Abstract
The paper discusses basic ideas and principles underlying methods, which have proved useful in the interpretation of diffraction and scattering phenomena by a smooth or slightly rough solid-liquid interface. Generally, the wave interaction may be formulated as an excitation problem; it involves (1) finding an equivalent dislocation or source distribution on the interface, and (2) evaluating the excited wave field. These steps are taken through perturbation theory and/or adopting the appropriate generalization of ray theory. In this context an explicit form of Green's function is also given. The methods have been applied to the core-mantle boundary, with a view toward the interpretation of recent data: (a) diffracted P and S waves around the core (in particular, their attenuation); (b) scattered short-period core phases (in particular, precursors to PKP and PKKP). Other types of wave interaction, and implications for models of the core-mantle boundary structure, are briefly mentioned.
Similar content being viewed by others
References
Adams, R. D. (1972),Multiple inner core reflections of a Novaya Zemlya explosion, Bull. seism. Soc. Am.62, 1063–1071.
Backus, G. andMulcahy, M. (1976),Moment tensors and other phenomenological descriptions of seismic sources — I. Continuous displacements, Geophys. J. R. astr. Soc.46, 341–361.
Ben-Menahem, A. andSingh, S. J. (1972), ‘Computation of models of elastic dislocations in the Earth’, inMethods in Computational Physics, Vol. 12, ed. by B. A. Bolt, pp. 299–375.
Bessonova, E. N., Fishman, V. M., Shnirman, M. G., Sitnikova, G. A. andJohnson, L. R. (1976),The tau method for inversion of travel times — II. Earthquake data, Geophys. J. R. astr. Soc.46, 87–108.
Bolt, B. A. andQamar, A. (1972),Observations of pseudo-aftershocks from underground nuclear explosions, Phys. Earth Planet. Int.5, 400–402.
Bremmer, H. (1949),Terrestrial Radio Waves, Elsevier Publishing Company, Amsterdam-New York.
Bremmer, H. (1960),On the theory of wave propagation through a concentrically stratified troposphere with a smooth profile, I. Discussion of the extended W.K.B. approximation, J. Res. natn. Bur. Stand.64D, 467–482.
Bremmer, H. (1962),Part II. Expansion of the rigorous solution, J. Res. natn. Bur. Stand.66D, 31–52.
Bremmer, H. (1976),A historical survey of the mathematical theories of radio-wave propagation, Ist. Naz. di Alta Mat., Symp. Math.18, 57–83.
Bullen, K. E. (1965),An Introduction to the Theory of Seismology, 3rd edn., Cambridge University Press.
Burridge, R. andKnopoff, L. (1964),Body force equivalents for seismic dislocations, Bull. seism. Soc. Am.54, 1875–1888.
Chang, A. C. andCleary, J. R. (1978),Precursors to PKKP, Bull. seism. Soc. Am.68, 1059–1079.
Chapman, C. H. (1973),The Earth flattening transformation in body wave theory, Geophys. J. R. astr. Soc.35, 55–70.
Chapman, C. H. (1978),A new method for computing theoretical seismograms, Geophys. J. R. astr. Soc.54, 481–518.
Chapman, C. H. andPhinney, R. R. (1972), ‘Diffracted seismic signals and their numerical solution’, inMethods in Computational Physics, Vol. 12, ed. by B. A. Bolt, pp. 165–230.
Chernov, L. A. (1960),Wave Propagation in a Random Medium, translated by R. A. Silverman, McGraw-Hill, New York.
Choy, G. L. (1977),Theoretical seismograms of core phases calculated by frequency-dependent full wave theory, and their interpretation, Geophys. J. R. astr. Soc.51, 275–312.
Cisternas, A. andJobert, G. (1977),Extension of matrix methods to structures of slightly irregular stratification, J. Geophys.43, 59–74.
Cormier, V. F. andRichards, P. G. (1976),Comments on ‘The damping of core waves’ by Anthony Qamar and Alfredo Eisenberg, J. Geophys. Res.81, 3066–3068.
Cormier, V. F. andRichards, P. G. (1977),Full wave theory applied to a discontinuous velocity increase: The inner core boundary, J. Geophys.43, 3–31.
Doornbos, D. J. (1974),Seismic wave scattering near caustics: Observations of PKKP precursors, Nature247, 352–353.
Doornbos, D. J. (1976),Characteristics of lower mantle inhomogeneities from scattered waves, Geophys. J. R. astr. Soc.44, 447–470.
Doornbos, D. J. (1978),On seismic-wave scattering by a rough core-mantle boundary, Geophys. J. R. astr. Soc.53, 643–662.
Doornbos, D. J. andMondt, J. C. (1979a),Attenuation of P and S waves diffracted around the core, Geophys. J. R. astr. Soc.57, 353–379.
Doornbos, D. J. andMondt, J. C. (1979b),P and S waves diffracted around the core and the velocity structure at the base of the mantle, Geophys. J. R. astr. Soc.57, 381–395.
Engdahl, E. R. (1968),Core phases and the Earth's core, Ph.D. Thesis, Saint Louis University.
Fuchs, K. (1971),The method of stationary phase applied to the reflection of spherical waves from transition zones with arbitrary depth-dependent elastic moduli and density, J. Geophys.37, 89–117.
Fuchs, K. andMüller, G. (1971),Computation of synthetic seismograms with the reflectivity method and comparison with observations, Geophys. J. R. astr. Soc.23, 417–433.
Fuchs, K. andSchulz, K. (1976),Tunneling of low-frequency waves through the subcrustal lithosphere, J. Geophys.42, 175–190.
Gilbert, F. andKnopoff, L. (1960),Seismic scattering from topographic irregularities, J. geophys. Res.65, 3437–3444.
Gilbert, F. andDziewonski, A. M. (1975),An application of normal mode theory to the retrieval of structural parameters and source mechanisms from seismic spectra, Phil. Trans. R. Soc. London, A.278, 187–269.
Haddon, R. A. W. (1972),Corrugations on the mantle core boundary or transition layers between inner and outer core? (abstract), Trans. Am. geophys. Un.53, 600.
Haddon, R. A. W. andCleary, J. R. (1974),Evidence for scattering of seismic PKP waves near the mantle-core boundary, Phys. Earth Planet. Int.8, 211–234.
Hill, D. P. (1972),An earth-flattening transformation for waves from a point source, Bull. seism. Soc. Am.62, 1195–1210.
Hudson, J. A. (1969),A quantitative evaluation of seismic signals at teleseismic distance — II. Body waves and surface waves from an extended source, Geophys. J. R. astr. Soc.18, 353–370.
Hudson, J. A. (1977),Scattered waves in the code of P, J. Geophys.43, 359–374.
Hudson, J. A. andKnopoff, L. (1967),Statistical properties of Rayleigh waves due to scattering by topography, Bull. seism. Soc. Am.57, 83–90.
Husebye, E. S., King, D. W. andHaddon, R. A. W. (1976),Precursors to PKIKP and seismic wave scattering near the mantle-core boundary, J. geophys. Res.81, 1870–1882.
Kennett, B. L. N. (1972a),Seismic wave scattering by obstacles on interfaces, Geophys. J. R. astr. Soc.28, 249–266.
Kennett, B. L. M. (1972b),The connection between elastodynamic representation theorems and propagator matrices, Bull. seism. Soc. Am.62, 973–983.
Kind, R. andMüller, G. (1977),The structure of the outer core from SKS amplitudes and travel times, Bull. seism. Soc. Am.67, 1541–1554.
Knopoff, L. andHudson, J. A. (1964),Scattering of elastic waves by small inhomogeneities, J. acoust. Soc. Am.36, 338–343.
Ludwig, D. (1970),Diffraction by a circular cavity, J. Math. Phys.11, 1617–1629.
Mondt, J. C. (1977a),SH waves: theory and observations for epicentral distances greater than 90 degrees, Phys. Earth Planet. Int.15, 46–59.
Mondt, J. C. (1977b),Full wave theory and the structure of the lower mantle, Ph.D. Thesis, University of Utrecht.
Mondt, J. C. andPootjes, H. J. (1980),A comparison of the reflectivity method and full wave theory, as applied to SH diffraction around the core, Pure Appl. Geophys,118, this issue.
Müller, G. (1973),Amplitude studies of core phases, J. geophys. Res.78, 3469–3490.
Müller, G. (1977),Earth-flattening transformation for body waves derived from geometric ray theory — Improvements, corrections and range of applicability, J. Geophys.42, 429–436.
Müller, G., Mula, A. H. andGregersen, S. (1977),Amplitudes of long-period PcP and the core-mantle boundary, Phys. Earth Planet. Int.14, 30–40.
Nussenzweig, H. M. (1965),High frequency scattering by an impenetrable sphere, Ann. Phys.34, 23–95.
Phinney, R. A. andAlexander, S. S. (1969),The effect of a velocity gradient at the base of the mantle on diffracted P waves in the shadow, J. geophys. Res.74, 4967–4971.
Richards, P. G. (1970),A contribution to the theory of high frequency elastic waves, with applications to the shadow boundary of the earth's core, Ph.D. Thesis, Cal. Inst. Techn.
Richards, P. G. (1973),Calculation of body waves for caustics and tunnelling in core phases, Geophys. J. R. astr. Soc.35, 243–264.
Richards, P. G. (1974),Weakly coupled potentials for high-frequency elastic waves in continuously stratified media, Bull. seism. Soc. Am.64, 1575–1588.
Richards, P. G. (1976),On the adequacy of plane-wave reflection/transmission coefficients in the analysis of seismic body waves, Bull. seism. Soc. Am.66, 701–717.
Scholte, J. G. J. (1956),On seismic waves in a spherical Earth, Koninkl. Ned. Meteor. Inst. Publ.65, 1–55.
Teng, T. andRichards, P. G. (1969),Diffracted P, SV and SH waves and their shadow boundary shifts, J. geophys. Res.74, 1537–1555.
Van den Berg, A. P., Cloetingh, S. A. P. L. andDoornbos, D. J. (1978),A comparison of PKP precursor data from several seismic arrays, J. Geophys.44, 499–510.
Wait, J. R. (1962),Electromagnetic Waves in Stratified Media, Pergamon Press.
Author information
Authors and Affiliations
Rights and permissions
About this article
Cite this article
Doornbos, D.J., Mondt, J.C. The interaction of elastic waves with a solid-liquid interface, with applications to the core-mantle boundary. PAGEOPH 118, 1293–1309 (1980). https://doi.org/10.1007/BF01593068
Received:
Issue Date:
DOI: https://doi.org/10.1007/BF01593068