Signal and noise separation: Art and science

Author:

Ulrych Tadeusz J.1,Sacchi Mauricio D.2,Graul J. Michael3

Affiliation:

1. University of British Columbia, Department of Earth and Ocean Science, 129-2219 Main Mall, Vancouver, British Columbia V6T 1Z4, Canada.

2. University of Alberta, Department of Physics, Avadh Bhatia Physics Laboratory, Edmonton, Alberta T6G 2J1, Canada.

3. Texseis Inc., 2618 Hollow Hook, Houston, Texas 7708-3814.

Abstract

The separation of signal and noise is a central issue in seismic data processing. The noise is both random and coherent in nature, the coherent part often masquerading as signal. In this tutorial, we present some approaches to signal isolation, in which stacking is a central concept. Our methodology is to transform the data to a domain where noise and signal are separable, a goal that we attain by means of inversion. We illustrate our ideas with some of our favorite transformations: wavelets, eigenvectors, and Radon transforms. We end with the notion of risk, baseball, and the Stein estimator.

Publisher

Society of Exploration Geophysicists

Subject

Geochemistry and Petrology,Geophysics

Reference14 articles.

1. Burg, J. P., 1975, Maximum entropy spectral analysis: Ph.D. thesis, Stanford Univ.

2. Donoho, D. L., 1994, De‐noising by soft‐thresholding: manuscript, Department of Statistics, Stanford Univ. Available at www.stat.stanford.edu/∼donoho/Reports/index.html.

3. Efron, B., and Morris, C., 1977, Stein’s paradox in statistics: Scientific American, May, 119–128.

4. Foster, D. J., Mosher, C. C., and Hassanzadeh, S., 1994, Wavelet transform methods for geophysical applications: 64th Ann. Internat. Mtg., Soc. Expl. Geophys., Expanded Abstracts, 1465–1468.

5. Application of singular value decomposition to vertical seismic profiling

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