Volumetric strain in relation to particle displacements for body and surface waves in a general viscoelastic half-space

Abstract

SUMMARY Dilatational earth strain, associated with the radiation fields for several hundred local, regional, and teleseismic earthquakes, has been recorded over an extended bandwidth and dynamic range at four borehole sites near the San Andreas fault, CA. The general theory of linear viscoelasticity is applied to account for anelasticity of the near-surface materials and to provide a mathematical basis for interpretation of seismic radiation fields as detected simultaneously by co-located volumetric strain meters and seismometers. The general theory is applied to describe volumetric strain and displacement for general (homogeneous or inhomogeneous) P and S waves in an anelastic whole space. Solutions to the free-surface reflection problems for incident general P and S-I waves are used to evaluate the effect of the free surface on observations from co-located sensors. Corresponding expressions are derived for a Rayleigh-type surface wave on a linear viscoelastic half-space. The theory predicts a number of anelastic wave field characteristics that can be inferred from observation of volumetric strains and displacement fields as detected by co-located sensors that cannot be inferred from either sensor alone. Volumetric strain meters respond to P waves but not S waves, with simultaneous observations permitting resolution of superimposed P and S wave fields into their respective components. The amplitude and phase for components of the displacement fields depend on angle of incidence, azimuth and inhomogeneity of the wave field. As volumetric strain shows no similar dependencies, simultaneous measurement permits inference of these characteristics as well as in situ material parameters. Conversion of S energy to dilatational strain energy by the free surface is largest at angles of incidence for which inhomogeneity of the reflected P wave is near its physical limit (that is, amplitudes vary rapidly along surfaces of constant phase). For such angles of incidence in a low-loss anelastic half-space, the particle motions for the reflected P waves are elliptical, amplitudes near the surface increase with depth and phase propagation is not parallel to the free surface. Volumetric strain for a Rayleigh-type surface wave shows an exponentially damped sinusoidal dependence on depth not evident for a Rayleigh wave on an elastic half-space.