Shear-wave polarizations on a curved wavefront at an isotropic free surface

Abstract

We present polarization diagrams of the particle motions at the free surface of an isotropic half-space generated by incident shear waves from a local buried point source. The reflectivity technique is used to calculate synthetic seismograms from which the particle motions are plotted. The particle motions are examined over a range of epicentral distances in a uniform isotropic half-space for different source frequencies and polarization angles, and for different Poisson's ratios. The particle motions due to a curved wavefront possess different characteristics from those generated by plane wavefronts at corresponding incidence angles. A curved wavefront generates a local SP-phase: a P-headwave which propagates along the free surface, and arrives shortly before the direct S-wave. These two arrivals give rise to cruciform particle motions in the sagittal and horizontal planes, which could be misinterpreted as anisotropy-induced shear-wave splitting. An examination of the particle motion in the transverse plane, mutually orthogonal to the sagittal and horizontal planes, can be used to discriminate between isotropic and anisotropic interpretations. The amplitude of the SP-phase is enhanced when it propagates in a low-velocity surface layer overlying the source layer, and may then become the dominant phase on radial-component seismograms. The presence of even a single surface layer may introduce considerable complexity into the seismogram, and we examine the effects of layer thickness, velocity contrast, and source depth on the corresponding polarization diagrams. Reliable information on the source and propagation path characteristics of shear waves from a buried local point source can only be obtained from free-surface records if they are recorded within a very limited epicentral distance range.

Seismic imaging of the geothermal field at Krafla, Iceland using shear-wave splitting

“…This window can be visualized as a right circular cone with vertex at the station and vertex angle i v = sin -1 (β/α), where α and β are the P-and Swave surface velocities, respectively. For angles of incidence greater than i v , shear waves interactive strongly with the free surface, distorting the incoming waveform (Booth and Crampin, 1985). For a half space with a typical Poisson's ratio of 0.25, the window's vertex angle, as measured from the vertical, is equal to 35°.…”

Variations in late syn‐rift melt alignment inferred from shear‐wave splitting in crustal earthquakes beneath the Ethiopian rift

“…24 earthquakes located beneath 18 stations provided 26 three-component seismograms where the S-wave incidentangle is within the shear-wave window (SWW). The SWW is the vertical cone bound by sin À1 (Vs/Vp) where S-wave particle motions are not disturbed by S-P conversions at the free surface [Booth and Crampin, 1985]. We use a Vp/Vs of 1.75, calculated from P-and S-wave travel-times from earthquakes in the MER, which corresponds to a SWW that is a cone within 35°of the vertical.…”

A review of shear-wave splitting in the compliant crack-critical anisotropic Earth

“…Note that it is the angle of incidence to the free surface that defines the shear-wave window. Surface recordings of shear waves on irregular topography, or above irregular internal interfaces, which modify the angle of incidence, may severely distort the shear-wave window [40]. However, a low-velocity layer at the surface may effectively widen the shear-wave window by refracting the upcoming shear waves towards vertical incidence.…”

“…An absolute requirement for useful observations of shear-waves at a free surface of an isotropic half-space is that the shear waves must be recorded within the shear-wave window defined by angles of incidence less than θ = sin −1 (V s /V p ), where V p and V s are the P-and shear-wave velocities, respectively [40]. For a Poisson's ratio of 1/4, θ is about 35 • .…”