The most common output of a 2-D shear-wave velocity (Vs) cross section shows only a general velocity (Vs) variation trend that often may not have sufficient resolution to detect small-scale anomalies such as underground utility pipes and tunnels. This is because MASW is not an imaging method that is based on the focusing principle (Claerbout, 1985) (Figure 1). The approach for normal MASW analysis is based on the layered-earth surface-wave propagation in which only the vertical variation is considered. Therefore, the solution of the individual 1-D (depth) velocity (Vs) profile obtained from each field record represents the "best" vertical velocity (Vs) model by laterally averaging subsurface properties under the receiver array used to acquire the record. In this case, an anomaly whose size (D) is smaller than a few receiver spacings (dx) (e.g., D ≤ 2dx for 24-channel acquisition) may not be able to make a significant impact on the dispersion property of surface waves. As a consequence, the 2-D velocity (Vs) cross section may not be the optimal approach to detect anomalies. On the other hand, a small object can generate strong back-scattered surface waves that can be visually identified sometimes over many receiver stations in the field records (Figure 2).
Horizontally travelling surface waves impinging into an object are scattered into all directions as if the object is a new source point (Huygen's Principle). Those travelling backward along the receiver line are called back-scattered surface waves (Figure 3), which make a distinctive arrival pattern of opposing slope in comparison to those of forward propagation travelling directly from the source (Figure 2). By observing the surface location where the feature originates, the anomaly is detected in its horizontal coordinate (Figures 2 and 3). Although the back-scattering does not noticeably influence dispersion analysis that focuses only to the forward propagation, the feature itself can be used to detect anomalies. In this case, the horizontal accuracy can be as high as one receiver spacing (1dx), although the vertical (depth) accuracy may be less (Figure 4).
The minimum dimension of an object to be detected by body (reflected) wave is ultimately determined by wavelength of the impinging wave. A shorter wavelength will be needed to detect a smaller object. The same principle must apply to the back scattering of surface waves. In surface waves, however, penetration depth (Zp) is in proportion to wavelength of surface waves (Lamda); the longer wavelength penetrates deeper. In general, one wavelength is considered the penetration depth (Zp ≈ 1Lamda) as most of the surface wave energy (≥ 99%) is confined for depths shallower than that (Richart et al., 1970) (Figure 5). Then, the minimum size of the (void) anomaly (Dmin) that can be detected by back scattering becomes a function of its depth of existence (Za); Dmin ≈ kZa with (k < 0.5). Although no such theoretical studies have been reported, observations made based on the real and numerical experiments indicate that it is a small fraction of Za; for example, Dmin ≈ 0.2Za. This relationship accounts for not only the wavelength-dependent aspect of detectability but also the amplitude (A) of surface wave that decreases exponentially with depth (Z) (Sheriff and Geldart, 1985); i.e., A ≈ exp (-aZ) with a > 0.0.
The approximate depth of the anomaly can be depicted from the spectral characteristics of the back-scattering feature by utilizing the wavelength (Lamda) dependent penetration depth (Zp) of surface waves (Zp ≈ Lamda). The back scattering can occur only when Zp exceeds the top of the anomaly of size D existing at depth Za (Figure 5); i.e., Zp > Za-D/2. Depending on the spectral characteristics of impinging surface waves and also on the ambient noise characteristics, the wavelength that gives the strongest back scattering may change. There are no systematic studies reported that address this subject through theoretical analysis. However, empirical observations indicate that an approximate relationship should follow the trend illustrated in Figure 6. It shows that, for a given size D (≈ 0.2Za), the back scattering amplitude increases with wavelength once it penetrates deeper than top of the anomaly (i.e., Zp ≈ Lamda > Za-D/2), and the maximum amplitude occurs when Zp ≈ Lamda ≈ 2Za (Figure 6). Then, the amplitude gradually decreases as Zp (or Lamda) further increases. The specific shape of the curve illustrated in Figure 6 and the wavelength that gives the strongest back scattering (i.e., Lamda ≈ 2Za) should change to a certain extent depending on the size (D) of the anomaly as well as the spectral characteristics of impinging surface waves.
A sample data set ["...\Sample Data\VOID\VOID(SR).dat"] is provided for the purpose of implementing the back-scattering-analysis (BSA) and common-offset (CO) section construction. It is a numerical (modeling) data set consisting of fifty (50) records of 24-channel acquisition (Figure 11) generated using the algorithm introduced in Park and Miller (2008). The data set is in PS format and has the source/receiver setup already encoded. The modeling algorithm simply introduces phase shifts to a given frequency band of seismic source wavelet according to the source-receiver distance and frequency-phase velocity relationship depicted in the input dispersion curve. The subsurface model used to generate the input dispersion curve consisted of two layers of overburden and bedrock (Figure 12). Then, a void of 2-m size was conceptually introduced at a depth of 5 m below the surface distance of 44-m (station #1044) (Figure 12). The void existence was incorporated into the modeling by adding wavefields that are generated from the source point, travel to the void, and then back scattered into receivers located at the back-scattering side (rather than forward propagation side). Amplitude of the scattered surface wave is calculated during modeling through a summation of surface wave amplitudes, which exponentially decrease with depth, only for those depths coinciding with depth range of the void. Figure 11 shows three (3) of these modeled records (from a total of 50) selected from the beginning, in the middle, and at the end of the survey line. The first two records in the figure contain the back-scattering feature (visible only with a high display gain), whereas the last record is free of back scattering. Although generation of the common-offset sections can be implemented from a seismic data set of PS format with or without the source/receiver (SR) setup encoded, application is recommended only after the SR setup has been applied (Figure 8).
Both BSA and common-offset sections are displayed in variable-area format by default, but such sections can be displayed in the conventional wiggle format by releasing the variable-area display button in the "View" tab of the display.