a Subsurface Imaging and Sensing Laboratory, Institute of Geophysics and Geomatics, China University of Geosciences, Wuhan 430074, China
b School of Earth Sciences, Zhejiang University, Hangzhou 310027, China
c School of Measurement and Testing Engineering, China Jiliang University, Hangzhou 310018, China
d Department of Geosciences, Boise State University, Boise, ID 83725, USA
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Received
Accepted
Published
2017-10-15
2018-08-16
2018-01-24
Issue Date
Revised Date
2018-08-24
2018-03-24
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(3360KB)
Abstract
Passive surface-wave utilization has been intensively studied as a means of compensating for the shortage of low-frequency information in active surface-wave measurement. In general, passive surface-wave methods cannot provide phase velocities up to several tens of hertz; thus, active surface-wave methods are often required in order to increase the frequency range. To reduce the amount of field work, we propose a strategy for a high-frequency passive surface-wave survey that imposes active sources during continuous passive surface-wave observation; we call our strategy 'mixed-source surface-wave (MSW) measurement.' Short-duration (within 10 min) passive surface waves and mixed-source surface waves were recorded at three sites with different noise levels: namely, inside a school, along a road, and along a railway. Spectral analysis indicates that the high-frequency energy is improved by imposing active sources during continuous passive surface-wave observation. The spatial autocorrelation (SPAC) method and the multichannel analysis of passive surface waves (MAPS) method based on cross-correlations were performed on the recorded time sequences. The results demonstrate the flexibility and applicability of the proposed method for high-frequency phase velocity analysis. We suggest that it will be constructive to perform MSW measurement in a seismic investigation, rather than exclusively performing either active surface-wave measurement or passive surface-wave measurement.
Surface-wave methods are increasingly used as non-destructive, noninvasive, inexpensive, and accurate seismic-imaging methods in multiscale engineering and geological applications. In order to obtain an objective investigation depth and specific resolution, the frequencies of surface waves are critical for geotechnical applications due to their dispersive properties. The capability of sources to generate low-frequency surface waves with deeper penetration has recently been a subject of increasing interest [1].
Two types of sources—active and passive—are generally used in surface-wave measurements. Common examples of active sources include a hammer, a dropped weight, and a harmonic shaker. Utilizing an active seismic source, the multichannel analysis of surface waves (MASW) method [2–6] can directly determine phase velocities from multichannel surface-wave data after transforming waveform data from the time-offset (t-x) domain into the frequency-velocity (f-v) domain. To increase the lateral resolution of surface-wave methods in heterogeneous environments, Hayashi and Suzuki [7] applied common midpoint cross-correlation analysis to MASW. Due to the difficulty in generating low-frequency energy, however, reasonably portable active sources are often limited in their ability to sample deep soils.
Passive surface waves such as those of microseisms (< 0.6 Hz, ocean-generated natural noise) and microtremors (> 1 Hz, cultural noise such as vehicle traffic, railways, or machinery) are typically of lower frequency. Therefore, passive surface-wave measurement would provide a wide range of penetration depths and, as a result, strong motivation to utilize such measurements. In fact, passive surface-wave utilization such as the microtremor survey method, which utilizes surface waves recorded at earthquake stations [8], has been intensively studied in Japan. Using microtremors and assuming a dominant Rayleigh-wave energy contribution, shear-wave velocity (Vs) can be derived by the inversion of spatial autocorrelation curves [9–11]. Louie [12] presented the refraction microtremor method as a fast and effective passive seismic method based on the τ-p transformation, or slant-stacking. Park et al. [13] introduced a strategy that combined the imaging dispersion of passive surface waves with an active scheme based on phase-shifts measurement. Cheng et al. [14] improved this passive surface-wave method with azimuthal adjustment based on cross-correlations, resulting in the method known as multichannel analysis of passive surface waves (MAPS).
In addition, active and passive measurements have been combined in order to extend the investigation depth of surface waves without sacrificing near-surface resolution [1,11,15–17]. However, when these two kinds of measurements (i.e., dispersion images or curves) are roughly combined together, the result can be potentially inappropriate for further analysis, for two reasons: ① The spatial resolution of the combined inverted Vs will be ambiguous, because the spatial sampling interval in passive surface-wave measurement is usually several—or even ten—times greater than the interval used in active surface-wave measurement; and ② passive and active measurements can show a large discrepancy in the overlapping frequency range, because phase velocities that are determined through active measurement usually appear slower due to insufficient information in the low-frequency range [18], whereas passive measurement are interfered with by higher modes, aliasing, and body waves in the high-frequency range.
If passive surface-wave methods are able to provide phase velocities up to several tens of hertz, then the active surface-wave method may not be necessary, and the amount of field work can be dramatically reduced. In this study, we propose a combined active-passive surface-wave method that imposes active sources during continuous passive surface-wave observation in order to obtain high-frequency passive surface-wave measurement; we call this kind of recording, which consists of passive surface waves (e.g., microtremors) and an active-source shot, “mixed-source surface-wave (MSW) measurement.” Passive surface-wave measurement using the spatial autocorrelation (SPAC) and MAPS methods, as well as active surface-wave measurement, were performed at three sites with different noise levels: namely, inside a school, along a road, and along a railway. As a preliminary work, the results presented here demonstrate the feasibility of the proposed combined active-passive surface-wave method in further extending the frequency band of passive surface-wave measurement.
2. Passive surface-wave methods
2.1. Spatial autocorrelation
Aki [9,19] proposed a technique to determine a phase velocity dispersion curve from microtremors recorded by a seismic array. He established that the SPAC coefficient ρ(r, w), as a function of frequency for a given interstation distance, r, and angular frequency, w, averaged over many different azimuths, can be written as follows:
where J0 is the zero-order Bessel function of the first kind and c is the phase velocity at frequency w at the site. The wavefield is assumed to consist of surface waves propagating with equal power in all directions. The phase velocity for each frequency can be obtained by inverting the observed SPAC coefficients. A common way of obtaining the phase velocity is to ensemble-average the observed cross-spectra and normalize the cross-spectra by the averaged power-spectra [20]. Weemstra et al. [21] normalized the cross-spectra before the ensemble-average and obtained the SPAC coefficient as follows:
where denotes the ensemble-average; takes the real part of a complex argument; and u(xk, w) is the power of the wavefield at the station xk.
Following the theory developed by Aki [9] and further discussed by Asten [22], we use the SPAC coefficients to fit the zero-order Bessel function of the first kind (Eq. (1)) in order to perform an inversion to obtain a one-dimensional (1D) phase velocity dispersion curve by defining the fitting residual, ε, as follows:
We then use a grid search over the phase velocity from 100 to 1000 m·s−1 and the frequency from 1 to 30 Hz in order to find the minimum L1-norm residual (step size 1 m·s−1 and 0.5 Hz, respectively).
In the ideal case of an isotropic noise wavefield, azimuthal averaging would not be needed in Eq. (2). For a real-world application, if the source distribution changes sufficiently over a certain time-span, then averaging over this time-span is similar to averaging over the azimuth for a fixed source distribution [23,24]. That means that it is possible to expand the applications of this method to a linear array with a fixed active source. The following applications will demonstrate the feasibility of this assumption.
2.2. Multichannel analysis of passive surface waves
The MASW scheme has been applied to roadside traffic noise in order to determine low-frequency dispersion information [13]. In order to reduce azimuthal effects and spatial aliasing in passive surface-wave measurement, Cheng et al. [14] improved this method with cross-correlations. In this preliminary work, only the inline plane-wave propagation case (Fig. 1) will be taken into account for the following field-data application. Interested readers are also referred to the articles cited in Ref. [14]. Receivers were installed on the road shoulder and used to detect plane waves propagating in the pavement. The active sources were imposed at the end of the receiver line. Our expectation was that high-frequency energy would be detected and improved by imposing active sources during continuous passive surface-wave (e.g., traffic noise) observation.
According to Cheng et al. [14], the relative dispersion energy matrix in the inline plane-wave propagation case can be calculated as follows:
where E(f, v) is the relative dispersion energy matrix for a particular frequency f and a scanning phase velocity v; and are the Fourier transformation of the causal and the acausal parts of the cross-correlation between traces j and k of the whitened records, respectively; xjk corresponds to the distance between traces j and k; and N is the total trace number.
To improve the quality of the relative dispersion energy matrix, we followed the seismic noise interferometry processing described by Cheng et al. [25], which contains single-station data preparation (splitting, removing mean, removing trend, band-pass filter, temporal normalization, and spectral normalization), cross-correlation between a pair of stations, and signal to noise ratio (SNR) weighted stacking.
3. MSW measurement at three sites
As described above, the SPAC method and the MAPS method were applied to three sites: namely, inside a school, along a road, and along a railway. We roughly classified the passive surface waves (e.g., traffic noise) in the common urban areas into three levels: light (L), moderate (M), and strong (S). The three field-data examples can be regarded as the corresponding representations of these three noise levels. In this section, we describe how to impose active sources for MSW measurement, and examine its applicability to high-frequency phase velocity analysis.
3.1. Site 1: L-level passive surface waves
A combined active-passive surface-wave experiment was performed in the backyard of the Institute of Geophysics and Geomatics at the China University of Geosciences, in the city of Wuhan, China (Fig. 2). A 48-channel active-source shot gather was collected. The source was a 6.3 kg hammer vertically impacting a 6 in (1 in = 2.54 cm) plate (the red rectangle in Fig. 2). Meanwhile, a comparable linear array with 15 RefTek digitizers (the red ellipse in Fig. 2) was synchronously deployed. Unfortunately, several digitizers were not connected well, and only nine digitizers worked well until the end of the experiment. All the receivers were 4.5 Hz vertical-component geophones. The trace intervals of the active and passive measurements were 0.5 and 1.5 m, respectively, and the sampling rates were 0.25 and 8.0 ms, respectively.
It is clear that the Rayleigh wave is fully developed and is recorded from 0.03 to 0.3 s in Fig. 3(a). The dispersion image (Fig. 3(b)) was generated by applying a high-resolution linear Radon transform [26] to the original active-source shot. The dispersion image indicates a good dispersion energy within the valid wavenumber zone restricted by the two dashed lines between the Nyquist wavenumber (1/(2·dx)) and the minimum wavenumber (1/(N·dx)). Obviously, the active surface-wave measurement is limited in its ability to sample deep soils (> 10 m) due to the lack of low-frequency (< 20 Hz) information.
To compensate for the shortage of low-frequency information in the active surface-wave measurement, the recorded passive surface waves were utilized and analyzed. Note that we separated the continuous time sequences into two 10 min subsets; the former subset consists exclusively of “quiet” passive surface waves, whereas the latter subset contains several active-source shots with a hammer—namely, MSW. Fig. 4 displays two typical 10 s time sequences for each of both subsets, respectively. An active-source shot event is noticeable in the right panel between 8.5 s and 9.0 s. The SPAC method was applied to both the preprocessed passive surface-wave data and the preprocessed MSW data. The obtained dispersion energy images (Fig. 5(a) and (b)) demonstrate that passive surface-wave measurement is able to obtain dispersion information at lower frequencies. Moreover, they indicate that MSW measurement (Fig. 5(b)) extends the high-frequency limit of the original passive surface-wave measurement from 30 to 55 Hz (Fig. 5(a)). Thus, active surface-wave measurement fieldwork can be avoided, given the full-frequency band that is provided by MSW measurement.
Spectral analysis was performed in order to further demonstrate the feasibility of MSW measurement on high-frequency phase velocity analysis. The results indicate that imposing active sources during continuous passive surface-wave observation clearly improved the higher frequency energy of the recorded time sequences at this site (Fig. 6(a) and (b)), and consequently allows the possibility of high-frequency dispersion analysis with MSW measurement. Compared with the MSW spectrum (Fig. 6(b)), the active surface-wave spectrum appears to be seriously distorted at low frequencies (< 15 Hz) (Fig. 6(c)).
We verified the accuracy of the passive surface-wave measurement using active surface-wave measurement. Because the fundamental model of active measurement in the high-frequency range (35 Hz < f < 55 Hz) is missing, we compared the passive measurement with the inverted active dispersion curve (black triangles in Fig. 7(a)). The largest misfit between the inverted active-source dispersion curve and the MSW measurement is about 7%, which demonstrates the accuracy of the proposed method. The picked dispersion curve (gray diamonds in Fig. 7(a)) was inverted to obtain the 1D Vs profile (as shown in Fig. 7(b)) using the Levenberg-Marquardt method [4,6,27,28].
3.2. Site 2: M-level passive surface waves
This test was carried out in the city of Changsha, China. A linear array of 12 vertical-component receivers of 2.5 Hz each was deployed on the road shoulder along the Xiaoxiang Road. The trace interval was fixed at 5 m and the sampling rate was 2 ms. The survey line parallels the river and road. To examine the effects of imposing active sources on passive surface-wave measurement, traffic noise was continuously recorded for 10 min and active sources were sequentially imposed five times during the last 5 min of the recording. The source was a 10 kg hammer vertically impacting a 6 in plate.
Fig. 8 shows two typical time sequences from 18 to 28 s for each of these two 5 min noise data subsets, respectively. Several linear events generated by vehicles can be distinguished in Fig. 8(a). An active-source shot event is noticeable in Fig. 8(b) between 26 and 27 s, as the black arrow indicates, but suffers strong attenuation at the far offsets. Unlike the “quiet” environment at Site 1, the active surface-wave measurement gave a poor performance due to serious interference from traffic noise and the strong soil attenuation. We do not present it here. We also found that the imposed active sources did not significantly improve the high-frequency (> 20 Hz) energy, because the active-source energy was buried in the powerful traffic noise. However, compared with the absolute amplitude of the original passive surface wave (Fig. 9(a)), the absolute amplitude of the MSW (Fig. 9(b)) still appears to be generally higher, especially in the frequency range from 8 to 18 Hz.
The SPAC method (Fig. 10(a) and (b)) and MAPS method (Fig. 10(c) and (d)) were performed on both the passive surface-wave data and the MSW data. The acceptable dispersion curves of the above measurements (Fig. 10(e)) were picked out and fitted well with each other, which corroborated the validity of these measurements. Compared with the passive surface wave, the MSW presents better applicability for high-frequency (> 10 Hz) dispersion analysis. In addition, incoherent energy, which polluted the dispersion image (Fig. 10(c)) at high frequencies from 14 to 18 Hz, was significantly suppressed in the MSW measurement (Fig. 10(d)); the effect of the coherent energy is discussed later in this paper.
3.3. Site 3: S-level passive surface waves
This test was carried out in the city of Yueyang, China. A linear array with 12 vertical-component receivers of 4.5 Hz each was deployed along the railway from Beijing to Guangzhou, which is one of the busiest railways in China. The trace interval was fixed at 10 m and the sampling rate was 2 ms. In this test, three kinds of noise subsets were recorded and analyzed. The first subset consisted of only “quiet” ambient noise; during the second observation, a passenger train and a freight train sequentially passed; and the third subset consisted of four shots with active sources. The source was a 20 kg rock that was found locally.
Fig. 11 displays the complete noise records of each subset. It is easy to distinguish the arrivals and loads of the two trains (Fig. 11(b)). Spectral analysis was performed on each subset (Fig. 12), and indicates that the imposed active sources indeed improved the high-frequency (> 5 Hz) energy of the MSW (white lines), compared with the “quiet” noise (gray lines). The train noise (black lines) showed the highest energy in the frequency range from 5 to 10 Hz, but the powerful high-frequency energy was greatly attenuated above 10 Hz due to the trains’ rapid departure. Note that the MSW displays great amplitude fluctuations among these traces with different offsets at high frequency (> 18 Hz), which reveals the effects of geometrical spreading and attenuation.
Dispersion energy images of each subset were obtained using the MAPS method (Fig. 13(a)–(c)) and the SPAC method (Fig. 13(d)–(f)), respectively. The acceptable dispersion curves of the above measurements (Fig. 13(g)) were picked out and fitted well with each other, which corroborated the validity of these measurements. Compared with the “quiet” noise (Fig. 13(a) and (d)), the MSW presents better applicability to high-frequency (>8 Hz) dispersion analysis (Fig. 13(b) and (e)). Although the train noise shows higher amplitude (Fig. 12), the rapid attenuation of the coherent signals at high frequency (> 10 Hz) makes it extremely difficult to utilize this kind of passive surface wave for high-frequency dispersion analysis (Fig. 13(c) and (f)), which is discussed later.
4. Discussion
Spatial aliasing should always be taken into consideration during passive surface-wave measurement. Utilizing cross-correlations, Cheng et al. [14] demonstrated the advantage of MAPS in suppressing spatial aliasing. Compared with using passive surface waves, we found that the MSW measurement was able to further reduce the effect of spatial aliasing. For example, the MSW measurement (Fig. 5(b)) displays less phase velocity disturbance than the passive surface-wave measurement (Fig. 5(a)) at low frequencies beyond the valid wavenumber zone. In addition, it is easy to find an aliasing energy trend from 7 to 20 Hz (Fig. 13(a)), whereas the aliasing energy is significantly suppressed in the MSW measurement (Fig. 13(b)). The suppression results from the effect of the coherent energy that is introduced by the active-source shots. It is noticeable that the temporal normalization option during preprocessing will only operate on the amplitude of passive surface waves; it will not affect the coherent phase [29].
Long-duration records used for passive surface-wave measurement not only provide high SNR, but also broaden the period range in which dispersion measurements can be made [30]. However, our results indicate that it is possible to utilize ultrashort-duration records (e.g., several seconds or minutes) for a passive surface-wave survey, rather than long-duration records over several hours or days. Although the use of ultrashort-duration records is beyond the scope of the present work, we suggest that short-duration records will be beneficial in amplifying the coherent energy effect of active-source shots for the MSW measurement due to the SNR weighted stacking operation [25].
The point we wished to emphasize in this paper is that it is possible to obtain higher frequency dispersion information for passive surface-wave methods by imposing active sources during continuous passive surface-wave observation. Therefore, we did not pay much attention to retrieving low-frequency information using passive surface waves in this context. Note that it was difficult to obtain low-frequency (< 5 Hz) phase velocities at Site 3 from MSW and train noise (Fig. 13(b), (c), (e), and (f)) because the powerful sources generated more near-field effects and scatter [31], and ultrashort-duration records (5 min) might be insufficient to ensemble-average this incoherent noise in such a low-frequency range. However, dispersion measurements within the valid wavenumber zone still showed a good performance. This indicates that a longer alignment spread—namely, lowering the lower limit of the wavenumber—is required in order to obtain sufficient depth coverage [32].
Three sites with totally different noise environments were used to demonstrate the flexibility and applicability of the MSW measurement in high-frequency phase velocity analysis. The MSW measurement can also be flexibly implemented in the field. For example, the active source at Site 3 was simply a rock picked on the site ground. It should be mentioned that the effect of the active source (i.e., offsets, weights, frequency, etc.) on the MSW measurement requires further study.
5. Conclusions
This paper proposes a simple procedure for a high-frequency passive surface-wave survey: It is possible to extend the frequency band by imposing active sources during continuous passive surface-wave observation, in a method we call “MSW measurement.” We have applied this method at three sites with different noise levels; the results indicate our method’s flexibility and applicability in high-frequency phase velocity analysis. Although this preliminary work is not backed up by a theoretical demonstration, the results presented here strongly suggest that it will be constructive to perform MSW measurement during seismic investigation, rather than exclusively performing either active surface-wave measurement or passive surface-wave measurement. The results suggest that the proposed strategy can be an alternative choice in engineering, environmental, and other seismic projects.
This study is supported by the National Natural Science Foundation of China (41774115) and the National Nonprofit Institute Research Grant of the Institute for Geophysical and Geochemical Exploration, Chinese Academy of Geological Sciences (WHS201306).()
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