall signal-to-noise ratio is good (the classical cone pattern of surface waves is visible in all the shots with good repeatability).
Performing also the following quality control in the field would allow the survey crew to adapt acquisition to actual results, but necessary numeric tools may not always be available in the field.
Analysis of the signals in the frequency domain can help in identifying the usable frequency band. In particular it is possible to assess energy content by applying low pass filters with decreasing frequency thresholds to evaluate the lower frequency bound of usable data and high pass filters with increasing frequency thresholds to evaluate the frequency upper bound (Fig. 9).
Fig. 9Example of check of the frequency content (data from Mirandola site, InterPACIFIC project). a Raw data, b data with low pass filter 10 Hz (OK), c data with low pass filter 6 Hz (signal is not dominant anymore), d data with high pass filter 27 Hz (OK), e data with high pass filter 60 Hz (both surface and air waves are dominant, but surface wave waveform changes a lot across the array)
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Ideally, it would be good practice to evaluate quantitatively the signal-to-noise ratio at each receiver and discard traces with values lower than about 10 dB. The noise level can be quantified with on-purpose records of background ambient vibrations (i.e. an acquisition with the same array and the same acquisition parameter without the activation of the source). Alternatively, it can be extracted from portions of the active records not affected by the active wavefield (e.g. the pretrigger window 0–0.2 s or the post-event window 1.8–2 s in Fig. 8), although this is not recommended because noise is a stochastic process and using a too narrow time window to estimate its spectral characteristics might lead to some misinterpretation. In practice however, such evaluation is rarely applied because it is not implemented in the common surface wave analysis software.
2.2
Passive surveyIn passive surface-wave analysis, ambient vibrations are recorded with no need for an on-purpose artificial seismic source. Ground vibrations are caused by natural phenomena (ocean waves, wind acting on trees, micro-seismicity, etc…) and by human activities (traffic, construction or industrial activities, etc…). Typically, low frequencies are generated by large-scale natural phenomena, whereas high frequencies come from local sources, often anthropic activities.
In general, analyzing the quality of a passive survey is more complex than for active acquisition. There is no simple rule that can predict without fail which kind of sensor or which sensor number is mandatory, which geometry is sufficient, etc. Often the term ambient noise is improperly adopted to designate ambient vibrations which are collected for passive surveys. Indeed, in the perspective of surface wave analysis it is necessary to clearly define “noise” and “signal” components in passive records: “signal” is what we wish to analyze and “noise” is what is disturbing our processing.
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Related links:For passive array techniques, “noise” comes from:
1.
effects that are not directly associated to wave propagation:
sensor instrumental self-noise (not-seismic);
weather actions on the sensor (wind, rain, thermal fluctuation…);
bad sensor coupling with soil;
2.
wave propagation features that are not accounted for in the analysis:
surface wave train that cannot be approximated as plane wave at the array size (sources too close to or within the array);
body wave components.
For passive array techniques, “signal” is:
Rayleigh (and, possibly Love) waves originating from distant sources (to satisfy the plane wave approximation at the array site).
The “signal” (ambient vibration level) for passive methods is highly variable from one site to the other one. This variability influences the potentiality to get reliable results. When a passive experiment is performed at a site where ambient vibrations are strong, coherent and dominated by surface wave components, reliable results could be obtained with a rather limited number of sensors and on a relatively short recording time. On the contrary, at “challenging” sites (where few noise sources are present and the wave field is particularly not coherent), a large number of sensitive sensors with optimal installation and coupling with the ground and long recording time are necessary.
Passive surveys allow the measurement of the dispersion from low frequencies (typically 0.2–5 Hz) to intermediate frequencies (typically 10–30 Hz), i.e. from long wavelengths (typically 200–2000 m) to short wavelengths (typically 5–80 m), depending on the location of the survey with respect to the location of the seismic sources, the attenuation between (unknown) sources and survey location, the velocity (and attenuation) structure of the site, and the acquisition approach (equipment, array geometry, array size).
For passive tests, 2D arrays of sensors deployed on the ground surface are recommended, as the ambient vibration wavefield is expected to propagate from different and unknown directions.
2.2.1
EquipmentVertical velocity sensors are adequate for acquisition of passive Rayleigh wave data when retrieving the dispersion curve is the main target. 3D sensors are used for the evaluation of H/V spectral ratio data or Rayleigh and Love wave dispersion (both horizontal and vertical components are analyzed). The natural frequency of the sensors must be sufficiently low with respect to the target depth of investigation, which is furthermore related to the array size and geometry.
As a rule of thumb, 4.5 Hz (or lower) natural frequency geophones (as used for MASW and shown on Fig. 5) are typically sufficient to investigate the uppermost tens of meters of a soil deposit if the ambient vibration level is high.
Nonetheless, passive surveys are often aimed at the characterization of very-deep velocity structures and, therefore, velocimeters/seismometers (e.g. Fig. 10) with natural periods of 1, 5 or 30 s are better suited. Even at higher frequencies on sites where the level of ambient vibration is low, the use of velocimeters/seismometers is more appropriate since these sensors are more sensitive than geophones. It must to be noted, however, that some long-period and broadband sensors require special attention during deployment (perfect leveling, long stabilization time of the feedback system) and processing (proper high-pass filtering before signal windowing), which makes them less appealing for commercial surveys and for non-expert users. The use of intermediate period seismometer is in most cases a good compromise. The use of accelerometers should be avoided as they are, at present, not sensitive enough for sites exhibiting low-amplitude ambient vibrations.
Fig. 10Example of 3D, 30 s seismometer used for passive measurements (on the right: 3D sensor, levelled, oriented, connected to its battery and equipped with an antenna for wireless connection with central data logger; on the left: GPS for synchronization fixed on the packing box
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The Appendix 3 gives some example and recommendations to evaluate sensors capabilities.
The sensor setup is very important in order to limit undesirable noises due to weather (wind or rain on sensors), unstable position of sensors, etc.
Different setups are possible (Fig. 11), from simply placing the sensor on a pavement or completely burying them. The sensor can also be protected from wind and rain using a plastic box (sufficiently “ballasted” to avoid any local vibration of the box itself). When the sensor is buried, the surrounding soil should be firmly packed to ensure a really good coupling. Best results are obtained when sensors are buried, at least for half of their height (as the example shown on Fig. 10), at the expense however of a longer setup time. The influence of the sensor installation on recorded signals depends on the frequency of excitation (see Fig. 41 in Appendix 3).
Fig. 11Different possible setups for the installation of seismometers for ambient vibration array measurements, ranging from least desirable (a) to most desirable (e) for high-quality data acquisition
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In view of the necessity to deploy wide 2D arrays of sensors, standalone or wireless solutions should be preferred over the common geophysical equipment, which requires use of seismic cables for connecting geophones to the acquisition device. Most often, a dedicated datalogger for each geophone/sensor is used and the acquisition is synchronized with GPS and wireless technologies.
As distances are used for velocity measurements, it is necessary to measure the exact location of each sensor relative to the others (at least with 5% location precision). The accuracy of the device to be used strongly depends on the wavelength range of investigation and consequently on the size of the array. For large arrays (e.g. diameter larger than about 200–300 m) it is usually sufficient to use a standard GPS system, either standalone or integrated into the seismometer. For small arrays, it is conversely appropriate to use a more accurate measuring device, such as differential GPS (with georeferenced or variable base station) and theodolites. The use of measuring tape is possible only for very small configurations, but practically recommended only for linear arrays.
In case of array measurements with vertical component sensors, the inclusion of at least one 3-component geophone or seismometer, typically at the array center, allows extraction of additional information via analysis of horizontal-to-vertical spectral ratios (H/V or HVSR; see Appendix 7), which typically provides valuable additional information, particularly for deep interface characterization. Alternatively, the same information can be obtained with an independent single-station measurement by a specific 3-component instrument placed near the array location.
2.2.2
Acquisition layoutAcquisition layout should fulfill the requirements of the processing technique(s) adopted to estimate the dispersion curve (see Sect. 3.2.1). In the following, we describe the most common geometries.
In the ambient vibration wavefield, the source positions are generally unknown. For this reason, 2D array geometries with no preferential direction(s) (e.g. circular or triangular, see Fig. 12) are highly recommended, as they provide a similar sensitivity of the array to wavefields impinging from different directions. T- or L-shapes are also possible, especially in complex and urban field conditions where the presence of obstacles can limit other more complex array shapes. In such cases it is recommended to carefully verify the theoretical array response (see examples in Appendix 2) and the presence of prevalent directional sources in the wavefield.
Fig. 12Commonly used array geometries for passive data acquisition (all examples are given with a total number of 10 sensors), a circular shape, b nested triangles, c T-shape, d L-shape, e sparse nested triangles
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The choice of a given geometry is a compromise between the available number of sensors, the level of ambient vibration on the given site, and the operating time that could be afforded at a given site. More information is given in Appendix 2.
On the other hand, the use of linear arrays, as for example in the Refraction Microtremor (ReMi) technique (Appendix 9), is strongly discouraged. The use of a linear array requires the assumption of homogeneous, isotropic distribution of the passive seismic sources around the site or passive sources in-line with the array direction. As it is not possible to verify the consistency of this assumption using data from a linear array, the results can be strongly biased in case of non-homogeneous source distribution around the testing site or strong off-line directional propagation.
The aperture of the array (maximum distance between two receivers) influences the maximum measured wavelength, and therefore the penetration depth of the measurement. On the other hand, the minimum spacing between receivers controls the smallest measurable wavelength, and therefore the resolution of the measurement close to the ground surface. Given the number of available sensors, arrays from small to large aperture/spacing are usually deployed successively in order to sample over a wide wavelength range.
Although maximum retrieved wavelength also depends on the chosen processing technique (see Sect. 3), the suggestion for non-expert users is to select the aperture of the largest array at least equal to one to two times the desired investigation depth. Minimum measured wavelength also depends on the propagating wavefield; however, the usual rule of thumb fixes the minimum receiver spacing of the smallest array equal to the desired resolution at shallow depth. Since it is often important to resolve near-surface layering for engineering purposes, it may be difficult to obtain short enough wavelengths from strictly passive surveys. Thus, it is recommended that passive surveys be complimented with active surveys if near-surface resolution is important.
The minimum number of receivers for passive surveys is still an open debate. Although acceptable results can often be obtained with a minimum of 4 sensors, especially using SPAC analysis, better results will be achieved using 8–10 sensors, which are still easily manageable in the field. At sites with low level of ambient vibrations, a higher number of receivers will enhance the chance to correctly measure the dispersion. The larger the number of sensors the better the results, but practical limitations are introduced by equipment cost and setup time.
2.2.3
Recording parametersAs for active tests, the sampling rate affects the usable frequency band. The sampling rate is typically lower than that used for active data because of the necessity of long duration records. Since analysis of passive data is typically limited to low frequency data, the use of mid-band seismometers with an upper corner frequency of 50–100 Hz is common. Typical sampling frequencies range from 100 to 200 Hz.
Acquisition of passive data requires much longer durations than those used for active data. Indeed, it is necessary to use statistical averages of distinct signal recording blocks to obtain stable estimates of wave propagation. Long duration records (30–120 min) are typically collected and divided into shorter windows (1–5 min) for processing (see Sect. 3.1.2). Depending on the frequency band of interest, acquisitions of tens of minutes to several hours are collected.
2.2.4
Signal quality controlChecking signal quality for passive data is typically more difficult than for active-source data. Appendix 3 gives information about the instrument testing and verification.
On site quality control during acquisition should be implemented to check the following:
all sensors are correctly recording, with appropriate (and identical) gain in order to have sufficient signal resolution without clipping of the records;
all stations are properly synchronized to a common time reference;
x,y coordinates are measured with sufficient precision (at most 5% of the minimum inter-sensor distance).;
All sensors are properly oriented if 3C sensors are used (a common reference is the magnetic North, which can be usually measured with a simple compass).
In case GPS is used, synchronization between recordings should be verified (e.g. by comparing low-pass filtered recordings). Gross errors in GPS timing can be identified by a noticeable time-shift of the low-frequency surface wavelets propagating across the array. Examples of bad synchronization and time-shift correction are given in Appendix 3.
If three-component seismometers are used, also the proper placement of the horizontal components to a given reference (e.g. the magnetic North) should be verified. The procedure for this verification is based on correlation analysis of the low-pass filtered horizontal components, rotated over different azimuths (see Poggi et al. 2012 for a detailed description). This procedure may be particularly useful at sites where magnetic North cannot be accurately identified with a compass (influence of electric lines, railways, etc.).
To check the usable frequency band of passive data, it is suggested to perform specific preliminary assessments of energy content in the spectral domain, and to compare it to reference levels of ambient vibrations (e.g. the High Noise Model—NHNM-and the Low Noise Model—NLNM-proposed by Peterson 1993) and instrumental self-noise. If possible, this check should be performed on site in order to adapt the acquisition parameters. At sites with low level of ambient vibrations, greatest care should be taken in the equipment settling (larger number of sensors, which should be carefully buried, protection of sensor and cables against wind), and recording length should be increased.
The above check may be also useful to identify frequency bounds in which signals are coherent or usable. Moreover, sharp narrow spectral peaks may indicate the presence of electromagnetic disturbances or machinery generated noise (see also the SESAME guidelines, SESAME Team 2004).
Figure 13 shows an analysis of power spectral density of the three sites investigated within the framework of the InterPacific project (Garofalo et al. 2016a, b), compared to the NHNM, NLNM and theoretical self-noise of the sensor used in the passive surveys. One can see that around 3 Hz the Cadarache site has a power spectral density 4 orders of magnitude lower in comparison with the Mirandola site. The lower ambient vibration level for the Cadarache site in a large frequency band above 3 Hz partially explains why this site was more complex to analyze. On the contrary, one can observe a drastic increase of power spectrum above 0.6 Hz in Mirandola.
Fig. 13Power spectral density of the three sites investigated within the InterPacific project, compared to the NHNM (high noise model), NLNM (low noise model) and theoretical self-noise of the sensor used in the passive surveys
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Another important check consists in verifying the one-dimensionality assumption for the testing site. This can be done by relative comparison of the spectral information from all the recordings along the array using different techniques, such as power spectral density, spectrogram or, more commonly, horizontal-to-vertical spectral ratios. If a sensor shows an anomalous spectral shape (compared to other stations), special attention should be given before including it in the processing, as the records could be biased by local heterogeneities of the subsurface structure, bad coupling or even uncalibrated sensor response.
2.3
Combination of active and passive surveysIn case both active and passive measurements are performed in view of measuring the VS vertical profile down to large depths, the acquisition layouts for active and passive data should be designed in order to optimize the complementarity of gathered frequency bands and to give a sufficient overlapping in the common frequency bands.
In order to measure the dispersion curve on the broadest possible frequency band, it is suggested to perform concentric passive acquisitions, from small (about 10 m) to large apertures (up to 1 km or more, depending on the targeted depth). Since all dispersion curves will be merged, it is suggested to perform the active measurements close to the center of the 2D passive array. Acquisition on several active profiles in the vicinity of the smallest passive arrays may give more insight into the possible lateral variations of the site at shallow depths. An example of a combined acquisition geometry following these specifications is reported in Fig. 14.
Fig. 14Example of active and passive combined acquisition layout for deep VS characterisation. The right plot is a zoom in the centre of the left plot. Active acquisition consists in 2 almost perpendicular profiles of 46 and 69 m length; passive acquisition consists in 3 successive recordings on 2 of the 4 concentric circles R1 to R4 (1st: R1R2, 2nd: R2R3, 3rd: R3R4)
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Finally, in order to avoid cross-contamination of the passive and active wavefields, it is recommended that simultaneous acquisition be avoided.
Appendix 10 reports a case study for site characterisation of a seismological station of the Réseau Accélérométrique Permanent (RAP, French seismological network).
2.4
General suggestions on measurement location2.4.1
Relative to target of investigationIn general, surface wave analysis provides an estimation of a representative velocity profile beneath the array. It is therefore better to place the arrays as close as possible to the target of the investigation. Particular care should be paid when extrapolating the retrieved velocity model to nearby sites, as this should be done only in case of evidences of later homogeneity.
2.4.2
Relative to strong or low sources of vibrationsIt is always suggested to avoid measuring in proximity of strong vibration sources (whenever known). Close sources, often of anthropogenic origin, are responsible for large amplitude transient signals with significant amount of body-waves and propagating non-planar wavefronts.
For active measurements, this reduces the signal-to-noise ratio and may be prohibitive. For passive measurements, a minimum distance on the order of the array aperture from the identifiable sources of vibration is suggested, in order to satisfy the assumption of surface-wave dominance and planar wave fronts. If not possible, especially in urban sites, an alternative is to increase the recording duration in order to perform a more robust statistical averaging of the recording windows.
Passive methods may face difficulties in very quiet sites where the level of ambient vibrations is very low or in case of stiff soil to rock conditions, where the mechanism of generation and propagation of surface waves is less efficient. Hence a preliminary on-site analysis of the signal power spectral density, preferably compared to instrumental self-noise level, is highly recommended before performing the test (see Sect. 2.2.4).
2.4.3
Relative to surface conditionsFor active-source measurements, placing the sensors in open fields is ideal, however placement on paved surfaces also gives satisfactory results, provided the sensors are shielded from wind-induced movement. When working in natural ground the sensors must be fixed on a firm base, either by spikes driven through grass cover, or where permitted by digging a hole to a firm base. When working on paved surfaces, ensure that service lines (buried cables or pipes) are not located beneath the sensor, and if near a building ensure that the site is not adjacent to machinery such as pumps or air-conditioners.
In the case of passive measurement sensors (often seismometers), the overall recommendations are the same, but when it is possible, it is preferable to bury the sensor, especially when recovery of low frequency data are required (e.g. large array for deep investigation), as shown on Fig. 11.
Installation on gentle slopes and mildly irregular topography are permitted, but sites with unusual topographic features (e.g. surface cracks, scarps, karstic dolines) should be avoided. A rule of thumb could be to avoid settling the array in areas with topographic variations larger than about 10% of the targeted wavelengths.
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