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Book Chapter

Seismic Traveltime Tomography

January 01, 2004


The word tomography comes from the Greek tomos, meaning to cut or slice. Thus, tomography is based on the premise that observed data sets are related to line integrals along lines or rays (i.e., projections) of some physical quantity. Tomography is used to reconstruct a model of the desired physical object so that the model's projected data agree approximately with measurements. A classic geophysical tomography problem is the reconstruction of a seismic velocity model of some portion of the earth in which the computed traveltimes agree with the observed traveltimes. In other words, traveltime tomography is a procedure that allows us to invert observed seismic traveltimes to estimate the subsurface velocity structure.

In geophysical tomography, the focus has been on the seismic-travel-time inversion problem. In seismic-traveltime tomography, we must consider two distinct cases. First is the reflection problem in which both source and receiver are at the surface of the earth. Second is the transmission problem in which the sources and/or receivers are in boreholes beneath the surface. Hybrid problems, such as VSP (vertical seismic profiling), in which both reflection and transmission are important, represent a straightforward generalization of these two cases. In any event, the essence of traveltime tomography is that the traveltime associated with a given ray is the integrated slowness along the ray. In the 2D case, one has 
where x and z are horizontal and vertical coordinates, dl is the differential distance along the ray, and s(x, z) = 1/v
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Geophysical Monograph Series

Fundamentals of Geophysical Interpretation

Laurence R. Lines
Laurence R. Lines
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Rachel T. Newrick
Rachel T. Newrick
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Society of Exploration Geophysicists
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Publication date:
January 01, 2004




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