Edge preserved denoising and singularity extraction from angles gathers
Felix J. Herrmann, Maarten V. de Hoop · 2002
this paper we present a method of recovering the geologic record from seismic data. First, we transform seismic data into a collection of images parametrized by angles. Under certain conditions, the angles within these scattering angles common image gathers (CIG's) correspond to the angles under which the subsurface singularities are being insonified by the seismic waves (Brandsberg-Dahl and de Hoop, 1998). Second, we subject these images to an adaptive atomic decomposition in one spatial direction, generally the vertical, and then perform this procedure for each of the remaining spatial directions, generally the horizontal. Inherent redundancy of the angles domain data is utilized by submitting the angles CIG's to an non-adaptive wavelet thresholding (Donoho and Johnstone, 1998) along the angles coordinates. This thresholding denoises the images and enforces smoothness in the angle directions. Conversely, we preserve the singularities in the depth-direction by a decomposition into transition sharpness-adaptive atoms. Noise in the data is removed because the decomposition extracts only the coherent structures. The parameterization of the selected atoms provides precise information on the location and shape of the important patterns within the geologic record