3-D ELECTROMAGNETIC MODELING FOR NEAR-SURFACE TARGETS USING INTEGRAL-EQUATIONS

Three-dimensional electromagnetic (EM) modeling in the frequency range from 100 kHz to about 200 MHz using integral equations is examined. T he modeling algorithm is formulated in the frequency domain. Time-doma in responses for ground-penetrating radar (GPR) and very early time ti me-decaying transients are computed via Fourier transforms. Of vital i mportance to the modeling problem is the computation of the Hankel tra nsforms in the Green's functions. The kernels of those Hankel transfor ms vary rapidly at high frequencies where displacement currents become important and are even singular for sources in the air, with poles ap proaching 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 tha t dielectric targets are very obvious in radargrams, with waves reflec ted by target boundaries arriving at distinctive times, depending on t he path they travel. While GPR signals are absorbed in conductive medi a, very early time-transient responses can detect conducting targets i n conductive media. Our modeling shows that 1-D shallow conductors can have large transient anomalies in the time window from 50 ns to 100 m s. Thus 1-D near-surface conductors may be detected by conventional sy stems operating at mu s ranges. However, shallow 3-D conductors of pra ctical interest can have much earlier anomaly time windows around 100 ns, These targets can only be detected by very early time-transient eq uipment. Moreover, very early time transients contain little informati on on dielectric permittivities, being primarily determined by the con ductivities of the media. Thus GPR and very early time transients are excellent complements to each other.