Joint Inversion of receiver functions and apparent incidence angles to determine the crustal structure of Mars

Abstract

Recent estimates of the crustal thickness of Mars show a bimodal result of either 20 km or 40 km beneath the InSight lander.We propose an approach based on random matrix theory applied to receiver functions to further constrain the subsurface structure. Assuming a spiked covariance model for our data, we first use the phase transition properties of the singular value spectrum of random matrices to detect coherent arrivals in the waveforms. Examples from terrestrial data show how the method works in different scenarios. We identify three new converted arrivals in the InSight data, including the second multiply reflected phase from a deeper third interface. We then use this information to jointly invert receiver functions with the absolute S-wave velocity information in the polarization of body waves. Results show a crustal thickness of 43±5 km beneath the lander with two mid-crustal interfaces at depths of 8.5±1.5 km and 22±3 km.

High‐Frequency Receiver Functions With Event S1222a Reveal a Discontinuity in the Martian Shallow Crust

“…The 𝐴𝐴 2𝜎𝜎 uncertainty of all the RFs are narrow, indicating that the RFs of all the selected events are reliable over different time windows (Figure 3a and Figure S3 in Supporting Information S1). The RFs clearly show the three positive converted P-to-S waves after the incident P-wave (between 2 and 3 s, 4 and 5 s, and 7 and 8 s, vertical orange shade boxes in Figure 3a), already highlighted in previous studies (Durán et al, 2022;Joshi et al, 2022;Kim et al, 2022;Knapmeyer-Endrun et al, 2021). The direct P-wave at the zero lag-time is weak for event S1000a, which might be attributed to the complex ray path of the PP wave of S1000a.…”

“…In this section, we first computed low-frequency RFs (0.25-1.0 Hz) for the seven events and validated our approach by retrieving the three positive converted P-to-S waves detected in previous RF studies (Durán et al, 2022;Joshi et al, 2022;Kim et al, 2022;Knapmeyer-Endrun et al, 2021). Then, we computed high-frequency RFs (0.25-2.0 Hz), observed a converted wave at approximately 1 s differential travel time, and investigated which velocity models fit this ∼1-s signal.…”

“…Finally, we retained a total of seven events, including S1222a (Figure 1 and Table S1 in Supporting Information S1). Five out of the selected events (S0173a, S0235b, S0809a, S1094b, and S1133c) have also already been included in previous papers (Durán et al, 2022;Joshi et al, 2022;Kim et al, 2022;Knapmeyer-Endrun et al, 2021), allowing us to confirm P-wave RF results from different studies.…”

Mars Seismology

“…The layered structure is also in agreement with a refraction seismic interpretation of P-wave arrivals from impacts within 300 km of InSight (Garcia et al 2022); however, due to the small number of data points, this analysis is not unique. Later RF studies including additional events (Duran et al 2022), phases , or more sophisticated data analysis (Joshi et al 2022) favor the three-layer crust on the order of 40 km thickness beneath InSight. This seismic anchor point has been used for a global crustal thickness map (Wieczorek et al 2022) based on orbital gravity and topography measurements (Figure 13) and suggests a global mean crustal thickness in the range of 30-72 km for the threelayer model.…”