Scattered Waves in the Coda of P
Article Sidebar
Published:
May 20, 1977
Keywords:
Elastic scattering theory,
Scattering in the Earth
Volumes
Vols. 1-18 (1924-1944), ISSN 0044-2801
Main Article Content
Abstract
This paper presents a survey of the development and use of first order elastic scattering theory in seismology. The various methods used to provide expressions for scattered waves from variations in structure are shown to lead to a single scattering formula. A ray theory approximation for the incident and scattered waves provides a simple formula from which the radiation patterns of different types of scatterer can be derived. As an illustration, the solution for a homogeneous 'average' structure is given in detail. The statistical properties of the signal in time are clearly related to those of the scatterers in space and, in particular, the correlation time of the signal is related to the correlation distance of the scatterers. The paper ends with a discussion of the possible use of first order (weak scattering) theory in cases when the scattered signals are large.
ARK: https://n2t.net/ark:/88439/y038723
Permalink: https://geophysicsjournal.com/article/88
Article Details
How to Cite
Hudson, J. (1977). Scattered Waves in the Coda of P. Journal of Geophysics, 43(1), 359-374. Retrieved from https://journal.geophysicsjournal.com/JofG/article/view/88
Section
References
Aki, K. (1969) Analysis of the seismic coda of local earthquakes as scattered waves. J. Geophys. Res. 74:615-631
Aki, K., Chouet, B.(1975) Origin of coda waves; attenuation and scattering effects. J. Geophys. Res. 80:3322-3342
Cleary, J.R., Haddon, R.A.W. (1972) Seismic wave scattering near the core-mantle boundary: A new interpretation of precursors to PKIKP. Nature 240:549-551
Cleary, J.R., King, D.W., Haddon, R.A.W. (1976) Seismic wave scattering in the earth's crust and upper mantle. Geophys. J. 43:861-872
Davies, D., Julian, B.R. (1972) A study of short period P wave signals from LONGSHOT. Geophys. J. 29:185-202
Doornbos, D.J., Vlaar, N.J. (1973) Regions of seismic wave scattering in the earth's mantle and precursors to PKP. Nature Phys. Sci. 243:58-61
Doornbos, D.J. (1974) Seismic wave scattering near caustics: observations of PKKP precursors. Nature 247:352-353
Doornbos, D.J. (1976) Characteristics of lower mantle inhomogeneities from scattered waves. Geophys. J. 44:447-470
Douglas, A., Marshall, P.D., Gibbs, P.G., Young, J.B., Blarney, C. (1973) P signal complexity reexamined. Geophys.J. 33:195-221
Dunkin, J.W. (1969) Scattering of transient, spherical P waves by a randomly inhomogeneous half-space. Geophysics 34:357-382
Gilbert, J.F., Knopoff, L. (1960) Seismic scattering from topographic irregularities, J. Geophys. Res. 65:3437-3444
Greenfield, R.J. (1971) Short-period P wave generation by Rayleigh wave scattering at Novaya Zemlya. J. Geophys. Res. 76:7988-8002
Haddon, R.A.W. (1972) Corrugations on the mantle-core boundary, or transition layers between inner and outer cores? Trans. Am. Geophys. Union 53 (Abstract only)
Haddon, R.A.W., Cleary, J.R. (1974) Evidence for scattering of seismic PKP waves near the mantle-core boundary. Phys. Earth Planet. Interiors 8:211-234
Haddon, R.A.W., Husebye, E.S., King, D.W. (1977) Origins of precursors to P'P'. Phys. Earth Planet. Interiors (in press)
Herrera, I., Mal, A.K. (1965) A perturbation method for elastic wave propagation, II - small inhomogeneities. J. Geophys. Res. 70:871-883
Herrera, I. (1965) A perturbation method for elastic wave propagation, III - Thin inhomogeneities. Geofis. Int. 5:1-14
Hudson, J.A. (1967) Scattered surface waves from a surface obstacle. Geophys. J. 13:441-458
Hudson, J.A. (1968) The scattering of elastic waves by granular media. Qu. J. Mech. Appl. Math. 21:487-502
Hudson, J.A., Knopoff, 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., Haddon, R.A.W. (1976) Precursors to PK/KP and seismic wave scattering near the mantle-core boundary. J. Geophys. Res. 81:1870-1882
King, D.W., Cleary, J.R. (1974) A note on the interpretation of precursors to PKPPKP. Bull. Seism. Soc. Amer. 64:721-723
King, D.W., Haddon, R.A.W., Cleary, J.R. (1973) Evidence for seismic wave scattering in the 'D' layer. Earth Planet. Sci. Lett. 20:353-356
King, D.W., Haddon, R.A.W., Cleary, J.R. (1974) Array analysis of precursors to PK/KP in the distance range 128° to 142°. Geophys. J. 37:157-173
King, D.W., Haddon, R.A.W., Husebye, E.S. (1975) Precursors to PP. Phys. Earth Planet. Interiors 10:103-127
Knopoff, L., Hudson, J.A. (1964) Scattering of elastic waves by small inhomogeneities. J. Acoust. Soc. Am. 36:338-343
Knopoff, L., Hudson, J.A. (1967) Frequency dependence of scattered elastic waves. J. Acoust. Soc. Am. 42:18-20
Miles, J.W. (1960) Scattering of elastic waves by small inhomogeneities. Geophysics 25:642-648
Takano, K. (1971) Analysis of seismic coda waves of ultramicroearthquakes in the Matsushiro area - A comparison with Parkfield, California. J. Phys. Earth 19:209-216
Vinnik, L.P. (1974) Scattering of longitudinal waves in the Earth. Izv. Acad. Sci. USSR Phys. Solid E:718-728
Wesley, J.P. (1965) Diffusion of seismic energy in the near range. J. Geophy. Res. 70:5099-5106
Wright, C. (1975) The origin of short-period precursors to PKP. Bull. Seism. Soc. Am. 65:765-786
Aki, K., Chouet, B.(1975) Origin of coda waves; attenuation and scattering effects. J. Geophys. Res. 80:3322-3342
Cleary, J.R., Haddon, R.A.W. (1972) Seismic wave scattering near the core-mantle boundary: A new interpretation of precursors to PKIKP. Nature 240:549-551
Cleary, J.R., King, D.W., Haddon, R.A.W. (1976) Seismic wave scattering in the earth's crust and upper mantle. Geophys. J. 43:861-872
Davies, D., Julian, B.R. (1972) A study of short period P wave signals from LONGSHOT. Geophys. J. 29:185-202
Doornbos, D.J., Vlaar, N.J. (1973) Regions of seismic wave scattering in the earth's mantle and precursors to PKP. Nature Phys. Sci. 243:58-61
Doornbos, D.J. (1974) Seismic wave scattering near caustics: observations of PKKP precursors. Nature 247:352-353
Doornbos, D.J. (1976) Characteristics of lower mantle inhomogeneities from scattered waves. Geophys. J. 44:447-470
Douglas, A., Marshall, P.D., Gibbs, P.G., Young, J.B., Blarney, C. (1973) P signal complexity reexamined. Geophys.J. 33:195-221
Dunkin, J.W. (1969) Scattering of transient, spherical P waves by a randomly inhomogeneous half-space. Geophysics 34:357-382
Gilbert, J.F., Knopoff, L. (1960) Seismic scattering from topographic irregularities, J. Geophys. Res. 65:3437-3444
Greenfield, R.J. (1971) Short-period P wave generation by Rayleigh wave scattering at Novaya Zemlya. J. Geophys. Res. 76:7988-8002
Haddon, R.A.W. (1972) Corrugations on the mantle-core boundary, or transition layers between inner and outer cores? Trans. Am. Geophys. Union 53 (Abstract only)
Haddon, R.A.W., Cleary, J.R. (1974) Evidence for scattering of seismic PKP waves near the mantle-core boundary. Phys. Earth Planet. Interiors 8:211-234
Haddon, R.A.W., Husebye, E.S., King, D.W. (1977) Origins of precursors to P'P'. Phys. Earth Planet. Interiors (in press)
Herrera, I., Mal, A.K. (1965) A perturbation method for elastic wave propagation, II - small inhomogeneities. J. Geophys. Res. 70:871-883
Herrera, I. (1965) A perturbation method for elastic wave propagation, III - Thin inhomogeneities. Geofis. Int. 5:1-14
Hudson, J.A. (1967) Scattered surface waves from a surface obstacle. Geophys. J. 13:441-458
Hudson, J.A. (1968) The scattering of elastic waves by granular media. Qu. J. Mech. Appl. Math. 21:487-502
Hudson, J.A., Knopoff, 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., Haddon, R.A.W. (1976) Precursors to PK/KP and seismic wave scattering near the mantle-core boundary. J. Geophys. Res. 81:1870-1882
King, D.W., Cleary, J.R. (1974) A note on the interpretation of precursors to PKPPKP. Bull. Seism. Soc. Amer. 64:721-723
King, D.W., Haddon, R.A.W., Cleary, J.R. (1973) Evidence for seismic wave scattering in the 'D' layer. Earth Planet. Sci. Lett. 20:353-356
King, D.W., Haddon, R.A.W., Cleary, J.R. (1974) Array analysis of precursors to PK/KP in the distance range 128° to 142°. Geophys. J. 37:157-173
King, D.W., Haddon, R.A.W., Husebye, E.S. (1975) Precursors to PP. Phys. Earth Planet. Interiors 10:103-127
Knopoff, L., Hudson, J.A. (1964) Scattering of elastic waves by small inhomogeneities. J. Acoust. Soc. Am. 36:338-343
Knopoff, L., Hudson, J.A. (1967) Frequency dependence of scattered elastic waves. J. Acoust. Soc. Am. 42:18-20
Miles, J.W. (1960) Scattering of elastic waves by small inhomogeneities. Geophysics 25:642-648
Takano, K. (1971) Analysis of seismic coda waves of ultramicroearthquakes in the Matsushiro area - A comparison with Parkfield, California. J. Phys. Earth 19:209-216
Vinnik, L.P. (1974) Scattering of longitudinal waves in the Earth. Izv. Acad. Sci. USSR Phys. Solid E:718-728
Wesley, J.P. (1965) Diffusion of seismic energy in the near range. J. Geophy. Res. 70:5099-5106
Wright, C. (1975) The origin of short-period precursors to PKP. Bull. Seism. Soc. Am. 65:765-786