In this chapter, we introduce the tomographic methods which are widely used to study three-dimensional (3-D) seismic velocity, attenuation and anisotropy structures of the Earth's interior. The fundamental mathematical equations of these methods are presented for a better understanding of the principles of seismic tomography.Keywords Seismic tomography · Model parameterization · Ray tracing · Inversion · Resolution · Damping parameter From seismological observations, such as P-and S-wave arrival times, amplitudes, and waveforms, basically three kinds of physical parameters can be determined to characterize the seismological structure of the Earth's interior. These parameters are seismic velocity, attenuation, and anisotropy. Applying tomographic methods to the seismological data, we can estimate the three-dimensional (3-D) distribution of these parameters, i.e., seismic velocity tomography, attenuation tomography, and anisotropy tomography. In this chapter, we introduce the general approaches to conduct the three kinds of tomographic inversions.In general, a study of seismic tomography includes the following operations: (1) Modeling the Earth's interior structure, i.e., model parameterization; (2) Forward modeling, such as ray tracing in travel-time tomography, earthquake relocation, and the construction of observation equations; (3) Inversion, i.e., solving the large system of observation equations; and (4) Resolution and error analysis, i.e., evaluating the resolution and uncertainty of the obtained tomographic image.
Seismic Velocity TomographySince the advent of seismology, P-and S-wave velocities (Vp, Vs) have been the primary physical parameters to characterize the Earth's structure because they are determined mainly from P-and S-wave arrival-time data which can be measured in high quality and great quantity by the routine processing of seismic networks deployed in many regions. Hence, earthquake arrival times have been the most