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Seismic Body Waves in Inhomogeneous Anisotropic Media - NGEO063
Title: Seismické prostorové vlny v nehomogenních anizotropních prostředích
Guaranteed by: Department of Geophysics (32-KG)
Faculty: Faculty of Mathematics and Physics
Actual: from 2022
Semester: summer
E-Credits: 3
Hours per week, examination: summer s.:2/0, Ex [HT]
Capacity: unlimited
Min. number of students: unlimited
4EU+: no
Virtual mobility / capacity: no
State of the course: cancelled
Language: Czech
Teaching methods: full-time
Teaching methods: full-time
Guarantor: RNDr. Ivan Pšenčík, CSc.
Classification: Physics > Geophysics
Annotation -
Last update: T_KG (23.05.2008)
Ray method for seismic body wave propagation in inhomogeneous anisotropic media. Differences in wave propagation in anisotropic and isotropic media. Derivation of eikonal and transport equations. Their solutions, ray tracing, dynamic ray tracing. Seismic body wave propagation in weakly anisotropic media. Approximate formulae for the computation of phase and group velocities, polarization vectors, travel times, rays, reflection and transmission coefficients in weakly anisotropic media. Quasi-isotropic approach for seismic wave propagation in inhomogeneous weakly anisotropic media.
Aim of the course -
Last update: T_KG (23.05.2008)

The lecture provides the students with basic theory of elastic wave propagation in inhomogeneous anisotropic media.

Literature - Czech
Last update: T_KG (19.01.2003)
  • Bulant,P. & Klimeš,L., 2002. Numerical algorithm of the coupling ray theory in weakly anisotropic media, PAGEOPH, 159.
  • Červený,V., 2001. Seismic Ray Theory, Cambridge University Press, Cambridge.
  • Červený,V.,1972. Seismic rays and ray intensities in inhomogeneous anisotropic media, Geophys.J.R.astr.Soc., 29, 1-13.
  • Červený,V., Molotkov,I.A. & Pšenčík,I., 1977. Ray Method in Seismology, Charles University Press, Praha.
  • Chapman,C.H. & Pratt,R.G.,1992. Traveltime tomography in anisotropic media-I. Theory, Geophys.J.Int., 109, 1-19.
  • Coates,R.T. & Chapman,C.H., 1990. Quasi-shear wave coupling in weakly anisotropic 3-D media, Geophys.J.Int., 103, 301-320.
  • Farra,V., 2001. High order expressions of the phase velocity and polarization of qP and qS waves in anisotropic media. Geophys. J. Int., 147, 93-105.
  • Farra,V. & Le Bégat,S., 1995. Sensitivity of qP-wave travel times and polarization vectors to heterogeneity, anisotropy and interfaces. Geophys. J. Int., 121, 371-384.
  • Fedorov, F.I., 1968. Theory of elastic waves in crystals. Plenum Press, New York.
  • Jech,J. & Pšenčík,I., 1989. First-order perturbation method for anisotropic media. Geophys. J. Int., 99, 369-376.
  • Jech,J. & Pšenčík,I., 1992. Kinematic inversion for qP and qS waves in inhomogeneous anisotropic structures. Geophys.J.Int., 108, 604-612.
  • Kravtsov, Yu.A. & Orlov,Yu.I., 1980. Geometrical optics of inhomogeneous media, Nauka, Moscow (in Russian).
  • Pšenčík,I., 1998. Green's functions for inhomogeneous weakly anisotropic media. Geophys.J. Int., 135, 279-288.
  • Pšenčík,I. & Gajewski,D., 1998. Polarization, phase velocity and NMO velocity of qP waves in arbitrary weakly anisotropic media, Geophysics, 63, 1754-1766.
  • Rueger,A., 1997. P-wave reflection coefficients for transversely isotropic models with vertical and horizontal axis of symmetry. Geophysics, 62, 713-722.
  • Rueger,A., 1998. Variation of P-wave reflectivity with offset and azimuth in anisotropic media. Geophysics, 63, 935-947.
  • Thomsen,L., 1986. Weak elastic anisotropy. Geophysics, 51, 1954-1966.
  • Thomsen,L., 1993. Weak anisotropic reflections, in Castagna, J.P., & Backus,M.M., Eds., Offset-dependent reflectivity - theory and practice of AVO Analysis, SEG, Investigations in Geophysics, 8, 103-111.
  • Vavryčuk,V., & Pšenčík,I., 1998. PP wave reflection coefficients in weakly anisotropic media, Geophysics, 63, 2129-2141.
  • Zheng,X. & Pšenčík,I., 2002. Local determination of weak anisotropy parameters from the qP-wave slowness and particle motion measurements, PAGEOPH, 159.

Teaching methods -
Last update: T_KG (23.05.2008)

Lecture
Syllabus -
Last update: T_KG (23.05.2008)
Plane waves in homogeneous anisotropic media

  • Christoffel matrix, Christoffel equation
  • slowness surface, wave surface
  • acoustical axes, longitudinal and singular directions
  • energy considerations
  • differences of propagation in anisotropic and isotropic media
  • effect of an interface, Snell's law

Ray theory for anisotropic media

  • basic system of ray equations
  • eikonal equation and its solution
  • various types of ray tracing equations
  • initial-value and boundary-value ray tracing
  • transport equation and its solution
  • various types of dynamic ray tracing equations
  • reflection/transmission at an interface
  • directivity functions of simple point sources
  • examples

Perturbation formulae for weakly anisotropic media

  • nondegenerate and degenerate situations
  • weak anisotropy parameters
  • approximate formulae for phase velocities a polarization vectors
  • approximate formulae for R/T coefficients
  • higher-order perturbation formulae
  • radiation patterns for weakly anisotropic media
  • examples

Perturbation formulae for travel time, amplitude and attenuation

  • perturbation formulae for travel time
  • perturbation formulae for shear wave delay time
  • perturbation formulae for slight absorption
  • quasi-isotropic (QI) approximation
  • relation of the QI approximation to the coupling theory
  • examples

Applications

  • travel time tomography
  • inversion of R/T coefficients
  • inversion of the slowness and polarization vectors
  • examples

 
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