Slip Area Research Articles

Evidence for a scale‐limited low‐frequency earthquake source process

AbstractWe calculate the seismic moments for 34,264 low‐frequency earthquakes (LFEs) beneath the Olympic Peninsula, Washington. LFE moments range from 1.4 × 1010 to 1.9 × 1012 N m (Mw = 0.7–2.1). While regular earthquakes follow a power law moment‐frequency distribution with a b value near 1 (the number of events increases by a factor of 10 for each unit increase in Mw), we find that while for large LFEs the b value is ~6, for small LFEs it is <1. The magnitude‐frequency distribution for all LFEs is best fit by an exponential distribution with a mean seismic moment (characteristic moment) of 2.0 × 1011 N m. The moment‐frequency distributions for each of the 43 LFE families, or spots on the plate interface where LFEs repeat, can also be fit by exponential distributions. An exponential moment‐frequency distribution implies a scale‐limited source process. We consider two end‐member models where LFE moment is limited by (1) the amount of slip or (2) slip area. We favor the area‐limited model. Based on the observed exponential distribution of LFE moment and geodetically observed total slip, we estimate that the total area that slips within an LFE family has a diameter of 300 m. Assuming an area‐limited model, we estimate the slips, subpatch diameters, stress drops, and slip rates for LFEs during episodic tremor and slip events. We allow for LFEs to rupture smaller subpatches within the LFE family patch. Models with 1–10 subpatches produce slips of 0.1–1 mm, subpatch diameters of 80–275 m, and stress drops of 30–1000 kPa. While one subpatch is often assumed, we believe 3–10 subpatches are more likely.

Subsidence at Cerro Prieto Geothermal Field and postseismic slip along the Indiviso fault from 2011 to 2016 RADARSAT‐2 DInSAR time series analysis

AbstractWe present RADARSAT‐2 Differential Interferometric Synthetic Aperture Radar (DInSAR) observations of deformation due to fluid extraction at the Cerro Prieto Geothermal Field (CPGF) and afterslip on the 2010 M7.2 El Mayor‐Cucapah (EMC) earthquake rupture during 2011–2016. Advanced multidimensional time series analysis reveals subsidence at the CPGF with the maximum rate greater than 100 mm/yr accompanied by horizontal motion (radial contraction) at a rate greater than 30 mm/yr. During the same time period, more than 30 mm of surface creep occurred on the Indiviso fault ruptured by the EMC earthquake. We performed inversions of DInSAR data to estimate the rate of volume changes at depth due to the geothermal production at the CPGF and the distribution of afterslip on the Indiviso fault. The maximum coseismic slip due to the EMC earthquake correlates with the Coulomb stress changes on the Indiviso fault due to fluid extraction at the CPGF. Afterslip occurs on the periphery of maximum coseismic slip areas. Time series analysis indicates that afterslip still occurs 6 years after the earthquake.

Frequency-dependent rupture process, stress change, and seismogenic mechanism of the 25 April 2015 Nepal Gorkha M w 7.8 earthquake

On 25 April 2015, an M w 7.8 earthquake occurred on the Main Himalaya Thrust fault with a dip angle of ~ 7° about 77 km northwest of Kathmandu, Nepal. This Nepal Gorkha event is the largest one on the Himalayan thrust belt since 1950. Here we use the compressive sensing method in the frequency domain to track the seismic radiation and rupture process of this event using teleseismic P waves recorded by array stations in North America. We also compute the distribution of static shear stress changes on the fault plane from a coseismic slip model. Our results indicate a dominant east-southeastward unilateral rupture process from the epicenter with an average rupture speed of ~3 km s‒1. Coseismic radiation of this earthquake shows clear frequency-dependent features. The lower frequency (0.05–0.3 Hz) radiation mainly originates from large coseismic slip regions with negative coseismic shear stress changes. In comparison, higher frequency (0.3–0.6 Hz) radiation appears to be from the down-dip part around the margin of large slip areas, which has been loaded and presents positive coseismic shear stress changes. We propose an asperity model to interpret this Nepal earthquake sequence and compare the frequency-dependent coseismic radiation with that in subduction zones. Such frequency-dependent radiation indicates the depth-varying frictional properties on the plate interface of the Nepal section in the main Himalaya thrust system, similar to previous findings in oceanic subduction zones. Our findings provide further evidence of the spatial correlation between changes of static stress status on the fault plane and the observed frequency-dependent coseismic radiation during large earthquakes. Our results show that the frequency-dependent coseismic radiation is not only found for megathrust earthquakes in the oceanic subduction environment, but also holds true for thrust events in the continental collision zone.

The Mw 8.3 Illapel earthquake (Chile): Preseismic and postseismic activity associated with hydrated slab structures

Abstract The accumulated stress in subduction zones is discharged with earthquake and aseismic activity; the latter is hosted in rheological complex regions, characterized by high pore fluid pressure, and is often accompanied by repeated earthquakes and earthquake swarms. The spatiotemporal analysis of seismic activity can reveal the presence of aseismic transients associated with large earthquakes. Here we study 20 years of seismicity prior to and after the Mw 8.3 earthquake that occurred in A.D. 2015 in central Chile. We identified several earthquake swarms before the main shock and repeating aftershocks at the border of the main slip area. Spatial clustering of the seismic activity shares similar orientation with the main fracture zones observed on the outer rise of the subducting Nazca plate. Our findings suggest that the fracture zones enclosing the rupture are playing a major role in accommodating the pre and post–main shock stress evolution. We further recognize how fracture regions have acted as barriers to the propagation of large earthquakes in the region.

3D vP and vS models of southeastern margin of the Tibetan plateau from joint inversion of body-wave arrival times and surface-wave dispersion data

A new 3D velocity model of the crust and upper mantle in the southeastern (SE) margin of the Tibetan plateau was obtained by joint inversion of body- and surface-wave data. For the body-wave data, we used 7190 events recorded by 102 stations in the SE margin of the Tibetan plateau. The surface-wave data consist of Rayleigh wave phase velocity dispersion curves obtained from ambient noise cross-correlation analysis recorded by a dense array in the SE margin of the Tibetan plateau. The joint inversion clearly improves the vS model because it is constrained by both data types. The results show that at around 10 km depth there are two low-velocity anomalies embedded within three high-velocity bodies along the Longmenshan fault system. These high-velocity bodies correspond well with the Precambrian massifs, and the two located to the northeast of 2013 MS 7.0 Lushan earthquake are associated with high fault slip areas during the 2008 Wenchuan earthquake. The aftershock gap between 2013 Lushan earthquake and 2008 Wenchuan earthquake is associated with low-velocity anomalies, which also acts as a barrier zone for ruptures of two earthquakes. Generally large earthquakes (M ≥ 5) in the region occurring from 2008 to 2015 are located around the high-velocity zones, indicating that they may act as asperities for these large earthquakes. Joint inversion results also clearly show that there exist low-velocity or weak zones in the mid-lower crust, which are not evenly distributed beneath the SE margin of Tibetan plateau.

Seismic structure off the Kii Peninsula, Japan, deduced from passive- and active-source seismographic data

We conduct seismic tomography to model subsurface seismicity between 2010 and 2012 and structural heterogeneity off the Kii Peninsula, southwestern Japan, and to investigate their relationships with segmentation of the Nankai and Tonankai seismogenic zones of the Nankai Trough. In order to constrain both the shallow and deep structure of the offshore seismogenic segments, we use both active- and passive-source data recorded by both ocean-bottom seismometers and land seismic stations. The relocated microearthquakes indicate a lack of seismic activity in the Tonankai seismogenic segment off Kumano, whereas there was active intraslab seismicity in the Kii Channel area of the Nankai seismogenic segment. Based on comparisons among the distribution of seismicity, age, and spreading rate of the subducting Philippine Sea plate, and the slip-deficit distribution, we conclude that seismicity in the subducting slab under the Kii Channel region nucleated from structures in the Philippine Sea slab that pre-date subduction and that fluids released by dehydration are related to decreased interplate coupling of these intraslab earthquakes. Our velocity model clearly shows the areal extent of two key structures reported in previous 2-D active-source surveys: a high-velocity zone beneath Cape Shionomisaki and a subducted seamount off Cape Muroto, both of which are roughly circular and of 15–20 km radius. The epicenters of the 1944 Tonankai and 1946 Nankai earthquakes are near the edge of the high-velocity body beneath Cape Shionomisaki, suggesting that this anomalous structure is related to the nucleation of these two earthquakes. We identify several other high- and low-velocity zones immediately above the plate boundary in the Tonankai and Nankai seismogenic segments. In comparison with the slip-deficit model, some of the low-velocity zones appear to correspond to an area of strong coupling. Our observations suggest that, unlike the Japan Trench subduction zone, in our study area there is not a simple correspondence between areas of large coseismic slip or strong interplate coupling and areas of high velocity in the overriding plate.

Fitting Earthquake Spectra: Colored Noise and Incomplete Data

Abstract Spectral analysis of earthquake recordings provides fundamental seismological information. It is used for magnitude calculation, estimation of attenuation, and the determination of fault rupture properties including slip area, stress drop, and radiated energy. Further applications are found in site‐effect studies and for the calibration of simulation and empirically based ground‐motion prediction equations. We identified two main limitations of the spectral fitting methods currently used in the literature. First, the frequency‐dependent noise level is not properly accounted for. Second, there are no mathematically defensible techniques to fit a parametric spectrum to a seismogram with gaps. When analyzing an earthquake recording, it is well known that the noise level is not the same at different frequencies, that is, the noise spectrum is colored. The different, frequency‐dependent, noise levels are mainly due to ambient noise and sensor noise. Methods in the literature do not properly account for the presence of colored noise. Seismograms with gaps are usually discarded due to the lack of methodologies to use them. Modern digital seismograms are occasionally clipped at the arrival of the strongest ground motion. This is also critical in the study of historical earthquakes in which few seismograms are available and gaps are common, significantly decreasing the number of useful records. In this work, we propose a method to overcome these two limitations. We show that the spectral fitting can be greatly improved and earthquakes with extremely low signal‐to‐noise ratio can be fitted. We show that the impact of gaps on the estimated parameters is minor when a small fraction of the total energy is missing. We also present a strategy to reconstruct the missing portion of the seismogram.

Anatomical Footprint of the Tibialis Anterior Tendon: Surgical Implications for Foot and Ankle Reconstructions.

This study aimed to analyze precisely the dimensions, shapes, and variations of the insertional footprints of the tibialis anterior tendon (TAT) at the medial cuneiform (MC) and first metatarsal (MT1) base. Forty-one formalin-fixed human cadaveric specimens were dissected. After preparation of the TAT footprint, standardized photographs were made and the following parameters were evaluated: the footprint length, width, area of insertion, dorsoplantar location, shape, and additional tendon slips. Twenty feet (48.8%) showed an equal insertion at the MC and MT1, another 20 feet (48.8%) had a wide insertion at the MC and a narrow insertion at the MT1, and 1 foot (2.4%) demonstrated a narrow insertion at the MC and a wide insertion at the MT1. Additional tendon slips inserting at the metatarsal shaft were found in two feet (4.8%). Regarding the dorsoplantar orientation, the footprints were located medial in 29 feet (70.7%) and medioplantar in 12 feet (29.3%). The most common shape at the MT1 base was the crescent type (75.6%) and the oval type at the MC (58.5%). The present study provided more detailed data on the dimensions and morphologic types of the tibialis anterior tendon footprint. The established anatomical data may allow for a safer surgical preparation and a more anatomical reconstruction.

Rupture area analysis of the Ecuador (Musine) Mw = 7.8 thrust earthquake on April 16, 2016, using GOCE derived gradients

The Ecuador Mw = 7.8 earthquake on April 16, 2016, ruptured a nearly 200 km long zone along the plate interface between Nazca and South American plates which is coincident with a seismic gap since 1942, when a Mw = 7.8 earthquake happened. This earthquake occurred at a margin characterized by moderately big to giant earthquakes such as the 1906 (Mw = 8.8). A heavily sedimented trench explains the abnormal lengths of the rupture zones in this system as inhibits the role of natural barriers on the propagation of rupture zones. High amount of sediment thickness is associated with tropical climates, high erosion rates and eastward Pacific dominant winds that provoke orographic rainfalls over the Pacific slope of the Ecuatorian Andes. Offshore sediment dispersion off the oceanic trench is controlled by a close arrangement of two aseismic ridges that hit the Costa Rica and South Ecuador margin respectively and a mid ocean ridge that separates the Cocos and Nazca plate trapping sediments. Gravity field and Ocean Circulation Explorer (GOCE) satellite data are used in this work to test the possible relationship between gravity signal and earthquake rupture structure as well as registered aftershock seismic activity. Reduced vertical gravity gradient shows a good correlation with rupture structure for certain degrees of the harmonic expansion and related depth of the causative mass; indicating, such as in other analyzed cases along the subduction margin, that fore-arc structure derived from density heterogeneities explains at a certain extent propagation of the rupture zones. In this analysis the rupture zone of the April 2016 Ecuador earthquake developed through a relatively low density zone of the fore-arc sliver. Finally, aftershock sequence nucleated around the area of maximum slips in the rupture zone, suggesting that heterogeneous density structure of the fore-arc determined from gravity data could be used in forecasting potential damaged zones associated with big ruptures along the subduction border.

<b>Wheel Slide Protection System by the Use of the Tangential Force in the Macro Slip Area</b>

<b>Wheel Slide Protection System by the Use of the Tangential Force in the Macro Slip Area</b>

Subduction megathrust creep governed by pressure solution and frictional–viscous flow

Subduction megathrust slip speeds range from slow creep at plate convergence rates (centimetres per year) to seismic slip rates (metres per second) in the largest earthquakes on Earth. The deformation mechanisms controlling whether fast slip or slow creep occurs, however, remain unclear. Here, we present evidence that pressure solution creep (fluid-assisted stress driven mass transfer) is an important deformation mechanism in megathrust faults. We quantify megathrust strength using a laboratory-constrained microphysical model for fault friction, involving viscous pressure solution and frictional sliding. We find that at plate-boundary deformation rates, aseismic, frictional–viscous flow is the preferred deformation mechanism at temperatures above 100 °C. The model thus predicts aseismic creep at temperatures much cooler than the onset of crystal plasticity, unless a boundary condition changes. Within this model framework, earthquakes may nucleate when a local increase in strain rate triggers velocity-weakening slip, and we speculate that slip area and event magnitude increase with increasing spacing of strong, topographically derived irregularities in the subduction interface.

Parametrizing Physics-Based Earthquake Simulations

Utilizing earthquake source parameter scaling relations, we formulate an extensible slip weakening friction law for quasi-static earthquake simulations. This algorithm is based on the method used to generate fault strengths for a recent earthquake simulator comparison study of the California fault system. Here we focus on the application of this algorithm in the Virtual Quake earthquake simulator. As a case study we probe the effects of the friction law’s parameters on simulated earthquake rates for the UCERF3 California fault model, and present the resulting conditional probabilities for California earthquake scenarios. The new friction model significantly extends the moment magnitude range over which simulated earthquake rates match observed rates in California, as well as substantially improving the agreement between simulated and observed scaling relations for mean slip and total rupture area.

Coseismic slip model of offshore moderate interplate earthquakes on March 9, 2011 in Tohoku using tsunami waveforms

We estimated the coseismic slip distribution associated with the Mw 7.2 and 6.5 foreshocks of the 2011 Tohoku-Oki earthquake based on analysis of the tsunami waveform records obtained just above their focal areas. The results show that the main rupture areas of each of the foreshocks do not overlap with each other, and show a distribution that is complementary to the postseismic slip area of the first Mw 7.2 foreshock as well as to the epicenters of smaller earthquakes during foreshock activity. After the second largest foreshock, seismicity increased in the area between the rupture area of the second largest foreshock and the mainshock epicenter, suggesting propagation of aseismic slip towards the mainshock epicenter. The calculated stress drop of the second largest foreshock was smaller than the largest one, implying strength reduction during the postseismic period of the largest foreshock. Based on a comparison of coastal tsunami records, it is suggested that the asperity ruptured in the M 7.0 earthquake in 1981 ruptured again during the largest foreshock in 2011, but it expanded to the updip side of the 1981 rupture area and became larger in magnitude, exemplifying the irregularity of earthquake recurrence in the area.

Characteristics of subevents and three-stage rupture processes of the 2015 Mw 7.8 Gorkha Nepal earthquake from multiple-array back projection

On 25 April 2015 an Mw 7.8 earthquake occurred in Nepal and caused about 9000 casualties. This earthquake ruptured part of the Main Himalaya Thrust fault, which is due to the convergence of the subducting Indian plate to the overriding Eurasian plate, and showed thrust mechanism with a very small fault dip angle (about 7–10°). We apply teleseismic multiple-array back projection analysis to study the rupture process of this earthquake and find 6 clear high frequency radiation sources (subevents). Our results illustrate a simple unilateral eastward rupture of ∼160km with relative stable rupture speed of ∼2.8km/s and a duration of 56s. The entire rupture processes can be divided into 3 stages. The high frequency radiation appears to be mainly located at the edge of the large slip area, but the subevents have different characteristics in the western and eastern rupture areas. For this 2015 Nepal earthquake, the scales of asperities appear to be mainly controlled by depth, which dominates the overall patterns of slip and high frequency radiation. We finally propose a multiple-scale asperity model with stress and structural heterogeneities along the rupture direction to explain the distribution of high frequency subevents, co-seismic slip, and aftershocks.

Source Process of the 1923 Kanto Earthquake Considering Subduction Interface Geometry and Amplification Effects Caused by the Large‐Scale and 3D Complex Sedimentary Basin

Abstract The 1923 Kanto earthquake occurred along the Sagami trough (central Japan), causing severe damage in the Tokyo metropolitan area. This study was able to characterize the source process for this event using geodetic, teleseismic, and strong‐motion data. The Kanto region is located above a large‐scale sedimentary basin. Therefore, 3D Green’s functions and a curved fault modeling the subduction interface geometry were used to account for 3D complex wave propagation inside the basin. The later phases of the 3D Green’s functions with long paths inside the basin had large amplitude and long duration, primarily because of amplification effects caused by the lateral heterogeneity of sedimentary layers. However, 3D static displacements were large mainly because of amplification effects caused by the presence of thick soft sedimentary layers in the basin. The geodetic inversions with 3D and 1D Green’s functions had smaller seismic moments than half‐space ones. This suggests that wave amplifications caused by large‐scale sedimentary basins exert significant effects on seismic moment determinations. The joint inversion with 3D Green’s functions showed two large slip areas with a maximum slip of >6 m and an estimated total seismic moment of about 4.1×10 20 N·m ( M w 7.7). Strong motions were recovered very well, even for the later phases, by slips in shallow areas. Furthermore, by comparing various source processes inverted by two fault models of 70 or 280 subfaults, 3D or 1D Green’s functions, and a curved or planar fault model, we verified these assumptions based on the inversion results.

Coseismic deformation due to the 2011 Tohoku-oki earthquake: influence of 3-D elastic structure around Japan

We investigated the effects of elastic heterogeneity on coseismic deformation associated with the 2011 Tohoku-oki earthquake, Japan, using a 3-D finite element model, incorporating the geometry of regional plate boundaries. Using a forward approach, we computed displacement fields for different elastic models with a given slip distribution. Three main structural models are considered to separate the effects of different kinds of heterogeneity: a homogeneous model, a two-layered model with crust–mantle stratification, and a crust–mantle layered model with a strong subducting slab. We observed two counteracting effects: (1) On large spatial scales, elastic layering with increasing rigidity with depth leads to a decrease in surface displacement. (2) An increase in rigidity from above the slab interface to below causes an increase in surface displacement, because the weaker hanging wall deforms to accommodate coseismic slip. Results for slip inversions associated with the Tohoku-oki earthquake show that slip patterns are modified when comparing homogeneous and heterogeneous models. However, the maximum slip only changes slightly: It increases from 38.5 m in the homogeneous to 39.6 m in the layered case and decreases to 37.3 m when slabs are introduced. Potency, i.e., the product of slip and fault area, changes accordingly. Layering leads to inferred slip distributions that are broader and deeper compared to the homogeneous case, particularly to the south of the overall slip maximum. The introduction of a strong slab leads to a reduction in slip around the slip maximum near the trench. We also find that details of the vertical deformation patterns for heterogeneous models are sensitive to the Poisson’s ratio. While elastic heterogeneity does therefore not have a dramatic effect on bulk quantities such as inferred potency, the mechanical response of a layered medium with a slab does lead to a systematically modified slip response, and such effects may bias studies of mega-thrust earthquakes.

High‐resolution seismic tomography of the 2015 Mw7.8 Gorkha earthquake, Nepal: Evidence for the crustal tearing of the Himalayan rift

AbstractThe Mw7.8 Gorkha earthquake struck Nepal and ruptured the boundary between the Indian and Eurasian plates. We conducted 2‐D Pg wave tomography to clarify the seismogenic structure and try to understand causal mechanisms for this large earthquake, using the aftershock data recorded by 15 broadband seismic stations located near the China‐Nepal border. Our high‐resolution results show that coseismic slip area of the main shock is consistent with the high P wave velocity anomaly, and the region of maximum slip has a larger area with higher velocity than the region of initial slip, possibly resulting in the dominant low‐frequency radiation of energy observed after the dominant high‐frequency radiation of energy in the source rupture process. The boundary between these regions of contrasting high and low seismic velocity anomalies suggests a potential crustal tearing at the southern end of the Tangra Yum Co Rift, possibly resulting from different thrust speeds in the Greater Himalaya.

Characteristics of postseismic deformation following the 2003 Tokachi-oki earthquake and estimation of the viscoelastic structure in Hokkaido, northern Japan

Postseismic deformation of the 2003 Tokachi-oki earthquake (M w 8.0) has been observed by GNSS. We analyzed the deformation observed in Hokkaido in the 2nd to the 7th year following the 2003 Tokachi-oki earthquake and examined the effect of two major mechanisms (i.e., afterslip and viscoelastic relaxation) for the observed postseismic deformation by fitting it with a model consisting of afterslip and viscoelastic relaxation. The thickness of the lithosphere, the viscosity of the asthenosphere, and the time decaying constant of afterslip were estimated to be 50 km, 2.0 × 1019 Pa s, and 0.110 year, respectively, which are concordant with those in the Tohoku region estimated in previous studies. The revealed characteristics of postseismic deformation are as follows. At most of the used stations, afterslip played the dominant role in the 2nd year and was still sustained near the coseismic area even in the 7th year. However, the calculated velocity due to viscoelastic relaxation was comparable to that due to afterslip at the stations in northern Hokkaido after the 5th year. Because the calculated velocity due to viscoelastic relaxation was landward near the coseismic slip area, afterslip near the coseismic slip area will be biased to be smaller if viscoelastic relaxation is ignored. A systematic spatial pattern of the residuals considering afterslip only highlights an importance for explaining the observation data. We also examined the effect of viscoelastic relaxation due to afterslip for the parameter estimation and found that it was too small to affect the estimated structure parameters.

Rupture Process and Strong-Motion Generation of the 2014 Iquique, Northern Chile, Earthquake

To investigate the rupture process and strong-motion generation of the [Formula: see text] 8.2 Iquique, Northern Chile, earthquake in 2014, we estimated kinematic source models from waveform inversion and back-projection analyses using strong-motion records. A slip model derived from the waveform inversion using the low-frequency (0.02–0.125[Formula: see text]Hz) velocities is characterized by a large slip area localized 50[Formula: see text]km south of the epicenter with a peak slip of 10[Formula: see text]m, and a deeper slip area with a peak slip above 2[Formula: see text]m located below the coast. The main rupture of these areas started 25[Formula: see text]s after the initial break generating two pronounced phases observed in most of the records. The landward slip area ruptured for about 10[Formula: see text]s generating the first impulsive phase, while the offshore largest slip area ruptured for 20[Formula: see text]s creating a longer duration phase observed later. Results from a back-projection analysis based on stacking of envelopes of 5–10-Hz accelerations indicate that the high-frequency radiation propagated down-dip towards the coast, reaching its maximum value from 25[Formula: see text]s to 40[Formula: see text]s, far away from the shallow main slip area obtained from low-frequency waveform inversion. Our results suggest a clear depth dependence of the seismic wave radiation during the Iquique earthquake.

New strategy for testing new high nitrogen bearing steel for offshore wind turbines

This article presents some results obtained during the first stage of the European Union project titled “STEELWIND,” a part of which has been dedicated to roller–race contact dynamics. Contact has been modeled qualitatively using viscous-elastic friction, in the sliding regions, and hysteresis-modified Hertzian pressure in the whole contact zone. Slip and stick areas are detected within the contact area where the sliding velocity may have both opposite directions parallel to the entraining velocity. Considering the complexity of the hybrid rolling–sliding–sticking conditions, the developed model, although simplified, can be helpful to develop a sliding–rolling test by means of a standard reciprocator stand, where nonsymmetrical and mobile configurations of the testing race samples are introduced.