Three‐dimensional determination of structure and velocity by seismic tomography

Abstract

A computerized seismic tomographic method was developed to obtain body‐wave velocities and three‐dimensional (3-D) structure of interfaces from reflection data simultaneously. The medium consists of layers with continuous arbitrary 3-D curved interfaces separating homogeneous material with different acoustic properties. The interface is defined by a polynomial surface. The elastic waves are assumed to be transmitted or reflected at curved interfaces in which the raypaths satisfy Snell's law. The ray tracing for each source‐receiver pair is determined by solving a system of nonlinear equations. This method of 3-D ray tracing is effective in computing many seismic rays, including converted phases and multiples. A damped least‐squares inversion scheme is formulated to reconstruct the interval velocity and 3-D structure of the interface by minimizing the difference between observed traveltimes and computed traveltimes. The results from a synthetic model indicate that the solutions converge quickly to the true model. The seismic tomographic method was applied to a Vibroseis seismic section obtained in 1984 on Vancouver Island as part of PROJECT LITHOPROBE. The method was found to be useful for imaging the 3-D subsurface of subducting plates by taking advantage of crooked lines in the nominally two‐dimensional seismic reflection survey.

Seismic Traveltime Tomography of the Crust and Lithosphere

“…Authors who have used DLS solutions to invert wide-angle traveltimes include Kanasewich & Chiu (1985), Chiu et al (1986), Farra & Madariaga (1988), White (1989), , , Zelt & Smith (1992), Lutter et al (1994), Kosloff et al (1996), Wang & Braile (1996), McCaughey & Singh (1997) and Zelt & Barton (1998). Similarly, DLS is also popular in local earthquake tomography (Aki & Lee, 1976;Thurber, 1983;Eberhart-Phillips, 1986;Graeber & Asch, 1999).…”

“…5d) is less common, mainly because methods for the inversion of 3-D layered structures are less wide spread. The ray tracing method of Gjøystdal et al (1984) parameterizes interfaces in terms of bicubic splines, and the reflection tomography method of Chiu et al (1986) describes interfaces using n th order polynomials (in practice, they use n ≤ 3). Like con-tinuous velocity variations, interfaces are also amenable to spectral parameterization.…”

“…Chiu et al (1986) use a bending method in the inversion of 3-D reflection traveltimes and Zhao et al (1997) use the pseudo-bending method in the inversion of refraction traveltimes for 2-D crustal structure. In local earthquake tomography, bending methods are probably most commonly used to find source-receiver paths and traveltimes (Eberhart-Phillips, 1990;Scott et al, 1994;Eberhart-Phillips & Reyners, 1997;Graeber & Asch, 1999).…”

“…Chiu et al (1986) developed and applied a scheme to vibroseis data collected on Vancouver Island. Their method assumes that subsurface structure can be adequately represented by constant velocity layers that separate interfaces described by n th -order polynomial surfaces.…”

Ultrasonic laboratory tests of geophysical tomographic reconstruction

“…Censor (1983) gives a good overview of the series expansion methods such as algebraic reconstruction technique (ART) and simultaneous iterative reconstruction technique (SIRT) and claims that the series expansion methods have a wider range of applicability to scanning geometries than the transform methods do. Most geophysical tomographic studies use series expansion methods (Dines and Lytle, 1979;McMechan, 1983;Kretzschmar et al, 1984;Menke, 1984;Bishop et al, 1985;Invansson, 1985;Peterson et al, 1985;Chiu et al, 1986;Cottin et al, 1986;Invansson, 1986;Gustavsson et al, 1986;Ramirez, 1986). The other kind of reconstruction algorithms, the transform methods, are widely used in commercial CT scanner for medical imaging.…”