Numerical simulation of a permittivity probe for measuring the electric properties of planetary regolith and application to the near-surface region of asteroids and comets

Abstract

We present a numerical simulation technique for the retrieval of the electric properties relative permittivity and conductivity of planetary, asteroid, and cometary regolith. Our simulation techniques aim at accompanying hardware development and conducting virtual experiments, e.g., to assess the response of arbitrary heterogeneous conductivity and permittivity distributions or to scrutinize possibilities for spatial reconstruction methods using inverse schemes. In a first step, we have developed a finite element simulation code on the basis of unstructured, adaptive triangular grids for arbitrary two-dimensional axisymmetric distributions of conductivity and permittivity. The code is able to take into account the spatial geometry of the probe and allows for possible inductive effects. In previous studies, the non-inductive approach has been used to convert potential and phase data into apparent material properties. By our simulations, we have shown that this approach is valid for the frequency range from 10² Hz to 10⁷ Hz and electric conductivities of 10−8 S/m that are typical for the near-surface region of asteroids and comets composed of chondritic materials and/or frozen volatiles such as H₂O and CO₂ ice. We prove the accuracy of our code to be better than 10%, using mixed types of boundary conditions and present a simulated vertical log through a horizontally stratified subsurface layer as a representative example of a heterogeneous distribution of the electrical properties. Resolution studies for the given electrode separation reveal that the material parameters of layers having thicknesses of less than about half the electrode spread are not reconstructible if only apparent quantities are considered. Therefore, spatial distributions of the complex sensitivity are presented having in mind a future data inversion concept that will permit the multi-dimensional reconstruction of material parameters in heterogeneous environments.