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Abstract

Seismic diffraction tomography is useful for reconstructing images of subsurface inhomogeneities which fall into two categories. The first category includes inhomogeneities that are smaller in size than the seismic wavelength and have a large velocity contrast with respect to the surrounding medium. Imaging these inhomogeneities with the seismic ray tomography methods presented in Chapter 2 is generally out of the question. The second category includes inhomogeneities that are much larger in size than the seismic wavelength and have a very small velocity contrast with the surrounding medium. Although seismic ray tomography is valid for imaging these inhomogeneities, it works best when the velocity contrasts are large. Note that both categories of inhomogeneity are capable of producing measurable scattered wavefields of similar power. The large velocity contrast of the first category inhomogeneity offsets its small size while the large size of the second category inhomogeneity makes up for its small velocity contrast.

The outline for this chapter closely parallels that of Chapter 2. First, in Section 3.2 we review acoustic wave scattering theory and derive two independent linear relationships between data functions representing scattered energy and the model function M(r). The model function M(r) used in this chapter is a measure of the velocity perturbation caused by an inhomogeneity at vector position r from a constant background velocity. Second, using either of the linear relationships between a data function and the model function M(r), the generalized projection slice theorem is derived in Section 3.3 which serves as

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