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We begin the study of seismic tomography with image reconstruction methods based on ray theory. We assume that the source produces seismic wave energy with wavelengths much smaller than the size of the inhomogeneities encountered in the medium. Only when this assumption is obeyed can the propagation of the seismic wave energy be properly modeled by rays. Otherwise, the seismic diffraction tomography in Chapter 3 must be applied to solve the problem.

Two groups of image reconstruction methods exist for doing seismic ray tomography. The transform methods in Section 2.2 comprise the first group. Applications of transform methods have their roots in astronomical and medical imaging problems. They are very limiting as far as seismic imaging problems are concerned since straight raypath propagation and full-scan aperture are generally assumed. However, the transform methods make an excellent introduction to the principles of tomography because of their simplicity and serve as a bridge between applications of tomography in other fields with applications in seismology. Also, the development of seismic diffraction tomography has a close relationship with the transform methods. The series expansion methods in Section 2.3 comprise the second group of image reconstruction methods. Out of all the methods presented in this book the series expansion methods presently see the most use in seismic tomography. Therefore, a large part of Chapter 2 is spent addressing the series expansion methods.

Before proceeding further one should have a good grasp of the Fourier transform concepts to understand the material in Section 2.2.

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