Christoph Statz

Properties of the 67P/Churyumov-Gerasimenko interior revealed by CONSERT radar

The Philae lander provides a unique opportunity to investigate the internal structure of a comet nucleus, providing information about its formation and evolution in the early solar system. We present Comet Nucleus Sounding Experiment by Radiowave Transmission (CONSERT) measurements of the interior of Comet 67P/Churyumov-Gerasimenko. From the propagation time and form of the signals, the upper part of the “head” of 67P is fairly homogeneous on a spatial scale of tens of meters. CONSERT also reduced the size of the uncertainty of Philae’s final landing site down to approximately 21 by 34 square meters. The average permittivity is about 1.27, suggesting that this region has a volumetric dust/ice ratio of 0.4 to 2.6 and a porosity of 75 to 85%. The dust component may be comparable to that of carbonaceous chondrites.

CONSERT suggests a change in local properties of 67P/Churyumov-Gerasimenko’s nucleus at depth

After the successful landing of Philae on the nucleus of 67P/Churyumov-Gerasimenko, the Rosetta mission provided the first opportunity of performing measurements with the CONSERT tomographic radar in November 2014. CONSERT data were acquired during this first science sequence. They unambiguously showed that propagation through the smaller lobe of the nucleus was achieved. Aims. While the ultimate objective of the CONSERT radar is to perform the tomography of the nucleus, this paper focuses on the local characterization of the shallow subsurface in the area of Philae’s final landing site, specifically determining the possible presence of a permittivity gradient below the nucleus surface. Methods. A number of electromagnetic simulations were made with a ray-tracing code to parametrically study how the gradient of the dielectric constant in the near-subsurface affects the ability of CONSERT to receive signals. Results. At the 90 MHz frequency of CONSERT, the dielectric constant is a function of porosity, composition, and temperature. The dielectric constant values considered for the study are based on observations made by the other instruments of the Rosetta mission, which indicate a possible near-surface gradient in physical properties and on laboratory measurements made on analog samples. Conclusions. The obtained simulated data clearly show that if the dielectric constant were increasing with depth, it would have prevented the reception of signal at the CONSERT location during the first science sequence. We conclude from our simulations that the dielectric constant most probably decreases with depth.

Three-dimensional reconstruction of a comet nucleus by optimal control of Maxwell's equations: A contribution to the experiment CONSERT onboard space craft Rosetta

COmet Nucleus Sounding Experiment by Radio Wave Transmission (CONSERT) is one of 20 experiments onboard the ESA mission Rosetta and aimed at the reconstruction of the unknown internal material parameter distribution of a comet nucleus. The details on the experiment setup can be found in [1], [2]. CONSERT consists of a lander module which attaches to the surface of the comet and an orbiter module which circulates the comet in space. An electromagnetic sounding of the comet nucleus will be achieved by a signal link between the lander and orbiter antenna system. We propose an optimal control approach to solve for the unknown 3D material parameter distribution of the comet nucleus. We optimize the computed electromagnetic field distribution at the receiver locations for the measured (observed) electromagnetic field distribution by controlling the material parameters. The target functional, the difference between computed and observed field for all receiver locations and time steps is minimized by means of a gradient-based quasi-Newton optimization algorithm. The optimal control problem is solved if the target functional yields its global minimum.

Hybrid CPU-GPU computation of adjoint derivatives in time domain

For the solution of large-scale inverse scattering problems - in either acoustic or electromagnetic domain - gradient based optimization approaches are a method of choice, especially when the derivatives regarding the parameter of interest can be obtained from adjoint fields [1], [2]. Gradients regarding a parameter can be effectively computed using an adjoint approach where the direct and adjoint fields are integrated in opposite temporal direction. This yielding high memory consumption, the memory reduced computation of the gradients using checkpointing and recomputation of states from the checkpoint is a method of choice. We propose the use of graphics processing units (GPU) to accelerate the computation by solving the direct problem on the GPU and the adjoint problem on the CPU of the computer. The implementation of pipelining based on CUDA streams and pinned memory masks the memory transfer between host and GPU and allows for the computation of the adjoint derivatives at only a little more than twice the time of the solution of the direct problem.

Noise mitigated compressive sensing for radar applications

During decades microwave imaging technology has achieved remarkable progress, and at the same time encountered increasing complexity in system implementation. Recently, the sparse systems, where the compressed sensing (CS) is applied, introduce the sparse signal processing theory to radar imaging to obtain a new system methodology of microwave imaging and facilitate the burden of computing large-scale data. Basically, CS recovery is a kind of sparse regularized optimization, where the regularization parameter λ plays an important role for a stable solution. Although there are a lots of methods to estimate λ, e.g. the L-curve method, the cross-validation method, etc., however, they are still complex and even only work for particular conditions. In this paper, we will introduce a novel approach, named noise mitigated method (NMM), to get a stable result even without a precise estimation of λ. For radar applications we will take the stepped frequency radar (SFR) as an example to present the feasibility of NMM.

PSTD-based approach to a large-scale inverse scattering problem

The three-dimensional finite-difference time-domain method (FDTD) simulation of electromagnetic wave propagation in large structures, like the cometary nucleus of 67P/Churyumov-Gerasimenko, as well as the inverse problem of reconstructing the permittivity distribution inside the comet nucleus is computationally expensive. With approximative methods not all propagation phenomena can be sufficiently modeled. For the efficient solution of this kind of inverse problem we propose the use of pseudo-spectral time-domain method (PSTD). This method overcomes the computational burdens and memory demands of the FDTD and allows accurate modeling of wave propagation for the CoNSERT case. In combination with optimal checkpointing and a state-of-the-art optimization tool, we demonstrate the solution of inverse problems at a scale of 50 wavelengths.

Enhanced GPR target classification by Compressed Sensing and radar polarimetry

Polarimetric technology has been one of the most important advances in microwave remote sensing during recent decades. The Entropy-α decomposition, which is a type of polarimetric analysis technique, has been common for terrain and land-use classification in polarimetric synthetic aperture radar. For certain scenarios, this kind of processing is also of interest for the interpretation of Ground Penetrating Radar (GPR) measurements. However, due to the limitation of the imaging resolution, which affects the performance of the polarimetric analysis, the classification of subsurface targets is not as reliable as in the original SAR scenario. In this paper we will apply blind support space (BSS) based compressed sensing (CS) to improve the performance of the polarimetric classification of GPR data. This is beneficial, because the support space is usually unknown and location-dependent. We demonstrate the feasibility of this approach based on full polarimetric data measured during a campaign in a controlled environment. The results from these measurements show that a BSS and CS based polarimetric GPR provides significant advantages in targets classification compared to standard GPR methods.

BETSi: An electromagnetic time-domain simulation tool for antennas and heterogeneous media in ground penetration radar and biomedical applications

The broadband electromagnetic time-domain simulation tool (BETSi) aims at the simple implementation of propagation and simulation models in ground penetrating radar and biomedical applications. Parallelism and numerical details of are hidden by BETSi from the user and developer of electromagnetic propagation kernels using the scientific partitioned global address space framework Maui.

Simulative Ultraschall-Untersuchung von Pitch-Catch-Messanordnungen für große zylindrische Stahl-Prüflinge und gradientenbasierte Bildgebung

Zusammenfassung Große zylindrische Stahlprüflinge werden mittels der Methode der finiten Differenzen im Zeitbereich (engl. finite differences in time domain, FDTD) simulativ untersucht. Dabei werden Pitch-Catch-Messanordnungen verwendet. Es werden zwei Bildgebungsansätze vorgestellt: ersterer basiert auf dem Imaging Principle nach Claerbout, letzterer basiert auf gradientenbasierter Optimierung eines Zielfunktionals.

Reconstructing surface permittivity distributions from RADAR measurements using a sparsity inducing regularized least-squares approach

The estimation of surface properties of small bodies in our solar system like asteroids, comets and small moons from RADAR observations is a particularly challenging task. Due to limitations in orbitography and instrument dynamics the associated inverse problems are usually ill-posed. Common methods in the solution of these kind of problems are regularized least-squares approaches where the proper selection of the parameter weighting target function and regularization penalty is of great importance and not trivial. In this paper we propose a methodology based on a compressive sensing technique and demonstrate its feasibility on a surface permittivity reconstruction based on the well known method of physical optics (PO). We show that the proposed algorithm yields proper and stable reconstruction results in a sparse representation of the surface permittivity distribution for sub-optimal choices of the regularization parameter.