Crust and Upper Mantle Structure of Mars Determined from Surface Wave Analysis

Abstract

The crust and upper mantle structure of Mars is determined in the depth range of 0 to 100 km, by means of dispersion analysis and its inversion, which is performed for the surface waves present in the traces of the seismic event: S1094b. From these traces, Love and Rayleigh waves are measured in the period range of 4 to 40 s. This dispersion was calculated with a combination of digital filtering techniques, and later was inverted to obtain both models: isotropic (from 0 to 100 km depth) and anisotropic (from 0 to 15 km depth), which were calculated considering the hypothesis of the surface wave propagation in slightly anisotropic media. The seismic anisotropy determined from 0 to 5 km depth (7% of S-velocity variation and ξ ~ 1.1) could be associated with the presence of sediments or lava-flow layering, and wide damage zones surrounding the long-term fault networks. For greater depths, the observed anisotropy (17% of S-velocity variation and ξ ~ 1.4) could be due to the possible presence of volcanic materials and/or the layering of lava flows. Another cause for this anisotropy could be the presence of layered intrusions due to a single or multiple impacts, which could cause internal layering within the crust. Finally, the Moho depth is determined at 50 km as a gradual transition from crust to mantle S-velocities, through an intermediate value (3.90 km/s) determined from 50 to 60 km-depth.

1. Introduction

The knowledge of the Martian crust and upper mantle structure with depth is an important key to understanding its origin and evolution, but this structure remains among the least studied structures in geophysics and planetary science, due to the long distance of Mars from Earth, which has made the development and operation of scientific instruments in satellites and/or on land very difficult. However, in the last few years and with huge scientific and economic effort, the Interior Exploration Using Seismic Investigations, Geodesy, and Heat Transport (InSight) mission (which landed on Mars in Elysium Planitia) has provided the first seismic data recorded on the Martian surface. These invaluable seismic data have been analyzed to obtain the deep structure from P and S waves (e.g., [1]), the shallow structure from ambient-noise wavefield [2], and the crust and upper mantle structure from surface waves (e.g., [3]). The present study will complement the very scarce quantity of previous studies performed on the crust and upper mantle structure of Mars, with the dispersion analysis of the surface waves present in the record of the seismic event S1094b, and the inversion of this dispersion to calculate an S-velocity distribution with depth, for a depth range of 0 to 100 km, in which the seismic anisotropy present in the first 15 km of the crust will be considered. The seismic anisotropy in Mars has already been reported in previous studies [3,4,5], but only for the event S1222a. The seismic records obtained from InSight were analyzed by Kim et al. to obtain surface group velocities [3,6]. Unfortunately, most of these records do not present surface waves, because they are affected by strong contamination with long-period wind noise and atmospheric pressure waves, as well as a strong crustal scattering; only the records of three seismic events are suitable for surface wave analysis: S1000a, S1094b, and S1222a. The largest marsquake recorded during all InSight missions was S1222a, providing the first clear signals of surface waves and their first overtones [3]. On the other hand, S1000a provided unclear surface waves and only Rayleigh wave dispersion was determined by Kim et al. [6] due to its relatively small magnitude and large epicentral distance. The records of S1094b also were analyzed by Kim et al. [6], and they only determined Rayleigh wave dispersion. In the present study, the seismic anisotropy is reported for the first time for the event S1094b, and is also related, for the first time, to the possible presence of sediments or lava flow layering for the first 5 km depth, and volcanic materials from a 5 to 15 km depth.

2. Data, Methodology, and Results

In the present study, the event S1094b (Supplement S1) recorded at the InSight seismic station (Supplement S2) has been revisited with the application of other filtering techniques [7], which have proven to be very useful techniques in several regions on Earth (e.g., [8]). This filtering analysis consists of a combination of the Multiple Filter Technique (MFT; [9]) and Time-Variable Filtering (TVF; [10]), as described by Corchete et al. [7], in which the MFT has been used to obtain the group-velocity dispersion curve from the time signals. The records of the vertical (Z), radial (R), and transverse (T) components of S1094b are obtained from its records in the three non-orthogonal components—UVW—of the seismic sensor [11], after instrument correction and removal of possible glitches [12]. Each of the ZRT records is a linear combination of all the UVW records, and all ZRT records have been analyzed in the present study, but the R and T records were discarded because they were affected by strong scattering. Thus, only the Z record (Figure 1, grey line) has been considered to determine the surface wave dispersion. Figure 2a (magenta points) and Figure 3 (black points) shows the initial group velocities calculated with the MFT, and applied to this record. TVF has been used to determine the smooth L- and R-signals shown in Figure 1 (black line), which are the time-variable filtered seismograms calculated from the original seismogram (Figure 1, grey line) and the initial group velocity (Figure 3, black points). Figure 3 (black line) shows the final group velocities calculated with the MFT (Figure 2b,c), applied to the L- and R-signals shown in Figure 1 (black line). The final dispersion curves for Love and Rayleigh waves shown in Figure 3 (black line) are considered as the observed data for the inversion process to be followed to calculate the S-velocity model, beneath the area crossed by the waves (Figure 4, [13]). The errors in the observed data are assumed as 0.1 km/s [7]. The initial model for this inversion process is listed in Supplement S3. This model has been prepared considering the previous models determined for the crust and mantle of Mars [3,6,14]. Figure 5 and Figure 6 show the inversion process for Love and Rayleigh waves, respectively [7]. The S-velocity models (Figure 5a and Figure 6a) and the resolving kernels (Figure 5b and Figure 6b) are plotted only for depths above 100 km, due to the poor resolution obtained for greater depths. The inversion process for Love wave dispersion gives an S-velocity model (Figure 5a), which is different to that calculated for the Rayleigh wave dispersion (Figure 6a), for the depth range of 0 to 15 km, i.e., the S-velocity model that satisfactorily fits the Love wave dispersion does not fit the Rayleigh wave dispersion (Figure 5c), and conversely, when the Rayleigh wave dispersion is properly fitted, the Love wave dispersion is not fitted (Figure 6c). The Love and Rayleigh wave dispersion are not compatible with a unique isotropic model (i.e., there is Love–Rayleigh discrepancy), and it is necessary to consider the existence of seismic anisotropy in the depth range of 0 to 15 km (Figure 5a and Figure 6a), defining an anisotropic model with hexagonal symmetry (i.e., azimuthal isotropy or transverse isotropy [15]). This model is calculated as described by Corchete [16]. In this methodology, the phase velocities are considered as observed data, and an isotropic model must be defined to calculate the anisotropic model, as a small perturbation of this isotropic model. In the present study, the Love and Rayleigh phase velocities (Figure 7, black rectangles) are calculated from the models shown in Figure 5a and Figure 6a by forward modelling [17,18], and it is selected as an isotropic model (Supplement S4) that is calculated from the inversion of the Rayleigh group velocities (Figure 6a). This methodology is improved in the present study considering the canonical harmonic components [19]: ${\mathrm{\gamma }}_{\mathrm{S}}^{00\mathrm{c}}$, ${\mathrm{\gamma }}_{\mathrm{A}}^{00\mathrm{c}}$, ${\mathrm{\gamma }}_{\mathrm{S}}^{20\mathrm{c}}$, ${\mathrm{\gamma }}_{\mathrm{A}}^{20\mathrm{c}}$ and ${\mathrm{\gamma }}_{\mathrm{S}}^{40\mathrm{c}}$, as linear functions of the P-velocities (α_H, α_V) and S-velocities (β_H, β_V), through to the perturbations γ_ijkl of the stiffness tensor [15,16,19]. Then, if a relation of $\mathrm{\alpha }=\sqrt{3}\mathrm{\beta }$ is assumed between the P- and S-velocities, the unknowns of the inverse problem can be reduced from 5 canonical harmonic components to 2 S-velocities, facilitating the fit of the observed data.

Table 1. S-velocities (β_H, β_V) calculated from the anisotropic inversion of the phase velocities shown in Figure 7 (black rectangles) for the first two layers of the isotropic model shown in Supplement S4. The P-velocities (α_H, α_V) are calculated as $\mathrm{\alpha }=\sqrt{3}\mathrm{\beta }$, and the parameters (ξ, φ) are calculated as defined by Babuska and Cara [15]. The S-velocity ratio (β_H − β_V)/β is given as a percentage, and β is given by Supplement S4.

Layer (n)	αH (km/s)	βH (km/s)	αV (km/s)	βV (km/s)	ξ (βH/βV)2	φ (αV/αH)2	$\frac{{\mathbf{\beta }}_{\mathbf{H}}-{\mathbf{\beta }}_{\mathbf{V}}}{\mathbf{\beta }}$
1	4.35 ± 0.12	2.51 ± 0.07	4.07 ± 0.14	2.35 ± 0.08	1.14	0.88	6.7
2	5.53 ± 0.16	3.19 ± 0.09	4.69 ± 0.14	2.71 ± 0.08	1.39	0.72	17.1

shows the results of this anisotropic inversion for the first two layers of Supplement S4 (from 0 to 15 km depth), and the values of the more frequently used quantities in anisotropic studies, as defined by Babuska and Cara [15]. The theoretical phase velocities calculated from this inversion are shown in Figure 7 (black lines), and their corresponding group velocities were computed by derivation [20]. Figure 7 shows the satisfactory fit obtained between the observed and theoretical dispersion curves, which was not possible with the isotropic inversion.

3. Interpretation and Discussion

Depth range: 0–5 km. There is a heterogeneous shallow crust that is constituted by several types of rocks, including sedimentary and igneous. This shallow crust is characterized by a wide range of densities and seismic velocities due to the presence of altered basalts, mudstones, shales, clays, sands, and loess, and it is expected to exhibit seismic anisotropy, as determined in the present study (7% of S-velocity variation for the layer 1 of Table 1), due to the presence of sediments or lava flow layering and wide damage zones surrounding the long-term fault networks [14].

Depth range: 5–15 km. The observed anisotropy at depths greater than 5 km is unlikely due to sedimentary layers, as in the previous depth range. For the present depth range, the presence of volcanic materials in the study area (Figure 4), such as andesite or altered basaltic rocks, could probably be the cause of the observed anisotropy (17% of S-velocity variation and ξ ~ 1.4 (layer 2 of Table 1)), which was also determined by Kim et al. [3] for another region of the Martian crust with 12% of S-velocity variation and ξ ~ 1.3. The layering of lava flows that could still exist for the present depth range could also be associated with this seismic anisotropy. Jiang et al. [21] have suggested that layered sill complexes can produce strong anisotropy (>8% S-velocity variation) at 5–18 km depth, but these complexes are usually very localized in depth and spatial extent, and are unlikely to be the cause of the observed anisotropy for this study area. Another cause for this anisotropy could be the presence of layered intrusions due to a single or multiple impacts [4]; such impacts could have caused internal layering within the crust, and the existence of seismic anisotropy.

Depth range: 15–100 km. In Figure 8, it is observed that all S-velocity models determined for Mars show similar values down to a 90 km depth, while these models show very different values up to this depth. This result is expected for Mars, because its Moho depth shows a great diversity of values from very shallow depths (< 10 km) to 90–100 km, depending on the region [14]: the northern lowlands show a uniformly thin crust (∼30 km thick), the southern highlands consist of a thick crust (∼60 km thick), and the Tharsis Rise (at the boundary between these two domains) is formed by a thick basaltic crust (∼100 km thick). For the study area (Figure 4), the Moho depth is determined at 50 km depth (Figure 8, black line), and this discontinuity is not sharp in terms of S-velocity, but a gradual transition from crust to mantle S-velocities, in which the S-velocity jumps from the crustal values (3.4 km/s) to mantle values (4.35 km/s) through an intermediate value (3.9 km/s) determined from 50 to 60 km depth. This Moho depth agrees well with that calculated in previous studies [6,22,23,24].

4. Conclusions

A dispersion analysis and its inversion is performed for the surface waves present in the record of the seismic event S1094b, and both models, isotropic (from 0 to 100 km depth) and anisotropic (from 0 to 15 km depth), are calculated considering the hypothesis of the surface wave propagation in slightly anisotropic media. From these models, the following conclusions are obtained:

Depth range: 0–5 km. The seismic anisotropy determined in the present study at this depth range (7% of S-velocity variation) could be associated with the presence of sediments or lava flow layering, and wide damage zones surrounding the long-term fault networks.

Depth range: 5–15 km. The observed anisotropy (17% of S-velocity variation and ξ ~ 1.4) at depths greater than 5 km could be due to the possible presence of volcanic materials in the study area, such as andesite or altered basaltic rocks. The layering of lava flows that still could exist for the present depth range of the study are, could also be associated with this seismic anisotropy. Another cause for this anisotropy could be the presence of layered intrusions due to a single or multiple impacts; such impacts could have caused internal layering within the crust and the existence of seismic anisotropy.

Depth range: 15–100 km. For Mars, the Moho depth shows a great diversity of values from very shallow depths (<10 km) to 90–100 km, depending on the region. For the present study area, the Moho depth is determined at 50 km, and this discontinuity is a gradual transition from crust to mantle S-velocities, in which the S-velocity jumps from the crustal values (3.4 km/s) to mantle values (4.35 km/s) through an intermediate value (3.90 km/s) determined from 50 to 60 km depth.