Dispersive characteristics of the first three Rayleigh modes for a single surface layer

abstract The dispersive characteristics of a single elastic layer overlying an elastic half-space are examined in detail for the fundamental and the first and second higher modes of Rayleigh waves. Phase velocity, group velocity, and the ratio of horizontal to vertical surface displacement are computed as functions of dimensionless quantities proportional to period and wave number. The significant range for the independent variable, B 1 T/H , proves to be largely independent of the parameters of the structure. The range is 1 to 20 for the fundamental, 0.3 to cutoff for the first higher mode, and 0.2 to cutoff for the second higher mode. The most important parameter of the structure for Rayleigh wave dispersion is the shear velocity ratio. Variations in the Poisson9s ratio in the surface layer and the density contrast may produce substantial effects. Poisson9s ratio in the half-space is of least significance. The dependence on model parameters of the long-period cutoff for the higher modes is determined. Specific results are given for the following geophysical examples: continental crust, continental ice cap, sedimentary basin, alluvial overburden, and laboratory seismic models.

[1]  R. L. Mills,et al.  ATTENUATION OF SHEAR AND COMPRESSIONAL WAVES IN PIERRE SHALE , 1958 .

[2]  F. Press,et al.  Crustal structure and surface-wave dispersion in Africa , 1956 .

[3]  W. M. Ewing,et al.  Elastic Waves in Layered Media , 2015 .

[4]  S. Crampin.  Higher modes of seismic surface waves: Phase velocities across Scandinavia , 1964 .

[5]  J. Dorman.  NUMERICAL SOLUTIONS FOR LOVE WAVE DISPERSION ON A HALF‐SPACE WITH DOUBLE SURFACE LAYER , 1959 .

[6]  K. Kanai,et al.  The M2 Seismic Waves , 1935 .

[7]  D. L. Anderson,et al.  Higher mode surface waves and their bearing on the structure of the earth's mantle , 1964 .

[8]  Eugene Usdin,et al.  Dispersive properties of stratified elastic and liquid media; a ray theory , 1953 .

[9]  W. Jardetzky,et al.  Rayleigh-wave coupling to atmospheric compression waves , 1952 .

[10]  M. Ewing,et al.  Normal modes of continental surface waves , 1958 .

[11]  M. Ewing,et al.  Higher modes of continental Rayleigh waves , 1957 .

[12]  M. B. Dobrin,et al.  Surface and near-surface waves in the Delaware Basin [Texas] , 1954 .

[13]  J. Oliver,et al.  The second shear mode of continental Rayleigh waves , 1959 .

[14]  D. L. Anderson,et al.  Surface waves on a spherical Earth: 1. Upper mantle structure from Love waves , 1963 .

[15]  W. M. Ewing,et al.  TWO‐DIMENSIONAL MODEL SEISMOLOGY , 1954 .

[16]  K. Kanai,et al.  Discontinuity in Dispersion Curves of Rayleigh-Waves , 1935 .

[17]  M. B. Dobrin,et al.  Rayleigh waves from small explosions , 1951 .

[18]  Katsutada Sezawa,et al.  Dispersion of Elastic Waves propagated on the Surface of Stratified Bodies and on Curved Surfaces , 1927 .

[19]  S. Stauder,et al.  Effect of sedimentary thickness on short-period Rayleigh wave dispersion , 1965 .

[20]  B. Bolt,et al.  Phase and group velocities of Rayleigh waves in a spherical, gravitating Earth , 1961 .

[21]  J. Butcher,et al.  Rayleigh Wave Dispersion for a Single Layer on an Elastic Half Space , 1960 .