Authors:P. Nenovski Pages: 555 - 577 Abstract: Recently several cases of observations of unipolar magnetic field pulses associated with earthquakes at different points (California, Italy, Peru) have been recorded. The paper attempts to model unipolar magnetic field pulses based on one mechanism that should be omnipresent for all measurement points, namely, the magnetic field diffusion through a conductive medium. The structure of magnetic fields supported by electric current sources is thoroughly modelled. The source of electric current is considered as an elongated volume of finite cross-section being immersed in a conductive medium. To model the unipolarity feature of the observed pulses prior to and at the earthquake main shock, the electric current of the source is of impulse form. Special attention is paid to the differences in the pulse structure (as amplitude envelope and the pulse width) that are measured by various magnetometers (fluxgate or search-coil). An analysis and comparison with recorded magnetic field pulse characteristics reveal that the observed unipolar pulses may have a common genesis, an electric current source within a conductive medium such as the earth crust. PubDate: 2018-12-01 DOI: 10.1007/s40328-018-0219-y Issue No:Vol. 53, No. 4 (2018)

Authors:Bapan Paul; Barin Kumar De; Anirban Guha Pages: 579 - 606 Abstract: The latitudinal ionospheric response of the three strongest geomagnetic storms of 2015 of the current solar cycle 24 during 16–19 March 2015, 21–24 June 2015 and 19–22 December 2015 is investigated using the total electron content data derived from a latitudinal chain of Global Positioning System (GPS) receivers extending from 70°N to 70°S. The storm time perturbations of the ionosphere during main and recovery phase is presented by the GPS derived vertical total electron content (VTEC) data which is further supported by ionospheric F region critical frequency (foF2) and F region peak height (hmF2) data. We observed symmetrical hemispheric response of the ionosphere during the strongest 17th March (St. Patrick’s Day) storm whereas asymmetrical hemispheric response of the ionosphere during 22nd June and 20th December storm over the Asian-Australian sector. The observations are explained by the combined transport of background inter-hemispheric seasonal wind and storm time disturbed meridional wind and by the global thermospheric compositional variation [O/N2] data. PubDate: 2018-12-01 DOI: 10.1007/s40328-018-0221-4 Issue No:Vol. 53, No. 4 (2018)

Authors:M. Radulian; A. Bălă; L. Ardeleanu; D. Toma-Dănilă; L. Petrescu; E. Popescu Abstract: The purpose of this paper is to present the most comprehensive catalogue of focal mechanisms for Romanian earthquakes which occurred between 1929 and 2000 in the Carpathian Orogen, the Moesian and Moldavian Platforms, and the Transylvanian Basin. The present catalogue (REFMC) is a first step toward creating a centralized and continuous database of earthquake mechanisms in Romania by revising and updating existing data for the twentieth century, which together with the Romanian earthquake catalogue (ROMPLUS)—continuously updated by the National Institute for Earth Physics, provides the fundamental information for any seismicity or seismic hazard assessment. In order to produce a close-to definitive version compatible with more recent and less uncertain focal mechanisms solutions, we revised multiple sets of data (some of which newly found), recalculated and corrected some of the fault-plane solutions and reached a consensus. The catalogue comprises 250 crustal events and 416 intermediate-depth events recorded in the twentieth century starting from 1929. On the basis of the new catalogue data and seismotectonic investigation, we propose a reconfiguration of the seismogenic zones located along Southern Carpathians toward the western side of Romania. PubDate: 2018-12-05 DOI: 10.1007/s40328-018-0243-y

Authors:Ya Mao; Qian-xin Wang; Chao Hu; Hong-yi Yang; Xu Yang; Wei-xuan Yu Abstract: During the on-orbit operation of BeiDou satellites, the on board atomic clocks of these satellites are easily affected by changes in the space environment. Since the clock offsets of BeiDou satellites derived from multi-satellite clock estimation exhibit correlation among one another. In this study, the correlation among the clock offsets of BeiDou satellites is analyzed and the influence of correlation among satellites on clock offset prediction accuracy is investigated. To obtain accurate analysis results, the Baarda outlier detection method is initially improved. The improved method can effectively eliminate small errors in clock offset data. Then, the correlation coefficient among BeiDou satellites is calculated, and the method based on the correlation among BeiDou satellite clocks is used to predict the clock offsets of the satellites. Experimental results show that clock offset prediction accuracy can be improved by 7.3% compared with that of the traditional method when the method that considers correlation among satellite clocks is used. PubDate: 2018-11-29 DOI: 10.1007/s40328-018-0242-z

Authors:Peng Feng; Fei Li; Jianguo Yan; J.-P. Barriot Abstract: In this study, done in the frame of the MGEX (Multi-GNSS Experiment) project, for 20 selected worldwide stations, and for the whole year of 2015, we compare zenithal total delay (ZTD) estimated values from BeiDou/GPS combined signals, to ZTD estimates from GPS-only signals, and also to ZTD estimates from the IGS analysis center CODE (CODE products), in order to assess the intrinsic accuracies of these ZTD estimates. We used the PANDA software from Wuhan university for all our data processing, with precise orbits (PPP) from the GFZ IGS analysis center. We found that the GPS-only ZTD estimates show a very good agreement with the CODE final ZTD products, but that a systematic negative bias of around 3 mm is showing up between the ZTD estimates from combined GPS/BeiDou data w.r.t. GPS-only data. This indicates that the accuracy of Beidou satellite orbits and clock errors still need to be improved w.r.t. to IGS standards. PubDate: 2018-11-26 DOI: 10.1007/s40328-018-0240-1

Authors:Huaien Zeng; Guobin Chang; Haiqing He; Yi Tu; Shuifa Sun; Yue Wu Abstract: The rigid motion involving both rotation and translation in the 3D space can be simultaneously described by a unit dual quaternion. Considering this excellent property, the paper constructs the Helmert transformation (seven-parameter similarity transformation) model based on a unit dual quaternion and then presents a rigid iterative algorithm of Helmert transformation using a unit dual quaternion. Because of the singularity of the coefficient matrix of the normal equation, the nine parameter (including one scale factor and eight parameters of a dual quaternion) Helmert transformation model is reduced into five parameter (including one scale factor and four parameters of a unit quaternion which can represent the rotation matrix) Helmert transformation one. Besides, a good start estimate of parameter is required for the iterative algorithm, hence another algorithm employed to compute the initial value of parameter is put forward. The numerical experiments involving a case of small rotation angles i.e. geodetic coordinate transformation and a case of big rotation angles i.e. the registration of LIDAR points are studied. The results show the presented algorithms in this paper are correct and valid for the two cases, disregarding the rotation angles are big or small. And the accuracy of computed parameter is comparable to the classic Procrustes algorithm from Grafarend and Awange (J Geod 77:66–76, 2003), the orthonormal matrix algorithm from Zeng (Earth Planets Space 67:105, 2015), and the algorithm from Wang et al. (J Photogramm Remote Sens 94:63–69, 2014). PubDate: 2018-11-20 DOI: 10.1007/s40328-018-0241-0

Authors:Luminiţa Ardeleanu Abstract: An inversion scheme using only few good quality high-frequency local waveforms was previously applied to estimate the source mechanism for a pilot set of crustal earthquakes with local magnitudes less than 4, from the bend of the South-eastern Carpathians. Taking advantage of the improved velocity and attenuation models recently determined for the study region, we reevaluate the focal mechanism of a couple of low-magnitude events (local magnitude ≥ 3), and assess the uncertainty of the fault plane solutions. The results evidence the increased reliability of the retrieved mechanisms and emphasize the capability of the approach to provide satisfactorily constrained fault plane solutions for the weak-to-moderate earthquakes in the study region. PubDate: 2018-11-16 DOI: 10.1007/s40328-018-0239-7

Authors:Dashuai Chai; Guoliang Chen; Shengli Wang; Xiushan Lu Abstract: A data gap of GNSS and INS may occur when data are collected by a vehicle. To obtain the pose information when this data gap appears, we use a combined auto regressive (AR) model for the forecasting of INS data so that the Strap-down Inertial Navigation System can still work. A forward process is initially implemented to forecast INS data using an AR model, and then inverse prediction is performed. Finally, the raw INS data are determined using forward and inverse results with different weights. The measurement data are applied to this method and the commercial software Inertial Explorer 8.60 (IE). The experimental result shows that the errors from the filtered results of the IE for loosely coupled and tightly coupled approaches reach the meter level after the data of the GNSS and INS are retrieved, and the error is at the meter level for conventional loosely coupled approach. Conversely, the maximum error from the proposed method is at the decimeter level. The smoother results have also been affected for the loosely coupled and tightly coupled approach of the IE before this data gap of GNSS and INS appears. However, a centimeter-level result can still be obtained via piecewise smoothing for the proposed method. The data gaps of 5 s and 10 s for GNSS and INS are simulated. These experiments show that the maximum errors of the smoother results are 0.4374 m and 4.0443 m for the proposed algorithm and these errors are better than the results for the loosely coupled and tightly coupled approach of the IE and the conventional loosely coupled approach. PubDate: 2018-11-15 DOI: 10.1007/s40328-018-0238-8

Authors:Guiwu Chen; Lei Song; Ray Ruichong Zhang Abstract: The acoustic response has many important roles in seismic exploration and nondestructive testing. It enables the development of fracture classification and sizing. In this paper, we combined Hudson’s effective medium scheme and finite-difference time-domain modeling method to simulate acoustic wave propagation in fractured media. Fractures are represented by discrete fracture networks, allowing for a state-of-the-art representation of natural fracture networks by a negative Exponential Law length distribution. The propagation of acoustic waves that are emitted by a point source and reflected from a fractured area in a 2D digital rock model are examined numerically with the purpose of developing an acoustic inference of fracture properties. In these fractured models, we vary the number and mean length of fractures to explore the relation between internal structure of rock and acoustic wave field characters. The modeling results indicate that acoustic wave field is more sensitive to the fracture number than to the mean of the fracture length. Moreover, a fracture-dependent attenuation analysis of the reflection records of discrete stochastic fractured models is obtained. The frequency- and time- dependent attenuation profiles feature two parts in frequency, (1) fracture-to-background at lower frequencies and (2) fracture-to-fracture at higher frequencies. Our results indicate that accounting for attenuation effects may not only allow for improving estimation of fracture number, but also provide information about geometrical characteristics of length distribution. Such an approach can be used to estimate nature fracture network properties with given acoustic records. PubDate: 2018-11-12 DOI: 10.1007/s40328-018-0237-9

Authors:Miloud Chermali; Fouzi Bellalem; Mohamed Walid Belgroun; Amar Boudella; Mohand Ouabdallah Bounif Abstract: The Wenner and offset Wenner array is among the quite recent configurations used to assess and reduce the disturbing lateral effect in resistivity soundings. Even if this system could be considered as one of the most efficient configurations for this purpose so far, the restricted number of measuring points makes its vertical resolution limited. To fix this limitation, Barker found out a specific equation by which resistance values at points halfway between the actual measuring ones are computed without being measured. This aim was reached by combining expressions of electric potentials at various electrode spacings. For the same purpose, three other equations were worked out and tested. For a single sounding, resistance values were computed at intermediate points by the mean of these equations. Observational errors were also calculated using Barker’s formulae. The computed resistance values were found to be contaminated by these errors, in varying degrees to the extent that some of them were lacking reliability. Furthermore, at each electrode spacing, the differences between the interpolated and the assumed resistivity values on a straight line joining the actual measuring points were calculated. After normalizing these differences to their corresponding averages, the RMS of these normalized differences were computed for a set of soundings using the four equations. Finally, a comparison of the obtained results with the errors of measurements from the reliability of the computed resistance values was made. This comparison allowed classifying these equations from the reliability of the intermediate resistivity values perspective. In addition, Barker’s choice of one of these equations as the one that gives the most satisfactory results is justified. PubDate: 2018-10-11 DOI: 10.1007/s40328-018-0236-x

Authors:Sumesh Gopinath; P. R. Prince Abstract: In the present study, information theoretic distance-based entropies have been employed for a better understanding of nonlinear features of the magnetosphere using proxies such as AE and Dst indices. Among the various distance-based entropies, approximate and sample entropies are considered as potential quantifiers which could track the nonlinear variations of the magnetospheric system. The generalized nonextensive Tsallis q-entropy and Fisher’s information measure are used to study the nonextensive entropy and complexity respectively of the magnetospheric dynamics. For the analysis, 1-min AE and Dst indices are considered during the period 1985–2007. The results indicate that nonlinearity and nonextensive entropy of Dst index are solar activity dependent. But, the nonlinearity and nonextensive measures of AE index are not having any solar activity dependence. This implies that, other than the modulating solar wind, certain other complex phenomena of internal origin are having influence on the dynamics of geomagnetic activity in the auroral zone. PubDate: 2018-09-19 DOI: 10.1007/s40328-018-0235-y

Authors:Alexandru Szakács; Zoltán Pécskay; Ágnes Gál Abstract: Based on a self-consistent K–Ar database completed with up-to-date geochronological information, this review paper addresses the general time–space evolution of Neogene magmatism in the Carpathian–Pannonian region, aiming at identifying significant patterns and trends. Grouped according to petrochemical criteria (felsic and intermediate calc-alkaline, alkaline) and major geotectonic units (Carpathian and intra-Carpathian, in turn divided into ALCAPA and TISZA-DACIA lithospheric blocks), the dated rocks reveal distinct evolution patterns. The intra-Carpathian area is characterized by (1) scattered, areal Eastward shifting magmatism, more developed on the ALCAPA block, involving felsic and intermediate calc-alkaline magmas in the early stage of evolution (21–7 My) and alkaline magmas in the later stages (11 to < 1 My), and (2) long-lasting magmatic activity spatially focused in an area ca. 200 km across located on the ALCAPA block, shifting in time from felsic to intermediate calc-alkaline and finally to alkaline compositions. We suggest that a mantle plume-type thermal anomaly was acting at the site of focused magmatism contributing to the development of higher volume areal-type magmatism in the same block, as compared with the later activated colder and more brittle TISZA-DACIA block. The Carpathian magmatism in turn displays two distinct time–space evolution patterns: (1) a long-lasting and slowly eastward migrating intermediate calc-alkaline magmatic front, active in the 15–9 My time interval along most of the Carpathian thrust-and-fold belt, generated in a subduction environment, and (2) a time-transient magmatism along the South-easternmost Carpathian segment, in the 11 to < 0.1 Ma time interval, whose purely subduction-related origin is questionable. Beyond these evolution patterns, two regional CPR-wide trends have also been identified: (1) the general Eastward shift of magmatic activity in time, irrespective of the chemical type, and (2) the convergence of magmatism in both time and space towards the South-eastern corner of the CPR (i.e. the Carpathian bend area in Romania), currently the geodynamically most active (and most hazardous) area of the whole CPR, including the Vrancea seismic structure. Eastward directed asthenospheric flow, possibly related to the inferred mantle plume responsible for the focused time-persistent volcanism on the ALCAPA block, might be considered as being at the origin of these evolutionary trends. PubDate: 2018-08-09 DOI: 10.1007/s40328-018-0230-3

Authors:Erman Şentürk; Murat Selim Çepni Abstract: In this study, daily mean vertical total electron content (VTEC) and daily mean 2-h VTEC values were obtained from Center for Orbit Determination in Europe–Global Ionosphere Maps (CODE–GIM) data over the region of Turkey between January 1, 2003, and December 31, 2016. The time interval is sufficient to reflect temporal changes of the ionosphere. The daily mean VTEC data was used to analyze the space weather effects on the VTEC variability and daily mean 2-h VTEC data was utilized to see the pattern of the diurnal, monthly, seasonal and yearly variation of VTEC values. The highest correlation was found between VTEC and F10.7 (r = 0.83). Totally, 40 major geomagnetic storms were identified that 45% of the storms are caused a decrease and 55% of the storms are caused an increase in VTEC variation. The maximum VTEC is shown at 13:00 LT and the minimum VTEC is shown at 03:00 LT according to diurnal variation of the 14-year mean 2-h VTEC. The maximum VTEC is shown on April and the minimum VTEC is shown on July according to diurnal variation of monthly mean VTEC. Diurnal variation of seasonal mean VTEC and its standard deviations are higher in equinox than solstices. Diurnal variation of yearly mean VTEC has a significant change from low to high solar activity periods. PubDate: 2018-08-09 DOI: 10.1007/s40328-018-0233-0

Authors:Ilke Deniz; Gokhan Gurbuz; Cetin Mekik Abstract: Studies of estimating precipitable water vapor (PWV) from continuous Global Navigation Satellite System (GNSS) stations with high temporal and spatial resolution continuously have become popular in recent years. In this estimation process, the weighted mean temperature (Tm) and the conversion parameter (Q) are the most important parameters to convert tropospheric zenith delay (ZTD) to PWV. In this study, Tm and Q time series are derived by assessing 4103 profile observations of eight Turkish radiosonde stations (RS) for approximately one year. The Tm − Ts linear regression model is developed. In analogy to Tm − Ts model, the Q values are modelled based on different combinations of surface temperature (Ts), station latitude (θ), station height (H) and day of the year (DOY). To test the validity of these models, the GNSS derived PWV (PWVGNSS) values are computed from the GNSS data of just over a year for the Istanbul and Ankara RS-GNSS stations using the most precise Tm and Q models, and later they are compared with the PWVRS values. The mean of the differences obtained for the Ankara and Istanbul stations are found to be 1.4–1.6 mm with a standard deviation of 1.7–1.8 mm, respectively. Moreover, modelling and interpolating meteorological parameters such as temperature, pressure, as well as PWV and ZTD are tested using the spherical harmonic functions (SHF). The results indicate that SHF can be safely and accurately used for modelling and interpolating meteorological parameters and ZTD. PubDate: 2018-08-07 DOI: 10.1007/s40328-018-0232-1

Authors:György Hetényi; Jean-Luc Epard; Leonardo Colavitti; Alexandre H. Hirzel; Dániel Kiss; Benoît Petri; Matteo Scarponi; Stefan M. Schmalholz; Shiba Subedi Abstract: The deformation pattern in active orogens is in general diffuse and distributed, and is expressed by spatially scattered seismicity and fault network. We select two relating datasets in the region encompassing Switzerland and analyse how they compare with each other. The datasets are not complete but are the best datasets currently available which fully cover the investigated area at a uniform scale. The distribution of distances from each earthquake to the nearest fault suggests that about two-thirds of the seismicity occurs near faults, yet about 10% occurs far from known faults. These numbers are stable for various selections of earthquakes and even when considering location uncertainties. Earthquake magnitudes in the catalogue are smaller than what could be expected from faults lengths. This suggests that the deep fracture pattern is more segmented than the superficial one, or mostly partial rupture during earthquakes, and (partly) the impropriety of the scaling law. Statistics on the distances from each fault to the nearest earthquake reveal that all supposedly-active faults in Switzerland have experienced a typically felt (magnitude 2.5 or larger) event, and only one out of six has not done so in the past four decades. Future applications of the presented approach to more complete or comprehensive fault databases may result in revised numbers regarding the connection between deep and superficial fracture patterns, representative of the stress regime of the region. The public and educational message: (1) in the region of Switzerland, earthquakes can happen in areas without known or mapped faults; (2) not all faults produce earthquakes within a human lifetime, but they seem to do so over long times. PubDate: 2018-08-06 DOI: 10.1007/s40328-018-0229-9

Authors:Eszter Szűcs; István Bozsó; István János Kovács; László Bányai; Ágnes Gál; Alexandru Szakács; Viktor Wesztergom Abstract: The Carpathian bend is amongst the tectonically most active areas in Europe where intraplate subduction triggers sub-crustal earthquakes releasing significant amount of seismic energy in a well-defined seismic zone. To constrain the deep processes by exploiting their linkage to the surface processes an accurate knowledge of surface deformations is required. Detection of small-magnitude tectonic processes with high reliability is a challenge in which the recent space geodetic techniques may bright a breakthrough. In this study we used the archive ENVISAT data set of the European Space Agency to investigate the feasibility limit of detecting crustal deformations in the region of the south Carpathian bend, where past geodetic observations failed to unravel the tectonic processes with high details. Despite the inherent limitations of radar interferometry our results show that coherent velocity field can be estimated with a magnitude of few mm/year. The vertical displacement field suggests subsidence in the Brasov basin which is in agreement with former studies, however radar interferometry can provide a more detailed picture. PubDate: 2018-08-01 DOI: 10.1007/s40328-018-0228-x

Authors:Rakesh K. Dumka; Bahadur Singh Kotlia; Girish Ch. Kothyari; Joydeep Paikrey; Siddharth Dimri Abstract: We present geodetically estimated crustal strain rates in Uttarakhand Himalaya, a region which has long been considered as a part of seismic gap. We processed and analyzed the GPS data, acquired from the sites enveloping all the litho-tectonic units from the Sub Himalaya in the south to the Tethys Himalaya in the north together with the major Himalayan thrust/fault systems. On the basis of the obtained dataset, we conclude that the maximum amount of crustal shortening takes place towards the hinterland in the vicinity of Main Central Thrust and Inner Lesser Himalaya which is also in agreement with high seismic activity in these sectors. The GPS velocities of the sites (Indian reference frame) show significant variation from the sub-Himalaya to the Tethys Himalaya. The Sub and Inner Lesser Himalayan parts exhibit low deformation rate in contrast to the maximum amount of deformation in the Inner Lesser and Higher Himalayan segments. The strain analysis reveals lateral variation with high strain zones (HSZ) and moderate strain zones (MSZ) within the compressional regime in the Uttarakhand Himalaya. The strain rate of 0.45 and 0.25 micro-strain/year is observed in the HSZ and MSZ respectively. By comparing the strain rate with the seismicity pattern for the past five decades, we suggest that the earthquakes in the HSZ are related with ramp structure of the MHT, whereas, part of accumulated strain in the MSZ is being released in form of the present day seismic activity. PubDate: 2018-07-23 DOI: 10.1007/s40328-018-0226-z

Authors:M. Soleimani; H. Aghajani; S. Heydari-Nejad Abstract: Accurate geological modeling of subsurface structures with all available geophysical data is a challenging task in geo-exploration studies. Concern in precise modeling will increase by increasing geological complexity of subsurface structures such as salt dome. Integrating various sources of geophysical data will reduce uncertainty in geological modeling in complex media. In this study, we introduce an integrated strategy for more appropriate detection of salt boundary in seismic image, by applying the normalized full gradient (NFG) method, used in processing of potential field data. In the proposed strategy, we initially, analyzed sensitivity of the NFG parameters by derivation of a synthetic model. Parameter analysis and optimization showed dependency of geometrical properties of the geological target to the harmonic number in the NFG method. Afterwards, seismic traces were processed by the NFG method. Results showed increase in vertical resolution of seismic envelope compared to the result of the well-known Hilbert Transform. The proposed strategy was applied on a synthetic seismic data contains complex salt model. Results have shown that application of the proposed strategy produced higher resolution seismic image compared to the Hilbert Transform method. The method also was applied on a field seismic data with a complex salt dome from southwest of Kazakhstan. Seismic image obtained by the integration procedure could better exhibit body of the salt dome, as well as better interpretation of faults, layer boundary truncation, salt bottom and subsalt layers. Thus, it was concluded that the proposed strategy could be considered as an alternative to resolve some of ambiguities in geological interpretation of seismic data in complex geological settings. PubDate: 2018-07-09 DOI: 10.1007/s40328-018-0222-3

Authors:Sermet Öğütcü Abstract: The geocentric datum of Turkish CORS Network (TUSAGA-Aktif) is a semi-kinematic datum realized with respect to the International Terrestrial Reference Frame (ITRF 96) at the reference epoch of 1 January 2005 (2005.00). This realization was maintained by ITRF no net rotation (NNR) velocities of CORS stations. Up-to-date ITRF NNR velocities were determined by General Command of Mapping in Turkey using 7 years of CORS stations data from 2008 to 2015. In accordance with Turkish surveying regulation, there are two types of coordinate computation of the control points performed with Global Navigation Satellite System relative positioning technique based on the datum. Coordinates of the first-order and the second-order control points are computed in semi-kinematic datum, whereas the third-order control points are computed in static datum. Generally, CORS stations of TUSAGA-Aktif are used as fiducial stations for coordinate computation of these control points. In this study, baseline deformation effect of static datum on the three-dimensional position of the points are investigated. 20 CORS stations within TUSAGA-Aktif were chosen to simulate the rover and the fiducial stations. The results show that relative displacement from the reference epoch (2005.00) between the rover-fiducial stations at the measurement time and the positioning error of the rover station are in a good agreement. The differences are in the order of mm to cm level. The results also show that when more than one fiducial station used in static datum processing, mean relative displacement between the rover-fiducial stations at the measurement time and the positioning error of the rover are also in a good agreement. The results emphasized that, velocities of the fiducial stations should be known by the users for conducting static datum processing with minimum baseline deformation as much as possible. PubDate: 2018-06-27 DOI: 10.1007/s40328-018-0223-2