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Electromagnetic full waveform inversion (FWI) is a high-resolution method to reveal the distribution of dielectric parameters of the medium. Traditionally, the electromagnetic FWI is usually performed using the $L_{2}$ norm misfit function, which suffers severely local minimum problems since the $L_{2}$ norm misfit function is nonconvex in the model space. To mitigate the local minimum problem, the quadratic Wasserstein metric ( $W_{2}$ ) derived from the optimal transport theory is proposed to replace the $L_{2}$ norm to define the misfit function. Since the computation of the $W_{2}$ metric requires the signal to be mass conservation and nonnegativity, the softplus function is applied to rescale the signal to meet these two requirements. Based on the softplus scaling method, a hierarchy inversion strategy that involves multiple scaling coefficients is proposed to mitigate the local minimum problem without sacrificing the inversion resolution. The numerical experiments prove that the FWI based on $W_{2}$ ( $W_{2}$ -FWI) is more independent on the initial model than the FWI based on the $L_{2}$ norm ( $L_{2}$ -FWI), and the $W_{2}$ -FWI could be more robust to zero-mean random noise than the $L_{2}$ -FWI. Finally, a comprehensive numerical experiment related to asteroid radar tomography is carried out to show the potential of $W_{2}$ -FWI in realistic applications.

Our knowledge of the internal structure of asteroids is currently indirect and relies on inferences from remote sensing observations of surfaces. However, it is fundamental for understanding small bodies' history and for planetary defense missions. Radar observation of asteroids is the most mature technique available to characterize their inner structure, and Synthetic Aperture Radar Tomography (TomoSAR) allows 3D imaging of their interior. However, as the geometry of observation of small asteroids is complex, and TomoSAR studies have always been performed in the Earth observation geometry, its results in a small body geometry must be simulated to assess the methods' performances. We adopt here two different tomography algorithms and evaluate their performances in our geometry by assessing the resolution and the difference between the scatterer's position and its retrieved position. The first method, the Frequency Domain Back Projection (FDBP) is based on correcting the Fourier transform of the received signal by a phase function built from the geometry. While it can provide a good resolution, a bias remains in the imaged scatterer's position. Meanwhile, Compressive Sensing (CS) relies on the hypothesis that few scatterers lie in the same direction from the subsurface. Its application in the small body geometry is studied, which results in a slightly impoverished resolution but an improved localization of the scatterer. High‐Frequency Radar (HFR) is an UWB Synthetic Aperture Radar (SAR) developed to retrieve the 3D structure of the first 10 m of an asteroid's subsurfaceSAR Tomography (TomoSAR) is crucial to improve the resolution in the vertical directionIn the specific asteroid geometry, simulations are necessary the assess the performances of the TomoSAR algorithms High‐Frequency Radar (HFR) is an UWB Synthetic Aperture Radar (SAR) developed to retrieve the 3D structure of the first 10 m of an asteroid's subsurface SAR Tomography (TomoSAR) is crucial to improve the resolution in the vertical direction In the specific asteroid geometry, simulations are necessary the assess the performances of the TomoSAR algorithms

Electromagnetic full waveform inversion in Debye dispersive medium (EFWI-D) is a promising technique to reconstruct the inner structure and electrical properties of the medium such as soil, rock and biological tissues. Same as conventional full waveform inversion, EFWI-D requires high computational cost, especially in the 3D case. To reduce the long computation time, we design and implement the EFWI-D algorithm in time domain using multiple GPU cards. The inversion method is based on the L-BFGS optimization algorithm, which can increase the convergence of the misfit function, while the auxiliary differential equation (ADE) method is employed for modeling the Debye dispersive medium by using exponential time differencing (ETD) finite-difference time-domain (FDTD) approach. Moreover, a multi-stream strategy is performed in the workflow to improve the computation performance. Numerical results illustrate the improvement of the computational performance and the preliminarily feasibility of the proposed inversion algorithm. Program title: 3D Electromagnetic Full Waveform Inversion in Debye Dispersive Medium Based on Multi-GPU Paralleling CPC Library link to program files: https://doi.org/10.17632/mjd9pp5dcm.1 Licensing provisions: LGPL Programming language: C/C++, CUDA Nature of problem: Electromagnetic FWI derives high-resolution distribution of electrical parameters by using additional information provided by the amplitude and phase of the received signals. It goes beyond ray-tracing tomography techniques, which use only the travel time kinematics of the signals. Mathematically, electromagnetic FWI is a kind of conditional extremum problem which is to minimize the difference between observed and modeled waveform of received signals under the condition of Maxwell's equation. Solution method: The basis of inversion is the solution of the forward problem. In this program, the forward simulation is based on Auxiliary Differential Equation (ADE) method. Since the inverse problem is nonlinear, it is solved by using iterative solution which is an optimization method. As it is well known that 3D FWI requires tremendous computation, multi-GPU paralleling is used in this program to accelerate the computing process. Additional comments including Restrictions and Unusual features: The program is mainly designed to solve the inverse problem in Debye dispersive medium, but it also can be used for solving the forward and inverse problem in nondispersive medium by setting the input parameter: poles_of_debye_dispersive_medium(non_dispersive=0,dispersive=1-5)=0. [ABSTRACT FROM AUTHOR]