Skip to main content Accessibility help

We use cookies to distinguish you from other users and to provide you with a better experience on our websites. Close this message to accept cookies or find out how to manage your cookie settings.

Close cookie message
×
Hostname: page-component-848d4c4894-v5vhk Total loading time: 0 Render date: 2024-06-25T22:40:11.369Z Has data issue: false hasContentIssue false

References

Published online by Cambridge University Press:  05 March 2015

Roel Snieder  and
Kasper van Wijk
Roel Snieder
Affiliation:
Colorado School of Mines
Kasper van Wijk
Affiliation:
University of Auckland
Get access
Type
Chapter
Information
A Guided Tour of Mathematical Methods for the Physical Sciences , pp. 547 - 554
Publisher: Cambridge University Press
Print publication year: 2015

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

Abramowitz, M., and Stegun, I.A. 1965. Handbook of mathematical functions with formulas, graph, and mathematical tables. Applied Mathematics Series, 55, 1046.
Aharonov, Y., and Bohm, D. 1959. Significance of electromagnetic potentials in the quantum theory. Physical Review, 115(3), 485.CrossRefGoogle Scholar
Aki, K., and Richards, P.G. 2002. Quantitative seismology. 4th edn. Sausalito, CA: Univ. Science Books.Google Scholar
Aldridge, D.F. 1994. Linearization of the eikonal equation. Geophysics, 59(10), 1631–1632.CrossRefGoogle Scholar
Alvarez, L.W., Alvarez, W., Asaro, F., and Michel, H.V. 1980. Extraterrestrial cause for the cretaceous-tertiary extinction. Science, 208(4448), 1095–1108.CrossRefGoogle ScholarPubMed
Arfken, G.B., and Weber, H.J. 2005. Mathematical methods for physicists. 4th edn. Amsterdam: Harcourt.Google Scholar
Ashby, N. 2002. Relativity and the global positioning system. Physics Today, 55(5), 41–47.CrossRefGoogle Scholar
Backus, M.N. 1959. Water reverberations—their nature and elimination. Geophysics, 24(2), 233–261.CrossRefGoogle Scholar
Bajec, I.L., and Heppner, F.H. 2009. Organized flight in birds. Animal Behaviour, 78(4), 777–789.CrossRefGoogle Scholar
Bakulin, A., and Calvert, R. 2006. The virtual source method: theory and case study. Geophysics, 71, SI139–SI150.CrossRefGoogle Scholar
Barish, B.C., and Weiss, R. 1999. LIGO and the detection of gravitational waves. Physics Today, 52(10), 44–50.CrossRefGoogle Scholar
Barton, G. 1989. Elements of Green's functions and propagation: potentials, diffusion, and waves. Oxford, UK: Oxford University Press.Google Scholar
Beissner, K. 1998. The acoustic radiation force in lossless fluids in Eulerian and Lagrangian coordinates. The Journal of the Acoustical Society of America, 103, 2321–2332.CrossRefGoogle Scholar
Bellman, R., Kalaba, R., and Wing, G.M. 1960. Invariant imbedding and mathematical physics. I. Particle processes. Journal of Mathematical Physics, 1, 280–308.CrossRefGoogle Scholar
Bender, C.M., and Orszag, S.A. 1999. Advanced mathematical methods for scientists and engineers I: asymptotic methods and perturbation theory. Vol. 1. New York, NY: Springer Verlag.CrossRefGoogle Scholar
Bennett, J.A. 1973. Variations of the ray path and phase path: a Hamiltonian formulation. Radio Science, 8(8–9), 737–744.CrossRefGoogle Scholar
Berry, M.V. 2013. Five momenta. European Journal of Physics, 34, 1337–1348.CrossRefGoogle Scholar
Berry, M.V., and Klein, S. 1997. Transparent mirrors: rays, waves and localization. European Journal of Physics, 18(3), 222–228.CrossRefGoogle Scholar
Berry, M.V., and Upstill, C. 1980. Catastrophe optics: morphologies of caustics and their diffraction patterns. Prog. Opt, 18, 257–346.Google Scholar
Blakeley, R.J. 1995. Potential theory in gravity and magnetics. Cambridge, UK: Cambridge Univ. Press.CrossRefGoogle Scholar
Bleistein, N., and Handelsman, R.A. 1975. Asymptotic expansions of integrals. Courier Dover Publications.Google Scholar
Boas, M.L. 2006. Mathematical methods in the physical sciences. Hoboken, NJ: John Wiley & Sons., Inc.Google Scholar
Brack, M., and Bhaduri, R.K. 1997. Semiclassical physics. Vol. 14. Reading, MA: Addison-Wesley Reading.Google Scholar
Brillouin, L., and Sommerfeld, A. 1960. Wave propagation and group velocity. Vol. 960. New York: Academic Press.Google Scholar
Buckingham, E. 1914. On physically similar systems; illustrations of the use of dimensional equations. Physical Review, 4(4), 345–376.CrossRefGoogle Scholar
Butkov, E. 1968. Mathematical physics. Addison-Wesley series in advanced physics. Reading, MA: Addison-Wesley Pub. Co.Google Scholar
Chopelas, A. 1996. Thermal expansivity of lower mantle phases MgO and MgSiO3perovskite at high pressure derived from vibrational spectroscopy. Physics of the Earth and Planetary Interiors, 98(1), 3–15.CrossRefGoogle Scholar
Choy, G.L., and Richards, P.G. 1975. Pulse distortion and Hilbert transformation in multiply reflected and refracted body waves. Bulletin of the Seismological Society of America, 65(1), 55–70.Google Scholar
Cipra, B. 2000. Misteaks… and how to find them before the teacher does: a calculus supplement. 3rd edn. Birkhäuser.Google Scholar
Claerbout, J. 1976. Fundamentals of seismic data processing. New York, NY: McGraw-Hill.Google Scholar
Claerbout, J.F. 1985. Imaging the earth's interior: Blackwell. Oxford, England.Google Scholar
Coveney, P.V., and Highfield, R. 1991. The arrow of time: a voyage through science to solve time's greatest mystery. New York: Fawcett Columbine, 1991. 1st American edn., 1.Google Scholar
Craig, G.M. 1997. Stop abusing Bernoulli! How airplanes really fly. Anderson, IN: Regenerative Press.Google Scholar
Curtis, A., Gerstoft, P., Sato, H., Snieder, R., and Wapenaar, K. 2006. Seismic interferometry – turning noise into signal. The Leading Edge, 25, 1082–1092.CrossRefGoogle Scholar
Dahlen, F.A. 1979. The spectra of unresolved split normal mode multiplets. Geophysical Journal International, 58(1), 1–33.CrossRefGoogle Scholar
Dahlen, F.A., and Henson, I.H. 1985. Asymptotic normal modes of a laterally heterogeneous Earth. Journal of Geophysical Research: Solid Earth (1978–2012), 90(B14), 12653–12681.CrossRefGoogle Scholar
Dahlen, F.A., and Tromp, J. 1998. Theoretical global seismology. Princeton, NJ: Princeton University Press.Google Scholar
Davies-Jones, R. 1984. Streamwise vorticity: the origin of updraft rotation in supercell storms. J. Atmosph. Sci., 41, 2991–3006.2.0.CO;2>CrossRefGoogle Scholar
de Broglie, L. 1952. La théorie des particules de spin 1/2: électrons de Dirac. Paris, France: Gauthier-Villars.Google Scholar
DeSanto, J.A. 1992. Scalar wave theory. Berlin, Germany: Springer.CrossRefGoogle Scholar
Dziewonski, A.M., and Woodhouse, J. H. 1983. Studies of the seismic source using normal-mode theory. Earthquakes: observations, theory and intepretation, edited by H., Kanamori and E., Boschi, North Holland, Amsterdam, 45–137.Google Scholar
Earnshaw, S. 1842. On the nature of the molecular forces which regulate the constitution of the luminiferous ether. Trans. Camb. Phil. Soc, 7, 97–112.Google Scholar
Edmonds, A.R. 1996. Angular momentum in quantum mechanics. Vol. 4. Princeton, NJ: Princeton University Press.Google Scholar
Farra, V., and Madariaga, R. 1987. Seismic waveform modeling in heterogeneous media by ray perturbation theory. Journal of Geophysical Research: Solid Earth (1978–2012), 92(B3), 2697–2712.CrossRefGoogle Scholar
Feynman, R.P. 1967. The character of physical law. Vol. 66. Cambridge, MA: MIT Press.Google Scholar
Feynman, R.P., Hibbs, A.R., and Styer, D.F. 1965. Quantum mechanics and path integrals. Vol. 2. New York: McGraw-Hill.Google Scholar
Fischbach, E., and Talmadge, C. 1992. Six years of the fifth force. Nature, 356, 207–215.CrossRefGoogle Scholar
Fletcher, C. 1996. The complete walker III. New York: Alfred A. Knopf.Google Scholar
Fokkema, J.T., and van den Berg, P.M. 1993. Seismic applications of acoustic reciprocity. Amsterdam, the Netherlands: Elsevier.CrossRefGoogle Scholar
Förste, Christoph, Schmidt, Roland, Stubenvoll, Richard, Flechtner, Frank, Meyer, Ulrich, König, Rolf, Neumayer, Hans, Biancale, Richard, Lemoine, Jean-Michel, Bruinsma, Sean, et al. 2008. The GeoForschungsZentrum Potsdam/Groupe de Recherche de Geodesie Spatiale satellite-only and combined gravity field models: EIGEN-GL04S1 and EIGEN-GL04C. Journal of Geodesy, 82(6), 331–346.CrossRefGoogle Scholar
Fowler, C.M.R. 2005. The solid Earth, an introduction to global geophyscis. Cambridge, UK: Cambridge Univ. Press.Google Scholar
French, S., Lekic, V., and Romanowicz, B. 2013. Waveform tomography reveals channeled flow at the base of the oceanic lithosphere. Science, 342, 227–230.CrossRefGoogle Scholar
Gabrielse, G. 2013. The standard model's greatest triumph. Physics Today, 66(12), 64–65.CrossRefGoogle Scholar
Garcia, Raphael F., Bruinsma, Sean, Lognonn, Philippe, Doornbos, Eelco, and Cachoux, Florian. 2013. GOCE: The first seismometer in orbit around the Earth. Geophysical Research Letters, 40(5), 1015–1020.CrossRefGoogle Scholar
Goldstein, H. 1980. Classical mechanics. Reading, MA: Addison-Wesley Pub. Co.Google Scholar
Gradshteyn, I.S., and Ryzhik, I.M. 1965. Table of integrals, series, and products. Prepared by Ju. V., Geronimus and M. Ju., Ceitlin. Translated from the Russian by Scripta Technica, Inc. Translation edited by Alan, Jeffrey. San Diego, CA: Academies Press.Google Scholar
Gubbins, D., and Snieder, R. 1991. Dispersion of P waves in subducted lithosphere: evidence for an eclogite layer. Journal of Geophysical Research: Solid Earth (1978–2012), 96(B4), 6321–6333.CrossRefGoogle Scholar
Guglielmi, A.V., and Pokhotelov, O.A. 1996. Geoelectromagnetic waves. Vol. 1. Bristol, UK: Institute of Physics Publishing.Google Scholar
Gutenberg, B., and Richter, C.F. 1956. Magnitude and energy of earthquakes. Annali di Geofisica, 9, 1–15.Google Scholar
Halbwachs, F. 1960. Théorie relativiste des fluides à spin. Vol. 10. Paris. Gauthier-Villars, Paris.Google Scholar
Hansen, P.C. 1992. Analysis of discrete ill-posed problems by means of the L-curve. SIAM Review, 34(4), 561–580.CrossRefGoogle Scholar
Hildebrand, A.R., Pilkington, M., Connors, M., Ortiz-Aleman, C., and Chavez, R.E. 1995. Size and structure of the Chicxulub crater revealed by horizontal gravity gradients and cenotes. Nature, 376(6539), 415–417.CrossRefGoogle Scholar
Holton, J.R., and Hakim, G.J. 2012. An introduction to dynamic meteorology. Waltham, MA: Academic Press.Google Scholar
Hutchings, Michael, Morgan, Frank, Ritor, Manuel, and Ros, Antonio. 2002. Proof of the Double Bubble Conjecture. Annals of Mathematics, 155(2), pp. 459–489.CrossRefGoogle Scholar
Ishimaru, A. 1978. Wave propagation and scattering in random media. Vol. 2. New York: Academic Press.Google Scholar
Iyer, H. M. 1993. Seismic tomography: theory and practice. London, UK: Chapman and Hall.Google Scholar
Jackson, J. D. 1998. Classical Electrodynamics. New York: John Wiley.Google Scholar
Jaynes, E.T. 2003. Probability theory, the logic of science. Cambridge, UK: Cambridge Univ. Press.CrossRefGoogle Scholar
Jeffreys, H. 1925. On Certain Approximate Solutions of Lineae Differential Equations of the Second Order. Proceedings of the London Mathematical Society, 2(1), 428–436.Google Scholar
Kanamori, H., Mori, J., Anderson, D.L., and Heaton, T.H. 1991. Seismic excitation by the space shuttle Columbia. Nature, 349, 781–782.CrossRefGoogle Scholar
Kanamori, H., Mori, J., Sturtevant, B., Anderson, D.L., and Heaton, T. 1992. Seismic excitation by space shuttles. Shock Waves, 2, 89–96.CrossRefGoogle Scholar
Kanamori, H.J., and Harkrider, D.G. 1994. Excitation of Atmospheric Oscillations by Volcanic Eruptions. Journal of Geophysical Research, 99(B11), 21947–21961.CrossRefGoogle Scholar
Kearey, P., Brooks, M., and Hill, I. 2002. An introduction to geophysical exploration. Oxford, UK: Blackwell.Google Scholar
Kermode, A.C., Barnard, R.H., and Philpott, D.R. 1996. Mechanics of flight. Harlow, UK: Longman.Google Scholar
Kline, S.J. 1986. Similitude and approximation theory. New York: Springer.CrossRefGoogle Scholar
Kravtsov, Yu. A. 1988. IV Rays and Caustics as Physical Objects. Progress in optics, 26, 227–348.Google Scholar
Kulkarny, V.A., and White, B.S. 1982. Focusing of waves in turbulent inhomogeneous media. Physics of Fluids, 25, 1770–1784.Google Scholar
Lambeck, K. 1988. Geophysical geodesy. Oxford: Oxford University Press.Google Scholar
Lanczos, C. 1970. The variational principles of mechanics. 4. New York, NY: Courier Dover Publications.Google Scholar
Larose, E., Margerin, L., Derode, A., van Tiggelen, B., Campillo, M., Shapiro, N., Paul, A., Stehly, L., and Tanter, M. 2006. Correlation of random wavefields: an interdisciplinary review. Geophysics, 71, SI11–SI21.CrossRefGoogle Scholar
Lauterborn, W., and Kurz, T. 2003. Coherent Optics: fundamentals and applications. Berlin, Germany: Springer Verlag.CrossRefGoogle Scholar
Lavenda, B.H. 1991. Statistical physics: A probabilistic approach. Wiley-Interscience.
Levenspiel, O. 2006. Atmospheric pressure at the time of dinosaurs. Chemical Industry and Chemical Engineering Quarterly, 12(2), 116–122.CrossRefGoogle Scholar
Lin, C.C., and Segel, L.A. 1974. Mathematics Applied to Deterministic Problems. New York, NY: SIAM.Google Scholar
Lin, F.C., Ritzwoller, M.H., and Snieder, R. 2009. Eikonal tomography: surface wave tomography by phase front tracking across a regional broad-band seismic array. Geophys. J. Int., 177, 1091–1110.CrossRefGoogle Scholar
Lister, G.S., and Williams, P.F. 1983. The partitioning of deformation in flowing rock masses. Tectonophysics, 92(1), 1–33.CrossRefGoogle Scholar
Lomnitz, C. 1994. Fundamentals of earthquake prediction. New York, NY: Wiley.Google Scholar
Love, S.G., and Brownlee, D.E. 1993. A direct measurement of the terrestrial mass accretion rate of cosmic dust. Science, 262(5133), 550–553.CrossRefGoogle ScholarPubMed
Madelung, E. 1927. Quantentheorie in hydrodynamischer Form. Zeitschrift für Physik A Hadrons and Nuclei, 40(3), 322–326.Google Scholar
Marchaj, C.A. 2000. Aero-hydrodynamics of sailing. 3rd edn. Easton, MD: Tiller Pub.Google Scholar
Marsden, J.E., and Tromba, A. 2003. Vector calculus. New York, NY: WH Freeman.Google Scholar
Merzbacher, E. 1961. Quantum mechanics. New York: John Wiley and Sons.Google Scholar
Meuel, T., Xiong, Y.L., Fisher, P., Bruneau, C.H., Bessafi, M., and Kellay, H. 2013. Intensity of vortices: from soap bubbles to hurricanes. Scientific Reports, 3, 3455.CrossRefGoogle ScholarPubMed
Middleton, G.V., and Wilcock, P.R. 1994. Mechanics in the Earth and environmental sciences. Cambridge, UK: Cambridge University Press.Google Scholar
Mikesell, D., and van Wijk, K. 2011. Seismic refraction interferometry with a semblance analysis on the crosscorrelation gathering. Geophysics, 76, SA77–SA82.CrossRefGoogle Scholar
Moler, C., and Van Loan, C. 1978. Nineteen dubious ways to compute the exponential of a matrix. SIAM Review, 20(4), 801–836.CrossRefGoogle Scholar
Morley, T. 1985. A simple proof that the world is three dimensional. SIAM Review, 27(1), 69–71.CrossRefGoogle Scholar
Mosegaard, K. 2011. Quest for consistency, symmetry, and simplicity – the legacy of Albert Tarantola. Geophysics, 76, W51–W61.CrossRefGoogle Scholar
Mosegaard, K., and Tarantola, A. 1995. Monte Carlo sampling of slutions to inverse problems. Journal Geophysical Research, 100, 12431–12447.CrossRefGoogle Scholar
Muirhead, H. 1973. The special theory of relativity. New York: Macmillan.CrossRefGoogle Scholar
Nayfeh, A.H. 2011. Introduction to perturbation techniques. New York, NY: Wiley.Google Scholar
Nolet, G. 1987. Seismic tomography: with applications in global seismology and exploration geophysics. Vol. 5. Dordrecht, the Netherlands: Kluwer.CrossRefGoogle Scholar
Ohanian, H.C., and Ruffini, R. 1976. Gravitation and spacetime. New York: Norton.Google Scholar
Olson, P. 1989. The encyclopedia of solid earth geophysics. Van Nostrand Reinholt. Chap. Mantle convection and plumes.
Özisik, M.N. 1973. Radiative transfer and interaction with conduction and convection. New York: John Wiley.Google Scholar
Paasschens, J.C.J. 1997. Solution of the time-dependent Boltzmann equation. Phys. Rev. E, 56, 1135–1141.CrossRefGoogle Scholar
Parker, R.L. 1994. Geophysical inverse theory. Princeton, NJ: Princeton University Press.Google Scholar
Parker, R.L., and Zumberge, M.A. 1989. An analysis of geophysical experiments to test Newton's law of gravity. Nature, 342, 29–32.CrossRefGoogle Scholar
Parsons, B., and Sclater, J.G. 1977. An analysis of the variation of ocean floor bathymetry and heat flow with age. Journal of Geophysical Research, 82(5), 803–827.CrossRefGoogle Scholar
Payne, R., and Webb, D. 1971. Orientation by means of long range acoustic signaling in baleen whales. Annals of the New York Academy of Sciences, 188(1), 110–141.CrossRefGoogle ScholarPubMed
Pedlosky, J. 1982. Geophysical fluid dynamics. Berlin, Germany: Springer-Verlag, 1.
Peixoto, J.P., and Oort, A.H. 1992. Physics of climate. Am. Inst. of Phys., New York.Google Scholar
Pissanetzky, S. 1984. Sparse matrix technology. London: Academic Press.Google Scholar
Popper, K.R. 1956. The arrow of time. Nature, 177, 538.CrossRefGoogle Scholar
Press, W.H., Flannery, B.P., Teukolsky, S.A., and Vetterling, W.T. 1992. Numerical Recipes in FORTRAN 77: Volume 1, Volume 1 of Fortran numerical recipes: the art of scientific computing. Vol. 1. Cambridge, UK: Cambridge University Press.Google Scholar
Price, H. 1996. Time's arrow & Archimedes' point: New directions for the physics of time. Oxford, UK: Oxford University Press.Google Scholar
Rayleigh, L. 1917. On the reflection of light from a regularly stratified medium. Proceedings of the Royal Society of London. Series A, 93(655), 565–577.CrossRefGoogle Scholar
Rhie, J., and Romanowicz, B. 2004. Excitation of Earth's continuous free oscillations by atmospere-ocean-seafloor coupling. Nature, 431, 552–556.CrossRefGoogle ScholarPubMed
Rhie, J., and Romanowicz, B. 2006. A study of the realation between ocean storms and the Earth's hum. Geochemistry Geophysics and Geosystems, 7, Q10004.CrossRefGoogle Scholar
Riley, K., Hobson, M., and Bence, S. 2006. Mathematical methods for physics and engineering. Cambridge, UK: Cambridge University Press.CrossRefGoogle Scholar
Robinson, D.K., and Bevington, P.R. 1992. Sample programs for date reduction and error analysis for the physical sciences. New York, NY: McGraw-Hill.Google Scholar
Robinson, E.A., and Treitel, S. 1980. Geophysical signal analysis., Englewood Cliffs, NJ: Prentice-Hall.Google Scholar
Rossing, T.D., Moore, R.R., and Wheeler, P.A. 1990. The science of sound. Reading, MA: Addison-Wesley.Google Scholar
Sakurai, J.J. 1978. Advanced quantum mechanics. Reading, MA: Addison Wesley.Google Scholar
Sambridge, M., and Mosegaard, K. 2002. Monte Carlo methods in geophysical inverse problems. Rev. Geophys., 40(3), 3.1–3.29.CrossRefGoogle Scholar
Scales, J.A., and Snieder, R. 1997. Humility and nonlinearity. Geophysics, 62(5), 1355–1358.CrossRefGoogle Scholar
Schneider, W.A. 1978. Integral formulation for migration in two and three dimensions. Geophysics, 43(1), 49–76.CrossRefGoogle Scholar
Schulte, P., Alegret, L., Arenillas, I., Arz, J.A., Barton, P.J., Bown, P.R., Bralower, T.J., Christeson, G.L., Claeys, P., Cockell, C.S., Collins, G.S., Deutsch, A., Goldin, T.J., Goto, K., Grajales-Nishimura, J.M., Grieve, R.A.F., Gulick, S.P.S., Johnson, K.R., Kiessling, W., Koeberl, C., Kring, D.A., MacLeod, K.G., Matsui, T., Melosh, J., Montanari, A., Morgan, J.V., Neal, C.R., Nichols, D.J., Norris, R.D., Pierazzo, E., Ravizza, G., Rebolledo-Vieyra, M., Reimold, W.U., Robin, E., Salge, T., Speijer, R.P., Sweet, A.R., Urrutia-Fucugauchi, J., Vajda, V., Whalen, M.T., and Willumsen, P.S. 2010. The Chicxulub asteroid impact and mass extinction at the Cretaceous-Paleogene boundary. Science, 327(5970), 1214–1218.CrossRefGoogle ScholarPubMed
Schuster, G. 2009. Seismic interferometry. Cambridge, UK: Cambridge Univ. Press.CrossRefGoogle Scholar
Silverman, M.P. 1993. And yet it moves: strange systems and subtle questions in physics. Cambridge, UK: Cambridge University Press.Google Scholar
Smith, D.R. 1974. Variational methods in optimization. Englewood Cliffs, NJ: Prentice-Hall.Google Scholar
Snieder, R. 1986. 3-D linearized scattering of surface waves and a formalism for surface wave holography. Geophysical Journal International, 84(3), 581–605.CrossRefGoogle Scholar
Snieder, R. 1996. Surface wave inversions on a regional scale. Seismic modelling of Earth structure, Eds. E., Boschi, G., Ekstrom and A., Morelli, Bologna: Editrice Compositori, 149–181. Amsterdam, the Netherlands: North Holland.Google Scholar
Snieder, R. 2002. Time-reversal invariance and the relation between wave chaos and classical chaos. Pages 1–16 of: Imaging of complex media with acoustic and seismic waves. Berlin, Germany: Springer.Google Scholar
Snieder, R., and Aldridge, D.F. 1995. Perturbation theory for travel times. The Journal of the Acoustical Society of America, 98, 1565–1569.CrossRefGoogle Scholar
Snieder, R., and Larose, E. 2013. Extracting Earth's elastic wave response from noise measurements. Ann. Rev. Earth Planet. Sci., 41, 183–206.CrossRefGoogle Scholar
Snieder, R, and Nolet, G. 1987. Linearized scattering of surface waves on a spherical Earth. J. Geophys., 61, 55–63.Google Scholar
Snieder, R., and Sambridge, M. 1992. Ray perturbation theory for travel times and raypaths in 3-D heterogeneous media. Geophysical Journal International, 109, 294–322.CrossRefGoogle Scholar
Snieder, R., and Sambridge, M. 1993. The ambiguity in ray perturbation theory. Journal of Geophysical Research, 98, 22021–22034.CrossRefGoogle Scholar
Snieder, R., Wapenaar, K., and Wegler, U. 2007. Unified Green's function retrieval by cross-correlation; connection with energy principles. Phys.Rev.E, 75, 036103.CrossRefGoogle ScholarPubMed
Snieder, R.K. 1985. The origin of the 100,000 year cycle in a simple ice age model. Journal of Geophysical Research: Atmospheres, 90(D3), 5661–5664.CrossRefGoogle Scholar
Spetzler, J., and Snieder, R. 2001. The effect of small scale heterogeneity on the arrival time of waves. Geophysical Journal International, 145(3), 786–796.CrossRefGoogle Scholar
Stacey, F.D. 1992. Physics of the Earth. Brookfield, New York.Google Scholar
Stein, S., and Wysession, M. 2003. An introduction to seismology, earthquakes, and earth structure. Malden MA: Blackwell.Google Scholar
Stephenson, F.R., and Morrison, L.V. 1995. Long-term fluctuations in the Earth's rotation: 700 BC to AD 1990. Philosophical Transactions of the Royal Society of London. Series A: Physical and Engineering Sciences, 351(1695), 165–202.CrossRefGoogle Scholar
Strang, G. 2003. Introduction to linear algebra. SIAM.Google Scholar
Strichartz, R.S. 1994. A guide to distribution theory and Fourier transforms. Singapore: World Scientific.Google Scholar
Tabor, M. 1989. Chaos and integrability in nonlinear dynamics: an introduction. New York: Wiley.Google Scholar
Tarantola, A. 1987. Inverse problem theory. Amsterdam: Elsevier.Google Scholar
Tarantola, A., and Valette, B. 1982. Generalized nonlinear inverse problems solved using the least squares criterion. Reviews of Geophysics Space Physics, 20, 219–232.CrossRefGoogle Scholar
Tennekes, H. 2009. The simple science of flight: from insects to jumbo jets. Cambridge, MA: MIT Press.Google Scholar
Thompson, P.A., and Beavers, G.S. 1972. Compressible-fluid dynamics. Journal of Applied Mechanics, 39, 366.CrossRefGoogle Scholar
Tritton, D.J. 1988. Physical fluid dynamics. Oxford: Clarendon Press.Google Scholar
Tromp, J., and Snieder, R. 1989. The reflection and transmission of plane P-and S-waves by a continuously stratified band: a new approach using invariant imbedding. Geophysical Journal International, 96(3), 447–456.CrossRefGoogle Scholar
Turcotte, D.L., and Schubert, G. 2002. Geodynamics. Cambridge University Press.CrossRefGoogle Scholar
Vallina, A.U. 1999. Principles of seismology. Cambridge, UK: Cambridge University Press.Google Scholar
Van Dyke, M. 1964. Perturbation methods in fluid mechanics. Vol. 964. New York: Academic Press.Google Scholar
van Wijk, K., Scales, J.A., Navidi, W., and Tenorio, L. 2002. Data and model uncertainty estimation for linear inversion. Geophysical Journal International, 149, 625–632.CrossRefGoogle Scholar
van Wijk, K., Channel, T., Smith, M., and Viskupic, K. 2013. Teaching geophysics with a vertical-component seismometer. The Physics Teacher, 51(December), 552–554.CrossRefGoogle Scholar
Vogel, S. 1998. Exposing life's limits with dimensionless numbers. Physics Today, 51(11), 22–27.CrossRefGoogle Scholar
Wapenaar, K., Slob, E., and Snieder, R. 2006. Unified Green's function retrieval by cross-correlation. Phys. Rev. Lett., 97, 234301.CrossRefGoogle ScholarPubMed
Watson, T.H. 1972. A real frequency, complex wave-number analysis of leaking modes. Bulletin of the Seismological Society of America, 62(1), 369–384.Google Scholar
Webster, G.M. (ed). 1981. Deconvolution. Tulsa, OK: Society of Exploration Geophysicists.
Weisskopf, V.F. 1939. On the self-energy and the electric field of the electron. Physical Review, 56, 72–85.CrossRefGoogle Scholar
Wheeler, J.A., and Taylor, E.F. 1966. Spacetime physics. San Francisco, CA: WH Freeman.Google Scholar
Whitaker, S. 1968. Introduction to fluid mechanics. Englewood Cliffs, NJ: Prentice-Hall.Google Scholar
Whitham, G.B. 2011. Linear and nonlinear waves. Pure and applied mathematics. Wiley.Google Scholar
Wigner, E.P. 1960. The unreasonable effectiveness of mathematics in the natural sciences. Communications on Pure and Applied Mathematics, 13(1), 1–14.Google Scholar
Wigner, E.P. 1972. The place of consciousness in modern physics. Pages 132–141 of: Muses, C. and Young, A.M. (eds.), Consciousness and reality. New York: Outerbridge and Lazard.Google Scholar
Wu, R., and Aki, K. 1985. Scattering characteristics of elastic waves by an elastic heterogeneity. Geophysics, 50(4), 582–595.CrossRefGoogle Scholar
Yilmaz, Ö. 2001. Seismic data analysis: processing, inversion, and interpretation of seismic data. 10. Tulsa, OK: Society of Exploration Geophysicists.CrossRefGoogle Scholar
Yoder, C.F., Williams, J.G., Dickey, J.O., Schutz, B.E., Eanes, R.J., and Tapley, B.D. 1983. Secular variation of Earth's gravitational harmonic J2 coefficient from LAGEOS and nontidal acceleration of Earth rotation. Nature, 303, 757–762.CrossRefGoogle Scholar
Zee, A. 2005. Quantum field theory in a nutshell. Universities Press.Google Scholar
Ziolkowski, A. 1991. Why don't we measure seismic signatures?Geophysics, 56, 190–201.CrossRefGoogle Scholar
Zumberge, M.A., Ridgway, J.R., and Hildebrand, J.A. 1997. A towed marine gravity meter for near-bottom surveys. Geophysics, 62, 1386–1393.CrossRefGoogle Scholar

Save book to Kindle

To save this book to your Kindle, first ensure coreplatform@cambridge.org is added to your Approved Personal Document E-mail List under your Personal Document Settings on the Manage Your Content and Devices page of your Amazon account. Then enter the ‘name’ part of your Kindle email address below. Find out more about saving to your Kindle.

Note you can select to save to either the @free.kindle.com or @kindle.com variations. ‘@free.kindle.com’ emails are free but can only be saved to your device when it is connected to wi-fi. ‘@kindle.com’ emails can be delivered even when you are not connected to wi-fi, but note that service fees apply.

Find out more about the Kindle Personal Document Service.

  • References
  • Roel Snieder, Colorado School of Mines, Kasper van Wijk, University of Auckland
  • Book: A Guided Tour of Mathematical Methods for the Physical Sciences
  • Online publication: 05 March 2015
  • Chapter DOI: https://doi.org/10.1017/CBO9781139013543.029
Available formats
×

Save book to Dropbox

To save content items to your account, please confirm that you agree to abide by our usage policies. If this is the first time you use this feature, you will be asked to authorise Cambridge Core to connect with your account. Find out more about saving content to Dropbox.

  • References
  • Roel Snieder, Colorado School of Mines, Kasper van Wijk, University of Auckland
  • Book: A Guided Tour of Mathematical Methods for the Physical Sciences
  • Online publication: 05 March 2015
  • Chapter DOI: https://doi.org/10.1017/CBO9781139013543.029
Available formats
×

Save book to Google Drive

To save content items to your account, please confirm that you agree to abide by our usage policies. If this is the first time you use this feature, you will be asked to authorise Cambridge Core to connect with your account. Find out more about saving content to Google Drive.

  • References
  • Roel Snieder, Colorado School of Mines, Kasper van Wijk, University of Auckland
  • Book: A Guided Tour of Mathematical Methods for the Physical Sciences
  • Online publication: 05 March 2015
  • Chapter DOI: https://doi.org/10.1017/CBO9781139013543.029
Available formats
×