Unified Analysis of Leap-Frog Methods for Solving Time-Domain Maxwell’s Equations in Dispersive Media

2010 ◽  
Vol 47 (1) ◽  
pp. 1-26 ◽  
Author(s):  
Jichun Li
Keyword(s):  
Time Domain ◽  
Maxwell’S Equations ◽  
Maxwell's Equations ◽  
Dispersive Media

3-D simulation of GPR surveys over pipes in dispersive soils

Geophysics ◽  
2000 ◽  
Vol 65 (5) ◽  
pp. 1560-1568 ◽  
Author(s):  
Tsili Wang ◽  
Michael L. Oristaglio
Keyword(s):  
Electrical Properties ◽  
Time Domain ◽  
Maxwell’S Equations ◽  
Maxwell's Equations ◽  
Displacement Vector ◽  
Electric Displacement ◽  
Field Vector ◽  
Dispersive Media ◽  
Dispersive Soils ◽  
Dispersive Soil

The finite‐difference time‐domain method is adapted to simulate radar surveys of objects buried in dispersive soils whose complex permittivity depends on frequency. The method treats dispersion through the constitutive relation between the electric field vector and the electric displacement vector, which is a convolution in the time domain. This convolution is updated recursively, along with Maxwell’s equations, after approximating the dispersion with a Debye (exponential) relaxation model. A novel feature of our work is the inclusion of dispersion in the perfectly‐matched layer formulation of Maxwell’s equations, which gives an absorbing boundary condition for dispersive media. We simulate 200-MHz ground‐penetrating radar surveys over metallic and plastic pipes buried at a depth of 2 m in soils whose electrical properties model are those of clay loams of different moisture contents. Radar reflections modeled for pipes in dispersive soil differ from those for pipes in soils whose electrical properties are constant (at the values of dispersive soil at the central frequency of the radar pulse). Because the permittivity decreases at higher frequencies in the soils modeled, energy in the reflections shifts toward the front of the waveform, and the amplitudes of trailing lobes in the waveform are suppressed. The effects are subtle, but become more pronounced in models of soils with 10% moisture content by weight.

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