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Dysorvequation method (which 1$ used in quantum field theory) have been analyzed (107).

The existence of a perlodic progressive wave solution to the nonlinear boundary value problem for Ray-leigh surface waves of finite amplitudę has been demonstrated using an extenslon of the method of strained co ord i na t es [108). The Cauchy problem for a system of first-order nonlinear ordinary dlf-ferentlal equatlons descrlblng the propagatlon of rays in a nonhomogeneous medium has been considered [1091. Nonlinear modę coupling between two co-directional quasi-harmonic Rayleigh surface waves on an isotropic solid has been analyzed [110] using a method of multiple scaies. A solution has been obtained for a nonlinear differential equation that describes an initlally sinusoidal flnite-amplitude elastic wave propagating in a solid; the solution eon* tains a static displacement term in additlon to the harmonie terms [111). An experimental study of the eiastic-wave static displacement in a solid was also considered.

HEAD WAYES

When a half-space z > 0 Is subjected to a point load or source of disturbance, energy will reach the interior in two ways: by flux along rays emanatlng dlrectly from the point of excitation and by paths consisting of a linę segment in the free surface and radlatlon into the interior from eech point of such segments. The most significant secondary radiation from the surface is due to the passage of the fastest wave front over the surface. The associated stress vector on the piane z - 0 is. in generał, nonzero. The stress-free condłtlon on z • 0 will requłre genera-tion of an equal and opposlte stress vector by dis-płacement components other than the polarlzation vector of the fastest wave front.

The displacement components resolved along the polarization vectors of slower waves propagate to the interior. Constructive lnterference of such secondary radiations gives rlse to loci of constant phase (wave fronts) known as head waves. The properties of such waves in anisotropic elastic media have been discussed (112-115). For a łayered structure sand-wiched by two half-spaces. the dynamie properties of head waves propagated along some Interface that Interferes with reflected waves or head waves along other interfaces have been irwestigated by calculatlng thelr theoretlcal selsmograms (116). The unlqueness of the solution has been proved for an irwerse klne-matlc problem for seismlc head waves [117); the waves were propagating in a medium with a curvi-linear boundary at constant yelocities according to a system of two oncomlng tlme curves with unknown yelocity in the upper layer.

OTHER FROBLEMS

The reflection and refraction of elastic waves at a piane interface between two (initlally stressed) solid media in contact [118) and of generał piane P and type - 1 S(SV) body waves incident on piane bound-aries for generał linear yiscoełastic solids [119) have been discussed. The effects of an inciined interface on the reflection and refraction of Rayleigh waves have been analyzed by the method of Green's func-tion (120). The reflection. refraction. and absorption of obliquely incident piane harmonie anti-plane strain (SH) waves at a frictional Interface between dis-similar semi-infinite elastic solids [121) have been studied, as have the reflection and transmission of P and SV waves at the Earth's core-mantle boundary (under initial stress) [1221 and of long sinusoidal tsunami waves (123). The pattern of amplitudes of a reflected-diffracted wave train has been found to depend on the dimensions of the fracture zonę 1124).

The diffraction of anti-plane sheer waves by a Grifflth crack or a rigid strip [125). and by an edge crack

(126)    have been investigated, as has the diffraction of Love waves by a stress-free crack of finite width

[127) . Diffraction of SH waves by a spherlcal strat)-fied medium [128) and normally incident SH waves by a rigid strip [ 129) have been discussed. The diffraction problem associated with the propagatlon of piane harr.ionic Love waves [130) and Iow frequency diffraction of a piane harmonie shear (SH) wave by an edge crack in a wedge of arbitrary vertex angle (131) have been considered. The diffraction and scattering of elastic waves by a smooth or slightly rough solid-liquid interface [132). with appllcation to the core-mantle boundary. and of SH waves by surface irregularities (133) have been studied.

The scattering of Rayleigh waves in 8n elastic quarter space [ 134), in a rectangular rough surface (135). at