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The method of layer matrices is applied to solve the problem of the static deformation of a multilayered elastic half‐space by buried sources. Each layer of the multilayered medium is assumed to be homogeneous and isotropic, and the interfaces are assumed to be in welded contact. The point source ia represented as a discontinuity in the z‐dependent coefficients of the displacement and stress integrands at the source level. Source functions are obtained for the six elementary displacement dislocations. Explicit expressions for the surface displacements are calculated for a vertical strike‐slip and a vertical dip‐slip fault.

The propagation of plane waves in fibre-reinforced, anisotropic, elastic media is discussed. The expressions for the phase velocity of quasi-P (qP ) and quasi-SV (qSV ) waves propagating in a plane containing the reinforcement direction are obtained as functions of the angle between the propagation and reinforcement directions. Closed form expressions for the amplitude ratios for qP and qSV waves reflected at the free surface of a fibre-reinforced, anisotropic, homogeneous, elastic half-space are obtained. These expressions are used to study the variation of amplitude ratios with angle of incidence. It is found that reinforcement has a significant effect on the amplitude ratios and critical angle.

SUMMARY Closed‐form expressions for the displacements and stresses at an arbitrary point of a homogeneous, isotropic, perfectly elastic half‐space caused by a dip‐slip line source obtained earlier are integrated analytically to derive the elastic residual field due to a long dip‐slip fault of finite width. The results are valid for an arbitrary dip of the fault and for arbitrary receiver locations inside the medium. The variation of the displacement and stress field with the distance from the fault is studied numerically. Contour maps showing the stress field around a long dip‐slip fault are obtained. Permanent surface deformations which occur as a result of faulting can be measured from geodetic surveys carried out before and after an earthquake. These observations can be used to obtain the fault parameters (dip, slip, width, depth) by inversion, using the theoretical expressions given in the paper. The features of the observational data which are diagnostic of the source properties are: the asymmetry of the data; the magnitude of various components of deformation; and the rate of fall of these components with distance. The asymmetry depends mainly on the dip, the magnitude on the slip and the rate of fall on the depth of the fault.

By using Volterra's relation, it is shown that a tangential dislocation in a gravitating radially inhomogeneous sphere can be characterized by discontinuities in the stress and displacement fields across the source surface r = r,,. This representation of the source facilitates the numerical evaluation of the displacement field.It is found that at the free surface of the Earth the six simultaneous linear differential equations governing the spheroidal field associated with the Legendre polynomial of the first degree (I = 1) degenerate into five.The two equations corresponding to the toroidal field for 1 = 1 degenerate into one. Therefore, when dealing with the case 1 = 1, one must incorporate additional conditions, namely, that the angular momentum of the sphere about its centre is zero and that the centre of mass of the sphere is not displaced.The changes in the inertia tensor due to an earthquake of arbitrary depth and orientation are calculated with the assumption that the Adams-Williamson condition holds at the core. No difference in the numerical results are obtained if the Adams-Williamson conditions does not hold. Comparison with homogeneous, non-gravitating Earth model shows that, in general, real Earth models render a smaller value for the changes in the inertia tensor. It appears from our results that earthquakes are insufficient to maintain the Chandler wobble.