Time-varying deconvolution of GPR data in civil engineering

Why Ricker wavelets are successful in processing seismic data: Towards a theoretical explanation

“…Similarly, the joint effect of several layers can be described by a formula (5) in which the corresponding function m(t) is a convolution of functions m i (t) corresponding to all the layers. So, to describe the joint effect of propagating the signal through several layers, we need to describe convolutions of several functions.…”

“…Since the original Ricker's paper, Ricker wavelets have been successfully used in processing seismic signal; see, e.g., [2], [3], [4], [5], [8], [9], [10], [12], [13], [18], [20] (see especially [4]). Ricker wavelet are also actively used when computational intelligence techniques are used for processing seismic data; see, e.g., [6].…”

“…The resulting seismic information helps geophysicists, petroleum and mining engineers, hydrologists to find mineral deposits and underground water reservoirs, helps civil engineers get a good understanding of the stability of the underground layers below the future structure (e.g., a building, a tunnel, a dam, or a landfill) [1], [5], [19], etc. ; see, e.g., [14].…”