Dynamic nucleation process of shallow earthquake faulting in a fault zone

Two distinct phases are commonly observed at the initial part of seismograms of large shallow earthquakes: low-frequency and low-amplitude waves following the onset of a P wave ( P ₁) are interrupted by the arrival of the second impulsive phase P₂ enriched with high-frequency components. This observation suggests that a large shallow earthquake involves two qualitatively different stages of rupture at its nucleation.
We propose a theoretical model that can naturally explain the above nucleation behaviour. The model is 2-D and the deformation is assumed to be anti-plane. A key clement in our model is the assumption of a zone in which numbers of pre-existing cracks are densely distributed; this cracked zone is a model for the fault zone. Dynamic crack growth nucleated in such a zone is intensely affected by the crack interactions, which exert two conflicting effects: one tends to accelerate the crack growth, and the other tends to decelerate it. The accelerating and decelerating effects are generally ascribable to coplanar and non-coplanar crack interactions, respectively. We rigorously treat the multiple interactions among the cracks, using the boundary integral equation method (BIEM), and assume the critical stress fracture criterion for the analysis of spontaneous crack propagation.
Our analysis shows that a dynamic rupture nucleated in the cracked zone begins to grow slowly due to the relative predominance of non-coplanar interactions. This process radiates the P₁ phase. If the crack continues to grow, coalescence with adjacent coplanar cracks occurs after a short time. Then, coplanar interactions suddenly begin to prevail and crack growth is accelerated; the P₂ phase is emitted in this process. It is interpreted that the two distinct phases appear in the process of the transition from non-coplanar to coplanar interaction predominance.     

Complex P waveforms from a Gulf of Aden earthquake

Summary. It is shown that complex teleseismic P waveforms from a shallow earthquake in a tectonic area can be interpreted using a simple source model embedded in a plane layer velocity structure (with sea layer) whose details are based upon independent evidence. This gives hope that structural complexity in tectonic regions may not always make distant P -wave seismograms impossible to interpret, and that, instead, source complexity may be responsible for some of the many complex waveforms observed, even for earthquakes below magnitude m _b 5.5.     

Determination of the fault plane using a single near-field seismic station with a finite-dimension source model

We explore the possibility of determining the actual fault plane of an earthquake from the inversion of near-source displacement seismograms of one station when a finite-dimension source is used instead of a point source model and when the complete displacement is taken into account, including near-field waves. Tests on synthetic seismograms and real data recorded at local distances show that this is possible even with a single, three-component station. A single accelerogram available for the Erzincan, Turkey, 1992 March 13, M _s = 6.8 earthquake is inverted and the solution found is compatible with other seismological studies and with the mechanism expected for the North Anatolian Fault.     

Dynamic rupture and stress change in a normal faulting earthquake in the subducting Cocos plate

A large nearly vertical, normal faulting earthquake ( M _w = 7.1) took place in 1997 in the Cocos plate, just beneath the ruptured fault zone of the great 1985 Michoacan thrust event ( M _w = 8.1). Dynamic rupture and resultant stress change during the 1997 earthquake have been investigated on the basis of near-source strong-motion records together with a 3-D dynamic model.
Dynamically consistent waveform inversion reveals a highly heterogeneous distribution of stress drop, including patch-like asperities and negative stress-drop zones. Zones of high stress drop are mainly confined to the deeper, southeastern section of the vertical fault, where the maximum dynamic stress drop reaches 280 bars (28 MPa). The dynamically generated source time function varies with location on the fault, and yields a short slip duration, which is caused by a short scalelength of stress-drop heterogeneities. The synthetic seismograms calculated from the dynamic model are generally consistent with the strong-motion velocity records in the frequency range lower than 0.5 Hz.
The pattern of stress-drop distribution appears, in some sense, to be consistent with that of coseismic changes in shear stress resulting from the 1985 thrust event. This consistency suggests that the stress transfer from the 1985 event to the subducting plate could be one of the possible mechanisms that increased the chance of the occurrence of the 1997 earthquake.     

Dynamic stress field of a kinematic earthquake source model with k-squared slip distribution

Source models such as the k -squared stochastic source model with k -dependent rise time are able to reproduce source complexity commonly observed in earthquake slip inversions. An analysis of the dynamic stress field associated with the slip history prescribed in these kinematic models can indicate possible inconsistencies with physics of faulting. The static stress drop, the strength excess, the breakdown stress drop and critical slip weakening distance D _c distributions are determined in this study for the kinematic k -squared source model with k -dependent rise time. Several studied k -squared models are found to be consistent with the slip weakening friction law along a substantial part of the fault. A new quantity, the stress delay, is introduced to map areas where the yielding criterion of the slip weakening friction is violated. Hisada's slip velocity function is found to be more consistent with the source dynamics than Boxcar, Brune's and Dirac's slip velocity functions. Constant rupture velocities close to the Rayleigh velocity are inconsistent with the k -squared model, because they break the yielding criterion of the slip weakening friction law. The bimodal character of D _c / D _tot frequency–magnitude distribution was found. D _c approaches the final slip D _tot near the edge of both the fault and asperity. We emphasize that both filtering and smoothing routinely applied in slip inversions may have a strong effect on the space–time pattern of the inferred stress field, leading potentially to an oversimplified view of earthquake source dynamics.     

Errors in travel times measured on paper seismograms

Summary. The investigation of temporal variations in seismic velocities sometimes requires the use of paper seismograms. For this reason, an investigation of all of the sources of random error in measuring travel times on seismograms has been undertaken using a mathematical model devised by Jeffreys and some additional results derived using elementary statistics. The most important contribution to the total error is often the error due to linear interpolation between minute markers or other time marks on the seismogram, which can be as high as 0.13 s on smoked paper seismograms recorded at 120 mm min⁻¹, and as high as 0.076 s on short-period seismograms of the Canadian network recorded at 60 mm min⁻¹. For 32 explosions at short distances (< 50 km) recorded on smoked paper, however, the median value of the total error in the travel times was 0.016 s. Interpolation errors are generally insignificant for travel-time studies of teleseisms, but may be important in some special studies of local earthquakes and explosions. The theoretical results are useful, not only in seismology, but wherever the accurate timing of an event relative to two reference time markers on a chart recorder is required.     

On the consistency of earthquake moment release and space geodetic strain rates: Europe

In this paper, approximately 100 VLBI/SLR/GPS velocities map European strain rates from <0.09 × 10⁻⁸ to >9.0 × 10⁻⁸ yr⁻¹ with regional uncertainties of 20 to 40 per cent. Kostrov's formula translates these strain-rate values into regional geodetic moment rates M¯˙ _geodetic . Two other moment rates, M¯˙ _seismic , extracted from a 100-year historical catalogue and M¯˙ _plate , taken from plate-tectonic models, contrast the geodetic rates. In Mediterranean Europe, the ratios of M¯˙ _seismic to M¯˙ _geodetic are between 0.50 and 0.71. In Turkey the ratio falls to 0.22. Although aseismic deformation may contribute to the earthquake deficit ( M¯˙ _seismic values less than M¯˙ _geodetic ), the evidence is not compelling because the magnitudes of the observed shortfalls coincide with the random variations expected in a 100-year catalogue. If the lack of aseismic deformation inferred from the 100-year catalogue holds true for longer periods, then much of Europe's strain budget would have to be accommodated by more frequent or larger earthquakes than have been experienced this century to raise the ratios of M¯˙ _seismic to M¯˙ _geodetic to unity. Improved geological fault data bases, longer historical earthquake catalogues, and densification of the continent's space geodetic network will clarify the roles of aseismic deformation versus statistical quiescence.     

On the linear relation between mb and Ms for discrimination between explosions and earthquakes

Summary. The statistical capability of the m _b: M _s discriminant for the discrimination of earthquake and explosion populations is examined by application of discriminant functions to a group of 83 explosions and 72 earthquakes in Eurasia. Equations are derived for the probability that an event is an earthquake or an explosion. The positive sign of DIS in the decision index equation, DIS _i = 34.3383 – 11.9569 mb _t + 7.1161 M _si , indicates that the event i is an earthquake. Its negative sign indicates that event i is an explosion. The probability of correct classification for an event, P _i , is related to its DIS _i value, by P _i = [1-exp (DIS _i )]⁻¹, where a large, positive DIS indicates a high probability that an event is an earthquake and a large, negative DIS indicates a high probability that an event is an explosion. The discrimination line M _s = 1.680 m _b– 4.825, or m _b= 0.595 M _s+ 2.872 very successfully separates the explosion population from the earthquake population. The points on this line have an equal chance of being an earthquake or an explosion; moreover, for any event, the distance parallel to the M _s-axis from the point representing that event in the m _b: M _s plane to this line is a measure of the probability for the correct classification of that event.     

Crust and upper mantle structure of the central Iberian Meseta (Spain)

Summary. Quarry blasts recorded along three lines on the central Iberian Meseta are used in an attempt to interpret the crustal structure. The results of the interpretation of the data, together with published surface wave and earthquake data, suggest a layered structure of the crust having the following features: the basement, in some areas covered by up to 4 km of sediments, has a P -velocity of 6.1 km s⁻¹; a low-velocity layer, between 7 and 11 km depth, seems to exist on the basis of both P and S interpretation of seismic data; a thick middle crust of 12 km has a P -velocity of 6.4 km s⁻¹ and overlies a lower crust with a mean P -velocity of 6.9 km s⁻¹ and a possible slight negative gradient; the mean v _p/ v _s ratio for the crust is about 1.75; the Moho is reached at about 31 km depth and consists of a transition zone at least 1.5 km thick. The P -velocity of the upper mantle is close to 8.1 km s⁻¹ and the S -velocity about 4.5 km s⁻¹, which gives a v _p /v _s ratio of 1.8 for the uppermost mantle. A tentative petrological interpretation of the velocities and composition of the layers is given.     

Strain accumulation along an oblique plate boundary: the Reykjanes Peninsula, southwest Iceland

We use annual GPS observations on the Reykjanes Peninsula (RP) from 2000 to 2006 to generate maps of surface velocities and strain rates across the active plate boundary. We find that the surface deformation on the RP is consistent with oblique plate boundary motion on a regional scale, although considerable temporal and spatial strain rate variations are observed within the plate boundary zone. A small, but consistent increase in eastward velocity is observed at several stations on the southern part of the peninsula, compared to the 1993–1998 time period. The 2000–2006 velocities can be modelled by approximating the plate boundary as a series of vertical dislocations with left-lateral motion and opening. For the RP plate boundary we estimate left-lateral motion  18⁺⁴₋₃ mm yr⁻¹  and opening of  7⁺³₋₂ mm yr⁻¹  below a locking depth of  7⁺¹₋₂ km  . The resulting deep motion of  20⁺⁴₋₃ mm yr⁻¹  in the direction of  N(100⁺⁸₋₆)°E  agrees well with the predicted relative North America–Eurasia rate. We calculate the areal and shear strain rates using velocities from two periods: 1993–1998 and 2000–2006. The deep motion along the plate boundary results in left-lateral shear strain rates, which are perturbed by shallow deformation due to the 1994–1998 inflation and elevated seismicity in the Hengill–Hrómundartindur volcanic system, geothermal fluid extraction at the Svartsengi power plant, and possibly earthquake activity on the central part of the peninsula.     

Inversion of sonic waveforms with unknown source and receiver functions

A seismogram that is several times the length of the source-receiver wavelet is windowed into two parts—these may overlap—to obtain two seismograms with approximately the same source function but different Green's functions. A similarly windowed synthetic seismogram gives two corresponding synthetic seismograms. The spectral product of the window 1 data with the window 2 synthetic is equal to the spectral product of the window 1 synthetic with the window 2 data only if the correct earth model is used to compute the synthetic. This partition principle is applied to well-log sonic waveform data from Ocean Drilling Project hole 806B, a slow formation, and used there to estimate Poisson's ratio from a single seismogram whose transmitter and receiver functions are unknown. A multichannel extension of the algorithm gives even better results. The effective borehole radius R _b, was included in the inversion procedure, because of waveform sensitivity to R _b. Inversion results for R _b agreed with the sonic caliper, but not the mechanical caliper; thus if R _b is not included in the inversion its value should be taken from the sonic caliper.     

The utility of regional Chinese seismograms for source and path studies in central Asia

Summary. Broadband seismograms from the National Seismic Network of the People's Republic of China (PRC) have recently become available through a data exchange programme between NOAA and the State Seismological Bureau of the PRC. In this study, regional surface waves recorded at the Urumchi station located about 700 km north of the Tibetan Plateau in the Sinkiang Province are used to study East Kazakh explosions and wave propagation in central Asia. The data consist of broadband (flat to displacement between 0.1 and 10 Hz), photographic records from an SK Kirnos galvanometric system. Simultaneous inversion of Rayleigh wave phase and group velocities for the path from East Kazakh through the Dzhungarian Basin yields a crustal model dominated by the presence of very low velocities and a strong positive velocity gradient above 15 km depth. Velocities below 15 km depth are not significantly different from other continental structures underlain by Palaeozoic or Precambrian basement. Seismic moments were estimated for seven East Kazakh explosions using models of explosion sources with associated tectonic strain release. The largest explosion studied occurred on 1980 September 14 and had an m_b of 6.2 and a seismic moment of 2.7 × 10²³ dyn cm. The observed amplitude spectra of Rayleigh waves are richer in high frequencies than spectra calculated from our models. This could be caused by a path effect involving seismic wave focusing by the Dzhungarian Basin, although source medium effects cannot be ruled out.     

Rayleigh-wave amplitudes from earthquakes in the range 0–150°

Summary . Vertical component Rayleigh-wave amplitudes from 1461 shallow earthquakes recorded in the distance range 0–150° are analysed to separate the effects of earthquake size, epicentral distance (Δ) and recording station.
The estimated decay of amplitude with distance has the form of a theoretical curve for the decay of Rayleigh waves with distance if the assumption is made that the decay due to dispersion for the data analysed is that of an Airy phase. Writing the decay due to anelastic attenuation as exp (- k Δ), k is estimated to be 0.676/rad over the whole range of distance. If the distance effects are represented by a straight line of the form h log Δ+ constant, h is estimated to be 1.15. The calibration function for computing M _s derived from the estimated distance effects is very similar to that of Marshall & Basham.
Station effects on Rayleigh-wave amplitudes though statistically significant are small, and can probably be ignored in the computation of M _s.
Comparing the estimated surface-wave magnitudes (earthquake size) obtained in this study with the long and short period body-wave magnitudes ( m ^LP_b and m ^SP_b respectively) obtained by Booth, Marshall & Young for the same earthquake shows that m ^LP_b is about equal to M _s over the magnitude range of interest (˜4.0–7.0). The m ^LP_b and M_s relationship shows that the greater the long-period energy radiated by an earthquake the smaller proportionately is the short-period energy.     

Shear-induced pressure changes and seepage phenomena in a deforming porous layer-III

We report the results of an analytical investigation into the deformation behaviour of rate-dependent granular material as a refinement of previous studies on seepage phenomena during shear. The rheology has two components—a compliant part of the constitutive law associated with grain contacts as deformation takes place (dilatancy), and a rate-dependent viscous force transmitted by the melt phase. This formulation allows intermediate, time-dependent behaviour to be assessed for the dilatant porous medium. A key result is that during shear, the magnitude of the excess pore pressure first decreases then increases back to its initial value. Two characteristic timescales are identified that control the rate-dependent dilatancy of the mixture, τ₁, the time constant that rules the increase of the magnitude of the excess pore pressure, and τ₀ that controls its decline. We consider the dilatant effect to be an internal constraint in deforming magmas in the lithosphere and other porous (partially molten) regions in the solid earth. When such regions are exposed to external loading, secular pressure changes should drive fluid flow independent of local buoyancy forces, for the duration of the governing rate-dependent timescales. The accumulated heave of the process is also estimated.     

Observed very long period Rayleigh-wave phase velocities across the Canadian shield

summary . The recent Indonesian earthquake (1977 August 19; M_s =8.0) makes possible a direct determination of Rayleigh-wave phase velocities at very long periods (200 to 300 s) over a pure shield path (College, Alaska-State College, Pennsylvania) by the two-station method. Results are in good agreement with previous models derived by regionalization of great-circle phase velocities and discussed in a previous paper (Okal, Paper I). Great-circle phase velocities computed at College and State College are correctly predicted by the models derived in Paper I, and further substantiate one of its main conclusions: no substantial structural differences between oceans and continents at depths greater than 240 km, are necessary to account for the presently available seismic data.     

Experimental study of the anisotropy of longitudinal and transverse waves from local earthquake records

Summary. The paper gives the results of a study of the anisotropy of seismic wave velocities within the Ashkhabad test field in Central Asia. The anisotropy was studied by analysing variations in the values of apparent velocities of first arrivals for epicentral distances ranging from 30 to 130 km and by analysing the delays (Δ t_s1-_s2 ) between the arrival times of shear waves with different polarizations.
The velocities of P -waves vary with azimuth from 5.3 to 6.27 km s^-1 and the velocities of S -waves vary from 3.15 to 3.5 km s^-1.
The delay times Δ t_S1 - _S2 depend on the direction of the propagation. The character of the variation of the propagation velocity of the longitudinal wave, the presence of two differently polarized shear waves S 1 and S 2 propagating at different velocities, and the character of the distribution of Δ t_S1 - _S2 on the stereogram suggest that the symmetry of the anisotropic medium is close to hexagonal with a nearly horizontal symmetry axis coinciding with the direction of maximal velocity. The azimuth of the symmetry axis of the medium is 140° and coincides with the direction of geological faults.     

Lateral variation and frequency dependence of coda-Q in the southern part of Iberia

b
A method based on the coda attenuation law: Q = Q ₀( f/f ₀)^v leads to the determination of the lateral variation of coda- Q in the southern part of the Iberian Peninsula using seismograms belonging to the seismological network of the Cartuja Observatory, located in Granada. The lateral variation of Q ₀ ( Q value corresponding to a reference frequency f ₀ of 1 Hz) and its frequency dependence for the 1 to 5 Hz frequency range are, in general, in agreement with coda- Q values for frequencies less than about 1 Hz, previously determined in the region under study.
To determine the coda- Q values analytical functions have been used to fit the magnification curves of the vertical component short-period seismographs belonging to the Cartuja network. The problem is solved by using least-squares techniques and non-linear inversion. The determined coda- Q ₀ values and its frequency dependence correlate well with several known geophysical parameters in the southern part of the Iberian Peninsula.     

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.     

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.     

Variation of effective seismic velocities of minerals with pressure and its use in velocity prediction

summary . Regression analyses of P -wave velocity measurements on rocks at variable confining pressure yield'effective'mineral velocities which can be used in conjunction with geological data to predict the variation of velocity with depth in major units of continental crustal layering. Such prediction equations are more reliable than those based on density, mean atomic weight, or single-crystal data from the literature, because they take into direct account the effects of cracks on velocity. This is particularly important in the upper crust where many cracks are likely to be partly open: a by-product of the technique is the statistical relationship of cracks and alteration to minerals present in the samples. The technique is demonstrated in measurements of V_p to 3 kbar in rocks sampled in the vicinity of the Lewisian Units Seismic Traverse, in north-west Scotland.