3-D electromagnetic modeling for near‐surface targets using integral equations

Abstract

Three‐dimensional electromagnetic (EM) modeling in the frequency range from 100 kHz to about 200 MHz using integral equations is examined. The modeling algorithm is formulated in the frequency domain. Time‐domain responses for ground‐penetrating radar (GPR) and very early time time‐decaying transients are computed via Fourier transforms. Of vital importance to the modeling problem is the computation of the Hankel transforms in the Green's functions. The kernels of those Hankel transforms vary rapidly at high frequencies where displacement currents become important and are even singular for sources in the air, with poles approaching the real axis or branch cuts lying on the real axis. We use high density Hankel filters and a singularity extraction technique to circumvent these problems. Our modeling for GPR applications shows that dielectric targets are very obvious in radargrams, with waves reflected by target boundaries arriving at distinctive times, depending on the path they travel. While GPR signals are absorbed in conductive media, very early time‐transient responses can detect conducting targets in conductive media. Our modeling shows that 1-D shallow conductors can have large transient anomalies in the time window from 50 ns to 100 ms. Thus 1-D near‐surface conductors may be detected by conventional systems operating at μs ranges. However, shallow 3-D conductors of practical interest can have much earlier anomaly time windows around 100 ns. These targets can only be detected by very early time‐transient equipment. Moreover, very early time transients contain little information on dielectric permittivities, being primarily determined by the conductivities of the media. Thus GPR and very early time transients are excellent complements to each other.