2D GPR monitoring without a source by interferometry in a 3D world

Creating virtual sources at locations where physical receivers have measured a response is known as seismic interferometry. The method does not use any information about the actual source's location. The source can be mobile phone radiation, already available in the air, as long as this background radiation can be represented by uncorrelated noise sources. Interferometry by multi-dimensional deconvolution (MDD) `divides the common path out of the data', resulting in amplitude and phase information. Meanwhile, interferometry by cross-correlation (CC) uses time-reversion to retrieve phase information only. CC works fine for low-dissipative media. A finite difference time-domain solver can create 3D line-array data of receiving antennas on a surface of which the subsurface is homogeneous perpendicular to this receiver-array, without having anything being transmitted, other than background radiation. By applying the MDD and CC techniques, the 2D GPR signal can be retrieved as if there would be a transmitting antenna at a receiving antenna's position. Numerical results show that both MDD and CC work well.