Abstract
This paper presents a systematic approach to the description of spatial resolution of seismic experiments and migration (or inversion) algorithms.
We give a brief description of the linearized seismic inverse problem and its solution by migration and inversion algorithms. To consider the spatial resolution at a given point in the medium, we define the domain of coverage in the space of spatial frequencies. This region determines the spatial resolution and is shown to depend on (i) the total domain of integration, which in turn depends on the configuration of sources and receivers and on the frequency band of the signal, and (ii) the mapping of this domain into the spatial frequency domain. This mapping is determined by the background model and can be obtained numerically by ray tracing. Together (i) and (ii) allow us to estimate the limits of spatial resolution at each point in the medium given the configuration of experiment and the background model.
As important examples, we illustrate our approach by considering the spatial resolution of surface seismics and VSP.
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References
Hagedoorn, J.G., A process of seismic reflection interpretation, Geophysical Prospecting, v. 2, 85: 127 (1954).
Claerbout, J. F., Toward a unified theory of reflector mapping, Geophysics, v. 36, 467: 481 (1971).
Claerbout, J., “Fundamentals of geophysical data processing”, McGraw-Hill, New York, (1976).
French, W.S., Two-dimensional and three-dimensional migration of model-experiment reflection profiles, Geophysics, v. 39, 265: 277 (1974).
Schneider, W. A., Integral formulation for migration in two and three dimensions, Geophysics, v. 43, 49: 76 (1978).
Stolt, R. M., Migration by Fourier Transform, Geophysics, v. 43, 23: 48 (1978).
Cohen, J. K. and Bleistein, N., Velocity inversion procedure for acoustic waves, Geophysics, v. 44, 1077: 1085 (1979).
Berkhout, A. J.,“Seismic migration”, Elsevier, Amsterdam/New York, (1980).
Norton, S. G., Linzer, M., Ultrasonic reflectivity imaging in three dimensions: Exact inverse scattering solutions for plane, cylindrical, and spherical apertures, IEEE Trans. on Biomedical Engineering, v. BME-28, No. 2, 202: 220 (1981).
Miller, D. E., Integral transforms and the migration of multiple-offset borehole seismic profiles, SDR Research Note, December 1983.
Gelchinsky, B., Ray Asymptotic Migration (Basic Concepts), inExpanded Abstracts of 53rd SEG Meeting, Society of Exploration Geophysics, Las Vegas, 385: 387, (1983).
Carter, J.A., Fraser L.N., Accommodating lateral velocity changes in Kirchhoff migration by means of Fermat’s principle, Geophysics, v. 49, 46: 53, (1984).
Rose, J.H., Exterior reconstruction of a three dimensional scatterer, Wave Motion, 6, 149: 154, 1984
Beylkin, G., “Generalized Radon transform and its applications”, Ph.D. thesis, NYU, (1982).
Beylkin, G., The inversion problem and applications of the generalized Radon Transform, Comm. Pure Appl. Math., v. 37, 5, 579: 599, (1984).
Beylkin, G., Imaging of Discontinuities in the Inverse Scattering Problem by Inversion of a Causal Generalized Radon Transform, J. Math. Phys., 26, 99: 108 (1985).
Devaney, A.J., Geophysical Diffraction Tomography, IEEE Trans. on Geoscience and Remote Sensing, vol.GE-22, 1, (1984).
Miller, D., Oristagiio, M., Beylkin, G., A new formalism and old heuristic for seismic migration, in Expanded Abstracts of 54th SEG Meeting, Society of Exploration Geophysics, Atlanta, 704:707, (1984).
Beylkin, G., Reconstructing discontinuities in multidimensional inverse scattering problems: smooth errors versus small errrors, to appear, Special issue of Applied Opticson Industrial Applications of Computed Tomography and NMR Imaging, May 1985.
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© 1985 Plenum Press, New York
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Beylkin, G., Oristaglio, M., Miller, D. (1985). Spatial Resolution of Migration Algorithms. In: Berkhout, A.J., Ridder, J., van der Wal, L.F. (eds) Acoustical Imaging. Acoustical Imaging, vol 14. Springer, Boston, MA. https://doi.org/10.1007/978-1-4613-2523-9_15
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DOI: https://doi.org/10.1007/978-1-4613-2523-9_15
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