Bootstrapping confidence bands for the instantaneous frequency

Abdelhak M. Zoubir; D. R. Iskander; Branko Ristic; Boualem Boashash

doi:10.1117/12.190831

28 October 1994 Bootstrapping confidence bands for the instantaneous frequency

Abdelhak M. Zoubir, D. R. Iskander, Branko Ristic, Boualem Boashash

Proceedings Volume 2296, Advanced Signal Processing: Algorithms, Architectures, and Implementations V; (1994) https://doi.org/10.1117/12.190831
Event: SPIE's 1994 International Symposium on Optics, Imaging, and Instrumentation, 1994, San Diego, CA, United States

Abstract

Data produced by a reproducible source contains redundant information which allows seismic inversion to simultaneously determine the high-frequency fluctuation in the p-wave velocity (or reflectivity) as well as the input energy source. The seismogram model is the plane-wave convolutional model derived from the constant density, variable sound velocity acoustic wave equation. The first step is to analyze this linearized model when the background velocity is constant. Then perturbations in the seismic data stably determine corresponding perturbations in the source and reflectivity. The stability of this determination improves as the slowness aperture over which the data is defined increases. Further, the normal operator for the convolutional seismogram model is continuous with respect to velocity. Thus the stability result for constant background velocities may be extended to more realistic background velocity models which vary slowly and smoothly with depth. The theory above is illustrated with four synthetic numerical examples derived from marine data. The examples indicate that for a wide slowness aperture, inversion is very effective in establishing the true shape of the reflectivity and the shape and location of the compactly supported energy source. As this aperture window narrows, the corresponding inversion-estimated model still describes the data quite accurately, but the inversion is not able to recover the original two distinct parameters.

Citation Download Citation

Abdelhak M. Zoubir, D. R. Iskander, Branko Ristic, and Boualem Boashash "Bootstrapping confidence bands for the instantaneous frequency", Proc. SPIE 2296, Advanced Signal Processing: Algorithms, Architectures, and Implementations V, (28 October 1994); https://doi.org/10.1117/12.190831

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