Recovery of Deep Moonquake Focal Mechanisms

Deep moonquakes are clustered not only in space but also in time: their recurrence times correspond to the durations of the anomalistic and draconic months, with some clusters preferring one of the two periods, while others are active with both periods. A key constraint for the understanding of the connection between the orbital motion of the Moon and its seismic activity is the focal mechanism: the orientation of the fault surface on which failure occurs during the quake. Due to the small aperture of the Apollo seismic network and the strong scattering of seismic waves within the lunar crust, the evaluation of P wave first motions to constrain the strike and dip of the fault planes is not feasible. Instead we evaluate the amplitude ratios of P and S waves. Seismograms are rotated into the P-SV-SH coordinate frame and amplitudes are determined as averages over short time windows after the arrival to reduce the impact of the scattering coda, which is independent of the source orientation. We allow for reversals of the fault motion, as observed for some clusters in previous studies, by taking into account the absolute amplitude only, without sign. An empirical site correction factor is applied to correct for amplitude distortions in the crust. We construct ensembles of fault plane solutions using an exhaustive grid search by accepting all orientations that reproduce the measured amplitude ratios within the observed standard deviations. Since all events of a given cluster are supposed to share the same fault plane, the combination of the individual inversion results further constrains the orientation. We evaluate 106 events from 25 different moonquake clusters. The most active cluster A001 contributes 37 events, while others contribute 1 to 9 events per cluster. Comparison of fault orientations with the variation of the tidal stress results in preferred orientations

Compressive strength and elastic modulus of Comet 67P interpreted from a material science point of view

The analysis of Cometary Acoustic Surface Sounding Experiment (CASSE) data yielded values of surface compression strength and elastic modulus at the landing site Agilkia. These data are interpreted with fracture mechanical concepts from material science taking into account the high porosity of Comet 67P

Re-evaluation of Apollo 17 Lunar Seismic Profiling Experiment data

We re-analyzed Apollo 17 Lunar Seismic Profiling Experiment (LSPE) data to improve our knowledge of the subsurface structure of this landing site. We use new geometrically accurate 3-D positions of the seismic equipment deployed by the astronauts, which were previously derived using high-resolution images by Lunar Reconnaissance Orbiter (LRO) in combination with Apollo astronaut photography. These include coordinates of six Explosive Packages (EPs) and four geophone stations. Re-identified P-wave arrival times are used to calculate two- and three-layer seismic velocity models. A strong increase of seismic velocity with depth can be confirmed, in particular, we suggest a more drastic increase than previously thought. For the three-layer model the P-wave velocities were calculated to 285, 580, and 1825 m/s for the uppermost, second, and third layer, respectively, with the boundaries between the layers being at 96 and 773 m depth. When compared with results obtained with previously published coordinates, we find (1) a slightly higher velocity (+4%) for the uppermost layer, and (2) lower P-wave velocities for the second and third layers, representing a decrease of 34% and 12% for second and third layer, respectively. Using P-wave arrival time readings of previous studies, we confirm that velocities increase when changing over from old to new coordinates. In the three-layer case, this means using new coordinates alone leads to thinned layers, velocities rise slightly for the uppermost layer and decrease significantly for the layers below

Modeling Approaches in Planetary Seismology

Of the many geophysical means that can be used to probe a planet's interior, seismology remains the most direct. Given that the seismic data gathered on the Moon over 40 years ago revolutionized our understanding of the Moon and are still being used today to produce new insight into the state of the lunar interior, it is no wonder that many future missions, both real and conceptual, plan to take seismometers to other planets. To best facilitate the return of high-quality data from these instruments, as well as to further our understanding of the dynamic processes that modify a planet's interior, various modeling approaches are used to quantify parameters such as the amount and distribution of seismicity, tidal deformation, and seismic structure on and of the terrestrial planets. In addition, recent advances in wavefield modeling have permitted a renewed look at seismic energy transmission and the effects of attenuation and scattering, as well as the presence and effect of a core, on recorded seismograms. In this chapter, we will review these approaches

Deep Moonquake Focal Mechanisms: Recovery and Implications

A defining characteristic of deep moonquakes is their tendency to occur with tidal periodicity, prompting previous studies to infer that they are related to the buildup and release of tidal stress within the Moon. In studies of tidal forcing, a key constraint is the focal mechanism: the fault parameters describing the type of failure moonquakes represent. The quality of the lunar seismic data and the limited source/receiver geometries of the Apollo seismic network prohibit the determination of deep moonquake fault parameters using first-motion polarities, as is typically done in terrestrial seismology. Without being able to resolve tidal stress onto a known failure plane, we can examine only gross qualities of the tidal stress tensor with respect to moonquake occurrence, so we cannot fully address the role of tidal stress in moonquake generation. We will examine the extent to which shear (S) and compression (P) wave amplitude ratios can constrain moonquake fault geometry by determining whether, for a given cluster, there exists a focal mechanism that can produce a radiation pattern consistent with the amplitudes measured by the Apollo instruments. Amplitudes are read in the ray coordinate frame, directly from seismograms for which the P and S arrivals are clearly identifiable on all long-period channels of the four Apollo stations. We apply an empirical station correction to account for site effects and the differences between P- and S-wave attenuation. Instead of focusing on the best fitting solution only, we formulate the inverse problem using a falsification criterion: all source orientations that do not reproduce the observed SV/P ratios within an error margin derived from the uncertainty of amplitude readings are rejected. All others are accepted as possible solutions. The inversion is carried out using an exhaustive grid search on a regular grid with predefined step size, encompassing all possible combinations of strike, dip and slip. To assess the sensitivity of the inversion for the uncertainty of the lunar interior structure, we carry out repeated inversions with different velocity structures. Our data set consist of a total of 106 events from 25 deep moonquake clusters. The largest contribution of 37 events originates from the most active cluster, A001, while other clusters are represented by 1 to 9 events. Since the definition of a cluster implies that all events share the same source orientation, a comparison of the inversion results of all events from one cluster will reduce ambiguities of the inversion. Once we obtain a suite of fault parameters for a given source, we can attempt to further constrain the focal mechanism with refined analyses of tidal stresses and predictions based on synthetic seismograms

Estimation of the Seismic Moment Release Rate of Mars from InSight Seismic Data

Seismicity models for Mars usually estimate the long-term average annual seismic moment rate, and also the average annual event rate. This holds for estimations based on geological evidence (Golombek et al., 1992, Golombek, 2002, Taylor et al., 2013) as well as for models based on thermal evolution and cooling of the Martian interior (Phillips, 1991, Knapmeyer et al., 2006, Plesa et al., 2018). All studies are compatible with the conclusion based on the non-observation of any unambiguous event by Viking (Anderson et al., 1977, Goins & Lazarewicz, 1979) that Martian seismicity lies somewhere between that of the Moon and that of the Earth. We developed tools to derive reasonable estimations of the annual seismic moment rate from a number of events as small as one, provided that the observed events are beyond the global completeness threshold for observable events. Numerical tests as well as evaluation of terrestrial data shows the feasibility of the approach

Influence of Body Waves, Instrumentation Resonances, and Prior Assumptions on Rayleigh Wave Ellipticity Inversion for Shallow Structure at the InSight Landing Site

Based on an updated model of the regolith’s elastic properties, we simulate the ambient vibrations background wavefield recorded by InSight’s Seismic Experiment for Interior Structure (SEIS) on Mars to characterise the influence of the regolith and invert SEIS data for shallow subsurface structure. By approximately scaling the synthetics based on seismic signals of a terrestrial dust devil, we find that the high-frequency atmospheric background wavefield should be above the self-noise of SEIS’s SP sensors, even if the signals are not produced within 100–200 m of the station. We compare horizontal-to-vertical spectral ratios and Rayleigh wave ellipticity curves for a surface-wave based simulation on the one hand with synthetics explicitly considering body waves on the other hand and do not find any striking differences. Inverting the data, we find that the results are insensitive to assumptions on density. By contrast, assumptions on the velocity range in the upper-most layer have a strong influence on the results also at larger depth. Wrong assumptions can lead to results far from the true model in this case. Additional information on the general shape of the curve, i.e. single or dual peak, could help to mitigate this effect, even if it cannot directly be included into the inversion. We find that the ellipticity curves can provide stronger constraints on the minimum thickness and velocity of the second layer of the model than on the maximum values. We also consider the effect of instrumentation resonances caused by the lander flexible modes, solar panels, and the SEIS levelling system. Both the levelling system resonances and the lander flexible modes occur at significantly higher frequencies than the expected structural response, i.e. above 35 Hz and 20 Hz, respectively. While the lander and solar panel resonances might be too weak in amplitude to be recorded by SEIS, the levelling system resonances will show up clearly in horizontal spectra, the H/V and ellipticity curves. They are not removed by trying to extract only Rayleigh-wave dominated parts of the data. However, they can be distinguished from any subsurface response by their exceptionally low damping ratios of 1% or less as determined by random decrement analysis. The same applies to lander-generated signals observed in actual data from a Moon analogue experiment, so we expect this analysis will be useful in identifying instrumentation resonances in SEIS data

The Use of Deep Moonquakes for Constraining the Internal Structure of the Moon

The installation of seismometers on the Moon s surface during the Apollo era provided a wealth of information that transformed our understanding of lunar formation and evolution. Seismic events detected by the nearside network were used to constrain the structure of the Moon s crust and mantle down to a depth of about 1000 km. The presence of an attenuating region in the deepest interior has been inferred from the paucity of farside events, as well as other indirect geophysical measurements. Recent re-analyses of the Apollo data have tentatively identified this region as a lunar core, although its properties are not yet constrained. Here we present new modeling in support of seismic missions that plan to build upon the knowledge of the Moon s interior gathered by Apollo. We have devised a method in which individual events can be linked to a known cluster using the observed S-P arrival time differences and azimuth to only two stations. Events can be further identified using each cluster's unique occurrence time signatur

Thermal fracturing on comets: Applications to 67P/Churyumov-Gerasimenko

We simulate the stresses induced by temperature changes in a putative hard layer near the surface of comet 67P/Churyumov-Gerasimenko with a thermo-viscoelastic model. Such a layer could be formed by the recondensation or sintering of water ice (and dust grains), as suggested by laboratory experiments and computer simulations, and would explain the high compressive strength encountered by experiments on board the Philae lander. Changes in temperature from seasonal insolation variation penetrate into the comet’s surface to depths controlled by the thermal inertia, causing the material to expand and contract. Modelling this with a Maxwellian viscoelastic response on a spherical nucleus, we show that a hard, icy layer with similar properties to Martian permafrost will experience high stresses: up to tens of MPa, which exceed its material strength (a few MPa), down to depths of centimetres to a metre. The stress distribution with latitude is confirmed qualitatively when taking into account the comet’s complex shape but neglecting thermal inertia. Stress is found to be comparable to the material strength everywhere for sufficient thermal inertia (≳ 50 J m−2 K−1 s−1∕2) and ice content (≳ 45% at the equator). In this case, stresses penetrate to a typical depth of ~0.25 m, consistent with the detection of metre-scale thermal contraction crack polygons all over the comet. Thermal fracturing may be an important erosion process on cometary surfaces which breaks down material and weakens cliffs