HR: 14:40h
AN: S33E-05    [Abstracts]
TI: On the recovery of missing low and high frequency information from bandlimited reflectivity data
AU: * Sacchi, M D
EM: msacchi@ualberta.ca
AF: Department of Physics University of Alberta, Department of Physics Room #238 CEB 11322 - 89 Avenue University of Alberta, Edmonton, AB T6G 2G7, Canada
AU: Ulrych, T J
EM: ulrych@eos.ubc.ca
AF: Department of Earth and Ocean Sciences, UBC, 6339 Stores Road, Vancouver, BC V6T 1Z4, Canada
AB: During the last two decades, an important effort in the seismic exploration community has been made to retrieve broad-band seismic data by means of deconvolution and inversion. In general, the problem can be stated as a spectral reconstruction problem. In other words, given limited spectral information about the earth's reflectivity sequence, one attempts to create a broadband estimate of the Fourier spectra of the unknown reflectivity. Techniques based on the principle of parsimony can be effectively used to retrieve a sparse spike sequence and, consequently, a broad band signal. Alternatively, continuation methods, e.g., autoregressive modeling, can be used to extrapolate the recorded bandwidth of the seismic signal. The goal of this paper is to examine under what conditions the recovery of low and high frequencies from band-limited and noisy signals is possible. At the heart of the methods we discuss, is the celebrated non-Gaussian assumption so important in many modern signal processing methods, such as ICA, for example. Spectral recovery from limited information tends to work when the reflectivity consist of a few well isolated events. Results degrade with the number of reflectors, decreasing SNR and decreasing bandwidth of the source wavelet. Constrains and information-based priors can be used to stabilize the recovery but, as in all inverse problems, the solution is nonunique and effort is required to understand the level of recovery that is achievable, always keeping the physics of the problem in mind. We provide in this paper, a survey of methods to recover broad-band reflectivity sequences and examine the role that these techniques can play in the processing and inversion as applied to exploration and global seismology.
DE: 3200 MATHEMATICAL GEOPHYSICS (0500, 4400, 7833)
DE: 3205 Fourier analysis (3255)
DE: 3260 Inverse theory
DE: 3285 Wave propagation (0689, 2487, 4275, 4455, 6934)
SC: Seismology [S]
MN: 2007 Fall Meeting