A FDTD Modeling Approach to Investigate Critical Refraction from Crosswell Radar

Abstract

First arrival travel times (FATTs) from critically refracted waves in crosswell radar applications have been known to cause incorrect estimates of electromagnetic wave velocities, if these waves are assumed to be a direct arrival. This is a particular problem when the FATTs are acquired from radar antennae placed near the ground surface. One way to accommodate critically refracted waves at the air-ground interface is to remove the upper [Formula: see text] of data and assume that the remaining FATTs within the profile travel directly from transmitter to receiver. An alternative method is to use simple ray-based inverse models that accommodate critically refracted waves to back calculate the near-surface electromagnetic wave velocity. In this work, we show the validity of these ray-based models in regions where critical refractions will occur, by first generating FATTs with a finite-difference time domain (FDTD) numerical model and assuming zero-offset profiling mode of acquisition. The ray-based inverse models were shown to reproduce the original electromagnetic wave velocity of the numerical model. A second test was also run using FDTD modeling, where an infiltrating wetting front moves past a set stationary antennae and the time series of FATTs were recorded for the duration of the infiltration experiment. The critically refracted waves occurring at the edge of the moving wetting front actually benefits the calculation of the hydraulic conductivity controlling the speed of the wetting front. Additionally, the sharper the wetting front, the more accurate the prediction for hydraulic conductivity. With the work presented here and elsewhere, obtaining reasonable estimates of electromagnetic wave velocity where critical refraction is known to occur should be easily applied and defended.