Re-evaluation of focal depths and source mechanisms of selected earthquakes in the Afar depression

We present a stepwise inversion procedure to assess the focal depth and model earthquake source complexity of seven moderate-sized earthquakes  (6.2 > M _w > 5.1)  that occurred in the Afar depression and the surrounding region. The Afar depression is a region of highly extended and intruded lithosphere, and zones of incipient seafloor spreading. A time-domain inversion of full moment tensor was performed to model direct P and SH waves of teleseismic data. Waveform inversion of the selected events estimated focal depths in the range of 17–22 km, deeper than previously published results. This suggests that the brittle–ductile transition zone beneath parts of the Afar depression extends more than 22 km. The effect of near-source velocity structure on the moment tensor elements was also investigated and was found to respond little to the models considered. Synthetic tests indicate that the size of the estimated, non-physical, non-isotropic source component is rather sensitive to incorrect depth estimation. The dominant double couple part of the moment tensor solutions for most of the events indicates that their occurrence is mainly due to shearing. Parameters associated with source directivity (rupture velocity and azimuth) were also investigated. Re-evaluation of the analysed events shows predominantly normal faulting consistent with the relative plate motions in the region.     

Quaternary normal faulting in southeastern Sicily (Italy):a seismic source for the 1693 large earthquake

We present geological and morphological data, combined with an analysis of seismic reflection lines across the Ionian offshore zone and information on historical earthquakes, in order to yield new constraints on active faulting in southeastern Sicily. This region, one of the most seismically active of the Mediterranean, is affected by WNW–ESE regional extension producing normal faulting of the southern edge of the Siculo–Calabrian rift zone. Our data describe two systems of Quaternary normal faults, characterized by different ages and related to distinct tectonic processes. The older NW–SE-trending normal fault segments developed up to ≈400  kyr ago and, striking perpendicular to the main front of the Maghrebian thrust belt, bound the small basins occurring along the eastern coast of the Hyblean Plateau. The younger fault system is represented by prominent NNW–SSE-trending normal fault segments and extends along the Ionian offshore zone following the NE–SW-trending Avola and Rosolini–Ispica normal faults. These faults are characterized by vertical slip rates of 0.7–3.3  mm  yr ⁻¹ and might be associated with the large seismic events of January 1693. We suggest that the main shock of the January 1693 earthquakes ( M ~ 7) could be related to a 45  km long normal fault with a right-lateral component of motion. A long-term net slip rate of about 3.7  mm  yr ⁻¹ is calculated, and a recurrence interval of about 550 ± 50  yr is proposed for large events similar to that of January 1693.     

Precursory seismic quiescence in the Mudurnu Valley, North Anatolian fault zone, Turkey

The seismicity rate in the Mudurnu Valley of Turkey was studied using an earthquake catalogue that reports events homogeneously down to magnitude 2.3 for the years 1985–1989, and covers the area between latitudes 40.2° and 41.0°N, and longitudes 30.0° and 31.5°E. During this period the only two main shocks, M = 4.0 and M = 4.3, occurred on 1988 September 6 and 1988 December 9 within about 30km of each other. A highly significant seismic quiescence is evident in the area surrounding these main shocks, while the seismicity rate in the rest of the area covered by the catalogue remains constant. the quiescence becomes more pronounced the smaller the area around the main shocks that is studied. the smallest areas that can be studied contain about 60 earthquakes and have dimensions of approximately 25km on each side. the decreases in seismicity rates are 50–80 per cent depending on the volume and period used for defining the quiescence. the quiescence started in 1988 January and lasted about seven months, with approximately 4.5 months of normal activity separating it from the main shock of December. the precursor time of 12 months for an M = 4.3 main shock is similar to those observed in California. It is concluded that it is possible to resolve precursory quiescence before moderate and large earthquakes in the Mudurnu area with the existing seismograph network.     

Evidence for different scaling of earthquake source parameters for large earthquakes depending on faulting mechanism

Scaling relationships between seismic moment, rupture length, and rupture width have been examined. For this purpose, the data from several previous studies have been merged into a database containing more than 550 events. For large earthquakes, a dependence of scaling on faulting mechanism has been found. Whereas small and large dip-slip earthquakes scale in the same way, the self-similarity of earthquakes breaks down for large strike-slip events. Furthermore, no significant differences in scaling could be found between normal and reverse earthquakes and between earthquakes from different regions. Since the thickness of the seismogenic layer limits fault widths, most strike-slip earthquakes are limited to rupture widths of between 15 and 30 km while the rupture length is not limited. The aspect ratio of dip-slip earthquakes is similar for all earthquake sizes. Hence, the limitation in rupture width seems to control the maximum possible rupture length for these events. The different behaviour of strike-slip and dip-slip earthquakes can be explained by rupture dynamics and geological fault growth. If faults are segmented, with the thickness of the seismogenic layer controlling the length of each segment, strike-slip earthquakes might rupture connected segments more easily than dip-slip events, and thus could produce longer ruptures than dip-slip events of the same width     

State of stress in the Southern Tyrrhenian subduction zone from fault-plane solutions

In this paper we present revised locations and original focal mechanisms computed for intermediate and deep earthquakes that occurred within the Southern Tyrrhenian subduction zone between 1988 and 1994, in order to improve our knowledge of the state of stress for this compressional margin. In particular, we define the stress distribution within a large portion of the descending slab, between 40 and about 450 km depth. The seismicity distribution reveals a continuous 40–50 km thick slab that abruptly increases its dip from subhorizontal in the Ionian Sea to a constant 70° dip in the Tyrrhenian. We computed focal mechanisms for events with magnitudes ranging from 2.7 and 5.7, obtaining the distribution of P - and T -axes for many events for which centroid moment tensor (CMT) solutions are not available, thus enabling the sampling of a larger depth range compared to previous studies. We define three portions of the slab characterized by different distributions of P - and T -axes. A general down-dip compression is found between 165 and 370 km depth, whereas in the upper part of the slab (40–165 km depth) the fault-plane solutions are strongly heterogeneous. Below 370 km the P -axes of the few deep events located further to the north have a shallower dip and are not aligned with the 70° dipping slab, possibly suggesting that they belong to a separated piece of subducted lithosphere. There is a good correspondence between the depth range in which the P -axes plunge closer to the slab dip (∼ 70°) and the interval characterized by the highest seismic energy release (190–370 km).     

Post-seismic relaxation following the great 2004 Sumatra-Andaman earthquake on a compressible self-gravitating Earth

The   M _w γ 9.0  2004 December 26 Sumatra-Andaman and   M _w = 8.7  2005 March 28 Nias earthquakes, which collectively ruptured approximately 1800 km of the Andaman and Sunda subduction zones, are expected to be followed by vigorous viscoelastic relaxation involving both the upper and lower mantle. Because of these large spatial dimensions it is desirable to fully account for gravitational coupling effects in the relaxation process. We present a stable method of computing relaxation of a spherically-stratified, compressible and self-gravitating viscoelastic Earth following an impulsive moment release event. The solution is cast in terms of a spherical harmonic expansion of viscoelastic normal modes. For simple layered viscoelastic models, which include a low-viscosity oceanic asthenosphere, we predict substantial post-seismic effects over a region several 100s of km wide surrounding the eastern Indian Ocean. We compare observed GPS time-series from ten regional sites (mostly in Thailand and Indonesia), beginning in 2004 December, with synthetic time-series that include the coseismic and post-seismic effects of the 2004 December 26 and 2005 March 28 earthquakes. A viscosity structure involving a biviscous (Burgers body) rheology in the asthenosphere explains the pattern and amplitude of post-seismic offsets remarkably well.     

Frequency–size distribution of global seismicity seen frombroad-band radiated energy

The frequency–energy distribution of global seismicity is studied using broad-band radiated energy of shallow earthquakes from January 1987 to December 1994 estimated by NEIC. Rank-ordering statistics are applied to enhance the resolution in retrieving the power-law distribution with undersampled data, namely a few tens of events. Seen in the perspective of broad-band radiated energy with higher resolution, a single (Gutenberg–Richter-type) power-law distribution can fit the data. For earthquakes with energy larger than 10¹⁴ J, the number N of events with energy E depends on E via N∝E ^−B , with the scaling constant B = 0.64 ± 0.04, corresponding to b = 0.95 ± 0.06. This relation is different from that of scalar seismic moment, which shows a transition of power-law distributions between small and large earthquakes. To demonstrate such a difference we use the same set of earthquakes with both broad-band energy estimation and CMT estimation. It is found that for the same data set, the energy distribution and the moment distribution show different patterns. The moment distribution has a clear kink between small and large earthquakes, while the energy distribution shows a single power law with no convincing kink between small and large earthquakes. To investigate the effect of different focal mechanisms and different seismic regions, events with strike-slip mechanisms and events within the Japan–Kuril region are considered. For these subsets of events, a similar pattern exists, in which the moment distribution shows a kink between small and large earthquakes, while the energy distribution shows a single power law.     

Upper-mantle structure of the Baltic Shield below the Swedish National Seismological Network (SNSN) resolved by teleseismic tomography

Upper-mantle structure under the Baltic Shield is studied using non-linear high resolution teleseismic P -phase tomography. Observed relative arrival-time residuals from 52 teleseismic earthquakes recorded by the Swedish National Seismological Network (SNSN) are inverted to delineate the structure of the upper mantle. The network consists of 47 (currently working) three-component broad-band stations located in an area about 450 km wide and 1450 km long. In order to reduce complications due to possible significant three-dimensionality of Earth structure, events chosen for this study lay close to in-line with the long-axis of the array  (±30°)  . Results indicate P -wave velocity perturbations of ±3 per cent down to at least 470 km below the network. The size of the array allows inversion for structures even at greater depths, and lateral variations of velocity at depths of up to 680 km appear to be resolved. Below the central part of the array (60°–64° N), where ray coverage is best, the data reveals a large region of relatively low velocity at depths of over about 300 km. At depths less than about 250–300 km, the models include a number of features, including an apparent slab-like structure dipping gently towards the north.     

Relocation of M ≥ 2 events of the 1989 Dôbi seismic sequence in Afar: evidence for earthquake migration

The Ethiopian side of central Afar was struck in August 1989 by the largest seismic sequence (three 6.1 ≤ M _s ≤ 6.3 events, 15 with M _s or m _b ≥ 5.0) since that of Serdo in 1969. Using the Djibouti seismological network, we relocated 297 of the events of that sequence. As most of the large events took place outside the network, we assessed the accuracy and stability of earthquake relocations by using three different velocity models and two relocation codes to try to relate individual shocks to distinct faults and surface breaks. A majority of the events apparently occurred underneath the floor of the Dôbi graben, an area about 45  km long and 15  km wide, rupturing boundary and inner floor faults, in agreement with the surface cracks and scarps that we mapped in the area. The relocation shows that the principal events propagated about 50  km northwestwards along the graben in the first 40  hr. A day and a half after the beginning of the sequence, smaller events ( M ≤ 4) started to propagate more than 55  km eastwards, towards Asal Lake. Using two three-component stations installed near the Ethiopian border, we could determine reliable depths for 21 events. The depths are compatible with a seismogenic crust about 14  km thick in the Dôbi and Hanle graben area. Although the Dôbi sequence ruptured about 50  km of the fault array extending from Serdo to Asal, where the regional stress was released by earthquakes in 1969 and 1978, respectively, a seismic gap about 50  km long still subsists along the northern part of the Gaggade region (Der'êla half-graben).     

Lower-crustal rifting in the Rukwa Graben, East Africa

An M_w 5.9 earthquake occurred in the Lake Rukwa rift, Tanzania, on 1994 August 18, and was well recorded by 20 broad-band seismic stations at distances of 160 to 800 km and 21 broad-band stations at teleseismic distances. The regional and teleseismic waveforms have been used to investigate the source characteristics of the main shock, and also to locate aftershocks that occurred within three weeks of the main shock. Teleseismic body-wave modelling yields the following source parameters for the main shock: source depth of 25 ± 2 km, a normal fault orientation, with a horizontal tension axis striking NE-SW and an almost vertical pressure axis (Nodal Plane I: strike 126°–142°, dip 63°–66°, and rake 280°–290°; Nodal Plane II: strike 273°–289°, dip 28°–31°, and rake 235°–245°), a scalar moment of 4.1 times 10¹⁷ N m, and a 2 s impulsive source time function. Four of the largest aftershocks also nucleated at depths of 25 km, as deduced from regional sPmp–Pmp times. The nodal planes are broadly consistent with the orientation of both the Lupa and Ufipa faults, which bound the Rukwa rift to the northeast and southwest, respectively. The rupture radius of the main shock, assuming a circular fault, is estimated to be 4 km with a corresponding stress drop of 6.5 MPa. Published estimates of crustal thickness beneath the Rukwa rift indicate that the foci of the main shock and aftershocks lie at least 10 km above the Moho. The presence of lower-crustal seismicity beneath the Rukwa rift suggests that the pre-rift thermal structure of the rifted crust has not been strongly modified by the rifting, at least to depths of 25 km.     

Simulations of strong ground motion for earthquakes in the Mexicali–Imperial Valley region

Summary. In this paper computer modelling is used to test simple approximations for simulating strong ground motions for moderate and large earthquakes in the Mexicali–Imperial Valley region. Initially, we represent an earthquake rupture process as a series of many independent small earthquakes distributed in a somewhat random manner in both space and time along the rupture surface. By summing real seismograms for small earthquakes (used as empirical Green's functions), strong ground motions at specific sites near a fault are calculated. Alternatively, theoretical Green's functions that include frequencies up to 20 Hz are used in essentially similar simulations. The model uses random numbers to emulate some of the non-deterministic irregularities associated with real earthquakes, due either to complexities in the rupture process itself and/or strong variations in the material properties of the medium. Simulations of the 1980 June 9 Victoria, Baja California earthquake ( M _L= 6.1) approximately agree with the duration of shaking, the maximum ground acceleration, and the frequency content of strong ground motion records obtained at distances of up to 35 km for this moderate earthquake. In the initial stages of modelling we do not introduce any scaling of spectral shape with magnitude, in order to see at what stage the data require it. Surprisingly, such scaling is not critical in going from M = 4–5 events to the M = 6.1 Victoria earthquake. However, it is clearly required by the El Centro accelerogram for the Imperial Valley 1940 earthquake, which had a much higher moment ( Ms ∼ 7). We derive the spectral modification function for this event. The resulting model for this magnitude ∼ 7 earthquake is then used to predict the ground motions at short distances from the fault. Predicted peak horizontal accelerations for the M ∼ 7 event are about 25–50 per cent higher than those observed for the M = 6.1 Victoria event.     

Aseismic fault movement before the 1995 Kobe earthquake detected by a GPS survey: implication for preseismic stress localization?

By inversion analysis of the baseline changes and horizontal displacements observed with GPS (Global Positioning System) during 1990–1994, a high-angle reverse fault was detected in the Shikoku-Kinki region, southwest Japan. The active blind fault is characterized by reverse dip-slip (0.7±0.2  m yr⁻¹ within a layer 17–26  km deep) with a length of 208±5  km, a (down-dip) width of 9±2  km, a dip-angle of 51°±2° and a strike direction of 40°±2° (NE). Evidence from the geological investigation of subfaults close to the southwestern portion of the fault, two historical earthquakes ( M _L=7.0, 1789 and 6.4, 1955) near the centre of the fault, and an additional inversion analysis of the baseline changes recorded by the nationwide permanent GPS array from 18 January to 31 December 1995 partially demonstrates the existence of the fault, and suggests that it might be a reactivation of a pre-existing fault in this region. The fact that hardly any earthquakes ( M _L>2.0) occurred at depth on the inferred fault plane suggests that the fault activity was largely aseismic. Based on the parameters of the blind fault estimated in this study, we evaluated stress changes in this region. It is found that shear stress concentrated and increased by up to 2.1 bar yr⁻¹ at a depth of about 20  km around the epicentral area of the 1995 January 17  Kobe earthquake ( M _L=7.2, Japan), and that the earthquake hypocentre received a Coulomb failure stress of about 5.6 bar yr⁻¹ during 1990–1994. The results suggest that the 1995  Kobe earthquake could have been induced or triggered by aseismic fault movement.     

Model of the geoelectrical structure of the mid- and lower mantle in the Europe–Asia region

The conductivity structure of the Earth's mantle was estimated using the induction method down to 2100  km depth for the Europe–Asia region. For this purpose, the responses obtained at seven geomagnetic observatories (IRT, KIV, MOS, NVS, HLP, WIT and NGK) were analysed, together with reliable published results for 11  yr variations. 1-D spherical modelling has shown that, beneath the mid-mantle conductive layer (600–800  km), the conductivity increases slowly from about 1  S  m⁻¹ at 1000  km depth to 10  S  m⁻¹ at 1900  km, while further down (1900–2100  km) this increase is faster. Published models of the lower mantle conductivity obtained using the secular, 30–60  yr variations were also considered, in order to estimate the conductivity at depths down to the core. The new regional model of the lower mantle conductivity does not contradict most modern geoelectrical sounding results. This model supports the idea that the mantle base, situated below 2100  km depth, has a very high conductivity.     

Small-scale heterogeneities below the Gräfenberg array, Germany from seismic wavefield fluctuations of Hindu Kush events

Small-scale elastic heterogeneities (<5  km) are found in the upper lithosphere underneath the Gräfenberg array, southeast Germany. The results are based on the analysis of broadband recordings of 17 intermediate-depth (201–272  km) events from the Hindu Kush region. The wavefront of the first P arrival and the following 40  s coda are separated into coherent and incoherent (scattered) parts in the frequency range from 0.05 to 5  Hz. The frequency-dependent intensities of the mean and fluctuation wavefields are used to describe the scattering characteristics of the lithosphere underneath the receivers. It is possible to discriminate a weak-fluctuation regime of the wavefield in the frequency range below approximately 1.5–2.5  Hz and a strong-fluctuation regime starting at 2.0–2.5  Hz and continuing to higher frequencies. In order to explain the observed wavefield fluctuations, an approach with seismic scattering at random media-type structures is proposed. The preferred model contains heterogeneities with 3–7 per cent perturbations in seismic velocity and correlation lengths of 0.6–4.8  km in the crust. This is compatible with models from active seismic experiments. Scattering in the lithospheric mantle is not required, but cannot be excluded at weak velocity contrasts (<3 per cent).     

Comment on 'Systematic determination of earthquake rupture directivity and fault planes from analysis of long-period P-wave spectra' by L. M. Warren and P. M. Shearer

Warren and Shearer describe a method of estimating the duration of P pulses radiated by earthquakes, on the assumption that the source is a unilateral fracture. The estimates are made in the frequency domain. The estimates obtained by Warren and Shearer for seven of the earthquakes are compared to durations estimated here in the time domain; the time-domain measurements being made on broad-band seismograms (∼0.1–4.0 Hz) derived by filtering from short-period recordings. Overall, the time-domain method indicates that the pulse duration of the earthquakes studied here range from 2.0 to 7.6 s, whereas the estimates from the results of Warren and Shearer range from 7.1 to 9.8 s. This suggests that the method of Warren and Shearer cannot resolve pulse lengths less than about 7 s. The suggestion is supported by the estimates of the duration of rupture—fault length/speed of rupture—implied by the results of Warren and Shearer. For, although the estimated fault-length ranges from 0.8 km to over 40 km most rupture durations are around 8 s.     

Teleseismic delay-time tomography of the upper mantle beneath southeastern India: imprint of Indo–Antarctica rifting

A 3-D P -velocity map of the crust and upper mantle beneath the southeastern part of India has been reconstructed through the inversion of teleseismic traveltimes. Salient geological features in the study region include the Archean Dharwar Craton and Eastern Ghat metamorphic belt (EGMB), and the Proterozoic Cuddapah and Godavari basins. The Krishna–Godavari basin, on the eastern coastal margin, evolved in response to the Indo–Antarctica breakup. A 24-station temporary network provided 1161 traveltimes, which were used to model 3-D P -velocity variation. The velocity model accounts of 80 per cent of the observed data variance. The velocity picture to a depth of 120 km shows two patterns: a high velocity beneath the interior domain (Dharwar craton and Cuddapah basin), and a lower velocity beneath the eastern margin region (EGMB and coastal basin). Across the array velocity variations of 7–10 per cent in the crust (0–40 km) and 3–5 per cent in the uppermost mantle (40–120 km) are observed. At deeper levels (120–210 km) the upper-mantle velocity differences are insignificant among different geological units. The presence of such a low velocity along the eastern margin suggests significantly thin lithosphere (<100 km) beneath it compared to a thick lithosphere (>200 km) beneath the eastern Dharwar craton. Such lithospheric thinning could be a consequence of Indo–Antarctica break-up.     

Coseismic deformation revealed by inversion of strong motion and GPS data: the 2003 Chengkung earthquake in eastern Taiwan

A moderate earthquake of   M _w= 6.8  occurred on 2003 December 10. It ruptured the Chihshang Fault in eastern Taiwan which is the most active segment of the Longitudinal fault as a plate suture fault between the Luzon arc of the Philippine Sea plate and the Eurasian plate. The largest coseismic displacements were 13 cm (horizontal) and 26 cm (vertical). We analyse 40 strong motion and 91 GPS data to model the fault geometry and coseismic dislocations. The most realistic shape of the Chihshang fault surface is listric in type. The dipping angle of the seismic zone is steep (about 60°–70°) at depths shallower than 10 km and then gradually decreases to 40°–50° at depths of 20–30 km. Thus the polygonal elements in Poly3D are well suited for modelling complex surfaces with curving boundaries. Using the strong motion data, the displacement reaches 1.2 m dip-slip on the Chihshang Fault and decreases to 0.1 m near surface. The slip averages 0.34 m, releasing a scalar moment of 1.6E26 dyne-cm. For GPS data, our model reveals that the maximal dislocation is 1.8 m dip-slip. The dislocations decrease to 0.1 m near the surface. The average slip is 0.48 m, giving a scalar moment of 2.2E26 dyne-cm. Regarding post-seismic deformation, a displacements of 0.5 m were observed near the Chihshang Fault, indicating the strain had not been totally released, as a probable result of near-surface locking of the fault zone.     

Spherical harmonic representation of the magnetic field in the presence of a current density

Summary. We present the results of a systematic study of events with M _s > 6 in northern Chile (20–33°S), for the period between 1963 and 1971. Medium to large earthquakes near the coast of this region are of three types: (1) Interplate events at the interface between the downgoing slab and the overriding South American plate. These events can be very large reaching magnitudes greater than 8. (2) Intra-plate earthquakes 20–30 km inside the downgoing slab. They have fault mechanisms indicating extension along the dip of the slab and may have magnitudes up to 7.5. (3) Less frequent, M _s∼ 6 events that occur near the top of the downgoing slab and have thrust mechanisms with an almost horizontal E-W compressional axis. This type of mechanism is very different from that of the events of type 1 which are due to shallow dipping reverse faulting. There is a rotation of about 30° of the compressional axis in the vertical plane between events of types (1) and (3). Three groups of events near 32.5°, 25.5° and 21°s were studied in detail. Depth and mechanisms were redetermined by P -wave modelling and relative locations were obtained by a master event technique. Near 32.5°S, only events of types 1 and 2 were found in the time period of this study. At the two other sites, the three types of events were identified. This shows clearly that there are compressive stresses at the top of the slab and extension at the centre, a situation which is usually found in the areas where a double Benioff-zone has been identified in the seismicity.     

Accurate hypocentre determination in the seismogenic zone of the subducting Nazca Plate in northern Chile using a combined on-/offshore network

The coupled plate interface of subduction zones—commonly called the seismogenic zone—has been recognized as the origin of fatal earthquakes. A subset of the after-shock series of the great Antofagasta thrust-type event (1995 July 30; M _w = 8.0) has been used to study the extent of the seismogenic zone in northern Chile. To achieve reliable and precise hypocentre locations we applied the concept of the minimum 1-D model, which incorporates iterative simultaneous inversion of velocity and hypocentre parameters. The minimum 1-D model is complemented by station corrections which are influenced by near-surface velocity heterogeneity and by the individual station elevations. By relocating mine blasts, which were not included in the inversion, we obtain absolute location errors of 1  km in epicentre and 2  km in focal depth. A study of the resolution parameters ALE and DSPR documents the importance of offshore stations on location accuracy for offshore events. Based on precisely determined hypo-centres we calculate a depth of 46  km for the lower limit of the seismogenic zone, which is in good agreement with previous studies for this area. For the upper limit we found a depth of 20  km. Our results of an aseismic zone between the upper limit of the seismogenic zone and the surface correlates with a detachment zone proposed by other studies; the results are also in agreement with thermal studies for the Antofagasta forearc region.     

Implications of a percolation model for earthquake 'nucleation'

A percolation model is applied to the explanation of some of the qualitative and quantitative aspects associated with the recent observations of earthquake 'nucleation'. An additional assumption is introduced that nucleation starts at the critical point of percolation. The model explains the order of magnitude of the seismic moment release during the nucleation, the dependence of the seismic moment of the main shock on the duration of the nucleation process, and the observation that the fraction of the moment release during the nucleation has no systematic variation with the size of the main shock. The model also suggests that the source time function of the nucleation phase may be complex, and also that not all earthquakes are accompanied by a nucleation process, which is supported by observational results. By assuming that there exists a scale invariance associated with the criticality, a Widom scaling model is proposed to describe the electromagnetic emission during earthquake rupture.