SOME PRACTICAL ASPECTS OF MASW ANALYSIS AND PROCESSING

Julian Ivanov, Kansas Geological Survey, Lawrence, KS Richard D. Miller, Kansas Geological Survey, Lawrence, KS

George Tsoflias, CReSIS, The University of Kansas, Lawrence, KS

Abstract

We use multi-channel analysis of surface waves (MASW) on seismic data in an attempt to test data acquisition parameters and compare those results to reaffirm existing general theoretical recommendations and rules of thumb. Of particular interest were optimum seismic receiver spread size, minimum and maximum receiver offsets and dominant geophone frequency for best-case fundamental-mode dispersion-curve evaluation of the Rayleigh wave. Recommended MASW parameter selection criteria are tested on seismic data collected at various sites, such as desert setting, river sediments, and glacier, for which shear-wave properties were estimated. Presented MASW results demonstrate that observing optimal parameter selection can improve the resolution and quality of the fundamental-mode dispersion-curve images of the surface wave and the final 2D Vs section. After comparing the optimal parameter selection approach with the general theoretical recommendations it was concluded that the rules of thumb are s a good starting point, especially when applying the MASW method at a site with unknown seismic characteristics. However, optimal acquisition and processing MASW parameter selection can be best achieved using field site tests and is the preferred approach over theoretical recommendations. Specifically testing a selected brand of geophones, it is expected that, in general, frequencies as low as one octave and a half bellow the natural geophone frequency can be recommended used for most MASW analysis.

Introduction

Estimation of shear-wave velocity (Vs) is important for the evaluation of the stiffness properties of the near-surface materials; Vs increases as material shear strength (rigidity) increases. The multi-channel analysis of surface-wave (MASW) method was developed to estimate near-surface S-wave velocity from high-frequency (≥ 2 Hz) Rayleigh-wave data (Park et al., 1999; Xia et al., 1999a). The practical application of MASW has provided reliable correlations to drill data. Using the MASW method, Xia et al. (2000) noninvasively measured Vs within 15% of Vs measured in wells. Miller et al. (1999a) mapped bedrock with 0.3-m (1-ft) accuracy at depths of about 4.5-9 m (15-30 ft), confirmed by numerous borings. Similar results were reported by Ismail and Anderson (2007). The MASW method has been applied to problems such as characterization of pavements (Ryden et al., 2004), the study of Poisson’s ratio (Ivanov et al., 2000a), study of levees and sub-grade (Ivanov et al., 2005b, Ivanov et al., 2006c), investigation of sea-bottom sediment stiffness (Park et al., 2005; Ivanov et al., 2000b), mapping of fault zones (Ivanov et al., 2006a), detection of dissolution features (Miller et al., 1999b), and measurement of S-wave velocity as a function of depth (Xia et al., 1999b). Studies on the MASW method have been extended to areas of utilization of higher modes (Xia et al., 2003; Beaty et al., 2002; Beaty and Schmitt, 2003), determination of near-surface Q (Xia et al., 2002), and the acquisition of more realistic seismic refraction models (Ivanov et al., 2006b, Ivanov et al., 2007).

A single MASW data record is recorded by a set of geophones evenly spaced along a line. The seismic data from each record is transformed into a phase-velocity – frequency image in which the fundamental-mode dispersion-curve trend is evaluated. The estimated dispersion curve is then inverted

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to produce a 1-D Vs model, which is assigned to the middle of the geophone spread. By assembling numerous 1-D Vs models derived from consecutively recorded seismic shot records along a seismic line, a 2-D Vs model can be obtained.

The imaging and quality of the fundamental-mode dispersion-curve trend, essential for the method, can be influenced by field data acquisition parameters such as source strength, receiver dominant frequency, minimum and maximum geophone offset from the source, etc. Optimum minimum receiver offset and spread size determination extended the spectral analysis of surface waves (SASW) method (which uses only 2 geophones) work (Heisey et al., 1982; Roesset et al., 1989) and has been subject to further research when using the MASW method (Park et al., 2001; Zhang et al., 2004; Xu et al., 2006) to offer recommendations and rules of thumb that could be easily implemented in practice. For example, a most simple but practical—and thus widely accepted—general rule of thumb that has emerged so far is that the spread size should be about the size of depth of investigation and the nearest offset 50% of it (with the understanding that it could be between 25% and 100%).

In this paper we present a series of test with varying spread size and nearest offset parameters to exemplify the optimum parameter selection and show the potential pitfalls of applying the rules of thumb without on-site testing.

After examining the dispersion-curve images from different offset ranges and selecting the optimum offset parameters for the sample data set, we observed some of the analyzed short-offset ranges produce erroneous dispersion curve trends. While theoretical analysis of shortening the spread has indicated decreased fundamental-mode dispersion-curve imaging resolution (Park et al., 2001; Zhang et al., 2004), research so far has fallen short of indicating the possibility for actual changes in the observed dispersion-curve trend pattern. Such a changes can be essential for the final Vs image accuracy because they could lead to completely different patterns of the Vs inversion model.

When recording surface-wave data, the lower dominant frequency geophones used, the lower surface-wave frequencies can be recorded. However, it has been unclear if and to what degree the data below the dominant frequency of the geophones can be used. We demonstrate that for the purposes of dispersion curve evaluation the lowest usable frequencies can be as low as 1 to 1.5 octaves lower than the dominant frequency of the receivers.

Testing Minimum and Maximum Geophone Offsets

There are several contradicting variables affecting the selection of minimum and maximum geophone offsets. Using a shorter spread while continuously acquiring MASW data provides relatively higher lateral resolution. However, larger spreads are needed to provide separation between different surface-wave modes (Park et al., 2000) and to record longer wavelengths (lower frequencies). Lower frequencies provide Vs information for the deeper part of the section, while higher frequencies for the shallow. Larger spreads, though, reduce lateral resolution. At relatively near offsets (smaller than the longer wavelengths) corresponding low frequencies are affected by the near-field effect (Heisey et al., 1982), while at far offsets fundamental-mode higher-frequencies are attenuated and affected by body-waves and higher-mode energies. Thus, the goal of the tests is to find the optimum spread, which would be the shortest possible spread that provides the widest possible fundamental-mode frequency range including both low and high frequencies.

Desert seismic data

We performed source offset and spread size tests on seismic data collected in the Sonora Desert, Arizona, using a 96-channel Geometric Geode distributed seismic recording system, 4.5-Hz pressure-coupled geophones spaced every 1 m and a hydraulic actuated, spring accelerated weight drop. Geological information suggests that the first 100 m of sediment are composed predominantly of silt,

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gravel, and sand. Seismic data acquired at four source offsets using eight spread-size ranges was transformed into phase-velocity – frequency domain images (Figures 1 to 4) with the goal of finding out which of the 32 source-spread size combinations provides the best quality fundamental-mode dispersion curve trend in terms of resolution and widest frequency range observation.

The largest spread (95 m) having the longest (30 m) source offset (Figure 4h) provided the best resolution of the fundamental-mode trend starting from 510 m/s at 7 Hz to 360 m/s at 33 Hz with corresponding wavelengths between 73 m and 11 m and expected approximate depth estimates (based on the rough 50% of the wavelengths assumption) between 36.5 m and 5.5 m. Such a dispersion-curve range does not provide sufficient information to reliably estimate (invert) the top 5.5 m, which are usually of interest for the near-surface investigations.

Now we can evaluate one of the recommendations. Using the formula proposed by Zhang et al. (2004) we determine that the minimum offset should be X1=42 m and spread size 84 m, which are close to the suggested parameters. However, this approach may not be sufficient if the goal is to image the shallower part of the section, including the top 1-6 m range, which would require the estimation of the fundamental-mode dispersion curve in the range of 30-70 Hz.

Changing the offsets (both minimum and maximum) by keeping the largest spread (95 m) but moving the source closer to the spread (Figures 4h, 3h, 2h, and 1h) allows the observation of funda-mental-mode energy in the desired frequency range (30-70 Hz) at about 380-300 m/s, while noticing that the low-frequency energy trend between at 500 m/s becomes more irregular and unreliable most likely due to the near-field effect. Selecting the spread with the closest source (Figure 1h) provides the widest frequency range for this seismic data set. Shortening the spread further by reducing the maximum offset makes the fundamental-mode energy more pronounced in the frequency range 30-70 Hz (Figures 1g –1d). The resulting 12-72 Hz dispersion curve provides approximate depth estimates between 18 m and 2 m. This observation is consistent with the common observations with other data sets that at longer offsets higher frequency fundamental-mode energy rapidly attenuates and that energy from other higher modes becomes stronger. The clearest fundamental-mode energy in the 30-70 Hz range can be observed with the 45 m spread (Figure 1d). While such energy can be even stronger using shorter spreads, it can be seen that the general trend of the fundamental mode is influenced by the first higher mode (Figures 1c and 1d) to the extent of a complete merger when using the shortest spread (as seen in Figure 1a).

The series of dispersion-curve images demonstrate the principle that longer spreads are needed to separate the fundamental mode from higher modes. The merger, observed above, not only brings error to the Vs estimates but the resulting change in the dispersion-curve trend pattern could lead to completely different patterns in the overall Vs inversion model and generate false anomalies and patterns in the final 2D Vs image. Almost all short spreads 15 to 35 m (Figures 1-4, a, b, and c), exhibit reverse trend of phase-velocity increasing with frequency.

Here is the place to compare our observations to the simplest rule of thumb that the spread size should be about the targeted investigation depth (Zmax≈spread size) and source offset the same or smaller, as much as 1/6th (Heisey et al., 1982). We see that none of the 35 m spreads were large enough to clearly separate fundamental-mode from higher-mode energies. Thus, regardless of our target depth of investigation (say, 30 m) and corresponding rules of thumb, we can notice that the shortest usable spread is 45 m long. This data set illustrates that it is the velocity structure of the investigation site that influences the acquisition parameters in the first place, not the goal of the survey, which is secondary.

The goal of the survey can influence our spread selection after knowing the offset ranges that provide reliable estimates of the fundamental mode of the Rayleigh wave. If for this specific site the goal were to map the top 15-20 m, the 1 m source offset and the 45 m spread (Figure 1d) would most likely be our first choice.

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a) e)

b) f)

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Figure 1. Dispersion curve images of MASW seismic data acquired near Yuma, Arizona, with source distance from the nearest receiver at X1=1m and varying spread size a) 15 m, b) 25 m, c) 35 m, d) 45 m, e) 55 m, f) 65 m, g) 75 m, and h) 95 m.

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a) e)

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Figure 2. Dispersion curve images of MASW seismic data acquired near Yuma, Arizona, with source distance from the nearest receiver at X1=9m and varying spread size a) 15 m, b) 25 m, c) 35 m, d) 45 m, e) 55 m, f) 65 m, g) 75 m, and h) 95 m.

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a) e)

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Figure 3. Dispersion curve images of MASW seismic data acquired near Yuma, Arizona, with source distance from the nearest receiver at X1=19m and varying spread size a) 15 m, b) 25 m, c) 35 m, d) 45 m, e) 55 m, f) 65 m, g) 75 m, and h) 95 m.

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a) e)

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Figure 4. Dispersion curve images of MASW seismic data acquired near Yuma, Arizona, with source distance from the nearest receiver at X1=29m and varying spread size a) 15 m, b) 25 m, c) 35 m, d) 45 m, e) 55 m, f) 65 m, g) 75 m, and h) 95 m.

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If the survey objective were to estimate Vs for the top 30 m (e.g., Vs30) or deeper, with little interest in the top 5-6 m, then the 30 m source offset and the 95 m spread (Figure 4h) would most likely be a good choice. Furthermore, if both shallow and deep parts are of interest, then both spreads could be used to come up with a combined MASW analysis.

We intentionally provided abundant combinations of minimum source offset and spread sizes with this data set to demonstrate the narrow range of favorable offsets (spreads) and the large amount of unfavorable parameters that provide inaccurate fundamental-mode dispersion-curve trend. Some of these combinations might be used if rules of thumb are applied and detailed field parameter tests are not performed at a given site. Such an abundant set can be compared with various existing rules of thumb. However, our goal is not to question the rules of thumb, which are scientifically sound, but to demonstrate that detailed testing is the preferred approach.

Arctic seismic data

The next MASW data receiver-offset estimation was applied to data originally acquired for a refraction survey in the Arctic. The goal of the survey was to evaluate the top near-surface section of the ice. Data were collected using a 10 lb hammer for source and twenty-four 28 Hz P-wave vertical phones on 20 m spacing. In an effort to include as many traces as possible, initially we selected a 320 m long spread size (16 traces) with the source located at the beginning of the spread, which was two-thirds of the original spread size. The phase-velocity – frequency image of data showed the high-resolution fundamental-mode dispersion-curve trend within a wide frequency range, 15-100 Hz (Figure 5a). With a phase velocity of 1500 m/s at 15 Hz and 1000 m/s at 100 Hz with corresponding wavelengths between 100 m and 10 m, the expected (50% of the wavelengths) approximate depth estimates were from 50 m to 5 m. It was possible to observe the same fundamental-mode trend using only 11 geophones with a shorter spread of 220 m (Figure 5a).

a) b) Figure 5. Dispersion curve images of arctic MASW seismic data acquired with source distance from the nearest receiver at 20 m and spread size a) 320 m, and b) 220 m.

In this example the analyzed spread is significantly larger than the estimated depth range. With such long offsets it was reasonable to expect a very narrow fundamental-mode frequency range similar to the large-offset desert MASW data (Figure 4h). Nevertheless, including longer offsets did not harm the observation of higher fundamental-mode frequencies (say, 35-100 Hz), which is probably due to the absence of strong higher-mode energy within that range.

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Dispersion Curve Estimation at Frequencies Lower than the Dominant Geophone Frequency

Selection of seismic equipment is determined by the effort to record the seismic signal in the frequency range, considered for analysis. In general, it is uncommon and not recommended to analyze signal frequencies that are outside the manufacturer’s equipment specifications. However, in some instances it may be possible to do so. For example, it is possible to apply MASW analysis on seismic data that was not recorded using geophones with a frequency range optimal for the MASW method. Likely reasons for following such an approach could include the use of old data sets and/or data recorded for different types of seismic analysis, such as reflection or refraction methods (recorded usually with higher frequency receivers), limitations with available equipment, and amount of funding and resources. As a result, a common question can arise whether one can estimate phase-velocities below the manufacturer-specified geophone natural frequency? While it is known that the formal answer to such a question is ‘No,’ it is also known that usually the geophone signal attenuation below the natural frequency is about 6 dB per octave. The question then can be reformulated, if phase-velocities at frequencies 6 dB weaker than the rest of the signal could be estimated? at, say, one octave lower, and if signal at even lower frequencies and thus weaker could be analyzed?

To obtain practical estimates, we analyzed another seismic data set collected in the Sonora Desert, Arizona, USA, which was acquired using 3 sets of geophones: 4.5 Hz Geospace 11D, 10-Hz Geospace Ultra phone, and 40 Hz Mark Product L23E that were spaced 1 m apart (Figures 6a, 6b, and 6c). The 4.5 Hz geophones are with the lowest natural frequency and are therefore optimal for recording low-frequency surface-wave data (Figure 6a). The seismic energy was recorded using a 240-channel Geometrics StrataView seismograph. Our source was a Rubberband Assisted Weight Drop (RAWD) (50-kg mass accelerated ½ m and impacting striker plate of equal mass). Geological logs from borings near the center of the site suggest that the first 100 m of sediment are composed predominantly of silt, gravel, and sand. To a depth of 7 m, the materials are silt with sand and minor amounts of gravel. Between 7 and 28 m depth, the sediments are mostly gravel with some suggestions of boulders.

a) b) c) Figure 6. Raw shot records of MASW seismic data recorded near Yuma, Arizona, using a) 4.5 Hz phones, b) 10 Hz phones, and c) 40 Hz phones.

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The corresponding phase-velocity – frequency images of the selected short records were examined for the fundamental mode of Rayleigh wave (Figure 7). Examining the dispersion-curve image of the shot record acquired with the optimal frequency geophones (4.5 Hz), the fundamental-mode trend can be observed from about 500 m/s at 8 Hz to 360 m/s at 33 Hz (Figure 7a). Identical fundamental-mode dispersion-curve trend (Figure 7b) can be estimated analyzing the seismic data recorded with the 10 Hz geophones. When analyzing the 40 Hz geophone seismic data, the lowest observable fundamental-mode frequency is about 15 Hz (Figure 7c), while the rest of the dispersion-curve estimates at higher frequencies are identical to those from 4.5 and 10 Hz geophones. The frequency of 15 Hz is about one and a half octave lower than the natural geophone frequency of 40 Hz. This example shows that, from a practical perspective, it might be reasonable, for purposes of MASW phase-velocity evaluation, to use frequencies one and a half octave lower than the natural geophone frequency of the recording receivers.

a) b)

c)

Figure 7. Dispersion-curve images of MASW seismic data recorded near Yuma, Arizona, using a) 4.5 Hz phones, b) 10 Hz phones, and c) 40 Hz phones.

Looking back at the Arctic data refraction survey, which was acquired using 28 Hz receivers, it

can be noticed that phase-velocities were evaluated at frequencies about one octave lower (15 Hz) than the natural frequency of the geophones. From a practical perspective, and in view of the tests mentioned above, it can be assumed that it is acceptable to make phase-velocities estimates at frequencies about one a half octave lower (15 Hz) than the natural frequency of the recording geophones.

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Conclusions

Presented results from MASW data demonstrate that optimal parameter selection can improve the resolution, imaging, and quality of the fundamental mode of the surface wave and, consequently, of the resulting final 2D Vs section. Applying offset-parameter tests on real-world MASW data sets, we demonstrate that optimum minimum and maximum receiver offsets can be different from the general theoretical recommendations. Therefore, we conclude that it is preferable to think about the general theoretical geophone-offset recommendations and rules of thumb as a good starting point when considering the application of the MASW method at a site with unknown seismic settings. Optimum minimum and maximum receiver offsets are most likely to be determined after site tests, while considering the goal (i.e., shallow or deep focusing) of the MASW survey.

We show that the use of minimum and maximum receiver offsets, which are not optimized for a given site, has the potential to provide erroneous fundamental-mode dispersion-curve patterns and resulting 2D Vs images.

The work described here illustrates that the velocity structure of the investigation site is the major factor that influences the acquisition parameters and the goal of the survey is of secondary importance.

Practical geophone-frequency tests show that frequencies as low as one and a half octave lower than the natural geophone frequency can be used to estimate phase-velocities for the purposes of MASW analysis. These tests indicate the MASW frequency potential of any seismic data set. However, confi-dent dispersion-curve evaluation of such seismic data can only be achieved after comparison with dispersion-curve images from seismic data acquired with geophones whose resonant frequency is low enough and includes the targeted frequency range. For example, a few shot records can be recorded (for comparison and evaluation purposes) using appropriate low-frequency geophone at site for which there is a significant quantity of (e.g., old) seismic data (e.g., refraction) recorded with higher frequency receivers.

This manuscript provides practical examples for the utilization of frequencies lower than the dominant frequency of the seismic receivers that are located at appropriate source offsets for MASW analysis. These examples can be used as a guide for processing non-MASW seismic data sets (old or current) that were not originally designed and configured for surface-wave analysis. Furthermore, the presented result could facilitate the design of a single-pass multi-wave (e.g., surface-wave, refractions, and reflections) seismic data acquisition approach for given sites.

Acknowledgments

We appreciate Mary Brohammer’s assistance in manuscript preparation. The authors would like to acknowledge assistance in the field by Don Voigt, Huw Horgan, Leo Peters and Paul Winberry during the arctic data collection. Arctic research was supported by the National Science Foundation, grant ANT-0424589 under the Center for Remote Sensing of Ice Sheets (CReSIS). However, any opinions, conclusions, or recommendations expressed herein are those of the authors and do not necessarily reflect the views of the NSF.

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Xia, J., Miller, R.D., and C.B. Park, 1999a, Estimation of near-surface velocity by inversion of Rayleigh waves: Geophysics, 64, 691-700.

Xia, J., R.D. Miller, C.B. Park, J. A. Hunter, and J. B. Harris, 1999b, Evaluation of the MASW technique in unconsolidated sediments: 69th Annual International Meeting, SEG, Expanded Abstracts, 437-440.

Xu, Y., J. Xia, and R.D. Miller, 2006, Quantitative estimation of minimum offset for multichannel surface-wave survey with actively exciting source: Journal of Applied Geophysics, 159, 117-125.

Zhang, S.X., Chan, L.S., and J. Xia, 2004, The selection of field acquisition parameters for dispersion images from multichannel surface wave data: Pure and Applied Geophysics, 161, 1-17.

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