Transmission and reflection of Rayleigh waves at vertical boundaries

McGarr, A.; Alsop, L. E.

doi:10.1029/jz072i008p02169

Cited by 86 publications

(19 citation statements)

References 6 publications

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“…(A2.1) is known to give the flux of energy carried by the mode (McGarr & Alsop 1967). Let us mention here how the normalization and the orthogonality of the radiation modes implied by eq.…”

Section: The O R T H O G O N a L I T Y R E L A T I O Nmentioning

confidence: 99%

The radiation modes of a vertically varying half-space: a new representation of the complete Green's function in terms of modes

Maupin

1996

Geophysical Journal International

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We prove that the complete Green's function for an isotropic vertically varying halfspace can be written in a dyadic form as a sum on the usual normal modes plus an integral over radiation modes. The radiation modes form the basis on which to represent the body waves, which are not trapped in the structure. The expressions f o r their eigenfunctions, the so-called improper eigenfunctions, are found for both the SH and the P-SV wave operators. We prove that they are orthogonal t o each other and to the normal-mode eigenfunctions. In a numerical example, we present improper eigenfunctions, and compare complete wavefield seismograms synthesized by the mode method and by the discrete wavenumber integration method.

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“…(A2.1) is known to give the flux of energy carried by the mode (McGarr & Alsop 1967). Let us mention here how the normalization and the orthogonality of the radiation modes implied by eq.…”

Section: The O R T H O G O N a L I T Y R E L A T I O Nmentioning

confidence: 99%

The radiation modes of a vertically varying half-space: a new representation of the complete Green's function in terms of modes

Maupin

1996

Geophysical Journal International

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“…Nolet et al 1989), but may be fully complex in the case of Rayleigh waves. Indications to the existence of Rayleigh modes with complex wavenumbers a r e given by Achenbach (1973) andMiklowitz (1966). In contrast t o modes with real wavenumbers, complex modes may be interpreted as being confined to a narrow sheet, required t o represent near-field displacements near a source o r a discontinuity.…”

Section: S Stunge and W Friederichmentioning

confidence: 99%

Guided wave propagation across sharp lateral heterogeneities: the complete wavefield at plane vertical discontinuities

Stange

Friederich

1992

Geophysical Journal International

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S U M M A R Y 3-D wave propagation in a waveguide composed of laterally homogeneous partitions separated by vertical interfaces is treated in an exact manner. In each laterally homogeneous subregion, the wavefield is represented by Love-and Rayleigh-type modes, combined in such a way that displacements and tractions are continuous at the vertical discontinuities. In order t o achieve exact continuity at the interfaces, near-field modes which exponentially decay in the propagation direction and are associated to fully complex wavenumbers, must be included in the modal representation. The expansion coefficients of the mode series are computed directly by exploiting orthogonality relations between modes of different type, order and propagation direction. Since the boundary conditions at the discontinuities are satisfied exactly, the resulting expansion of the wavefield is valid even on the interfaces themselves. Numerical results are presented for a single vertical discontinuity and a lamella.

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“…Alsop 1966;McGarr & Alsop 1967;Malischewsky 1976Malischewsky , 1987Meier et al 1997a). Alsop 1966;McGarr & Alsop 1967;Malischewsky 1976Malischewsky , 1987Meier et al 1997a).…”

Section: Introductionunclassified

Approximation of surface wave mode conversion at a passive continental margin by a mode-matching technique

Meier¹,

Malischewsky²

2000

Geophys. J. Int.

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Summary At a continental margin sharp structural changes cause strong lateral heterogeneityin S‐wave velocity, P‐wave velocity and density. Therefore, mode conversion of surface wave modes is expected. Passive continental margins may be modelled by vertical discontinuities. Mode conversion is then expressed in terms of reflection and transmission coefficients. Long‐period seismograms are calculated by mode summation over incident, reflected and transmitted modes. Reflection and transmission coefficients for surface waves are approximated by a mode‐matching technique that is adapted to a spherical earth model. An orthogonality relation for surface wave eigenfunctions on a spherical earth is given that allows one to simplify the linear system of equations for the determination of reflection and transmission coefficients. Transmission of fundamental Love and Rayleigh modes is strongly influenced by upper crustal heterogeneity for frequencies larger than 40 Hz for fundamental Love modes and larger than 60 Hz for fundamental Rayleigh modes. Mode conversion to neighbouring modes can be strong but mode conversion is not necessarily confined to neighbouring modes. Fundamental modes in particular can couple with more distant higher modes. In synthetic seismograms calculated for epicentral distances up to 40°, mode conversion between higher modes and fundamental modes results inshear‐coupled Rayleigh waves.

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Transmission and reflection of Rayleigh waves at vertical boundaries

Cited by 86 publications

References 6 publications

The radiation modes of a vertically varying half-space: a new representation of the complete Green's function in terms of modes

The radiation modes of a vertically varying half-space: a new representation of the complete Green's function in terms of modes

Guided wave propagation across sharp lateral heterogeneities: the complete wavefield at plane vertical discontinuities

Approximation of surface wave mode conversion at a passive continental margin by a mode-matching technique

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