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 or ∼40 km beneath the InSight lander. We propose an approach based on random matrix theory applied to receiver functions (RFs) 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 previously undetected converted arrivals in the InSight data, including the first multiple from a deeper third interface. We then use this information to jointly invert RFs 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 ± 1 and 21 ± 3 km.

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

“…The $$2\sigma $$ 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 ). 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.…”

“…Finally, we retained a total of seven events, including S1222a (Figure 1 and Table S1 in Supporting Information ). 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.…”

“…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.…”

“…The gray shade in each RF stands for the $$2\sigma $$ uncertainty. The vertical orange shaded boxes mark the arrival times of the converted phases detected before (Durán et al., 2022; Joshi et al., 2022; Kim et al., 2022; Knapmeyer‐Endrun et al., 2021). The pink shade box marks the newly detected converted wave at approximately 1 s in the high‐frequency RFs of type 2 events.…”

Constraints for the Martian Crustal Structure From Rayleigh Waves Ellipticity of Large Seismic Events

“…The parameter space is configured as 3‐uniform‐layers over a half‐space (3LOH), where the depths of the discontinuities are constrained by Joshi et al. (2023). We inverted for shear‐wave velocity V s , P‐wave velocity V p and bottom depth z of each layer.…”