GPR Without a Source: Cross-Correlation and Cross-Convolution Methods

Several formulations exist for retrieving the Green´s function from cross correlation of (passive) recordings at two locations. For media without losses, these known formulations retrieve Green´s functions from sources on a closed boundary. Until recent, these formulations were only developed for acoustic waves in fluids and elastodynamic waves in solids. Now, Green´s function representations for electromagnetic (EM) waves in matter exist and can be exploited for passive ground-penetrating radar (GPR) applications using transient or ambient noise sources, either natural or man-made. We derive general exact EM Green´s function retrieval formulations based on cross correlations and cross convolutions of recorded wave fields. For practical applications, simplified forms are derived that directly apply to field recordings due to unknown uncorrelated noise or transient sources. Only naturally present sources are needed, which allows for all kinds of applications of ldquoGPR without a source.rdquo We illustrate the consequences of using the simplified forms for Green´s function retrieval with 2-D numerical examples. We show that in dissipative media, the Green´s function is most accurately retrieved using the cross-convolution method when the sources are located on a sufficiently irregular boundary.