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

Summary. 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.     

Temporal variations of shear-wave splitting in field and laboratory studies in China

Observations of shear-wave splitting at seismic stations above a swarm of small earthquakes on Hainan Island, China, and other examples world-wide, suggest that the time-delays of split shear-waves monitor the build up of stress before earthquakes and the stress release as earthquakes occur. Rock physics experiments on marble specimens also show variations of shear-wave time-delays with uniaxial pressure analogous to the field observations. The rock experiments show an abrupt decrease in time-delays immediately before fracturing occurs. Similar precursory behaviour has been observed before earthquakes elsewhere, and is believed to be important for two reasons. Precursory changes in shear-wave splitting could be used for short-term forecasting, but of greater importance may be the information such behaviour provides about the source processes in earthquake preparation zones.     

Comment on: 'The 3D shear experiment over the Natih field in Oman: the effects of fracture-filling fluids on shear propagation' by C.M. van der Kolk, W.S. Guest and J.H.H.M. Potters

We find errors in theory and application in the paper by van der Kolk et al. (Geophysical Prospecting 49 , 179–197 (2001)) that invalidate their arguments for the cause of the reduction in the velocity of the vertically propagating slower split shear-wave in the gas cap over the Natih field in Oman. We suggest that existing theories are adequate and can explain the anomaly.     

Modelling the compliance of crustal rock—II. Response to temporal changes before earthquakes

There have been several claims that seismic shear waves respond to changes in stress before earthquakes. The companion paper develops a stress-sensitive model (APE) for the behaviour of low-porosity low-permeability crystalline rocks containing pervasive distributions of fluid-filled intergranular microcracks, and this paper uses APE to model the behaviour before earthquakes. Modelling with APE shows that the microgeometry and statistics of distributions of such fluid-filled microcracks respond almost immediately to changes in stress, and that the behaviour can be monitored by analysing seismic shear-wave splitting. The physical reasons for the coupling between shear-wave splitting and differential stress are discussed.
In this paper, we extend the model by using percolation theory to show that large crack densities are limited at the grain-scale level by the percolation threshold at which interacting crack clusters lead to pronounced increases in rock-matrix permeability. In the simplest formulation, the modelling is dimensionless and almost entirely constrained without free parameters. Nevertheless, APE modelling of the evolution of fluid-saturated rocks under stress reproduces the observed fracture criticality and the narrow range of shear-wave azimuthal anisotropy in crustal rocks. It also reproduces the behaviour of temporal variations in shear-wave splitting observed before and after the 1986, M = 6, North Palm Springs earthquake, Southern California, and several other smaller earthquakes.
The agreement of APE modelling with a wide range of observations confirms that fluid-saturated crystalline rocks are stress-sensitive and respond to changes in stress by critical fluid-rock interactions at the microscale level. This means that the effects of changes in stress and other parameters can be numerically modelled and monitored by appropriate observations of seismic shear waves.     

Shear-wave anisotropy: spatial and temporal variations in time delays at Parkfield, Central California

Shear-wave splitting is analysed on data recorded by the High Resolution Seismic Network (HRSN) at Parkfield on the San Andreas fault, Central California, during the three-year period 1988-1990. Shear-wave polarizations either side of the fault are generally aligned in directions consistent with the regional horizontal maximum compressive stress, at some 70° to the fault strike, whereas at station MM in the immediate fault zone, shear-wave polarizations are aligned approximately parallel to the fault. Normalized time delays at this station are found to be about twice as large as those in the rock mass either side. This suggests that fluid-filled cracks and fractures within the fault zone are elastically or seismically different from those in the surrounding rocks, and that the alignment of fault-parallel shear-wave polarizations are associated with some fault-specific phenomenon.
Temporal variations in time delays between the two split shear-waves before and after a M_L = 4 earthquake can be identified at two stations with sufficient data: MM within the fault zone and VC outside the immediate fault zone. Time delays between faster and slower split shear waves increase before the M_L = 4 earthquake and decrease near the time of the event. The temporal variations are statistically significant at 68 per cent confidence levels. Earthquake doublets and multiplets also show similar temporal variations, consistent with those predicted by anisotropic poroelasticity theory for stress modifications to the microcrack geometry pervading the rock mass. This study is broadly consistent with the behaviour observed before three other earthquakes, suggesting that the build-up of stress before earthquakes may be monitored and interpreted by the analysis of shear-wave splitting.     

Inversion of arrival-times in a region of dilatancy anisotropy

Shear-wave splitting has been identified in many three-component seismograms from two separate field experiments on a section of the North Anatolian Fault in North-West Turkey. These observations are consistent with shear-wave propagation through a zone of extensive-dilitancy anisotropy. A preliminary attempt has been made to confirm this interpretation by simultaneously inverting suites of arrival-times for hypocentral locations and for parameters describing an anisotropic halfspace. Although the inversion procedure is not globally convergent, it is possible to recognize the true solution by systematically varying the initial conditions. Applied to selected data sets, the inversion defines several anisotropic models that fit the data significantly better than a simple isotropic model, and display the anisotropy required by the shear-wave splitting. However, most of these anisotropic models are not superior when they are used to individually locate events in a much larger data set. However, for each experiment, there is a single model that produces clearly superior locations for the larger data sets than those of other anisotropic or simple isotropic models. Both models display similar velocity variations which are characteristic of propagation through distributions of biplanar cracks displaying orthorhombic symmetry. The principal axes of the two models are oriented in similar directions and are within 20° of the principal axis of regional stress derived from fault-plane solutions. The solutions indicate low velocities close to the tensional axis, as would be expected in extensive-dilatancy anisotropy.     

Numerical comparisons of the damping of internal gravity waves in stratified fluids

Summary Comparisons are made of the attenuation of progressive internal waves in stratified fluids consisting of (a) a representation of a single thermocline, (b) a weak exponential density distribution and (c) a two-layer system. Effects of the earth's rotation are neglected, as also are heat and salt diffusion. Significant differences are found in the decay characteristics of the three density structures. Internal waves are most strongly damped in the layered system (c) whilst the calculated attenuation rates are least for the thermoclinic structure (a). All the internal modes investigated are, however, shown to be more strongly damped than the associated surface wave.