A Hitch-hiker’s Guide to Stochastic Differential Equations

In this review, an overview of the recent history of stochastic differential equations (SDEs) in application to particle transport problems in space physics and astrophysics is given. The aim is to present a helpful working guide to the literature and at the same time introduce key principles of the SDE approach via “toy models”. Using these examples, we hope to provide an easy way for newcomers to the field to use such methods in their own research. Aspects covered are the solar modulation of cosmic rays, diffusive shock acceleration, galactic cosmic ray propagation and solar energetic particle transport. We believe that the SDE method, due to its simplicity and computational efficiency on modern computer architectures, will be of significant relevance in energetic particle studies in the years to come.     

Inversion of Meteor Rayleigh Waves on Earth and Modeling of Air Coupled Rayleigh Waves on Mars

Meteor impacts and/or meteor events generate body and surface seismic waves on the surface of a planet. When meteoroids burst in the atmosphere, they generate shock waves that subsequently convert into acoustic waves in the atmosphere and seismic waves in the ground. This effect can be modeled as the amplitude of Rayleigh and other Spheroidal modes excitation, due to atmospheric/ground coupling effects.First, an inversion of the seismic source of Chelyabinsk superbolide is performed. We develop an approach in order to model a line source in the atmosphere, corresponding to the consecutive generation of shock waves by the interaction with the atmosphere. The model is based on the known trajectory. We calculate the synthetic seismograms of Rayleigh waves associated with the event by the summation of normal modes of a model of the solid part and the atmosphere of the planet. Through an inversion technique based on singular value decomposition, we perform a full Rayleigh wave inversion and we provide solutions for the moment magnitude.SEIS will likely detect seismic waves generated by impacts and the later might be further located by remote sensing differential processing. In the case of Mars, we use the same method to obtain waveforms associated with impacts on the planetary surface or in low altitudes in the Martian atmosphere. We show that the contribution of the fundamental spheroidal solid mode is dominating the waveforms, compared to that of the first two overtones. We perform an amplitude comparison and we show that small impactors (diameter of 0.5 to 2 m), can be detected by the SEIS VBB seismometer of InSight mission, even in short epicentral distances, in the higher frequencies of the Rayleigh waves. We perform an analysis based on impact rate estimations and we calculate the number of detectable events of 1 meter diameter meteor impacts to be 6.7 to 13.4 per 1 Martian year for a \(Q=500\).     

Crustal S-Wave Velocity from Apparent Incidence Angles: A Case Study in Preparation for InSight

Retrieval of crustal structure and thickness of Mars is among the main goals of InSight. Here we investigate which constraints on the crust at the landing site can be provided by apparent P-wave incidence angles derived from P-receiver functions. We consider receiver functions for six different Mars models, calculated from synthetic seismograms generated via Instaseis from the Green’s function databases of the Marsquake Service, in detail. To allow for a larger range of crustal thicknesses and structures, we additionally analyze data from five broad-band stations across Central Europe. We find that the likely usable epicentral distance range for P-wave receiver functions on Mars lies between \(35^{\circ}\) and the core shadow, and can be extended to more than \(150^{\circ}\) by also using the PP-phase. Comparison to models for the spatial distribution of Martian seismicity indicates that sufficient seismicity should occur within the P-wave distance range around InSight within the nominal mission duration to allow for the application of our method. Apparent P-wave incidence angles are derived from the amplitudes of vertical and radial receiver functions at the P-wave onset within a range of period bands, up to 120 s. The apparent incidence angles are directly related to apparent S-wave velocities, which are inverted for the subsurface S-wave velocity structure via a grid search. The veracity of the forward calculated receiver functions and apparent S-wave velocities is ensured by benchmarking various algorithms against the Instaseis synthetics. Results indicate that apparent S-wave velocity curves provide valuable constraints on crustal thickness and structure, even without any additional constraints, and considering the location uncertainty and limited data quantity of InSight. S-wave velocities in the upper half of the crust are constrained best, but if reliable measurements at long periods are available, the curves also provide constraints down to the uppermost mantle. Besides, it is demonstrated that the apparent velocity curves can differentiate between crustal velocity models that are indistinguishable by other methods.     

Experimental Investigation of InSight HP<Superscript>3</Superscript> Mole Interaction with Martian Regolith Simulant

The InSight mission launches in 2018 to characterize several geophysical quantities on Mars, including the heat flow from the planetary interior. This quantity will be calculated by utilizing measurements of the thermal conductivity and the thermal gradient down to 5 meters below the Martian surface. One of the components of InSight is the Mole, which hammers into the Martian regolith to facilitate these thermal property measurements. In this paper, we experimentally investigated the effect of the Mole’s penetrating action on regolith compaction and mechanical properties. Quasi-static and dynamic experiments were run with a 2D model of the 3D cylindrical mole. Force resistance data was captured with load cells. Deformation information was captured in images and analyzed using Digitial Image Correlation (DIC). Additionally, we used existing approximations of Martian regolith thermal conductivity to estimate the change in the surrounding granular material’s thermal conductivity due to the Mole’s penetration. We found that the Mole has the potential to cause a high degree of densification, especially if the initial granular material is relatively loose. The effect on the thermal conductivity from this densification was found to be relatively small in first-order calculations though more complete thermal models incorporating this densification should be a subject of further investigation. The results obtained provide an initial estimate of the Mole’s impact on Martian regolith thermal properties.     

Venus: The Atmosphere,Climate, Surface,Interior and Near-Space Environment of an Earth-Like Planet

This is a review of current knowledge about Earth’s nearest planetary neighbour and near twin, Venus. Such knowledge has recently been extended by the European Venus Express and the Japanese Akatsuki spacecraft in orbit around the planet; these missions and their achievements are concisely described in the first part of the review, along with a summary of previous Venus observations. The scientific discussions which follow are divided into three main sections: on the surface and interior; the atmosphere and climate; and the thermosphere, exosphere and magnetosphere. These reports are intended to provide an overview for the general reader, and also an introduction to the more detailed topical surveys in the following articles in this issue, where full references to original material may be found.     

Impact risk analysis for a spacecraft in Cosmo-Skymed orbit

This paper presents a case study of Micrometeoroids and Orbital Debris risk assessment for a spacecraft flying in an orbit close to that of the Italian Cosmo-Skymed constellation. The aim of the analysis was to calculate the failure flux impinging on the satellite external shell, taking into account both geometry and materials of satellite surfaces. Furthermore the analysis included the evaluation of the contribution to debris population at the selected orbit of the fragments produced by a Chinese Anti-SATellite experiment, which caused the catastrophic break-up of the satellite Fengyun 1C in January 2007.     

Michelson Interferometer for Global High-Resolution Thermospheric Imaging (MIGHTI): Instrument Design and Calibration

The Michelson Interferometer for Global High-resolution Thermospheric Imaging (MIGHTI) instrument was built for launch and operation on the NASA Ionospheric Connection Explorer (ICON) mission. The instrument was designed to measure thermospheric horizontal wind velocity profiles and thermospheric temperature in altitude regions between 90 km and 300 km, during day and night. For the wind measurements it uses two perpendicular fields of view pointed at the Earth’s limb, observing the Doppler shift of the atomic oxygen red and green lines at 630.0 nm and 557.7 nm wavelength. The wavelength shift is measured using field-widened, temperature compensated Doppler Asymmetric Spatial Heterodyne (DASH) spectrometers, employing low order échelle gratings operating at two different orders for the different atmospheric lines. The temperature measurement is accomplished by a multichannel photometric measurement of the spectral shape of the molecular oxygen A-band around 762 nm wavelength. For each field of view, the signals of the two oxygen lines and the A-band are detected on different regions of a single, cooled, frame transfer charge coupled device (CCD) detector. On-board calibration sources are used to periodically quantify thermal drifts, simultaneously with observing the atmosphere. The MIGHTI requirements, the resulting instrument design and the calibration are described.