Minimum entropy regularization in frequency-wavenumber migration to localize subsurface objects

Optimized versions of frequency-wavenumber (F-K) migration methods are introduced to better focus ground-penetrating radar (GPR) data in applications of shallow subsurface object localization, e.g., landmine remediation. Migration methods are based on the wave equation and operate by backpropagating the received data into the earth so as to localize buried objects. Traditional F-K migration is based on an underlying assumption that the wavefields propagate in a homogeneous medium. The presence of a rough air-ground interface in the GPR case degrades the localization ability. To overcome this problem in the context of the F-K algorithm, we introduce lateral variations in the velocity of waves in the medium. An optimization approach is employed to choose that velocity function that results in a well-focused image where an entropy-like criterion is used to quantify the notion of focus. Extension of the basic method to lossy medium is also described. The utility of these techniques is demonstrated using field data from a number of GPR systems.