Crustal structure of the Moon determined from short-period Rayleigh wave analysis

Abstract

The lunar crustal structure is determined to be in a depth range of 0 to 40 km by means of Rayleigh wave analysis. The traces of three moonquakes were used to obtain Rayleigh wave dispersion (group velocities) in the short period range (fundamental mode: 0.5–12.5 s, first mode: 0.5–5.5 s, and second mode: 1–4 s). These moonquakes were registered by two stations placed on the Moon during the Apollo program. The dispersion was calculated with a combination of filtering techniques and was later inverted to the fundamental-mode dispersion to obtain an S-velocity model—an S-velocity distribution with depth. The S-velocity increased with depth, and a rapid S-velocity gradient was observed from 0 to 5 km in depth, while the S-velocity gradient became smaller down to 5 km in depth. While the present S-velocity model contributes to lunar crustal structure determination, more research is needed to precisely determine this structure, which will be possible when higher-quality data are acquired in future missions. Plain language summary: A rapid S-velocity gradient was determined from 0 to 5 km in depth. The low S-velocities (<2 km/s) determined for the first layers (0–2 km-depth) can be associated with the presence of broken and fractured materials at the uppermost lunar strata. The S-velocity increases with depth, but its gradient becomes slower deeper than 5 km.

1 Introduction

An important key for understanding the origin and evolution of the Moon is found in knowledge about its internal structure. Fortunately, the Moon is a body of our solar system for which seismic data have been successfully obtained. The Active Seismic Experiment and Passive Seismic Experiment during the Apollo program (Nunn et al., 2022) provided invaluable seismic data which were analysed to obtain the deep structure from P and S waves (e.g., Matsumoto et al., 2015) and the shallow structure from Raleigh wave modes of high frequency (e.g., Dal (2015) in the frequency range of 1 to 80 Hz. However, the Rayleigh-wave modes have not been analyzed for periods greater than 1 s. This is the goal of the present study, which complements previous research by filtering and inverting the short-period Rayleigh-wave modes to obtain an S-velocity model (i.e., an S-velocity distribution with depth) for a depth range of 0 to 40 km. This methodology has proven to be very useful in several regions of the Earth (Corchete, 2021; 2022).

2 Data, methodology, and results

Seismic records obtained from seismometers placed on the Moon during the Apollo program (Nunn et al., 2022) corresponding to 63 seismic events (Garcia et al., 2011) were used to compute Rayleigh-wave group velocities (dispersion curves) (Corchete et al., 2007) by means of dispersion analysis: multiple filter technique (MFT; Dziewonski et al., 1969) and time variable filtering (TVF; Cara, 1973). Unfortunately, most of these records do not present Rayleigh waves; only a few seismic waves have provided adequate Rayleigh-wave trains (Supplementary Material S1, 2). In Supplementary Material S1, the parameters (date, origin time, latitude, and longitude) are provided by Garcia et al. (2011). Figure 1 shows the paths of the Rayleigh waves; the Rayleigh-wave analysis (dispersion analysis) is shown in Figure 2 and Supplementary Materials S3, 4. This analysis consists of a combination of MFT and TVF (Corchete et al., 2007) in which MFT is used to obtain the group-velocity dispersion curve (e.g., Figures 2b,d) from an instrument-corrected seismic record (e.g., Figure 2a, red line; Bath, 1974) or a filtered seismic signal (e.g., Figure 2a, blue line). MFT analysis is improved by performing a polynomial fit of the envelope before the calculation of its maximum because lunar-quake seismic records are highly noisy signals (e.g., Figure 2a, red line). The time of this maximum corresponds to the group time for the considered period (Dziewonski et al., 1969). In Figures 2e and f, the improvements introduced to analyze these noise signals are shown for the trace in Figure 2a (red line) at periods of 2.5 and 7.5 s, respectively. This improvement is applied to all MFT computations performed in this study. The TVF is the filtering technique used to compute a smooth signal (a time-variable filtered signal) in which the energy of all undesirable perturbations has been removed (Figure 3, black lines). The final results of this analysis (MFT and TVF combination) are the dispersion curves shown in Figure 2c (blue line) and Supplementary Materials S3c, 4c (blue lines). The dispersion curve shown in Figure 2c (blue line) is considered the observed data for the inversion process (Supplementary Materials S5–7; Corchete et al., 2007). The errors in these observed data are assumed to be 0.1 km/s (Corchete et al., 2007). The initial model for this inversion process is listed in Supplementary Material S5, and their S-velocity values are plotted in Figure 4a (red line) from 0 to 40 km in depth. This model consists of three principal layers: crust (0–44 km deep, upper mantle (44–500 km deep), and middle mantle (considered a semi-infinite layer) (Matsumoto et al., 2015). These principal layers are subdivided into more layers with an adequate layer thicknesses (Figure 4a and Supplementary Material S6a) selected to improve the solution reliability of the inversion process (Supplementary Material S6b; Corchete et al., 2007). The values of the P- and S-velocities and the density considered for these layers were determined by Matsumoto et al. (2015). The theoretical group velocity calculated by means of forward modeling, from the initial model listed in Supplementary Material S5 (Figure 4a and Supplementary Material S6a, red lines), is plotted with a red line in Figure 4b (and Supplementary Material S6c). The S-velocity models (Figure 4a and Supplementary Material S6a) and the resolving kernels (Supplementary Material S6b) are plotted only for depths above 40 km due to the poor resolution obtained for greater depths. The resolving kernels are representation of the resolution matrix (Corchete et al., 2007). Good coincidence between the maxima of these functions and the reference depths (Supplementary Material S6b), with the absolute maxima of these functions narrow, shows good resolution of the final model determined from the inversion process (Corchete et al., 2007). The S-velocity model shown in Figure 4a (black line) is the final model calculated from the inversion process (Supplementary Material S6). From this model, the Rayleigh-wave phase velocities can be computed for the first and second higher modes (Abo-Zena, 1979; Aki and Richards, 1980), and their corresponding group velocities (theoretical group velocities) can be calculated by derivation of these phase-velocity curves (Ben-Menahem and Singh, 1981). These theoretical group velocities are shown in Figure 4b (black lines) and compared with those (Figure 4b, dots) determined by filtering for events #1 (Supplementary Material S4c, blue line), #2 (Supplementary Material S3c, blue line), and #3 (Figure 2c, blue line). The errors in the dispersion curves shown in Figure 4b (black vertical bars) are assumed as 0.1 km/s (Corchete et al., 2007). It should be noted that all theoretical curves (black lines) fit all observed curves (black dots) within the errors (black vertical bars), showing that the S-velocity model determined in this study (Figure 4a, black line) can be considered valid to describe the subsurface structure beneath the seismic paths (Figure 1). Thus, the results of this study show that the crustal structure beneath the paths (Figure 1) may be considered approximately uniform because a unique S-velocity model fits the observations performed for all paths, and no hypothesis is assumed a priori about this uniformity. This uniformity is a result of the Rayleigh-wave analysis performed.

FIGURE 1

FIGURE 2

FIGURE 3

FIGURE 4

3 Discussion and conclusions

A rapid S-velocity gradient was determined from 0 to 5 km in depth (Figure 4a, black line) as observed in previous studies (Toksöz et al., 1974; Vinnik et al., 2001; Khan and Mosegaard, 2002; Lognonné et al., 2003; Gagnepain-Beyneix et al., 2006). The low S-velocities (<2 km/s) determined for the first layers (0–2 km-depth) can be associated with the presence of broken and fractured materials at the uppermost lunar strata (Vinnik et al., 2001; Lognonné et al., 2003; Figure 4a). In addition, very low velocities of between 0 and 2 km deep were determined by Kovach and Watkins (1973a), Kovach and Watkins (1973b), and Goins et al. (1977). The S-velocity increases with depth (Figure 4a, black line) as expected, but the S-velocity gradient becomes smaller below 5 km in depth (Larose et al., 2005; Sens-Schönfelder and Larose, 2010). This conspicuous feature is also observed in some publicly available 1-D S-velocity models, as shown in Figure 4 of Garcia et al. (2019). The present S-velocity model (Figure 4a, black line), determined from Rayleigh-wave analysis, is a first step for lunar crustal structure determination. More work is needed to precisely determine this structure, which will be possible when more quality data are measured in future missions.

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