Seismic Tomography

The inversion of seismic travel-time data for radially varying media was initially investigated by Herglotz, Wiechert, and Bateman (the HWB method) in the early part of the 20th century [1]. Tomographic inversions for laterally varying media began in seismology starting in the 1970's. This included early work by Aki, Christoffersson, and Husebye who developed an inversion technique for estimating lithospheric structure beneath a seismic array from distant earthquakes (the ACH method) [2]. Also, Alekseev and others in Russia performed early inversions of refraction data for laterally varying upper mantle structure [3]. Aki and Lee [4] developed an inversion technique using travel-time data from local earthquakes. The first global tomographic images were then obtained using both body waves and surface waves [5,6]. In this chapter, we provide an overview of seismic tomography mostly applied to seismic body waves. We first describe travel-time tomography using different approaches including variable damping, iterative methods, irregular gridding, autoregressive extrapolation, nonlinear inversions , and multi-grid methods. We next provide an overview of applications of seismic tomography to cross-hole, refraction and reflection data, local earthquake data, and teleseismic data. An example is given for the inversion of data from the TomoVes experiment to image beneath the Mt. Vesuvius volcano. Finally,