Modeling and Simulation of Low Frequency Subsurface Radar Imaging in Permafrost
- K. van den Doel - Adrok Ltd. 49-1, West Bowling Green St., Edinburgh EH6 5NX, Scotland
- G. Stove - Adrok Ltd. 49-1, West Bowling Green St., Edinburgh EH6 5NX, Scotland
Abstract
We describe simulated low frequency subsurface radar scans targeting the detection of a liquid water layer, or some other reflector such as conductive sulfides, under permafrost. A finite-difference time-domain (FDTD) and ray tracing simulation framework is used to model measurements and data analysis at depths from 350m to 800m. Operating characteristics such as pulse shape and noise levels of the measurement apparatus were obtained from an existing com- mercial radar scanning system. Results were used to test and optimize data analysis methods, predict maximum detection depth under realistic time constraints, and guide experimental design parameters such as the amount of replications required for denoising and length of the wide angle reflection and refraction (WARR) scan lines used for velocity estimation.
Keywords
Radar, Simulation, Electromagnetic, Geophysics, Imaging
1 INTRODUCTION
Applications of ground penetrating radar [1, 2] are currently mostly limited to shallow depths of a few tens of meters, because of the strong attenuation of radio waves in most subsurface materials at a typical frequency range of 20 − 1000MHz. Losses are caused by conductivity and polarization effects due to moisture content or inherent material properties. Deeper penetration up to several kilometres has been achieved with much lower frequencies (1 − 5Mhz) using very large antenna’s in resistive environments such as Martian rock, ice, and permafrost [3, 4, 5, 6]. In this article we present results of simulations of scans with a low frequency pulsed radar system through permafrost. The scenario we consider is the detection of a water rich layer at depths of 350m to 800m. Electrical properties (conductivity and Debye polarization model parameters) of limestone were measured previously in-situ by trans illumination scans through large underground pillars [7], which we use as representative for permafrost, though perhaps these values are somewhat pessimistic in terms of generated losses [8]. Material parameters were used in a one dimensional full waveform FDTD simulator similar to [9], and a two dimensional simulator based on the ray approximation to Maxwell’s equations. The radar system was modeled after the Adrok scanner [10] for which we measured the transmitted pulse shape and noise levels.
Two types of radar scans were simulated. In Stare scans transmitter and receiver are placed about 1m apart on the surface and reflections from transmitted pulses are measured repeatedly and stacked (averaged) for denoising. From the arrival times of observed returns, reflecting boundaries can be localized if the propagation velocity is known. To estimate velocity we perform a WARR [11] scan, where data is acquired with transmitter and receiver at varying distances. Using triangulation methods such as normal move out analysis or velocity spectrum analysis allows the estimation of average velocity at a specific reflection time. Velocity v is related to relative permittivity εr (referred to as “the dielectric” below) by v = c/√εr with c the speed of light in vacuum. Pulse dispersion is negligible in the frequency range under consideration so we ignore the small variations of εr with frequency. Results are used to test efficacy of data analysis methods, determine the effect of backscatter caused by irregularities in the ground, estimate how much stacking is required, and estimate maximum achievable penetration depth with the modeled system.
2 Wave propagation model
We implemented a 1 + 1 dimensional time-domain finite difference simulation of Maxwell’s equations in a medium described by dielectric εr(x), static conductivity σ(x) and a Debye polarization model [12] with relaxation time τ to account for frequency dependent losses. The model is similar to the one described in [5], except we added a polarization component. Material properties are assumed to be constant in time but can depend on location. The model is summarized by the following system of partial differential equations:
with E the electrical field, P the polarization, ε0 = 8.85 × 10−12F/m and μ0 = 4π × 10−7H/m. The equations are discretized with a fourth order finite difference approximation for the spatial derivatives and a leap-frog method for the time stepping [13]. At the simulation boundaries we use perfectly matched layers [14]. A spatial grid spacing of 10cm and a time step of 0.15ns was used and found to be accurate enough for frequencies up to 100MHz. The size of the absorbing boundaries were 400m on the top and 200m on the bottom. See Fig, 1.
This model permits the simulation of Stare scans, where transmitter and receiver are at (almost) the same position on the surface. During WARR scans we measure returns with transmitter and receiver at increasing separations, with the transmitter moving away from the receiver. For this a two dimensional simulation is required. Due to the small grid spacing necessary and the long simulation times to capture deep reflections a FDTD simulator would require very large computational resources. An interesting alternative manner to reduce computational requirements was proposed in [15] using a finite difference model in the frequency domain.
We used a ray tracing method instead. A