The three electromagnetic properties appearing in Maxwell's equations are dielectric permittivity, electrical conductivity and magnetic permeability. The study of point diffractors in a homogeneous, isotropic, linear medium suggests the use of logarithms to describe the variations of electromagnetic properties in the earth. A small anomaly in electrical properties (permittivity and conductivity) responds to an incident electromagnetic field as an electric dipole, whereas a small anomaly in the magnetic property responds as a magnetic dipole. Neither property variation can be neglected without justification. Considering radiation patterns of the different diffracting points, diagnostic interpretation of electric and magnetic variations is theoretically feasible but is not an easy task using Ground Penetrating Radar. However, using an effective electromagnetic impedance and an effective electromagnetic velocity to describe a medium, the radiation patterns of a small anomaly behave completely differently with source-receiver offset. Zero-offset reflection data give a direct image of impedance variations while large-offset reflection data contain information on velocity variations.
Effective modeling of ground penetrating radar in fractured media using analytic solutions for propagation, thin-bed interaction and dipolar scattering
Hydrogeophysical characterization of transport processes in fractured rock by combining push-pull tracer tests and single-hole ground penetrating radar
Modelling Arbitrary Complex Dielectric Properties -- an automated implementation for gprMax
在对探地雷达（GPR）建模时，需要准确地模拟具有复杂电磁特性的材料，因为GPR遇到的许多物体都含有水，例如土壤，固化混凝土和充水管道。gprMax是一个广泛使用的模拟电磁波传播的开源软件。它使用Yee算法来求解Maxwell方程，并采用时域有限差分法（FDTD）。FDTD方法的一个显著缺点是对具有色散特性的材料建模的能力有限，目前仅限于特定的弛豫机制，即多德拜，德鲁德和洛伦兹介质。因此，任何复杂材料的建模都应该通过将其近似为这些函数的组合来完成。本文描述了作为Google Summer of Code（GSoC）计划2021的一部分而开展的工作，该计划旨在开发gprMax中的一个新模块，该模块可用于以自动方式使用多德拜展开来模拟复杂的色散材料。该模块能够对Havriliak-Negami、Cole-Cole、Cole-Davidson、Jonscher、复折射率模型以及用户指定的具有实部和虚部介电常数的任意色散材料进行建模。
