Tomographic inversion of gravity gradient field for a synthetic Itokawa model

Abstract

This article investigates reconstructing the internal mass density of a numerical asteroid model using the gradient of a simulated gravity field as synthetic measurement data. Our goal is to advance the mathematical inversion methodology and find feasibility constraints for the resolution, noise and orbit selection for future space missions. We base our model on the shape of the asteroid Itokawa as well as on the recent observations and simulation studies which suggest that the internal density varies, increasing towards the center, and that the asteroid may have a detailed structure. We introduce randomized multiresolution scan algorithm which might provide a robust way to cancel out bias and artifact effects related to the measurement noise and numerical discretization. In this scheme, the inverse algorithm can reconstruct details of various sizes without fixing the exact resolution a priori, and the randomization minimizes the effect of discretization on the solution. We show that the adopted methodology provides an advantageous way to diminish the surface bias of the inverse solution. The results also suggest that a noise level below 80 Eotvos will be sufficient for the detection of internal voids and high density anomalies, if a sparse set of measurements can be obtained from a close-enough distance to the target.

Modelling and computation of gravitational attraction, gradient tensors, rotational and horizontal invariants of Asteroid Bennu (101955), Itokawa (25143) and Eros (433) via 2D Non-Uniform FFT

“…To detect variations in forward modelled gravity anomaly with constant density contrast, tensor gradient and invariant applications tend to produce more interpretable output than first derivative anomalies (Figure 7). In figure 7, surficial heterogeneity analysis presents anomalous characteristics in the body part, and this is compatible with the previous findings Sorsa et al, 2020). Tensor gradients 𝑇𝑇 𝑥𝑥𝑥𝑥 and 𝑇𝑇 𝑦𝑦𝑦𝑦 delineate the edge of the structural heterogeneity zone along the x and y axes.…”

“…In figure 6c and 6d, the body part produces a distinctly higher gravity anomaly, while the head part has a lower gravity anomaly. Although the head part has higher density values Sorsa et al, 2020), lower gravity anomalies are estimated in 𝑔𝑔 𝑧𝑧 and 𝑔𝑔 𝑥𝑥 . It is worth noting that using constant density models during the computation of gravity anomaly does not provide a reliable density distribution.…”

“…It is possible to say that, we assume the head and body parts of Itokawa have the same density and variations in the computed gravity anomaly should be linked to surficial heterogeneity. Sorsa et al, (2020) proposed that both lobes of Itokawa have a uniform structure and surface composition. Furthermore, the differences between lobes might be linked to void space distribution or high density metallic fragments.…”