Fréchet kernels for finite-frequency traveltimes-I. Theory

Geophysical Journal International

Volumn 141, Issue 1, 2000, Pages 157-174

  Dahlen, F A ^a   Hung, S H ^a   Nolet, Guust ^a  

^a PRINCETON UNIVERSITY   (United States)

Author keywords

Body waves; Fr chet derivatives; Global seismology; Ray theory; Tomography, traveltime

Indexed keywords

RAY TRACING; SEISMIC TOMOGRAPHY; SEISMIC WAVE; TRAVEL TIME; WAVE PROPAGATION;

EID: 0034010082     PISSN: 0956540X     EISSN: None     Source Type: Journal    
DOI: 10.1046/j.1365-246X.2000.00070.x     Document Type: Article

References (25)

1. Brune, J.N., Nafe, J.E. & AIsop, L.E., 1961. The polar phase shift of surface waves on a sphere, Bull, seisin. Soc. Am., 51, 247-257.
2. Cerveny, V., 1985. The application of ray tracing to the numerical modeling of seismic wavefields in complex structures, in Seismic Shear Waves, Par, A: Theory, Handbook of Geophysical Exploration, Vol. 15A, pp. 1-124, ed. Dohr, G.P., Geophysical Press, London.
3. Cerveny, V. & Hron, F., 1980. The ray series method and dynamic ray tracing systems for 3-D inhomogeneous media, Bull, seism. Soc. Am., 70, 47-77.
4. Cerveny, V., Molotkov, I.A. & Psencik, 1977. Ray Method in Seismology, Univerzita Karlova, Praha.
5. Coates, R.T. & Chapman, C.H., 1990. Ray perturbation theory and the Born approximation, Geophys. J. Int., 100, 379-392.
6. Dahlen, F.A. & Tromp, J., 1998. Theoretical Global Seismology, Princeton University Press, Princeton.
7. Dziewonski, A.M., 1984. Mapping the lower mantle: determination of lateral heterogeneity in P velocity up to degree and order 6, J. geophys. Res., 89, 5929-5952.
8. Grand, S.P., 1994. Mantle shear structure beneath the Americas and surrounding oceans, J. geophys. Res., 99, 11591-11 621.
9. Hudson, J.A., 1977. Scattered waves in the coda of P, J. Geophys., 43, 359-374.
10. Hung, S.-H., Dahlen, F.A. & Nolet, G., 2000. Fréchet kernels for finite-frequency traveltimes-II. Examples, Geophys. J. Int., 141, 175-203 (this issue).
11. Inoue, H., Fuk? \Y., Tanabe, K. & Ogata, Y, 1990. Whole mantle P-wave travel time tomography, Phys. Earth planet. Inter., 59, 294-328.
12. Kravstov, Yu.A. & Orlov, Yu.I., 1990. Geometrical Optics of Inhomogeneous Media, Springer-Verlag, New York.
13. Kuo, B.-Y., Forsyth, D.W. & Wysession, M., 1987. Lateral heterogeneity and azimuthal anisotropy in the North Atlantic determined from SS-S differential traveltimes, J. geophys. Res., 92, 6421-6436.
14. Luo, Y. & Schuster, G.T., 1991. Wave-equation traveltime tomography, Geophysics, 56, 645-653.
15. Marquering, H., Dahlen, F.A. & Nolet, G., 1999. Three-dimensional sensitivity kernels for finite-frequency traveltimes: the bananadoughnut paradox, Geophys. J. Int., 137, 805-815.
16. Masters, G., Johnson, S., Laske, G. & Bolton, H., 1996. A shearvelocity model of the mantle, Phil. Trans. R. Soc. Land., A354, 1385-1411.
17. Pulliam, R.J., Vasco, D.W. & Johnson, L.R., 1993. Tomographie inversions for mantle P wave velocity structure based on the minimization of 12 and 11 norms of International Seismological Centre travel time residuals, J. geophys. Res., 98, 699-734.
18. Sheehan, A. & Solomon, S., 1991. Joint inversion of shear wave traveltime residuals and geoid and depth anomalies for long-wavelength variations in upper mantle temperature and composition along the Mid-Atlantic Ridge, J. geophys. Res., 96, 19981-20009.
19. Snieder, R. & Chapman, C.H., 1998. The reciprocity properties of geometrical spreading, Geophys. J. Int., 132, 89-95.
20. Su, W.-J. & Dziewonski, A.M., 1992. On the scale of mantle heterogeneity, Phys. Earth planet. Inter., 74, 29-54.
21. VanDecar, J. & Crosson, R., 1990. Determination of teleseismic relative phase arrival times using multi-channel cross-correlation and least squares, Bull, seism. Soc. Am.. 80, 150-159.
22. Van der Hilst, R.D., Widiyantoro, S. & Engdahl, E.R., 1997. Evidence for deep mantle circulation from global tomography, Nature, 386, 578-584.
23. Woodward, R.L. & Masters, G., 1991. Global upper mantle structure from long-period differential traveltimes, J. geophys. Res., 96, 6351-6377.
24. Wu, R.S. & Aki, K., 1985. Elastic wave scattering by a random medium and the small-scale inhomogeneities in the lithosphère, J. geophys. Res., 90, 10261-10273.
25. Zhao, L. & Dahlen, F.A., 1996. Mode-sum to ray-sum transformation in a spherical and aspherical Earth, Geophys. J. Int., 126, 389-412.