Practical representations of electromagnetic interferometry for GPR applications: a tutorial

Starting from the reciprocity theorems of the time-convolution and time-correlation types, several exact interferometric representations for electric and magnetic field Green's functions due to electric dipole and quadrupole Sources are derived. The abundance of ambient noise, over a wide electromagnetic spectrum from sources in the atmosphere or in space, is used to define three different practical acquisition geometries that can be used to create new data from cross-correlations of the noise recordings. Similar setups are given for band limited transient sources to create new data from cross-correlations or cross-convolutions of the recordings from these transient sources. In all these applications the Earth can be arbitrarily anisotropic and dissipative as long as one receiver is located at the Earth's Surface or in the air above. In applications where both receivers are located in the Earth we show that cross-correlations of such recordings lead to accurate new GPR data when the Earth is almost lossless.