Uniqueness of reflector depths and characterization of the slowness null space in linearized seismic reflection tomography

Journal Article · Wed Feb 01 04:00:00 EST 1995 · SIAM Journal of Applied Mathematics

DOI:https://doi.org/10.1137/S0036139992241169· OSTI ID:28005

Bube, K P ^[1]

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1. Univ. of Washington, Seattle, WA (United States). Dept. of Mathematics

Seismic reflection tomography attempts to match traveltimes obtained from surface seismic data with the corresponding traveltimes of rays traced through a model of the subsurface. Traveltimes along rays from surface shot locations down to reflecting interfaces and then back up to surface receiver locations are used; the goal is to determine both the position of the reflectors and the slowness field above the reflectors. Seismic reflection tomography is closely related to the inversion of a limited-angle Radon transform. The author formulates a continuum version of reflection tomography analogous to the discrete version appropriate for much of surface seismic data; the continuum version models a finite cable length with positive minimum offset, where the shot and receiver spacing are small compared with the cable length. It is proven that in a continuum formulation of reflection tomography with infinite horizontal extent, linearized about a constant background, the reflector depth perturbations are uniquely determined by the travel time perturbations. Moreover, the slowness perturbations in the null space of this linearized problem can be completely characterized: they are polynomials in the horizontal variable with coefficients which are functions of the depth variable satisfying integral orthogonality constraints.

• Sponsoring Organization: USDOE
• OSTI ID: 28005
• Journal Information: SIAM Journal of Applied Mathematics, Journal Name: SIAM Journal of Applied Mathematics Journal Issue: 1 Vol. 55; ISSN SMJMAP; ISSN 0036-1399
• Country of Publication: United States
• Language: English

Related Subjects

02 PETROLEUM
58 GEOSCIENCES
DATA ANALYSIS
EXPLORATION
GEOLOGIC MODELS
GEOPHYSICS
PETROLEUM DEPOSITS
REFLECTION
SEISMIC SURVEYS
SEISMIC WAVES
WAVE PROPAGATION