Simulating radio propagation in ice with Parabolic Equations: applications to terrestrial glaciers and ice moons

We investigate the use of Parabolic Equation (PE) simulations in modelling the propagation of radio waves in inhomogeneous ice environments, such as the firn layer of terrestrial glaciers in the Alps and Antarctic. In particular PEs allow for an accurate and efficient means to simulate pulsed radar on a multi-km scale for depth-dependent permittivity profiles, and inhomogeneities that are the targets of radar scans.

PEs are an approximate solution to Maxwell's equations which are valid within a cone that is perpendicular to the source, which defines the 'paraxial direction'. For monochromatic (single-frequency) radio emission, the electric field can be solved using a numerical step-wise solver, where the next range increment can be solved from the previous step. The emission profile of the source is used to define the starting condition. To solve in the time-domain for pulses, the pulse is decomposed into its Fourier spectrum, and the electric field throughout the geometry is solved for each frequency. By sampling the frequency dependent field amplitude at a given range and depth in the geometry, one can reconstruct the pulse and measure the time of flight. We implement a two-stage PE solver which first models propagation in the forwards direction from a transmitter, and then solves in the 'backwards' direction in order to calculate reflected signals. 

We present a Python based PE solver which simulates emission from a high frequency (300 MHz to 2000 MHz) radar transmitter into ice on a multi km-scale, using depth dependent permittivity profiles and a list of objects, such as boulders, crevasses and aquifers, which cause scattering. We find that we can accurately solve pulsed radar emission, and test target reconstruction techniques. We compare radar images for targets with constant permittivity and varying permittivity. We apply our simulation method to the firn layer of numerous real-world glaciers, with their permittivity estimated from density profiles, and observed birefringence and wave-guide-like behaviour between bands of solid ice, caused by melting and refreezing of the firn. 

Additionally we apply PE simulations to assess the viability of a future melting probe mission on Saturn's ice moon Enceladus, in which the melting probe would seek a near surface water pocket, which it localized with a combined orbital and surface radar scan.