Further Constraints and Uncertainties on the Deep Seismic Structure of the Moon

The Apollo Passive Seismic Experiment (APSE) consisted of four 3-component seismometers deployed between 1969 and 1972, that continuously recorded lunar ground motion until late 1977. The APSE data provide a unique opportunity for investigating the interior of a planet other than Earth, generating the most direct constraints on the elastic structure, and hence the thermal and compositional evolution of the Moon. Owing to the lack of far side moonquakes, past seismic models of the lunar interior were unable to constrain the lowermost 500 km of the interior. Recently, array methodologies aimed at detecting deep lunar seismic reflections found evidence for a lunar core, providing an elastic model of the deepest lunar interior consistent with geodetic parameters. Here we study the uncertainties in these models associated with the double array stacking of deep moonquakes for imaging deep reflectors in the Moon. We investigate the dependency of the array stacking results on a suite of parameters, including amplitude normalization assumptions, polarization filters, assumed velocity structure, and seismic phases that interfere with our desired target phases. These efforts are facilitated by the generation of synthetic seismograms at high frequencies (approx. 1Hz), allowing us to directly study the trade-offs between different parameters. We also investigate expected amplitudes of deep reflections relative to direct P and S arrivals, including predictions from arbitrarily oriented focal mechanisms in our synthetics. Results from separate versus combined station stacking help to establish the robustness of stacks. Synthetics for every path geometry of data were processed identically to that done with data. Different experiments were aimed at examining various processing assumptions, such as adding random noise to synthetics and mixing 3 components to some degree. The principal stacked energy peaks put forth in recent work persist, but their amplitude (which maps into reflector impedance contrast) and timing (which maps into reflector depth) depend on factors that are not well constrained -- most notably, the velocity structure of the overlying lunar interior. Thus, while evidence for the lunar core remains strong, the depths of imaged reflectors have associated uncertainties that will require new seismic data and observations to constrain. These results strongly advocate further investigations on the Moon to better resolve the interior (e.g., Selene missions), for the Moon apparently has a rich history of construction and evolution that is inextricably tied to that of Earth

Towards Simulating a Realistic Planetary Seismic Wavefield: The Contribution of the Megaregolith and Low-Velocity Waveguides

Lunar seismograms are distinctly different from their terrestrial counterparts. The Apollo lunar seismometers recorded moonquakes without distinct P- or S-wave arrivals; instead waves arrive as a diffuse coda that decays over several hours making the identification of body waves difficult. The unusual character of the lunar seismic wavefield is generally tied to properties of the megaregolith: it consists of highly fractured and broken crustal rock, the result of extensive bombardment of the Moon. The megaregolith extends several kilometers into the lunar crust, possibly into the mantle in some regions, and is covered by a thin coating of fine-scale dust. These materials possess very low seismic velocities that strongly scatter the seismic wavefield at high frequencies. Directly modeling the effects of the megaregolith to simulate an accurate lunar seismic wavefield is a challenging computational problem, owing to the inherent 3-D nature of the problem and the high frequencies (greater than 1 Hz) required. Here we focus on modeling the long duration code, studying the effects of the low velocities found in the megaregolith. We produce synthetic seismograms using 1-D slowness integration methodologies, GEMINI and reflectivity, and a 3-D Cartesian finite difference code, Wave Propagation Program, to study the effect of thin layers of low velocity on the surface of a planet. These codes allow us generate seismograms with dominant frequencies of approximately 1 Hz. For background lunar seismic structure we explore several models, including the recent model of Weber et al., Science, 2011. We also investigate variations in megaregolithic thickness, velocity, attenuation, and seismogram frequency content. Our results are compared to the Apollo seismic dataset, using both a cross correlation technique and integrated envelope approach to investigate coda decay. We find our new high frequency results strongly support the hypothesis that the long duration of the lunar seismic codes is generated by the presence of the low velocity megaregolith, and that the diffuse arrivals are a combination of scattered energy and multiple reverberations within this layer. The 3-D modeling indicates the extreme surface topography of the Moon adds only a small contribution to scattering effects, though local geology may play a larger role. We also study the effects of the megaregolith on core reflected and converted phases and other body waves. Our analysis indicates detection of core interacting arrivals with a polarization filter technique is robust and lends the possibility of detecting other body waves from the Moon

Imaging the Moon's Core with Seismology

Constraining the structure of the lunar core is necessary to improve our understanding of the present-day thermal structure of the interior and the history of a lunar dynamo, as well as the origin and thermal and compositional evolution of the Moon. We analyze Apollo deep moonquake seismograms using terrestrial array processing methods to search for the presence of reflected and converted energy from the lunar core. Although moonquake fault parameters are not constrained, we first explore a suite of theoretical focal spheres to verify that fault planes exist that can produce favorable core reflection amplitudes relative to direct up-going energy at the Apollo stations. Beginning with stacks of event seismograms from the known distribution of deep moonquake clusters, we apply a polarization filter to account for the effects of seismic scattering that (a) partitions energy away from expected components of ground motion, and (b) obscures all but the main P- and S-wave arrivals. The filtered traces are then shifted to the predicted arrival time of a core phase (e.g. PcP) and stacked to enhance subtle arrivals associated with the Moon s core. This combination of filtering and array processing is well suited for detecting deep lunar seismic reflections, since we do not expect scattered wave energy from near surface (or deeper) structure recorded at varying epicentral distances and stations from varying moonquakes at varying depths to stack coherently. Our results indicate the presence of a solid inner and fluid outer core, overlain by a partial-melt-containing boundary layer (Table 1). These layers are consistently observed among stacks from four classes of reflections: P-to-P, S-to-P, P-to-S, and S-to-S, and are consistent with current indirect geophysical estimates of core and deep mantle properties, including mass, moment of inertia, lunar laser ranging, and electromagnetic induction. Future refinements are expected following the successful launch of the GRAIL lunar orbiter and SELENE 2 lunar lander missions

A Retrospective on (Meta) Kernelization

International audienceIn parameterized complexity, a {\em kernelization algorithm} can be seen as a reduction of a parameterized problem to itself, so that the produced equivalent instance has size depending exclusively on the parameter. If this size is polynomial, then then we say that the parameterized problem in question admits a polynomial kernelization algorithm. Kernelization can be seen as a formalization of the notion of preprocessingand has occupied a big part of the research on Multi-variate Algorithmics. The first algorithmic meta-theorem on kernelizationappeared in \href{https://arxiv.org/pdf/0904.0727}{\green{[{\sl H.~L. Bodlaender, F.~V. Fomin, D.~Lokshtanov, E.~Penninkx, S.~Saurabh, and D.~M. Thilikos. (Meta) kernelization. J. {ACM}, 63(5):44:1--44:69, 2016}\,]}} and unified a large family of previously known kernelization results on problems defined on topologically embeddable graphs.In this exposition we present the central results of this paper. During our presentation we pay attention to the abstractions on which the results where founded and take into account the subsequent advancements on this topic