Ambient seismic noise eikonal tomography for near-surface imaging at Valhall |

Appendix: Bicubic Spline reguarization

(12) |

To fit datapoints using forcing functions weighted by , we have the system

(13) |

Using the defined Green's function, we have the system

(14) |

or in matrix notation

(15) |

where is a kernel with Green's functions. The system is solved using an f90 library that performs LU decomposition (Press et al., 1986; Moreau, 2011). Green's function solutions for cubic splines in various dimensions have been derived and are summarized by Wessel (2009). This paper uses the two dimensional solution

(16) |

where .

Ambient seismic noise eikonal tomography for near-surface imaging at Valhall |

2011-05-24