Improving Constraints on Planetary Interiors With PPs Receiver Functions

Abstract

Seismological constraints obtained from receiver function (RF) analysis provide important information about the crust and mantle structure. Here, we explore the utility of the free-surface multiple of the P-wave (PP) and the corresponding conversions in RF analysis. Using earthquake records, we demonstrate the efficacy of PPs-RFs before illustrating how they become especially useful when limited data is available in typical planetary missions. Using a transdimensional hierarchical Bayesian deconvolution approach, we compute robust P-to-S (Ps)- and PPs-RFs with InSight recordings of five marsquakes. Our Ps-RF results verify the direct Ps converted phases reported by previous RF analyses with increased coherence and reveal other phases including the primary multiple reverberating within the uppermost layer of the Martian crust. Unlike the Ps-RFs, our PPs-RFs lack an arrival at 7.2 s lag time. Whereas Ps-RFs on Mars could be equally well fit by a two- or three-layer crust, synthetic modeling shows that the disappearance of the 7.2 s phase requires a three-layer crust, and is highly sensitive to velocity and thickness of intra-crustal layers. We show that a three-layer crust is also preferred by S-to-P (Sp)-RFs. While the deepest interface of the three-layer crust represents the crust-mantle interface beneath the InSight landing site, the other two interfaces at shallower depths could represent a sharp transition between either fractured and unfractured materials or thick basaltic flows and pre-existing crustal materials. PPs-RFs can provide complementary constraints and maximize the extraction of information about crustal structure in data-constrained circumstances such as planetary missions.

Keywords: InSight; Mars; Martian crust; Receiver function; Seismology; Transdimensional hierarchical Bayesian.

Figure 1

The receiver function (RF) analysis on Earth using a pair of earthquake recordings. (a) Vertical and radial component seismograms from Mw6.3 Norwegian Sea (2012‐05‐24UTC22:47:46) and Mw7.7 Mariana Islands (2016‐07‐29UTC21:18:25) earthquakes recorded by broadband station US.AGMN. Gray lines indicate body wave phases predicted by iasp91. The ray paths of P (blue) and PP (red) for each event are shown on the right. (b and c) Ensemble Ps‐ and PPs‐RFs combining all models for events in panel (a). The ensemble mean RF for each event is shown in red. Ray parameter estimates and the bandpass filter range used for processing are noted at the bottom left and right side at each panel, respectively. Note that due to the epicentral distances chosen, the Ps and PPs phases in the lower and upper panels of Figures 1B and 1C are expected to arrive at similar lag times. (d) Theoretical thickness versus V _P/V _s (H‐κ) curves for Ps (dashed red) and PPs (gray) phases in panel (b) for the bulk crustal V _P of 6.5 km/s. Calculation is made for those H‐κ values estimated by EarthScope Automated Receiver Survey (black cross). The hypothetical PPs H‐κ curve for a much larger ray parameter is shown in blue. Comparison of the H‐κ stacks using average RFs in panels (b and c) with panel (e) Ps phase alone versus (f) both Ps and PPs phases. The maximum amplitude found in the H‐κ space is marked by white symbol.

Figure 2

Five marsquake low‐frequency (LF) event waveforms. Vertical and radial component data from five marsquake LF events: (a) S0235b, (b) S0407a, (c) S0820a, (d) S0173a, and (e) S0809a recorded by Seismic Experiment for Interior Structure Very Broad Band. Waveforms are bandpass filtered with the frequency ranges as noted at the bottom of each panel. Phase picks are shown in gray. All five events used in this study are in The Marsquake Service event quality A‐B and show relatively high signal‐to‐noise ratio with dominant seismic energy below 1 Hz. By definition, event quality A‐B in InSight data denotes events that show multiple clear and identifiable phases with coherent polarization (J. F. Clinton et al., ; InSight Marsquake Service, 2021) allowing epicentral locations to be robustly determined (e.g., Figure 3).

Figure 3

Location of marsquakes. The Marsquake Service (MQS)‐reported epicenters of marsquake events used in this study (InSight Marsquake Service, 2021) are indicated by yellow stars, while the black symbol denotes the InSight lander. All of these events originate in the general area of Cerberus Fossae located to the east of the InSight landing site at Elysium Planitia. Note S0407a is not shown due to the absence of the MQS reported back azimuth. Uncertainties associated with the event distance and back azimuth are denoted by gray circles and white ellipses, respectively. The background topography is from the Mars Orbiter Laser Altimeter (e.g., Smith et al., 1999).

Figure 4

Transdimensional hierarchical Bayesian deconvolution (THBD) P‐to‐S‐ (Ps) and P‐waves (PPs)‐receiver functions (RFs) on Mars using five low‐frequency (LF) marsquake events. (a and b) Ensemble Ps‐RFs combining all models of the simultaneous analysis on five LF marsquakes that are located ∼30° away from the InSight lander. The ensemble mean RF is shown in red. Histograms in panel (a) indicate the corresponding relative amplitudes across the entire RF solutions in the ensemble examined at each peak (marked by purple, green, and blue ticks on panel (b)) for the first few stable phases discussed in the main text. The ray path of P (blue) is shown on the right. Our LF marsquake waveform data are bandpass filtered between 0.2 and 0.7 Hz prior to THBD. Both evolution of the model likelihood (black) and the number of Gaussian (gray) as a function of iteration are plotted on the right side of the RF ensemble. Below, we denote the average free surface transform parameters used in our analysis. Panels (c and d) same as panels (a and b), but the resulting PPs‐RF counterparts. The ray path of PP (red) is shown on the right. Color markers in panel (b) are faded in panel (d). Waveform data are bandpass filtered between 0.2 and 0.6 Hz. Note the 2.4 and 4.8 s phases in panels (a and b) are slightly delayed by 0.1 and 0.2 s, respectively in panels (c and d), while the instability of the 7.2 s is observed across the two ensembles.

Figure 5

Synthetic receiver functions (RFs) using the two‐ and three‐layer Martian crustal models. Simple synthetic RF (Z/R) gather calculated based on Thomson‐Haskell matrix method using (a) two‐ and (b) three‐layer crustal models. Velocity profiles in black indicate the average of the best 5,000 models, plotted in colors, from Knapmeyer‐Endrun et al. (2021). Dashed and solid lines in panels (a and b) indicate expected arrivals based on each model, respectively. Note, the multiples (blue, PpP₁s) exist in both models while the three‐layer model produces an additional direct conversion at the deepest interface (black, P₃s). Traces in bold denote synthetic RFs predicted by two representative ray parameters of the incoming P‐wave from marsquakes used in this study. Comparison of the transdimensional hierarchical Bayesian deconvolution ensemble assemblages and distributions of relative amplitudes associated with observed phases at 2.4, 4.8, and 7.2 s (purple, green, and blue) based on synthetic waveforms with ray parameter of (c and d) 7.2 s/° and (e and f) 8.0 s/°. Panels on the left column correspond to the two‐layer model while those on the right correspond to the three‐layer model.

Figure 6

H‐κ‐V _P triple stacking of the P‐to‐S (Ps)‐receiver functions (RFs) focused on the first interface. (a) Ensemble Ps‐RF results from Figure 4b with timings of the phases related to the direct and multiples associated with the uppermost crustal interface corresponding to the best‐fitting parameters resulting from the H‐κ‐V _P analysis in panels (b–d). See Figure S7 in Supporting Information S1 for the enlarged version of this panel including labels of all of the converted phases discussed in the main text. Colorbar shown beneath panel (a) denotes relative amplitude of the H‐κ‐V _P in panels (b–d). Schematic raypaths of the analyzed phases are shown below. As discussed in the main text, the origin of the 7.2 s phase is debated. Note, the presence of the negative phase associated with PpS₁s multiple is unclear. (b–d) The cross‐sections sliced through the parameter space at the maximum of the H‐κ‐V _P triple stack. Black cross with cross‐hair denotes the maximum value ±1σ.

Figure 7

Transdimensional hierarchical Bayesian deconvolution (THBD) S‐to‐P (Sp)‐receiver functions (RFs) analysis of the S0235b marsquake. (a) A series of ensemble Sp‐RFs combining all models of individual low‐frequency event S0235b when the maximum number of Gaussian pulses (i.e., maximum number of pulses) allowed in THBD is set as 1, 2, and 3 (the average RF for each case is color coded by green, red, and black). (b) Comparison of the S0235b P‐component data and the corresponding waveform predictions generated by the average RFs in panel (a). Bold and dashed gray lines indicate P‐ and SV‐component raw waveforms, respectively. Note, only the average RF with three positive phases (black, a) allows the prediction that fits all three S‐precursors (see those records prior to the S‐arrival denoted by black dashed line) in the raw data. Chi‐squared misfit between the Sp‐RFs and the corresponding predictions from RFs with different maximum number of pulses values does not decrease as additional pulses past the third are allowed (see Figure S8 in Supporting Information S1).

Figure 8

Yearly expected number of earthquake appropriate for (a) P‐to‐S (Ps) and (b) P‐waves (PPs) analysis on Earth. Given the distribution of sufficiently large (Mw > 6) and shallow (depth < 300 km) earthquakes, the number of events suitable for computing Ps‐ and PPs‐RFs varies geographically due to the difference in epicentral distance ranges of 35–85 and >50° appropriate for crustal Ps and PPs analysis, respectively. The maps show complementary coverage with more events suitable for PPs analysis being expected in locations where fewer events are appropriate for Ps analysis.