Time-dependent Cauchy-Navier splines and their application to seismic wave front propagation

ZAMM Zeitschrift fur Angewandte Mathematik und Mechanik

Volumn 88, Issue 3, 2008, Pages 155-178

  Kanunann, Paula ^a   Michel, Volker ^a  

^a University of Koblenz Landau   (Germany)

Author keywords

Cauchy Navier equation; Elasticity; Reproducing kernel; Seismic wave; Sphere; Spline; Time dependence

Indexed keywords

EID: 41349118528     PISSN: 00442267     EISSN: 15214001     Source Type: Journal    
DOI: 10.1002/zamm.200610362     Document Type: Article

References (32)

1. N. Aronszajn, Trans. Amer. Math. Soc. 68, 337-404 (1950).
2. A. Ben-Menahem and S.J. Singh, Seismic Waves and Sources (Springer, New York, Heidelberg, Berlin, 1981).
3. V. Bolotnikov and L. Rodman, Houston J. Math. 30, 559-576 (2004).
4. J. M. Brudowsky, Über die elementare Darstellung von Cauchy-Navierschen Splines (Diploma Thesis, Geomathematics Group, Department of Mathematics, University of Kaiserslautern, 1992).
5. J. Dalkolmo, Synthetische Seismogramme für eine sphärisch symmetrische, nichtrotierende Erde durch direkte Berechnung der Greenschen Funktion (Diploma Thesis, Institut für Geophysik, Universität Stuttgart, 1993).
6. P. Davis, Interpolation and Approximation (Dover Publications Inc., New York, 1975).
7. H. Engl, M. Hanke, and A. Neubauer, Regularization of Inverse Problems (Kluwer Academic Publishers, Dordrecht, Boston, London, 1996).
8. M. Fengler, D. Michel, and V. Michel, ZAMM 86, 856-873 (2006).
9. W. Freeden, Manuscr. Geod. 6, 193-244 (1981).
10. W. Freeden, Math. Methods Appl. Sci. 3, 551-575 (1981).
11. W. Freeden, Metaharmonic Splines for Solving the Exterior Dirichlet Problem for the Helmholtz Equation, in: Topics in Multivariate Approximation, edited by F. Utreras, C. Chui, and L. Schumaker (Academic Press, Boston, 1987), pp. 99-110.
12. W. Freeden, Multiscale Modelling of Spaceborne Geodata (Teubner, Stuttgart, Leipzig, 1999).
13. W. Freeden, T. Gervens, and M. Schreiner, Constructive Approximation on the Sphere (With Applications to Geomathematics) (Oxford Science Publications, Clarendon, 1998).
14. W. Freeden and V. Michel, Multiscale Potential Theory (with Application to Geoscience) (Birkhäuser, Boston, 2004).
15. W. Freeden, M. Schreiner, and R. Franke, Surv. Math. Ind. 7, 29-85 (1997).
16. P. Kammann, Modelling Seismic Wave Propagation Using Time-Dependent Cauchy-Navier Splines (Diploma Thesis, Geomathematics Group, Department of Mathematics, University of Kaiserslautern, 2005).
17. R. Kress, Numerical Analysis (Springer, Berlin, Heidelberg, New York, 1998).
18. V. Michel, Revista Matemática Complutense 16, 519-554 (2003).
19. V. Michel and K. Wolf, Schriften zur Funktionalanalysis und Geomathematik 28, accepted for publication in: Geophysical Journal International, 2007 (2006).
20. C. Müller, Math. Ann. 124, 235-264 (1952).
21. C. Müller, Spherical Harmonics (Springer, Berlin, Heidelberg, New York, 1966).
22. R. Reuter, Über Integralformeln der Einheitssphäre und harmonische Splinefunktionen (Veröffentlichungen des Geodätischen Instituts, RWTH Aachen, Heft 33, 1982).
23. S. Saitoh, Kodai Math. J. 28, 519-554 (2005).
24. S. Saitoh, T. Matsuura, and M. Asaduzzaman, J. Anal. Appl. 1, 131-142 (2003).
25. T. Sato, Y. Murono, and T. Kawanishi, Proc. JSCE (Japan Society of Civil Engineers) 710, 225-234 (2002).
26. R. Schaback and H. Wendland, Approximation by Positive Definite Kernels, in: Advanced Problems in Constructive Approximation, edited by M. D. Buhmann and D. H. Mache (Birkhäuser Verlag, Basel, 2002), pp. 203-221.
27. R. Schaback and H. Wendland, Acta Numer. 15, 543-639 (2006).
28. H. Schwarz, Numerische Mathematik (B.G. Teubner, Stuttgart, 1997).
29. P. Spudich and D. Miller, Bull. Seismol. Soc. Am. 80(6A), 1504-1532 (1990).
30. M. Tücks, Navier-Splines und ihre Anwendung in der Deformationsanalyse (PhD Thesis, Geomathematics Group, Department of Mathematics, University of Kaiserslautern, Shaker, Aachen, 1996).
31. W. Walter, Einführung in die Theorie der Distributionen, 3rd edn (BI-Wissenschafts-Verlag, Mannheim, 1994).
32. K. Wolf, Numerical Aspects of Harmonie Spline-Wavelets for the Satellite Gravimetry Problem (Diploma Thesis, Geomathematics Group, Department of Mathematics, University of Kaiserslautern, 2006).