Surface waves across 2-D structures: a method based on coupled local modes

SUMMARY The propagation of surface waves across 2-D structures is treated by a coupled-mode approach, expressing the wavefield as a laterally varying sum of local modes. The propagation direction may differ from normal incidence to the 2-D structure. The continuity conditions across tilted interfaces, including a fluid-solid interface, are fulfilled by transforming the part of the continuity condition related to the slope into a volume force. The lateral heterogeneity introduces energy transfers between modes, including transfers between Love and Rayleigh waves, leading to a lateral variation of the different mode-amplitude coefficients. This variation is described by a first-order coupling equation which is established using the orthogonality properties of the local modes. The coupling matrix is cast into a form where the role of the lateral derivatives of the elastic constants and density appears explicitly. This method can be applied to a wide variety of structures since no restriction has to be put on the rate or the extent of the lateral variation in the model.

[1]  B. Kennett,et al.  On the use of truncated modal expansions in laterally varying media , 1987 .

[2]  B. Romanowicz.  Multiplet-multiplet coupling due to lateral heterogeneity: asymptotic effects on the amplitude and frequency of the Earth's normal modes , 1987 .

[3]  R. Odom.  A coupled mode examination of irregular waveguides including the continuum spectrum , 1986 .

[4]  B. Bolt,et al.  Love mode dispersion across subduction zones by finite element modelling , 1986 .

[5]  M. Hall.  The effects of variations in sound speed on coupling coefficients between acoustic normal modes in shallow water over a sloping bottom , 1986 .

[6]  B. Kennett,et al.  Mapping of crustal heterogeneity in the North Sea basin via the propagation of Lg-waves , 1985 .

[7]  S. Gregersen.  Lg-wave propagation and crustal structure differences near Denmark and the North Sea , 1984 .

[8]  B. Kennett.  Guided wave propagation in laterally varying media — I. Theoretical development , 1984 .

[9]  B. Kennett,et al.  Guided wave propagation in laterally varying media — II. Lg-waves in north-western Europe , 1984 .

[10]  B. Kennett,et al.  Seismic Wave Propagation in Stratified Media , 1983 .

[11]  S. Gregersen.  Seismicity and observations of Lg wave attenuation in Greenland , 1982 .

[12]  K. E. Hawker,et al.  Consistent coupled mode theory of sound propagation for a class of nonseparable problems , 1981 .

[13]  S. Rutherford.  An examination of multipath processes in a range dependent environment within the context of adiabatic mode theory , 1979 .

[14]  P. Molnar,et al.  Propagation of Lg and lateral variations in crustal structure in Asia , 1977 .

[15]  P. Malischewsky.  Surface waves in media having lateral inhomogeneities , 1976 .

[16]  S. Gregersen.  Surface waves in isotropic, laterally inhomogeneous media , 1976 .

[17]  B. Isacks,et al.  Conversion of Sn to Lg at a continental margin , 1975, Bulletin of the Seismological Society of America.

[18]  S. Gregersen,et al.  Amplitudes of horizontally refracted Love waves , 1974, Bulletin of the Seismological Society of America.

[19]  Lawrence A. Drake,et al.  Love and Rayleigh waves in nonhorizontally layered media , 1972 .

[20]  B. Kennett.  Seismic Waves in Laterally Inhomogeneous Media , 1972 .

[21]  Stuart Crampin,et al.  The Dispersion of Surface Waves in Multilayered Anisotropic Media , 1970 .

[22]  D. Milder.  Ray and Wave Invariants for SOFAR Channel Propagation , 1969 .

[23]  A. McGarr,et al.  Transmission and reflection of Rayleigh waves at vertical boundaries , 1967 .

[24]  L. Knopoff,et al.  Phase velocity of surface waves in the transition zone of continental margins: 1. Love waves , 1967 .

[25]  Leon Knopoff,et al.  Body Force Equivalents for Seismic Dislocations , 1964 .

[26]  I. Herrera.  On a method to obtain a Green's function for a multi-layered half space , 1964 .

[27]  Valérie Maupin.  Etude des caracteristiques des ondes de surface en milieu anisotrope : application a l'analyse d'anomalies de polarisation a la station de port-aux-francais , 1987 .

[28]  L. Felsen,et al.  Coupled mode theory of intrinsic modes in a wedge , 1986 .

[29]  E. N. Its,et al.  Propagation of surface waves in a half-space with vertical, inclined or curved interfaces , 1985 .

[30]  A. Pierce.  Extension of the Method of Normal Modes to Sound Propagation in an Almost‐Stratified Medium , 1965 .