Effect of the mixing of s-wave and chiral p-wave pairings on electrical shot noise properties of normal metal/superconductor tunnel junctions

We study theoretically the electrical shot noise properties of tunnel junctions between a normal metal and a superconductor with the mixture of singlet s-wave and chiral triplet p-wave pairing due to broken inversion symmetry. We investigate how the shot noise properties vary as the relative amplitude between the two parity components in the pairing potential is changed. It is demonstrated that some characteristics of the electrical shot noise properties of such tunnel junctions may depend sensitively on the relative amplitude between the two parity components in the pairing potential, and some significant changes may occur in the electrical shot noise properties when the relative amplitude between the two parity components is varied from the singlet s-wave pairing dominated regime to the chiral triplet p-wave pairing dominated regime. In the chiral triplet p-wave pairing dominated regime, the ratio of noise power to electric current is close to 2e both in the in-gap and in the out-gap region. In the singlet s-wave pairing dominated regime, the value of this ratio is close to 4e in the inner gap region but may reduce to about 2e in the outer gap region as the relative amplitude of the chiral triplet pairing component is increased. The variations of the differential shot noise with the bias voltage also exhibit some significantly different features in different regimes. Such different features can serve as useful diagnostic tools for the determination of the relative magnitude of the two parity components in the pairing potential.

Joint inversion of Rayleigh group and phase velocities for S-wave velocity structure of the 2021 M_(S)6.0 Luxian earthquake source area,China

On September 16,2021,a MS6.0 earthquake struck Luxian County,one of the shale gas blocks in the Southeastern Sichuan Basin,China.To understand the seismogenic environment and its mechanism,we inverted a fine three-dimensional S-wave velocity model from ambient noise tomography using data from a newly deployed dense seismic array around the epicenter,by extracting and jointly inverting the Rayleigh phase and group velocities in the period of 1.6–7.2 s.The results showed that the velocity model varied significantly beneath different geological units.The Yujiasi syncline is characterized by low velocity at depths of~3.0–4.0 km,corresponding to the stable sedimentary layer in the Sichuan Basin.The eastern and western branches of the Huayingshan fault belt generally exhibit high velocities in the NE-SW direction,with a few local low-velocity zones.The Luxian MS6.0 earthquake epicenter is located at the boundary between the high-and low-velocity zones,and the earthquake sequences expand eastward from the epicenter at depths of 3.0–5.0 km.Integrated with the velocity variations around the epicenter,distribution of aftershock sequences,and focal mechanism solution,it is speculated that the seismogenic mechanism of the main shock might be interpreted as the reactivation of pre-existing faults by hydraulic fracturing.

Impacts of anisotropy coefficient and porosity on the thermal conductivity and P-wave velocity of calcarenites used as building materials of historical monuments in Morocco

It is essential to study the porosity,thermal conductivity,and P-wave velocity of calcarenites,as well as the anisotropy coefficients of the thermal conductivity and P-wave velocity,for civil engineering,and conservation and restoration of historical monuments.This study focuses on measuring the thermal conductivity using the thermal conductivity scanning(TCS)technique and measuring the P-wave ve-locity using portable equipment.This was applied for some dry and saturated calcarenite samples in the horizontal and vertical directions(parallel and perpendicular to the bedding plane,respectively).The calcarenites were selected from some historical monuments in Morocco.These physical properties were measured in the laboratory to find a reliable relationship between all of these properties.As a result of the statistical analysis of the obtained data,excellent linear relationships were observed between the porosity and both the thermal conductivity and porosity.These relationships are characterized by relatively high coefficients of determination for the horizontal and vertical samples.Based on the thermal conductivity and P-wave velocity values in these two directions,the anisotropy coefficients of these two properties were calculated.The internal structure and the pore fabric of the calcarenite samples were delineated using scanning electron microscopy(SEM),while their chemical and mineral compositions were studied using the energy dispersive X-ray analysis(EDXA)and X-ray diffraction(XRD)techniques.

P-wave velocity structure beneath reservoirs and surrounding areas in the lower Jinsha River

The lower reaches of the Jinsha River are rich in hydropower resources because of the high mountains,deep valleys,and swift currents in this area.This region also features complex tectonic structures and frequent earthquakes.After the impoundment of the reservoirs,seismic activity increased significantly.Therefore,it is necessary to study the P-wave velocity structure and earthquake locations in the lower reaches of the Jinsha River and surrounds,thus providing seismological support for subsequent earthquake prevention and disaster reduction work in reservoir areas.In this study,we selected the data of 7.670 seismic events recorded by the seismic networks in Sichuan.Yunnan,and Chongqing and the temporary seismic arrays deployed nearby.We then applied the double-difference tomography method to this data,to obtain the P-wave velocity structure and earthquake locations in the lower reaches of the Jinsha River and surrounds.The results showed that the Jinsha River basin has a complex lateral P-wave velocity structure.Seismic events are mainly distributed in the transition zones between high-and low-velocity anomalies,and seismic events are particularly intense in the Xiluodu and Baihetan reservoir areas.Vertical cross-sections through the Xiangjiaba and Xiluodu reservoir areas revealed an apparent high-velocity anomaly at approximately 6 km depth:this high-velocity anomaly plays a role in stress accumulation,with few earthquakes distributed inside the high-velocity body.After the impoundment of the Baihetan reservoir,the number of earthquakes in the reservoir area increased significantly.The seismic events in the reservoir area north of 27°N were related to the enhanced activity of nearby faults after impoundment:the earthquakes in the reservoir area south of 27°N were probably induced by additional loads(or regional stress changes),and the multiple microseismic events may have been caused by rock rupture near the main faults under high pore pressure.

3D S-wave velocity structure of the Ningdu basin in Jiangxi province inferred from ambient noise tomography with dense array

The Ningdu basin,located in southern Jiangxi province of southwest China,is one of the Mesozoic basin groups which has exploration prospects for geothermal energy.A study on the detailed velocity structure of the Ningdu basin can provide important information for geothermal resource exploration.In this study,we deployed a dense seismic array in the Ningdu basin to investigate the 3D velocity structure and discuss implications for geothermal exploration and geological evolution.Based on the dense seismic array including 35 short-period(5 s-100 Hz)seismometers with an average interstation distance of~5 km,Rayleigh surface wave dispersion curves were extracted from the continuous ambient noise data for surface wave tomographic inversion.Group velocity tomography was conducted and the 3D S-wave velocity structure was inverted by the neighborhood algorithm.The results revealed obvious low-velocity anomalies in the center of the basin,consistent with the low-velocity Cretaceous sedimentary rocks.The basement and basin-controlling fault can also be depicted by the S-wave velocity anomalies.The obvious seismic interface is about 2 km depth in the basin center and decreases to 700 m depth near the basin boundary,suggesting spatial thickness variations of the Cretaceous sediment.The fault features of the S-wave velocity profile coincide with the geological cognition of the western boundary basincontrolling fault,which may provide possible upwelling channels for geothermal fluid.This study suggests that seismic tomography with a dense array is an effective method and can play an important role in the detailed investigations of sedimentary basins.

The experimental studies on electrical con-ductivities and P-wave velocities of anortho-site at high pressure and high temperature

Results of P-wave velocity (vP) and electrical conductivity measurements on anorthosite are presented from room temperature to 880 C at 1.0 GPa using ultrasonic transmission technique and impedance spectra technique respec-tively. The experiments show that the P-wave velocities in anorthosite decrease markedly above 680 C following the dehydration of hydrous minerals in the rock, and the complex impedances collected from 12 Hz to 105 Hz only indicate the grain interior conduction mechanism at 1.0 GPa, from 410 C to 750 C. Because the fluids in the rock have not formed an interconnected network, the dehydration will not pronouncedly enhance the electrical conduc-tivity and change the electrical conduction mechanism. It is concluded that the formation and evolution of the low-velocity zones and high-conductivity layers in the crust may have no correlations, and the dehydration can result in the formation of the low-velocity zones, but cannot simultaneously result in the high-conductivity layers.

Rock critical porosity inversion and S-wave velocity prediction

A critical porosity model is often used to calculate the dry frame elastic modulus by the rock critical porosity value which is affected by many factors. In practice it is hard for us to obtain an accurate critical porosity value and we can generally take only an empirical critical porosity value which often causes errors. In this paper, we propose a method to obtain the rock critical porosity value by inverting P-wave velocity and applying it to predict S-wave velocity. The applications of experiment and log data both show that the critical porosity inversion method can reduce the uncertainty resulting from using an empirical value in the past and provide the accurate critical porosity value for predicting S-wave velocity which significantly improves the prediction accuracy.

The bound weighted average method(BWAM)for predicting S-wave velocity

The shear-wave velocity is a very important parameter in oil and gas seismic exploration, and vital in prestack elastic-parameters inversion and seismic attribute analysis. However, sheafing-velocity logging is seldom carried out because it is expensive. This paper presents a simple method for predicting S-wave velocity which covers the basic factors that influence seismic wave propagation velocity in rocks. The elastic modulus of a rock is expressed here as a weighted arithmetic average between Voigt and Reuss bounds, where the weighting factor, w, is a measurement of the geometric details of the pore space and mineral grains. The S-wave velocity can be estimated from w, which is derived from the P-wave modulus. The method is applied to process well-logging data for a carbonate reservoir in Sichuan Basin, and shows the predicted S-wave velocities agree well with the measured S-wave velocities.

Classification and assessment of rock mass parameters in Choghart iron mine using P-wave velocity

Engineering rock mass classification,based on empirical relations between rock mass parameters and engineering applications,is commonly used in rock engineering and forms the basis for designing rock structures.The basic data required may be obtained from visual observation and laboratory or field tests.However,owing to the discontinuous and variable nature of rock masses,it is difficult for rock engineers to directly obtain the specific design parameters needed.As an alternative,the use of geophysical methods in geomechanics such as seismography may largely address this problem.In this study,25 seismic profiles with the total length of 543 m have been scanned to determine the geomechanical properties of the rock mass in blocks Ⅰ,Ⅲ and Ⅳ-2 of the Choghart iron mine.Moreover,rock joint measurements and sampling for laboratory tests were conducted.The results show that the rock mass rating（RMR） and Q values have a close relation with P-wave velocity parameters,including P-wave velocity in field(V;).P-wave velocity in the laboratory(V;) and the ratio of V;V;(i.e.K;= V;/V;.However,Q value,totally,has greater correlation coefficient and less error than the RMR,In addition,rock mass parameters including rock quality designation（RQD）,uniaxial compressive strength（UCS）,joint roughness coefficient（JRC） and Schmidt number（RN） show close relationship with P-wave velocity.An equation based on these parameters was obtained to estimate the P-wave velocity in the rock mass with a correlation coefficient of 91%.The velocities in two orthogonal directions and the results of joint study show that the wave velocity anisotropy in rock mass may be used as an efficient tool to assess the strong and weak directions in rock mass.

Inconsistency of changes in uniaxial compressive strength and P-wave velocity of sandstone after temperature treatments

It is generally accepted that the uniaxial compressive strength(UCS)and P-wave velocity of rocks tend to decrease simultaneously with increasing temperature.However,based on a great number of statistical data and systematic analysis of the microstructure variation of rocks with temperature rising and corresponding propagation mechanism of elastic wave,the results show that(1)There are three different trends for the changes of UCS and P-wave velocity of sandstone when heated from room temperature(20C or 25C)to 800C:(i)Both the UCS and P-wave velocity decrease simultaneously;(ii)The UCS increases initially and then decreases,while the P-wave velocity decreases continuously;and(iii)The UCS increases initially and then fluctuates,while the P-wave velocity continuously decreases.(2)The UCS changes at room temperaturee400C,400Ce600C,and 600Ce800C are mainly attributed to the discrepancy of microstructure characteristics and quartz content,the transformation plasticity of clay minerals,and the balance between the thermal cementation and thermal damage,respectively.(3)The inconsistency in the trends of UCS and P-wave velocity changes is caused by the change of quartz content,phase transition of water and certain minerals.

A method to model the effect of pre-existing cracks on P-wave velocity in rocks

Crack closure is one of the reasons inducing changes of P-wave velocity of rocks under compression.In this context,a method is proposed to investigate the relationships among P-wave velocity,pre-existing cracks,and confining pressure based on the discrete element method(DEM).Pre-existing open cracks inside the rocks are generated by the initial gap of the flat-joint model.The validity of the method is evaluated by comparing the P-wave velocity tested on a sandstone specimen with numerical result.As the crack size is determined by the diameter of particles,the effects of three factors,i.e.number,aspect ratio,and orientation of cracks on the P-wave velocity are discussed.The results show that P-wave velocity is controlled by the(i.e.number) of open micro-cracks,while the closure pressure is determined by the aspect ratio of crack.The reason accounting for the anisotropy of P-wave velocity is the difference in crack number in measurement paths.Both of the number and aspect ratio of cracks can affect the responses of P-wave velocity to the applied confining pressure.Under confining pressure,the number of open cracks inside rocks will dominate the lowest P-wave velocity,and the P-wave velocity of the rock containing narrower cracks is more sensitive to the confining pressure.In this sense,crack density is difficult to be back-calculated merely by P-wave velocity.The proposed method offers a means to analyze the effect of pre-existing cracks on P-wave velocity.

Laboratory investigation on relationship between degree of saturation, B-value and P-wave velocity

Laboratory tests were performed on Toyoura sand specimens to investigate the relationship between degree of saturation Sr, B-value and P-wave velocity Vp. Different types of pore water （de-aired water or tap water） and pore gas （air or CO2） as well as different magnitudes of back pressure were used to achieve different Sr （or B-value）. The measured relationship between B-value and Vp was not consistent with the theoretical prediction. The measurement shows that the Vp value in the specimen flushed with de-aired water is independent of B-value （or St） and is always around the one in fully saturated condition. However, the Vp value in the specimen flushed with tap water increases with B-value, but the shape of the relationship between Vp and B-value is quite different from the theoretical prediction. The possible explanation for the discrepancy between laboratory measurement and theoretical prediction lies in that the air exists in the water as air bubbles and therefore the pore fluid （air-water mixture） is heterogeneous instead of homogenous assumed in the theoretical prediction.

Effect of CO_(2)on coal P-wave velocity under triaxial stress

As P-wave velocity is sensitive to the variations in coal reservoir parameters,it is possible to monitor the injected CO_(2)through P-wave velocity during CO_(2)sequestration in coal.However,the effects of CO_(2)on the coal P-wave velocity under triaxial stress are not clearly discerned.In the present study,different boundary conditions and gases were utilised to investigate the factors affecting the P-wave velocity after the interaction of coal with CO_(2).Experiments with helium indicated that the pore pressure primarily affected the P-wave velocity by altering the effective stress.Experiments with CH4 and CO_(2)indicated that matrix swelling induced-cleats porosity decline significantly promoted P-wave velocity.Moreover,CO_(2)caused a wider scale and severe weakening of coal matrix than CH4,thereby significantly decreasing the P-wave velocity,and the decline in P-wave velocity increases with vitrinite content.Furthermore,experiments under different boundary conditions showed that with the boundary condition having more constraints,the decrement of pore pressure on P-wave velocity is more weaken,whereas the improvement of matrix swelling on P-wave velocity is more evident.This study contributes to understanding the mechanism of effect of CO_(2)on P-wave velocity under triaxial stress condition and provides guidance for monitoring CO_(2)sequestration in coal.

Pure S-waves in land P-wave source VSP data

Conventional land vertical seismic profiling （VSP） exploration usually uses P-wave sources and three-component geophones for receivers, emphasizing P- and converted S-waves. Previous studies show that both dynamite borehole shots and vertical vibrations from controllable seismic sources at the surface will produce relatively strong pure P-waves and weaker pure S-waves. Interfaces with a large Poisson＇s ratio difference have a positive influence on the formation of strong transmitted converted S-waves. By a comparative analysis of pure S-waves from sources and converted downgoing S-waves, we believe that the main frequency of pure S-waves is usually lower than pure P-waves while the main frequency of downgoing converted S-waves is close to that of P-waves. We have studied zero-offset and offset VSP data from land P-wave sources. Results show that pure S-waves commonly exist in these data with differences in wave intensity. S-wave velocity can be obtained from the P-wave source zero-offset VSP data. Finally, we discuss the bright future of joint application of VSP P-and S-waves and the full use of S-waves in P-wave source VSP data.

Three-dimensional crustal P-wave velocity structure in the Yangbi and Eryuan earthquake regions, Yunnan, China

A magnitude 5.5 earthquakes occurred in Eryuan County,Dali Bai Autonomous Prefecture,Yunnan Province,China,on March 3.And a magnitude 5.0 earthquake occurred in the same place on April 17,2013,i.e.,45 days later.Then,on May 21,2021,multiple earthquakes,one with magnitude 6.4 and several at 5.0 or above,occurred in Yangbi County,Dali Bai Autonomous Prefecture,Yunnan Province,China.All of these occurred in the Weixi-QiaohouWeishan fault zone.In this study,1,874 seismic events in Yangbi and Eryuan counties were identified by automatic micro-seismic identification technology and the first arrivals were picked up manually.Following this,a total of 11,968 direct P-wave absolute arrivals and 73,987 high-quality Pwave relative arrivals were collected for joint inversion via the double difference tomography method.This was done to obtain the regional three-dimensional fine crustal P-wave velocity structure.The results show that the travel time residuals before and after inversion decreased from the initial–0.1–0.1 s to–0.06–0.06 s.The upper crust in the study area,which exhibited a low-velocity anomaly,corresponded to the basin region;this indicated that the low-velocity anomaly in the shallow part of the study area was affected by the basin.Results also showed some correlation between the distribution of the earthquakes and velocity structure,as there was a lowvelocity body Lv1 with a wide distribution at depths ranging from 15–20 km in the Yangbi and Eryuan earthquake regions.In addition,earthquakes occurred predominantly in the highlow velocity abnormal transition zone.The low-velocity body in the middle and lower crust may be prone to concentrating upper crustal stress,thus leading to the occurrence of earthquakes.

A graphical model for haloanhydrite components and P-wave velocity:A case study of haloanhydrites in Amu Darya Basin

Wave velocities in haloanhydrites are difficult to determine and significantly depend on the mineralogy. We used petrophysical parameters to study the wave velocity in haloanhydrites in the Amur Darya Basin and constructed a template of the relation between haloanhydrite mineralogy （anhydrite, salt, mudstone, and pore water） and wave velocities. We used the relation between the P-wave rnoduli ratio and porosity as constraint and constructed a graphical model （petrophysical template） for the relation between wave velocity, mineral content and porosity. We tested the graphical model using rock core and well logging data.

P-Wave Velocity in Rocks of Dabieshan, China at High Pressure and High Temperature: Constraints for Composition of Lower Crust and Crust-Mantle Recycling

P-wave velocities in the rocks of Dabieshan, central China were measured at pressures up to 5.0 GPa and temperatures up to 1 300℃. The ultrahigh pressure eclogites have the highest density and P-wave velocity (Vp) and lower anisotropy. Pressure derivatives of the eclogites range from 0. 22 to 0. 33 km. s-1 GPa-1. Average temperature derivative of the eclogites is - 3. 41×10-4 km. s-1. °C -1. The density and VP of the eclogites imply that there will be two united possibilities related to crust-mantle recycling after the eclogite formed in the deep lithosphere. One is that some eclogites in the deep lithosphere were detached and sunk into deeper mantle due to their denser density. Another is that some eclogites returned to the crust and exposed to the surface.Small amounts (<12%) of eclogites may be still exist in the deep crust beneath Dabieshan based on our calculation.

Estimation of Shallow S-Wave Velocity Structure of Two Practical Sites from Microtremors Array Observation in Tangshan Area

Microtremors array observation for estimating S-wave velocity structure from phase velocities of Rayleigh and Love wave on two practical sites in Tangshan area by a China-US joint group are researched.The phase velocities of Rayleigh wave are estimated from vertical component records and those of Love wave are estimated from three-component records of microtremors array using modified spatial auto-correlation method.Haskell matrix method is used in calculating Rayleigh and Love wave phase velocities,and the shallow S-wave velocity structure of two practical sites are estimated by means of a hybrid approach of Genetic Algorithm and Simplex.The results are compared with the PS logging data of the two sites,showing it is feasible to estimate the shallow S-wave velocity structure of practical site from the observation of microtremor array.

Three-dimensional P-wave Velocity Structure Modelling of the Middle and Lower Reaches of the Yangtze River Metallogenic Belt: Crustal Architecture and Metallogenic Implications

In this study,we compiled and analyzed 69310 P-wave travel-time data from 6639 earthquake events.These events(M≥2.0)occurred from 1980 s to June 2019 and were recorded at 319 seismic stations(Chinese Earthquake Networks Center)in the study area.We adopted the double-difference seismic tomographic method(tomo DD)to invert the 3-D P-wave velocity structure and constrain the crust-upper mantle architecture of the Middle and Lower Reaches of the Yangtze River Metallogenic Belt(MLYB).A 1-D initial model extracted from wide-angle seismic profiles was used in the seismic tomography,which greatly reduced the inversion residual.Our results indicate that reliable velocity structure of th e uppermost mantle can be obtained when Pn is involved in the tomography.Our results show that:(1)the pattern of the uppermost mantle velocity structure corresponds well with the geological partitioning:a nearly E-W-trending low-velocity zone is present beneath the Dabie Orogen,in contrast to the mainly NE-trending low-velocity anomalies beneath the Jiangnan Orogen.They suggest the presence of thickened lower crust beneath the orogens in the study area.In contrast,the Yangtze and Cathaysia blocks are characterized by relatively high-velocity anomalies;(2)both the ultra-high-pressure(UHP)metamorphic rocks in the Dabie Orogen and the low-pressure metamorphic rocks in the Zhangbaling dome are characterized by high-velocity anomalies.The upper crust in the Dabie Orogen is characterized by a low-velocity belt,sandwiched between two high velocity zones in a horizontal direction,with discontinuous low-velocity layers in the middle crust.The keel of the Dabie Orogen is mainly preserved beneath its northern section.We infer that the lower crustal delamination may have mainly occurred in the southern Dabie Orogen,which caused the mantle upwelling responsible for the formation of the granitic magmas emplaced in the middle crust as the low-velocity layers observed there.Continuous deep-level compression likely squeezed the granitic magma upward to intrude the upper crustal UHP metamorphic rocks,forming the'sandwich'velocity structure there;(3)high-velocity updoming is widespread in the crust-mantle transition zone beneath the MLYB.From the Anqing-Guichi ore field northeastward to the Luzong,Tongling,Ningwu and Ningzhen orefields,high-velocity anomalies in the crust-mantle transition zone increase rapidly in size and are widely distributed.The updoming also exists in the crust-mantle transition zone beneath the Jiurui and Edongnan orefields,but the high-velocity anomalies are mainly stellate distributed.The updoming high-velocity zone beneath the MLYB generally extends from the crust-mantle transition zone to the middle crust,different from the velocity structure in the upper crust.The upper crust beneath the Early Cretaceous extension-related Luzong and Ningwu volcanic basins is characterized by high velocity zones,in contrast to the low velocity anomalies beneath the Late Jurassic to Early Cretaceous compression-related Tongling ore field.The MLYB may have undergone a compressive-to-extensional transition during the Yanshanian(Jurassic-Cretaceous)period,during which extensive magmatism occurred.The near mantle-crustal boundary updoming was likely caused by asthenospheric underplating at the base of the lower crust.The magmas may have ascended through major crustal faults,undergoing AFC(assimilation and fractional crystallization)processes,became emplaced in the fault-bounded basins or Paleozoic sequences,eventually forming the many Cu-Fe polymetallic deposits there.

Estimation of S-wave Velocity for Gas Hydrate Reservoir in the Shenhu Area,North South China Sea

Estimation of S-wave velocity using logging data has mainly been performed for sandstone, mudstone and oil and gas strata, while its application to hydrate reservoirs has been largely overlooked. In this paper we present petxophysical methods to estimate the S-wave velocity of hydrate reservoirs with the P-wave velocity and the density as constraints. The three models used in this paper are an equivalent model （MBGL）, a three-phase model （TPBE）, and a thermo-elasticity model （TEM）. The MBGL model can effectively describe the internal relationship among the components of the rock, and the estimated P-wave velocities are in good agreement with the measured data （2.8% error）. However, in the TPBE model, the solid, liquid and gas phases axe considered to be independent of each other, and the estimation results are relatively low （46.6% error）. The TEM model is based on the sensitivity of the gas hydrate to temperature and pressure, and the accuracy of the estimation results is also high （3.6% error）. Before the estimation, the occurrence patterns of hydrates in the Shenhu area were examined, and occurrence state one （the hydrate is in solid form in the reservoir） was selected for analysis. By using the known P-wave velocity and density as constraints, a reasonable S-wave velocity value （ranging from 400 to 1100 m s 1 and for a hydrate layer of 1100 m s 1） can be obtained through multiple iterations. These methods and results provide new data and technical support for further research on hydrates and other geological features in the Shenhu area.