A versatile tuneable curvelet-like directional filter with application to fracture detection in two-dimensional GPR data

The present work introduces a curvelet-like directional filter and discusses its application to edge detection in general images and fracture detection in GPR data. The filter is essentially a curvelet of adjustable anisotropy and orientation that can be tuned on any given (target) wavenumber; while retaining the properties of curvelets, it is not bound to the scaling rules of the Curvelet Frame but is individually steerable to any local trait of the data, hence it is dubbed “Curveletiform”. Curveletiforms can be used in single- or multi-directional modes in a manner simple, computationally inexpensive and demonstrably efficient. GPR data generally contains straight or curved edge-like objects comprising reflections from planar interfaces and is notoriously susceptible to broadband noise. Fractures are an important class of interfaces as they determine the health state of rocks or man-made structures and are primary targets of GPR surveys in geotechnical, engineering and environmental applications. As demonstrated with examples, Curveletiforms can efficiently recover information of specific scale and geometry from straight or curved edges in general images. In GPR data they may distinguish reflections from small and large fractures, discriminate between groups of fractures, resolve fracture density and aid the assessment of damage in rocks and structures.