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.     

The basis for earthquake prediction

Summary. Recent advances in understanding the behaviour of shear waves propagating in the crust make the routine prediction of earthquakes seem practicable. Accumulating evidence suggests that most of the Earth's crust is pervaded by distributions of fluid-filled cracks and microcracks that are aligned by the contemporary stress-field so that the cracked rockmass is effectively anisotropic to seismic waves. This causes shear-waves to split, and shear-wave splitting is observed whenever shear-waves propagating along suitable raypaths in the crust are recorded by three-component instruments. These distributions of cracks are known as extensive-dilatancy anisotropy or EDA. Many characteristics of the crack- and stress-geometry can be monitored by analyzing shear-waves propagating through the cracked rockmass. Observations of temporal variations of the behaviour of shear-wave splitting in seismic gaps confirm these hypotheses, and suggest that stress changes before earthquakes may be monitored by analyzing shear-waves. In particular, monitoring earthquake preparation zones with three-component shear-wave vertical-seismic-profiles could lead to techniques for the routine prediction of earthquakes.     

Shear-wave polarizations near the North Anatolian Fault – II. Interpretation in terms of crack-induced anisotropy

Summary. The polarizations of shear waves recorded by networks of digital three-component seismometers immediately above small earthquakes near the North Anatolian Fault in Turkey display shear-wave splitting on almost all shear-wave seismograms recorded within the shear-wave window. This splitting is incompatible with source radiation-patterns propagating through simple isotropic structures but is compatible with effective anisotropy of the internal structure of the rock along the ray paths. This paper interprets the phenomena in terms of widespread crack-induced anisotropy. Distributions of stress-induced cracks model many features of the observations, and synthetic polarization diagrams calculated for propagation through simulated cracked rock are similar to the observed patterns. This evidence for widespread crack-induced anisotropy lends strong support to the hypothesis of extensive-dilatancy anisotropy (EDA) suggested by laboratory experiments in subcritical crack-growth. The crucial evidence confirming some form of EDA would be observations of temporal changes in shear-wave splitting as the stress field alters the crack density and crack geometry. There is some weak evidence for such temporal changes at one site, but further analysis of suitable digital three-component seismometer networks in seismic areas is required to confirm EDA.     

Shear-wave anisotropy and the stress field from borehole recordings at 2.5 km depth at Cajon Pass

53 local earthquakes recorded at 2.5 km depth in the Cajon Pass scientific borehole are analysed for shear-wave splitting. The time delays between the split shear waves can be positively identified for 32 of the events. Modelling these observations of polarizations and time delays using genetic algorithms suggests that the anisotropic structure near Cajon Pass has orthorhombic symmetry. The polarization of the shear waves and the inferred strike of the stress-aligned fluid-filled intergranular microcracks and pores suggests that the maximum horizontal compressional stress direction is approximately N13°W. This is consistent with previous results from earthquake source mechanisms and the right-lateral strike-slip motion on the nearby San Andreas Fault, but not with stresses measured within the uppermost 3 km of the borehole. This study suggests that the San Andreas Fault is driven by deeper tectonic stresses and the present understanding of a weak and frictionless San Andreas Fault may need to be modified. The active secondary faulting and folding close to the fault are probably driven by the relatively shallow stress as measured in the 3.5 km deep borehole.     

Shear-wave polarizations in the Peter the First Range indicating crack-induced anisotropy in a thrust-fault regime

Summary. Three-component seismograms of small local earthquakes recorded in the Peter the First Range of mountains near Garm, Tadzhikistan SSR, display shear-wave splitting similar to that previously observed near the North Anatolian Fault in Turkey. The Peter the First Range is in a region of compressional tectonics, whereas the North Anatolian Fault is a comparatively simple strike-slip fault. Detailed analysis of the Turkish records suggests that the splitting is diagnostic of crack-induced anisotropy caused by vertical microcracks aligned parallel to the direction of maximum compression. Preliminary examination of paper records from Garm shows that most shear waves arriving within the shear-wave window display shear-wave splitting, and that the polarizations of leading shear-waves are consistently aligned in a NE/SW direction. The area is complicated and the tectonics are not well-understood, but the NE/SW direction is approximately perpendicular to the compressional axis in many of the fault-plane mechanisms of the earthquakes. These earthquakes are usually at depths between 5 and 12 km, although there are some deeper events nearby.
Parallel shear-wave polarizations, such as those observed, are expected to indicate the strike of nearly vertical parallel microcracks, which would be aligned parallel to the direction of maximum compression. Thus the shear-wave polarizations in the Peter the First Range indicate that the directions of principal stress are reversed in the rock above the earthquake foci where thrust faulting is taking place.     

Temporal changes in shear-wave splitting at an isolated swarm of small earthquakes in 1992 near Dongfang, Hainan Island, southern China

An isolated swarm of small earthquakes occurred in 1992, near Dongfang on Hainan Island, southern China. The Institute of Geophysics, State Seismological Bureau of China, monitored the swarm with five DCS-302 digital accelerometers for three months from 1992 June 1. 18 earthquakes, with magnitudes M _L ranging from 1.8 to 3.6, were well located by five stations, and shear-wave splitting varying azimuthally was analysed on 27 seismic records from these events. The mean polarization azimuth of the faster shear wave was WNW. Time delays between the split shear waves at two stations varied with time and space. The time delays at one station fell abruptly after earthquakes of magnitudes 3.1 and 3.6, but did not change significantly at the second station. This behaviour is consistent with the delay-time changes being caused by changes in the aspect ratio of vertical liquid-filled (EDA) cracks. Thus, the variation in shear-wave-splitting time delay could be due to changes in crustal stress related to nearby small-magnitude earthquake activity. The connection between earthquake activity and crustal stress variation measured by shear-wave splitting leaves the door open for possible observations of crustal stress transients related to the onset of an earthquake; however, our data cannot be considered as definite evidence for such precursors.     

The variation of delays in stress-induced anisotropic polarization anomalies

Summary. Polarization anomalies in seismic shear wavetrains, diagnostic of propagation through anisotropic media, have now been observed in dilatancy zones in seismic regions. Stress-induced dilatancy will open cracks with preferred orientations, which will be effectively anisotropic to short-period seismic waves. The polarization anomalies are due to the shear waves splitting, in propagation through anisotropic media, into components with different polarizations and different velocities. This writes characteristic signatures into the shear wavetrains. The paper examines ways in which the differential shear-wave anisotropy (the delay between the split shear-waves) varies with direction by plotting stereograms of the relative delays, and their polarizations, for possible dilatancy symmetry-systems. It seems likely, that if sufficient observations of these anomalies can be obtained at each stage of the dilatancy episode, it will be possible to estimate the symmetry directions of the dilatancy and the geometry of the stress-induced crack-system, as well as monitoring the progress of the dilatancy episode.     

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.     

Shear-wave polarizations near the North Anatolian Fault – III. Observations of temporal changes.

Summary. Almost all shear-waves from local earthquakes recorded on closely-spaced three-component seismometer networks deployed near the North Anatolian Fault, Turkey, in two experiments in 1979 and 1980, display shear-wave splitting. The observations are consistent with the presence of EDA (extensive-dilatancy anisotropy), distributions of fluid-filled cracks and microcracks aligned by the regional stress field. Temporal changes in the stress-field, which may occur before an earthquake, may modify the geometry and possibly the orientation of the EDA-microcracks, and lead to corresponding changes in the behaviour of the split shear-waves. A third experiment was undertaken in 1984 to investigate EDA further and to search for possible temporal variations of the polarization of the leading split shear-wave and the time delay between split shear-waves. Observations indicate that the polarization alignments, which are parallel to the strike of the parallel vertical EDA-cracks, are unaltered between 1979 and 1984, implying that the direction of the regional stress field has not changed significantly. Temporal changes in the stress field are more likely to cause changes in the crack density and/or aspect ratio, which would result in a corresponding change in time delay between the split shear-waves. We examine observations of time delay in relation to their propagation path with respect to the crack geometry since it is then possible to separate the effects of changes in crack density and changes in aspect ratio. With this procedure, a small temporal variation of time delays is found between 1979 and 1984, consistent with a decrease in crack density, and consequently a relaxation of stress, in this time period. No evidence was found for any observable variation of time delay over a six month observation span in 1984. We suggest that analysis of repeated shear-wave VSPs offers a technique for monitoring stress changes before earthquakes.     

Finite-frequency sensitivity of body waves to anisotropy based upon adjoint methods

We investigate the sensitivity of finite-frequency body-wave observables to mantle anisotropy based upon kernels calculated by combining adjoint methods and spectral-element modelling of seismic wave propagation. Anisotropy is described by 21 density-normalized elastic parameters naturally involved in asymptotic wave propagation in weakly anisotropic media. In a 1-D reference model, body-wave sensitivity to anisotropy is characterized by 'banana–doughnut' kernels which exhibit large, path-dependent variations and even sign changes. P -wave traveltimes appear much more sensitive to certain azimuthally anisotropic parameters than to the usual isotropic parameters, suggesting that isotropic P -wave tomography could be significantly biased by coherent anisotropic structures, such as slabs. Because of shear-wave splitting, the common cross-correlation traveltime anomaly is not an appropriate observable for S waves propagating in anisotropic media. We propose two new observables for shear waves. The first observable is a generalized cross-correlation traveltime anomaly, and the second a generalized 'splitting intensity'. Like P waves, S waves analysed based upon these observables are generally sensitive to a large number of the 21 anisotropic parameters and show significant path-dependent variations. The specific path-geometry of SKS waves results in favourable properties for imaging based upon the splitting intensity, because it is sensitive to a smaller number of anisotropic parameters, and the region which is sampled is mainly limited to the upper mantle beneath the receiver.     

Earthquake prediction: a new physical basis

Summary. Subcritical crack growth in the laboratory occurs slowly but progressively in solids subjected to low stresses at low strain rates. The cracks tend to grow parallel to the maximum compressive stress so that, when this stress is aligned over a large enough region, the cracks will also be aligned and possess effective seismic anisotropy. It is suggested that such subcritical crack growth produces extensive-dilatancy anisotropy (EDA) throughout earth-quake preparation zones. This process is a possible driving mechanism for earthquake precursors observed at substantial distances from impending focal zones, and provides, in the shear-wave splitting which has been observed in several seismic regions, a possible technique for monitoring the build-up of stress before earthquakes.     

The Turkish Dilatancy Project (TDP3): multidisciplinary studies of a potential earthquake source region

Summary. The section of the North Anatolian Fault lying near the city of Izmit, at the east of the Marmara Sea, has been identified as a seismic gap and the possible site of a future major earthquake. Previously published studies of records from an earthquake swarm within the gap (TDP1 and TDP2) provided the first evidence that shear-wave splitting occurs in earthquake source regions, a conclusion since verified by many studies at other locations. A third field study (TDP3) was mounted in the Izmit region during the summer of 1984. Observations were made over an eight-month period and included geomagnetic and geoelectric measurements in addition to a series of observations utilising dense arrays of three-component seismometers. Earthquake activity in the principal study area was monitored over a period of eight months. Records showed features similar to those observed in the earlier studies. In particular: (1) almost all shear waves emerging within the shear-wave window displayed shear-wave splitting; and (2) the polarizations of the first arriving (faster) split shear-waves showed sub-parallel alignments, characteristic of propagation through a distribution of parallel vertical cracks striking perpendicular to the minimum compressional stress.
These and other observations support the conclusion of earlier studies – that the upper crust is pervaded by distributions of micro-cracks aligned by stress, known as extensive-dilatancy anisotropy. A search for time dependence in shear-wave phenomena has revealed temporal variations in the delays between the split shear-waves throughout the course of the TDP3 study, but as yet this has not been correlated with specific earthquake activity.     

Effects of the free surface on shear wavetrains

Summary. The behaviour of shear-waves is of great importance in identifying and investigating seismic anisotropy in the Earth. However, shear wavetrains recorded at the Earth's surface do not always reflect the motion at depth, introducing practical problems of interpretation. Shear wavetrains incident on the surface of an isotropic half-space at angles less than critical (about 35°) are broadly preserved, but at greater angles substantial distortions can occur. For stations situated close to the source, as in local earthquake studies, the local SP phase, a radially polarized precursor to S , may occur. The behaviour at the surface of an anisotropic half-space is further complicated by the divergence of phase and energy propagation vectors. All of these complications suggest that detailed seismogram modelling is essential to any study of shear wave propagation in the Earth, and in particular to investigations of anisotropy-induced shear-wave splitting.     

On the anisotropy of sedimentary rocks from shear-wave analysis

Summary. The paper describes some results of experimental seismic prospecting investigations of the anisotropic properties of sedimentary rocks at depths of less than 2.5 km. Shear and converted PS -waves were recorded. Examples of SV and SH velocity distributions and shear-wave polarization are given. The main conclusion is that the medium essentially differs from that usually adopted for sedimentary rocks in that the symmetry axis is not normal to the layering.     

Measuring anisotropy in rocks using laser-generated ultrasound

Summary. Measurements using standard contacting piezoelectric transducers and non-contacting laser sources and detectors, have been investigated for the study of ultrasonic anisotropy in rocks. An ultrasonic polariscope has been constructed in order to obtain reproducible travel-time and amplitude measurements. Three case studies are described to demonstrate the apparatus, namely isotropic halite, anisotropic calcite and transversely anisotropic mudstone. A novel technique has been developed in order to construct pseudo-particle motion diagrams, to highlight shear-wave birefringence in rock samples using 2.25 MHz transducers. A pulsed laser has been used to generate compressional and shear waves for comparison with piezoelectric transducer results. The pulses generated by laser irradiation have many advantages for the study of velocity and attenuation anisotropy because of their known characteristics, broad bandwidth and high level of reproducibility. The use of a non-contacting laser source and detector eliminates the need for elaborate coupling agents, stress bonding or immersion techniques. Point-source and line-focusing of the laser beam provides an indirect method of studying shear-wave polarization phenomena. Results from rotation of the line-focused laser beam and rotation of piezoelectric shear-wave transducers with respect to anisotropy, are compared for both velocity and amplitude phenomena in an anisotropic rock sample.     

Extensive-Dilatancy Anisotropy (Eda) Inferred From Observations of Crustal Shear Waves Generated By A Refraction Experiment In Northern Scandinavia

Summary. Particle-motion plots of shear waves have been studied for the section FG of the FENNOLORA seismic experiment. Shear-wave splitting is observed on some records and the polarization of the first arriving shear waves show two peaks at about N35°W and N65°E. These results can be interpreted as being due to crack-induced anisotropy with the crack direction dominated by a (dominant) horizontal stress around N35°W. This is consistent with in situ stress measurements and focal mechanism studies in Scandinavia. the results show that seismic refraction experiments may be useful in providing evidence of crack-induced anisotropy in the stable continental crust.     

Experimental study of shear-waves from shots in anisotropic media

Summary. A complex array of vertical-seismic-profiles and reflection surveys in the Taman Peninsula, Krasnodar, using geophones with inclined axes, is used to investigate shear-wave splitting in thick Maikopian clays characterised by pronounced diapirism. The shear waves split into SH (faster) and SV (slower) components and display transverse isotropy with a vertical axis of symmetry with a maximum shear-wave delay of up to 0.5 s . Within the accuracy of the observations there is no azimuthal anisotropy.     

Acoustoelasticity in cracked solids

A new model that accounts for the stress dependence of the phase velocity of elastodynamic waves propagating in a cracked solid under compression is presented. The phase velocities of longitudinal and shear waves are derived from the effective elastic properties of a cracked solid, which are evaluated within the framework of Kachanov's approach. Following Kachanov, the extra-compliance tensor of the cracked solid is related to the crack compliances, which display a marked non-linear behaviour when subjected to a compressive load. Such non-linear behaviour is shown to be derived from the elastic interaction between the contacting crack faces under compression. This work does not address the effect of mutual interaction among cracks and the generation of higher harmonics due to the medium non-linearity. Numerical examples are presented that illustrate the phase velocity changes occurring in a solid with a random distribution of parallel cracks as a function of an external compressive load. A distinctive feature of the acoustoelastic effect in solids with large parallel fractures and in solids with distributions of aligned microcracks is also illustrated.     

Shear-wave polarizations near the North Anatolian Fault – I. Evidence for anisotropy-induced shear-wave splitting

Summary. The Turkish Dilatancy Projects (TDP1 in 1979 and TDP2 in 1980) recorded small earthquakes near the North Anatolian Fault with closely-spaced networks of three-component seismometers in order to investigate the possibility of diagnosing dilatancy from its effects of shear-wave propagation. This paper examines the polarizations of shear wavetrains recorded in the shear-wave window immediately above the earthquake foci. Abrupt changes in the orientation and/or ellipticity of the shear-wave polarizations are almost always observed during the first few cycles following the initial shear-wave arrival on each seismogram. The horizontal projections of the polarizations of the first shear-wave arrivals at any given station show nearly parallel alignments with approximately the same orientations at each of the recording sites (with one exception). It is difficult to explain this uniform alignment over a wide area in terms of scattering at the irregular surface topography or by earthquake focal mechanisms. We demonstrate that the shear-wave splitting is likely to be the result of anisotropy in the region above the earthquake foci, which could produce polarizations displaying the observed alignments. The temporal change of the azimuth of alignment, observed at one locality between 1979 and 1980, may be due to the release of a local stress anomaly by a very near earthquake.     

P-SH conversions in a flat-layered medium with anisotropy of arbitrary orientation

P-SH conversion is commonly observed in teleseismic P waves, and is often attributed to dipping interfaces beneath the receiver. Our modelling suggests an alternative explanation in terms of flat-layered anisotropy. We use reflectivity techniques to compute three-component synthetic seismograms in a 1-D anisotropic layered medium. For each layer of the medium, we prescribe values of seismic velocities and hexagonally symmetric anisotropy about a common symmetry axis of arbitrary orientation. A compressional wave in an anisotropic velocity structure suffers conversion to both SV -and SH -polarized shear waves, unless the axis of symmetry is everywhere vertical or the wave travels parallel to all symmetry axes. The P-SV conversion forms the basis of the widely used 'receiver function' technique. The P-SH conversion occurs at interfaces where one or both layers are anisotropic. A tilted axis of symmetry and a dipping interface in isotropic media produce similar amplitudes of both direct ( P ) and converted ( Ps ) phases, leaving the backazimuth variation of the P-Ps delay as the main discriminant. Seismic anisotropy with a tilted symmetry axis leads to complex synthetic seismograms in velocity models composed of just a few flat homogeneous layers. It is possible therefore to model observations of P coda with prominent transverse components with relatively simple 1-D velocity structures. Successful retrieval of salient model characteristics appears possible using multiple realizations of a genetic-algorithm (GA) inversion of P coda from several backazimuths. Using GA inversion, we determine that six P coda recorded at station ARU in central Russia are consistent with models that possess strong (> 10 per cent) anisotropy in the top 5 km and between 30 and 43 km depth. The symmetry axes are tilted, and appear aligned with the seismic anisotropy orientation in the mantle under ARU suggested by SKS splitting.