Parametrizing surface wave tomographic models with harmonic spherical splines

Abel Amirbekyan, Volker Michel¹, and Frederik J Simons²

1 Department of Mathematics
University of Kaiserslautern
67653 Kaiserslautern, Germany

2 Geosciences Department
Princeton University
Princeton NJ 08544, USA

Abstract

We present a mathematical framework and a new methodology for the parametrization of surface-wave phase-speed models based on travel-time data. Our method is neither purely local like block-based approaches, nor is it purely global like those based on spherical harmonic basis functions. Rather, it combines the well-known theory and practical utility of the spherical harmonics with the spatial localization properties of spline basis functions. We derive the theoretical foundations for the application of harmonic spherical splines to surface-wave tomography and summarize the results of numerous numerical tests illustrating the performance of a practical inversion scheme based upon them. Our presentation is based on the notion of reproducing-kernel Hilbert spaces, which may lend itself to the parametrization of fully-three dimensional tomographic Earth models including body waves as well.

Figures

1. Figure 01 The Abel-Poisson kernel: spatial and spectral behavior
   
2. Figure 02 Sources, receivers, and great-circle ray paths for the tomographic experiments in this study
   
3. Figure 03 Results of a checkerboard test with global path coverage
   
4. Figure 04 Results of a checkerboard test test with regional path coverage
   
5. Figure 05 Results of a hidden-object test with global path coverage
   
6. Figure 06 Comparison of the localizing and resolving power of spherical harmonics versus splines