# Seismic Traveltime Tomography

## Seismic Traveltime Tomography

Seismograms yield a lot of interesting information about the Earth's interior. For instance, every earthquake is connected to a shadow zone for the compressional waves (P waves). This means that there is a belt, which is defined by a range of angular distances to the epicentre, where no P waves can be observed. The reason is that the waves are refracted at the core-mantle boundary because they enter a zone with a material where the speed of wave propagation is much smaller. Moreover, apparently no shear waves travel through the outer core. For this reason, in the present model of the Earth, the outer core is believed to consist of a liquid.

Seismic traveltime tomography goes far beyond such an analysis of seismograms. Thousands of rays from different epicentres to different seismic stations are analyzed with respect to the traveltime, i.e. the time that a wave needed to travel from the epicentre to the seismic station. These data are used to compute the speed of the waves at different points inside the Earth's body or at the Earth's surface (depending on the analysis of body or surface waves). In cooperation with Frederik J. Simons at the University of Princeton, the Geomathematics Group has developed and applied spline methods for solving this problem.

References:

- A. Amirbekyan: The Application of Reproducing
Kernel Based Spline Approximation to Seismic
Surface and Body Wave Tomography: Theoretical
Aspects and Numerical Results, PhD thesis, Geomathematics Group, Department of Mathematics, University of Kaiserslautern. The thesis is
published on-line at http://kluedo.ub.uni-kl.de/volltexte/2007/2103/
- A. Amirbekyan, V. Michel: Splines on the three-dimensional ball and their application to seismic body wave tomography, Inverse Problems, 24 (2008) , doi:10.1088/0266-5611/24/1/015022.
- A. Amirbekyan, V. Michel, F.J. Simons: Parameterizing surface-wave tomographic models with harmonic spherical splines, Geophysical Journal International, 174 (2008), 617-628 .