Convert Msor To Sor
Bridgette Kubis
Despite the earliest applications of surface waves in the 1950s (Van der Pol 1951; Jones 1955, 1958), surface waves methods were not widely used until the 1980s when the Spectral Analysis of Surface Waves (SASW) method was developed to process the surface wave information of seismic records (Nazarian et al. 1983; Stokoe et al. 1994). Eventually, the Multichannel Analysis of Surface Waves (MASW) method was developed in the late 1990s by a team at the Kansas Geological Survey (KGS) to address some of the limitations of the SASW and to provide practitioners with a robust surface wave testing method (Park et al. 1999; Xia et al. 1999). MASW uses several receivers along the ground surface to measure surface waves from either active sources or background seismic noise. The dispersion information derived from the multichannel recording is used to deduce a Vs profile, which is a direct measurement of the small-strain shear modulus and a proxy for subsurface stiffness at a given site. Thus far, MASW has been used in different engineering applications including seismic site classification (e.g., Kanli et al. 2006; Anbazhagan and Sitharam 2010; Coe et al. 2016), evaluation of liquefaction potential (e.g., Lin et al. 2004), bedrock profiling (e.g., Miller et al. 1999; Casto et al. 2010), assessment of ground improvement (e.g., Burke and Schofield 2008; Waddell et al. 2010; Finno et al. 2015; Mahvelati et al. 2016), and detection of underground anomalies (e.g., Miller et al. 2000; Ivanov et al. 2003).
Very few studies have employed active and/or passive surface wave measurements to produce lunar subsurface structures. Early applications of surface waves employed the horizontal-to-vertical spectral ratio (HVSR) method to estimate regolith thickness (e.g., Mark and Sutton 1975; Nakamura et al. 1975). It was only a few decades later that major technical advancement in surface wave analysis caused a new wave of studies in lunar near-surface characterization. Larose et al. (2005) used Apollo 17 passive measurements to generate Rayleigh wave dispersion images. Tanimoto et al. (2008) developed near-surface (
One of the challenges that has likely prevented such analysis is the lack of true multichannel data from previous exploration efforts. A Multichannel Simulation with One Receiver (MSOR) approach could address this limitation and generate an MASW record, which would allow a multichannel analysis to be performed. MSOR generates a multichannel record by only using a single receiver attached to a fixed location and multiple impacts delivered at successively increasing distance from the receiver (Ryden et al. 2001). Combining all the individual traces would then produce a multichannel record. MSOR assumes that there is source-receiver reciprocity whereby the recorded waveforms would be the same if source and receiver were interchanged (Rayleigh 1873; Knopoff and Gangi 1959).
Previous numerical simulations have confirmed that MASW and MSOR do indeed yield similar dispersion curves in one-dimensional layered profiles, soil profiles with a dipping interface, or even in profiles with a vertical fault (Lin and Ashlock 2016). Moreover, MSOR has been successfully applied in several real-world field experiments as a viable alternative to MASW to characterize soil sites (e.g., Tokeshi et al. 2013; Lin and Ashlock 2016; Dal Moro et al. 2018; Kumar and Mahajan 2020) and pavements (e.g., Ryden et al. 2001, 2004; Yuan et al. 2014; Lin and Ashlock 2015). Direct comparisons made between MASW and MSOR at soil sites that exhibit natural spatial variability comparable to the lunar subsurface demonstrated that MASW and MSOR are equivalent for practical purposes (Lin and Ashlock 2016). Similar comparisons demonstrated that for testing on pavements, MASW provides surface wave energy up to higher frequencies than MSOR (Lin and Ashlock 2015). However, in the frequency range covered by both, MSOR and MASW exhibited similar phase velocities on average. Although MSOR alleviates the problem of having only a few receivers, it necessitates the use of a repeatable impact source that generates waves with consistent timing (Park et al. 2002). Moreover, it is still somewhat unclear whether MSOR maintains reciprocity with a multichannel receiver approach given the nature of the significant variability present in the lunar near surface (i.e., interspersed soft lunar regolith and boulders).
Given the preceding discussion, the objective of this study was to re-analyze the active lunar seismic records in the context of a multichannel surface wave approach. In doing so, first, we used numerical simulation of seismic wave propagation to evaluate the differences between the results of a true MASW record and a multichannel record compiled with the MSOR approach in two highly heterogeneous domains with different scales of fluctuations. Then, we produced multichannel records from lunar active data acquired during Apollo 16 and processed such records for their surface wave information. For the purpose of this study, the focus was on the active seismic records from the Apollo 16 mission.
Figure 3 plots a sample trace of a thumper firing performed during the Apollo 16 exploration. There are two distinctive features about many of the lunar active records. First, many suffer from clipped (saturated) signals, especially at close source offset locations due to the limited dynamic range of the equipment used at the time. Second, the seismic traces exhibit a significant amount of ringy behavior. The ringy and scattered nature of traces has been attributed to low attenuation and the highly heterogeneous nature of the lunar regolith (Dainty et al. 1974; Dal Moro 2015b). Multiple studies have suggested that the low attenuation of the regolith is most likely due to multiple factors, including the absence of fluids in a highly-fractured material, the vacuum conditions present in the atmosphere, and the high temperature oscillations (Tittmann 1972, 1977; Dainty et al. 1974). These ringy signals were used to generate MSOR dispersion images and mimic multichannel analysis for the acquired surface waves.
Prior to MSOR analysis, we conducted a numerical study that explored whether the MSOR assumption of source-receiver reciprocity was valid to model MASW in a highly heterogeneous domain similar to the one present in the near surface of the Moon. Previous studies have identified this reciprocity when characterizing terrestrial soil sites with spatial variability (Lin and Ashlock 2016), but the distinct nature of the lunar subsurface with its interspersed soft regolith and significant presence of boulders warranted additional study. We therefore employed the Spectral Element Method (SEM) research code SPECFEM2D (Tromp et al. 2008) to simulate wave propagation throughout a lunar regolith model.
Figure 5 plots a sample of the waveform acquired by a receiver when simulating MASW with the source and receiver 22.85 m apart. The seismic trace appears to exhibit a ringy quality similar to the experimental seismogram acquired during the Apollo 16 ASE (Fig. 3). As previously noted, this attribute has been partially attributed to scattering from the heterogeneities present in the lunar near surface (Dainty et al. 1974; Dal Moro 2015a, b). The numerical modeling reinforces this theory that the complex nature of the lunar seismic traces is in part because of the heterogeneity in the shallow subsurface and scattering of the waves.
The results from both models suggest that in the absence of MASW records, an MSOR approach can be a candidate for the analysis of surface waves in the large-contrast highly-heterogeneous domain of the lunar subsurface. Consequently, this method will be used in the following section to process actual lunar seismic records.
Dispersion images during MASW processing are generated by applying wavefield transforms to convert multichannel recordings from the space-time domain to the phase velocity-frequency domain. An ideal MASW survey therefore requires a multichannel (e.g., 24 channels) data acquisition system to be deployed. However, as described earlier, the testing setup from the Apollo 16 mission only acquired measurements from three receivers. To mimic a multichannel survey from this dataset, we adopted the MSOR approach and generated two different multichannel records. The MSOR requirement of a consistent source was satisfied in the Apollo 16 exploration efforts given that the small explosives of the thumper were of the same charge. Figure 8 shows the first compiled MSOR record. The second multichannel record involves stacking traces of the same source-offset distance to reduce the noise and to improve the low-frequency response of the averaged record. Stacking is a common practice in seismic geophysics to overcome the adverse influences of ambient and random experimental noise (Foti et al. 2015). Multiple individual records collected with the same source-receiver offset are stacked to suppress the incoherent ambient noise and improve the low-frequency response of dispersion image. Again, there is an assumption of a layered profile with negligible lateral variation when averaging traces acquired with the same source offset, but from different shot/receiver combinations. Figure 9 presents a hypothetical example where 5 individual records collected from the same source-receiver configuration were stacked. Table 1 lists the details of the (shot, receiver) pairs used to compile the untreated and treated records in this study.
Figure 11 plots the one-dimensional Vs profile developed for the test site. The color-coded lines represent velocity models with misfit values below 5%. Consequently, the color-coded area provides a range of acceptable velocity models all of which practically describe the observed dispersion pattern well. This accounts for the non-uniqueness of surface wave dispersion inversion and is a measure of uncertainty often employed in other surface wave studies (e.g., Griffiths et al. 2016; Teague et al. 2018; Gouveia et al. 2019). Additionally, the horizontal dashed lines represent the minimum and maximum wavelength limitations. These limits are based on the one-third wavelength approximation for penetration depth of Rayleigh waves (Hayashi 2008). Also depicted on Fig. 11 are the inverted results from a recent surface wave study (Dal Moro 2015b). Multiple velocity models were acquired in Dal Moro (2015b) for the area bounded by the two gray lines. The dashed gray line is an estimated Vs profile from the Apollo 16 Preliminary Science Report.
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