Ground Penetrating Radar: Analysis of point diffractors for modeling and inversion

TL;DR

This paper analyzes how point diffractors affect electromagnetic properties in ground penetrating radar, using Maxwell's equations to interpret dielectric permittivity, conductivity, and magnetic permeability variations for improved subsurface imaging.

Contribution

It introduces a theoretical framework for modeling electromagnetic anomalies as electric and magnetic dipoles and discusses how different data offsets reveal impedance and velocity variations.

Findings

Zero-offset data directly image impedance variations.

Large-offset data contain information on velocity variations.

Electromagnetic property variations can be described using logarithms.

Abstract

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.