Full Waveform Teleseismic Tomography: Theory and Applications

We have adapted a 2D spectral domain finite difference waveform tomography algorithm previously used in active source seismological imaging to the case of a plane wave propagating through a 2.5D viscoelastic medium in order to recover P and S wavespeed variations from body waves recorded at teleseismic distances. A transferable efficacy that permits recovery of arbitrarily heterogeneous models on moderately sized computers provides the primary motivation for choosing this algorithm. Synthetic waveforms can be generated either by specifying an analytic solution for a background plane wave in a 1D model and solving for the source distribution that would produce it, or by solving for a scattered field excited by a plane wave source and then adding the background wavefield to it. Because the former approach typically involves a concentration of sources at the free surface, the latter tends to be more stable numerically. We adapt a gradient approach to solve the inverse problem to maintain tractability; calculating the gradient does not require much more computational effort than does the forward problem. The waveform tomography algorithm can be applied in a straightforward way to perform receiver function migration and travel time inversion. We will discuss an application of this technique to imaging the crust and upper mantle beneath the Tien Shan range in central Asia.