Virginie Dejoux
email: virginie.dejoux@inrets.fr

Inrets-Dest

SURVEY ON PEOPLE WITH TRAVEL DIFFICULTIES IN FRANCE

Keywords: handicap, mobility, national travel survey

The regular population's ageing, leaded to a decline in mortality and birthrate may affect the mobility of the whole population. Moreover, in France since few years there is a will to fully integrate persons with disabilities into society, in particular with the passing of the law of February 2005. This law reminds the need for accessibility to the whole chain of travel at all. In this context, the knowledge of people with reduced mobility seems nowadays essential. The objective of this research is to analyze the mobility of disabled people. This research is based on the French National Survey on Transport (FNTS) conducted in France in 2007-2008 by the Ministry of Transport and the National Institute of Statistics with the scientific support of INRETS. It is the data source providing the most transverse and consistent overview of mobility, whatever the modes and the transport situations of people living in France. This study should allow us to provide a detailed knowledge of the mobility of people involved.

reshaping the environment and eliminating the obstacles for people with disability. Thus, to understand and try to compensate for disability the focus has moved from the person with disability to analyzing the disability situation, with its individual and environmental components (WHO/OMS, 1998). It has thus been shown by a Canadian team led by Patrick Fougeyrollas that a disability situation arises from a reduction in the ability to carry out day-to-day activities caused by the interaction between personal factors (impairments, activity limitations, and other personal characteristics) and environmental factors [START_REF] Fougeyrollas | Documenting Environmental Factors for Preventing the Handicap Creation Process : Quebec contributions relating to ICIDIH and social participation of people with functional differences[END_REF]1998). Measures that aim to improve individuals' capacities are nowadays accompanied by measures that aim to change the environment by removing any potential barriers [START_REF] Ravaud | Recherches sur les déplacements et l'accès aux transports des personnes handicapées[END_REF]. Thus the difficulties encountered by people during their travel are influenced by their personal characteristics and their environment.

The demographic and social changes that are currently taking place in the developed country are likely to affect the future travel practices of the whole population. Factors such as the disappearance of local services and the increasing fragmentation of social and family networks affect lifestyles and may make it more difficult to meet travel needs. In addition, the ageing of the population caused by a reduction in mortality and birth rates (Brutel, 2002) will change travel patterns and may induce new needs in terms of transport.

The aim of this paper is to analyze the mobility of disabled people with disability and to compare this mobility with the patterns of those without difficulties. Mobility will be studied in term of number of trip, distance and daily travel time.

METHODS

Our study is based on the last National Transportation and Travel Survey (Enquête Nationale sur les Transports et les Déplacements -ENTD) that was conducted in France in 2007-2008(Armoogum et al., 2007)). The survey is design to study the travel practices and the use of personal and public transport modes of households living in France. The national transport survey is the largest mobility survey in France, with a sample size of 20,000 households, and considers all trips irrespective of their purpose, length, duration, transport mode, or the period of year or time of day. Data collection is spread over six waves covering 12 months, in order to neutralize the seasonal variations which affects mobility (especially for long distance travel).The aim of this survey is the description of short and long distance trips made by households living in France, as well as their access to and use of public and private transport means. As we have seen above, today, disability is seen as being "…the expression of a conflict between an individual's activity limitations, i.e. functional reduction, and daily life" (Minaire, 1992). It therefore seems worthwhile to identify those persons who are in disability situations when they travel on the basis of the difficulties they report rather than a priori by identifying their activity limitations. Therefore, situations of disability are identified on the basis of respondent's self-reported travel difficulties According to the survey, in France in 2007-2008, about 10% of individuals of 15 years of age or over (i.e. 5.1 million individuals) report difficulties when moving around outside their home. In the following analysis we differentiate people with difficulties from those without difficulty from their answer to this question.

RESULTS

LESS TRAVEL FOR PEOPLE WITH DISABILITY

People reporting travel difficulties make 1.8 trips per day, on average, which is almost half of those without difficulties (Table 1). Even if this difference was largely due to a higher level of immobility, those with travel difficulties still make slightly fewer trips: 3.3 trips per person per day compared with 3.9 for those reporting no difficulties. To remove the impact of immobility on the average number of trips, we take into account for next analysis only people who make a trip. A number of sociodemographic characteristics affect travel difficulties, in particular advancing age, the lack of professional occupation, and not owning a car [START_REF] Dejoux | The travel practices of disabled travellers in France, 89 th Annual meeting of Transportation Research Board[END_REF]. It seems interesting to compare the number of trips of persons with disabilities and of the others according to these sociodemographic characteristics. Graph 1 represents the evolution of the number of trips per day per person by age for people with and without difficulties, and it can be seen that the two curves are fairly similar. This result confirm that the number of trips per day decreases with age (Dejoux et al., à paraître) and this for people with and without difficulties.

GRAPH 1 Number of trips per person per day according to the age

The number of daily trips diminishes with age: it falls in the case of people with difficulties by 3.9 trips per day per person of under 45 years of age to 2.6 trips per day for the over 75 year-old. This reduction was almost similar in the case of people without difficulties whose number of trips fell from 4.2 to 3.0.

Regarding professional occupation, in the whole population, the number of trips is higher for active than inactive people and retired. Whatever the occupation, the average number of trips of people with difficulties is lower than of those not reporting difficulty (graph 2). Thus, if this difference is quite low for active people (3.9 against 4.1), it is slightly higher for inactive (3.4 against 3.7) and more for retired (3.1 against 3.5). Regarding inactive people, several hypotheses can be made: the inactive can be having severe disabilities, limiting their ability to move, or the difficulties of travel of these people are the reason for unemployment.

In the whole population, persons belonging to a non-motorized household move less than those in households with a car and even less than multi-motorized households. The motorization is indeed a very important determinant of mobility patterns. People with difficulties are moving less whatever the level of car ownership in their household (graph 2). But, the difference is greater among households nonmotorized. Different factors explain these results: people with disabilities are not always able to drive a car, because of impairments (eg visual impairment) or cost of car's adaptation (eg for severe physical disabilities) and conversely the availability of a car in the household, for use either as driver or as passenger, can reduce the discomfort of people for their travel.

SHORTER TRIPS FOR PEOPLE WITH DISABILITY

To study the distance of travel, we have the « crow flies » distance between the origin and destination of travel. From the table below (table 2), we can see that the trips of people reporting difficulties are shorter than those reporting no difficulty: Indeed, while about 60% of the trips of people with difficulties are performed in the same municipality, it is the case for 48% of the others. Travel distance depends strongly on the transport modes; we have in a second time analysed the distribution of distances by mode (graph 3). Whatever the transport mode used, the proportion of travel for people with difficulties whose origin and destination are the same municipality is higher. However, if the distribution of travel distances is almost similar in the case of walk and car, the difference is higher for urban transport. More than half of all trips made by public transport by people with difficulties are made in the same municipality, when that is the case for 31% of trips of people reporting any difficulty. Corollary to previous results, the daily travel time is lower for people with difficulties when they travel (graph 4): 43 % of these people are moved less than 30 minutes against 26% for those reporting any difficulty. Nevertheless, the daily travel time is related to the number of trips. We must therefore also analyse the travel time per trip. We observe that the trips of people with disability (18 minutes) are shorter than the trips of the others (20 minutes). We also note that trips made as a pedestrian or by transport public are longer for people with difficulties; and conversely those made by car are shorter. We can assume that the difficulties encountered during travel made as a pedestrian or by public transport extend travel time. And, as we have seen, people reporting difficulties and who have access to cars use them for shorter trips.

  -ENTD 2007-08 The age groups used in this graph are: 35-54 years, 55-64 years, 65-74 years, 75 years and over

TABLE 1 Number of trips per person per day according to their level of difficulties

 1

	Average number of trips per day	people reporting any difficulty	people reporting difficulties	Whole population
	per trip-maker	3,4	1,8	3,3
	all respondents	3,9	3,3	3,9
	Sources: INSEE -ENTD 2007-08

TABLE 2 Crow flies distance between the origin and destination municipalities

 2

	Crow flies distance	people reporting any difficulty (%)	people reporting difficulties (%)
	same municipality	48,1	59,8
	different municipality : less than 5 km	17,6	15,3
	different municipality : 5 -10 km	15,1	12,1
	different municipality : more than 10 km	19,2	12,8
	Sources: INSEE -ENTD 2007-08

4 the number of people with disabilities under age 35 is too small in the sample, so we did not represented on this graph.

Sources: INSEE -ENTD 2007-08

CONCLUSION

As the disability situations are nowadays defined as a conflict between personal factors and environmental factors, the French ENTD survey has allowed us to detect people in disability situations during their trips, on the basis of their responses to the question about their travel difficulties. In France, in 2007-08, about 10 % of the respondents reported being in a disability situation.

Our research has compared the mobility of people with difficulties to those without difficulty. People with disability travel less than people who report no difficulties (Bakker and Val Hal, 2006), whether in terms of the number of trips, distances covered or travel time.

Our study showed that age, the professional occupation and the household car ownership influence the mobility. Finally, as the elderly have been identified as more frequently being in a situation of disability when they makes trips than other groups, the ageing process which is currently taking place in developed countries should have a major impact on travel difficulties and, more generally, travel practices (Bush, 2003). Brutel, C (2002).La population de la France métropolitaine en 2050 : un vieillissement inéluctable. Economie et statistiques. Vol.355-356.pp. 57-71 Bush, S. (2003). "Forecasting 65+ Travel: An Integration of Cohort Analysis and Travel Demand Modeling," Massachusetts Institute of Technology, Department of Civil and Environmental Engineering, Cambridge, MA, USA.

BIBLIOGRAPHY


F Covello
email: fabio.covello@asi.

F Battazza

A Coletta

E Lopinto

C Fiorentino

L Pietranera

G Valentini

S Zoffoli

COSMO-SkyMed an existing opportunity for observing the Earth

Keywords: Announcement of Opportunity, Background Mission) COSMO-SkyMed, Satellite Constellation, Synthetic Aperture Radar, Dual-Use, X-Band

COnstellation of small Satellites for Mediterranean basin Observation (COSMO-SkyMed) is the largest Italian investment in Space Systems for Earth Observation, commissioned and funded by Italian Space Agency (ASI) and Italian Ministry of Defence (MoD). COSMO-SkyMed is a Dual-Use (Civilian and Defence) end-to-end Earth Observation System aimed at establishing a global service supplying provision of data, products and services compliant with well-established international standards and relevant to a wide range of applications, such as Risk Management, Scientific and Commercial Applications and Defence Applications. The system consists of a constellation of four LEO mid-sized satellites, each equipped with a multi-mode high-resolution SAR operating at Xband. Three out of four COSMO-SkyMed satellites have been successfully launched the 8 th of June, the 9 th of December 2007 and the 25 th of October 2008 respectively, while the remaining satellite will be deployed within 2010. COSMO-SkyMed 1 and 2 completed their Commissioning phase to test, verify and qualify the overall System and from the 1 st of August 2008 both satellites are in the

INTRODUCTION

COSMO-SkyMed is the first italian dual Space System dedicated to the Earth Observation. COSMO-SkyMed is the largest Italian investment in Space Systems for Earth Observation, commissioned and funded by Italian Space Agency (ASI) and Italian Ministry of Defence (MoD). It is a Dual-Use (Civilian and Defence) end-to-end Earth Observation System aimed at establishing a global service supplying provision of data, products and services compliant with well-established international standards and relevant to a wide range of applications, such as Risk Management, Scientific and Commercial Applications and Defence Applications.

The system consists of a constellation of four LEO mid-sized satellites, each equipped with a multimode high-resolution SAR operating at X-band. ASI in cooperation with MoD manages the contract assigned to an Italian industrial team, that is in charge of the project development. Thales Alenia Space Italia (TAS-I) is the Prime Contractor.

The results coming from the utilisation of the two operative satellites reveal the significant achievement of the X-band SAR and the importance of fast response time in a wide variety of A c c e p t e d M a n u s c r i p t applications. In this paper ASI will be presented some analysis and results related to a set of X-band SAR applications conducted during 2008. Moreover it will be given an overview of the mission exploitation strategy.

BRIEF MISSION NOTES

The object of the COSMO-SkyMed Program is to develop an End-to-End, turn-key system for "dual use" for both civilian and Defense purposes.

Primary Mission objective is thus to meet Customer's needs, under economical, schedule and political constraints, for a spaceborne Earth Observation System capable to provide:  Environmental Risk Management for both civilian Institutional and Defence needs, through monitoring and surveillance applications assessing exogenous, endogenous, and anthropogenic risks.

 Provision of commercial products and services (e.g. for agriculture, territory management) to world-wide civilian user community In order to reach these objectives the system has been conceived with the following main features:

 It is able to acquire images all over the world in every atmospheric condition during night and day,  It is able to produce a large number of images with high resolution, accuracy (geolocation, radiometry etc) and quality,  It is able to produce images for polarimetric and interferometric applications, A c c e p t e d M a n u s c r i p t  It is able to acquire images with very short revisit and response times according to a specific product order. Indeed COSMO-SkyMed Space Segment, at fully deployed constellation (4 satellites), will be capable to collect up to 1800 images per day; while the Ground Segment is currently downgraded in order to archive up to 560 images per day and to process 200 level 1C/1D products per day.

Obviously the Ground Segment capacity can be scaled in order to fully exploit the constellation capacity when needed.

In order to supply data for a wide variety of application that range from cartography to emergency response the SAR payload has been designed to acquire a scene in various modes (see Table . 1) according to the image area and the resolution that is requested.

The Ground Segment can process this data in order to obtain product at the following standard processing level:  Level 0 (RAW): containing for each sensor acquisition mode the unpacked echo data in complex in-phase and quadrature signal (I and Q) format.

 Level 1A (SCS), whose processing is aimed at generating Single-look Complex Slant (SCS) products.

 Level 1B (MDG), whose processing is aimed at generating Detected Ground Multi-look (MDG) products.

 Level 1C Products (GEC), whose processing is aimed at generating Geocoded Ellipsoid Corrected (GEC) products.

A c c e p t e d M a n u s c r i p t  Level 1D Products (GTC), whose processing is aimed at generating Geocoded Terrain Corrected (GTC) products.

Operative Modes

COSMO-SkyMed can operate in three different operative modes:

 Routine,  Crisis,  Very Urgent.
Each operative mode allows to satisfy different needs in terms of timeliness:

 Routine mode: The image order can be satisfied in less than 72 hours.

 Crisis mode:

The image order can be satisfied in less than 36 hours on a specific crisis area.

 Very Urgent mode:

The image order can be satisfied in less than 18 hours.

Time Performance

Four definitions apply to the time performances:

A c c e p t e d M a n u s c r i p t

The time performance values depend by the target coordinates, the active Ground Segment, the constellation configuration and the operative mode.

The following tables (Table . 2 andTable. 3) report the values of the revisit time and the response time, scaled from the current configuration (2 satellites) to 4 satellites in orbit, in the average and worst cases. These values are referred to the nominal operative mode (Routine mode).

At the time being these time performances are the best that can be obtained among civilian SAR Systems.

THE SPACE SEGMENT

Orbital Configuration

In the nominal configuration, satellites are equi-phased in the same orbital plane, as shown in Fig. 1.

The nominal orbital configuration is conceived to grant access all over the globe in few hours, with at least two access opportunities per day with different incidence angles.

The mutual position of the satellites can be modified in order to make it more suitable for interferometric acquisition. Indeed the system can produce interferometric and DEM products, combining two radar acquisitions of the same target area detected by two satellites of the constellation with the same geometry. Obviously for some applications the more the two acquisition are close each other the more the decorrelation between the two images is low resulting in a better quality of the product. In COSMO SkyMed two interferometric configuration are foreseen: Tandem and Tandem-like (one-day interferometry).

A c c e p t e d M a n u s c r i p t

In Fig. 2 is depicted the interferometric Tandem configuration. The two satellites are separated both in phase and in LTAN, with two different orbital planes with slightly different nodes (0.08 degrees of separation), such to obtain the "same" ground-track. This corresponds to a mutual distance of 151 km along track and allows to acquire the same scene with the same geometry with a delay of 20 seconds. The interval of the normal baseline can vary in a range of [100 m, 3500 m] (with 20% of accuracy) according to the acquisition mode.

In the Tandem-like configuration, two satellites are on the same orbit plane at a distance of 67,5°. This configuration allows to revisit any place on the earth with the same geometrical conditions (i.e. incident angle, etc.) after one day. The current configuration of the constellation is shown in Fig. 3: COSMO-SkyMed 1 and 2 are positioned at 180° each other, meanwhile COSMO-SkyMed 3 and 2 at 67,5° in tandem-like configuration (also called "one-day interferometry configuration").

Platform

The following Fig. 4 shows the COSMO-SkyMed satellite in "stowed" configuration, i.e. when it is mounted in the launcher, and in fully deployed configuration. The platform architecture has been conceived to monitor each on-board equipment, to collect and distribute data to al the satellite unit, to receive and decrypt telecommands sent from the ground, to control the attitude and the orbit manoeuvres and for the transmission of satellite telemetries and the images to the ground stations.

One of the main characteristics of the platform is its agility since it makes possible acquisitions in left and right looking allowing to extend the access area of the System. This can be obtained by an attitude manoeuvre. The nominal side looking mode is the right looking.

A c c e p t e d M a n u s c r i p t

SAR Antenna

The SAR antenna operates in X-band, with various resolutions (from 1 to 100 meters) and a number of polarizations over a large access region. It is equipped with a fixed antenna, having electronic scanning capabilities and it can manage a number of operative modes for the image acquisition but also for internal calibrations.

The nominal incidence angles (where the system grants the image quality requested) vary between 25° and 50°. The extended incidence angles vary between 20°-25° and 50°-59° but also in this case the image quality is very close to the nominal condition.

The access area, using the extended incidence angles, can reach 630 km.

THE GROUND SEGMENT

Overview

The COSMO-SkyMed system is dual, hence the applications are for civilian and defence users, assuring at the same time the data confidentiality and the integrity in each operative configuration.

The principles of a dual system are obtained through a specific architecture based on the innovative concept and the implementation of:

 the Ground Segment elements, with the aim to satisfy the civilian and defence user needs at the same time;

 the common centres, where the information are melted and processed together, adequately protected in terms of security.  User Ground Segment (UGS) whose aim is to receive and process the user requests, to acquire, archive, process and deliver the data received from the satellites of the constellation;  Communication Network;  GPS Fiducial Network: a support service to give the GPS ephemeris and the necessary data to increase the products geolocalisation.

Integrated Logistics and Operations Segment

Given the complexity and heterogeneity of the system, a big emphasis has been given since the design stage to Integrated Logistics and Operations Segment (ILS&OPS), that include the design and development of all the necessary resources processes and services needed to grant the availability and sustainability needed to operate the overall system.

A c c e p t e d M a n u s c r i p t

LEOP AND COMMISSIONING PHASES

Overview

The first three satellites have been successfully launched from Vandenberg Air Force Base in California (US) by BOEING DELTA II Rocket. The outstanding performance of the Rocket allowed the satellites to be in the expected orbit and to preserve important amount of propellant.

At the current time the system with two satellites is in the operational phase and the civilian institutional and commercial users, as well as the defence users, are ordering images over a wide variety of areas.

The third COSMO-SkyMed satellite has been launched on October 28 th 2008, and after the successful completion of LEOP, is entering its commissioning phase. The satellite has been positioned in Tandem-like configuration allowing, when operational, to perform 1-day interferometry.

The entire constellation will be completed by the end of 2010 and it will be fully operative by the end of 2010.

LEOP

During this phase the launch completion, the correctness of the orbital parameters and the start-up of the satellite have been verified. It is important to highlight that COSMO-SkyMed guarantees this performances within the very tight time constraints shown in 2.2. Indeed the localization error can be improved gathering and integrating GPS measure of the site over a long time (weeks) but this is not applicable when the response time is of the essence as shown in 7.3 and 7.4. Therefore these characteristics make COSMO-Skymed very well suited for disaster management application .

OPERATIONAL PHASE

The System with two satellites entered in the operational phase on the 1st of August and is currently used by both civilian and defence users.

ACQUISITIONS DURING THE COMMISSIONING PHASE

Overview

During the Commissioning Phase the first two satellites have begun to acquire thousands of images all over the globe, showing the full potentiality of the System.

In the following there are some examples of applications realised using the images of COSMO-SkyMed 1 and 2 during the Commissioning Phase, to give an idea of the capability of the System and also to highlight the activities already performed to help rescue actions in emergency and natural disaster situations (Myanmar Flood and China Earthquake). Furthermore the next image (Fig. 6) makes even more evident as the X-band can show the internal difference of the ice sheets, for example the rescue ways, traced by icebreakers in the previous months (that are not visible in the optical spectral range), are clearly shown in the X-band image (circle and arrows highlight the rescue ways).

At the end of March after the alert based on the images collected by ENVISAT satellite of the European Space Agency (ESA), COSMO-SkyMed acquired some images of the disintegration of the Wilkins Ice Shelf as reported in Fig. 7 (Stripmap HIMAGE of the 31st of March 2008). COSMO-SkyMed constellation makes possible the monitoring of these fenomena with a fast revisit time and the identification of large and small ice pieces thanks to its high resolution. The COSMO-SkyMed acquisition (ScanSAR Huge Region collected on the 6th of May) is reported in Fig. 8.

The flood areas are recognisable in the dark areas (highlighted by the circles). Another COSMO-SkyMed image of the disaster is reported in Fig. 9.

The World Food Programme (WFP) used COSMO-SkyMed images to create maps to be used for rescue actions. The flood evolution (between 6th and 8th of May) has been represented in the following picture (Fig. 10) elaborated by the WFP (red areas are affected by the flood):

China Earthquake (May 2008)

A powerful earthquake has killed at least 10,000 people in China's south-western Sichuan province, up to 5,000 of them in just one county. Many more have been killed and injured in other parts of In Fig. 11 is reported an image of the Guan-Xian area (in Sichuan province). The image was relevant for monitoring the damage and the general situation of Guan-Xian area and the potential damage of the dike (see top left of the image). The image in Fig. 12 clearly shows the damage of a building after the quake. Indeed the pictures shows two buildings that in nominal condition should appear as two parallel bright straight lines; the collapsed walls of one of them are evident because the line is no more straight (see red arrows) and the debris produce an high backscattered energy due to their irregular shape.

The images acquired by COSMO-SkyMed, in the days immediately after the earthquake, were of a great importance to help the rescue actions. This event showed the huge contribution of the COSMO-SkyMed space constellation in monitoring and observation of natural disasters of this relevance.

Agriculture Multi-Temporal Acquisition (May-July 2008)

A multi-temporal acquisition over agricultural fields have been performed on the 25th of May, 26th of June and 28th of July 2008 over Kumagaya (Japan) area, near Tokyo city (Fig. 13). The area of acquisition is essentially composed of agricultural fields. The three COSMO-SkyMed images are acquired in the Spotlight mode and the multi-temporal acquisition is a Co-registered product obtained using the three Spotlight images.

The multi-temporal acquisition highlights a strong signal on the 28th of July (red-violet colour) that should be due to the presence of the rice fields (confirmed by observations in situ).

A c c e p t e d M a n u s c r i p t

On May the rice fields are just at the beginning of the cultivation status and on May-June the presence of the water becomes quite relevant (in such cases the radar signal is weak), on July the first rice plants begin to grow up and their presence makes stronger the SAR signal.

Remarks

These are just examples of the capability of the COSMO-SkyMed constellation. Now with the beginning of the operational phase, COSMO-SkyMed becomes an important vehicle for the study of the Planet.

COSMO-SKYMED SYSTEM ACCESS

The access to the COSMO-SkyMed products for civilian use is ruled by the COSMO-SkyMed data Policy. According to this policy there are two main classes of Civilian users:

1.
Institutional Users

Commercial Users

The institutional users are "entities" that pursue institutional, scientific (no profit oriented) and public objectives.

The access to COSMO-SkyMed civilian institutional user is granted through a web site:

www.cosmo-skymed.it. On this site the potential user will find all the information about COSMO-SkyMed available products and services and the general terms and condition of the service.

The Institutional Use status needs to be assessed via a process managed by ASI under the data policy regulation.

A c c e p t e d M a n u s c r i p t

A specific agreement will be settled identifying the user class and the relative quota of the COSMO-SkyMed System resources (including data and products) to be assigned to the end-user.

At the end of the process the user will get the information (user-name and password) necessary to log-in the system allowing to request data through a relevant web-form.

SCIENTIFIC MISSION EXPLOITATION STRATEGY

The Scientific Mission Exploitation Strategy is focused mainly on two projects:

 The COSMO-SkyMed Announcement of Opportunity;

 The Background Mission.

The main scopes of the Scientific Mission Exploitation Strategy is to grant the access to the System to the Scientific community, supporting them with the provision of COSMO-SkyMed data to conduct scientific projects in several thematic areas.

The First Cosmo-Skymed Announcement Of Opportunity

In May 2007 ASI issued the Announcement of Opportunity (AO) through the web pages of the Agency, to stimulate the use of COSMO SkyMEd system for civilian research purposes and Earth Observation application development, using the products of the Mission for:

 development of scientific applications;

 development and validation of Level 2 geophysics products algorithms;

 demonstration of the capabilities of COSMO-SkyMed in the thematic areas of GMES and GEO;

A c c e p t e d M a n u s c r i p t

 new ideas for system exploitation.

The first Announcement of Opportunity has been a success since the CSK AO has attracted a great interest from over 600 scientists in more than 40 nations. In response to the CSK AO these scientists have proposed around 200 complex and interdisciplinary projects covering a wide spectrum of applications.

The Italian scientific community answered strongly but it must be highlighted that great part of the projects are conceived by international scientific teams, demonstrating an excellent cohesion and interest of the scientists at world wide level.

Some statistics on the first Announcement of Opportunity are reported in the following:

 Requested observation areas are focused mainly on global coverage, Italy and Europe, as shown in Fig. 14.

 Research project proposals cover wide thematic areas specified in the announcement. A strong interest can be noted on land use monitoring, ocean and ice and landslides phenomena observation as shown in Fig. 15:

Selected projects will start in the first half of 2010 and will last two years providing the opportunity to exploit at least the data collected by three satellites of the constellation.

Background Mission

The Background Mission has been conceived by ASI with the aim to collect images all over the world for the catalogue fulfilling. The Background Mission implements the lowest level of priority plan, i.e. when no further activity (so called foreground activity) is defined.

The Background Mission is based on the COSMO-SkyMed primary mission objectives: The Commissioning Phase confirms that the system meets the performance required showing, for instance, that in the worst case the resolution stays below the threshold shown in For the scientific community the main project dedicated to the exploitation of the COSMO-SkyMed data is the Announcement of Opportunity.

In response to the first COSMO-SkyMed AO more than 600 scientists, coming from more than 40 nations, have proposed around 200 complex, interdisciplinary and international projects.

Selected projects will be activated by mid 2010 and they will last two years. These are two buildings whose walls in nominal condition should appear as two parallel bright straight lines; debris produce an high backscattered energy due to their irregular shape and the wall of one building is no more evident (see red arrows).



  Reaction time: time between the deposit and the acceptance of the user request at the User Ground Segment (UGS) until the SAR image on-board acquisition;  Information age: from the SAR image on-board acquisition to the product availability at UGS;  Response time: sum of Reaction time and Information age (The time needed for the delivery is not considered in the Response Time);  Revisit time: period between two successive acquisitions over the same target.

  The main components of the Common Ground Segment are:Centro Pianificazione e Controllo Missione (Mission Planning and Control Centre, CPCM), in charge of coordinating the on-board and on ground operations through the generation of the acquisition plan and the management of all the activities including the resources sharing and the acquisition requests conflict solving;  Core Ground Segment (CGS), composed of Centro di Controllo Satellite (Satellite Control Centre -CCS), Flight Dynamic System (FDS) and TT&C stations;

  All satellites have been placed in a stable orbital configuration showing nominal parameters in terms of thermal and power stabilisation, telecommands and control correctness and nominal deployment of the satellite appendices.

  A c c e p t e d M a n u s c r i p t5.3 Commissioning PhaseThe Commissioning Phase has been performed at the same time for COSMO-SkyMed 1 and COSMO-SkyMed 2, at the end of this phase both satellites entered in the Operational Phase. COSMO-3 successfully performed the commissioning first two stages (LEOP and In Orbit Test) devoted to performance requirements verification. Current activities are dedicated to check the system capability to maintain such performances in a quasi-operational context [12]. It is worth of mention that, though not yet formally commissioned, COSMO-3 has been used for Abruzzo earthquake acquisition campaign on April 2009, and it is expected to enter in operation in the second half of 2009. During the Commissioning Phase the verification of the functionality, the performance and the operations of both satellites and of the overall System have been completed. All the payloads, subsystems and elements of the satellites have been verified in orbit through the utilisation of the Ground Segment. All the calibration activities have been completed testing and verifying the SAR antenna of each satellite. The verification and validation of the whole System (satellites, sites and support System) have been completed. The results coming from the Commissioning Phase confirm the high nominal performances of the constellation in terms of quality of product, system capacity and time performances already mentioned in the previous sections and scaled to the constellation with two satellites (see Table.

A

  c c e p t e d M a n u s c r i p t

A c c e p t e d M a n u s c r i p t 7 . 2

 72 Ocean And Ice Applications (February-March 2008) The images acquired by the COSMO-SkyMed satellites during February and March over the Northern Caspian Sea and the Antarctic Region show the great potentiality of the X-band SAR data in Ocean and Ice applications. The penetration of the X-band electromagnetic waves allows volumetric analyses of the ice, as shown in Fig. 5 (Stripmap HIMAGE collected on the 9th of February 2008). The same image acquired by an optical sensor should show the sea surface completely covered by ice.

7. 3

 3 Myanmar Flood (May 2008) Devastating Cyclone Nargis hit the Yangon region (southern Myanmar) on May 3rd 2008. The following acquisitions have been done by COSMO-SkyMed 1 after the flood:  ScanSAR Huge Region: May 6th A c c e p t e d M a n u s c r i p t  ScanSAR Wide Region: May 7th  StripMap HIMAGE: May 8th  Spotlight-2: May 10th  Spotlight-2: May 11th  StripMap HIMAGE: May 14 th On the 6th of May over Rangoon area COSMO-SkyMed 1 acquired an image (SCANSAR -Huge Region) with a fast Response Time equal to 20 hours, allowing to know in a short time the situation of the areas affected by the flood and to identify the main zones where the rescue actions had to take part.

A

  c c e p t e d M a n u s c r i p t China after the 7.8 magnitude quake struck on the 12th of May. COSMO-SkyMed processed the first image with a Response Time of 16 hours from the alarm.

A c c e p t e d M a n u s c r i p t 

 t Risk Management Applications (guideline field) Scientific indications specified in the projects of the first CSK Announcement of Opportunity  Institutional Users  Commercial users 10. CONCLUSIONS At worldwide level COSMO-SkyMed is the only SAR constellation currently operative dedicated to the civilian and defence use. At present COSMO-SkyMed constellation allows to reach high performance in terms of Revisit and Response Time, number of images, image quality, short gap for interferometric acquisitions, these A c c e p t e d M a n u s c r i p t performances will be further enhanced when the third and the fourth satellite will complete the constellation (end of 2010).

  Coletta A. et al., "Interferometric Missions: Applications within ASI Space Programs", Proceedings of SPACEOPS06 -9th International Conference on Space Operations, Rome, Italy, 19-23 June 2006 [9] Caltagirone F. et al., "The COSMO-SkyMed Mission Description", Proceedings of IGARSS 2003, Toulouse, France, 21-25 July 2003.

A c c e p t e d M a n u s c r i p tFig. 1 .Fig. 2 .Fig. 3 .Fig. 4 .Fig. 5 .Fig. 6 .Fig. 7 .

 1234567 Fig. 1. COSMO-SkyMed constellation in nominal configuration

Fig. 8 .

 8 Fig. 8. ScanSAR Huge Region collected on the 6th of May over Rangoon Area, Myanmar.

Fig. 9 .

 9 Fig. 9. Stripmap collected on the 8th of May over Rangoon Area, Myanmar.

Fig. 10 .

 10 Fig. 10. Flood evolution Map [Credits to WFP].

Fig. 13 .

 13 Fig. 13. Spotlight collected on the 25th of May, 26th of June and 28th of July 2008 over

A c c e p t e d M a n u s c r i p t

Fig. 15 .

 15 Fig. 15. Research thematic areas.

Fig. 1 .

 1 Fig. 1. COSMO-SkyMed constellation in nominal configuration

Fig. 2 .

 2 Fig. 2. Tandem Interferometric Configuration in different orbit

Fig. 3 .Fig. 4 .Fig. 5 .Fig. 6 .Fig. 7 .Fig. 8 .Fig. 9 .Fig. 11 .Fig. 12 .Fig. 15 .

 3456789111215 Fig. 3. COSMO-SkyMed constellation in current configuration.

1 ,

 1 Table. 2 and Table.3). In Table.4 are reported some results obtained with a stripmap image during the calibration campaign performed in this phase, also in this case COSMO-Skemed confirm the expected results concerning the geometric resolution and a substantial overperformace concerning the geolocation accuracy.

  Table. 1 and time performaces are better than those in Table. 2 and Table.3. . The constellation has been successfully used in various applications in the field of risk and emergency management such as China's earthquake, Myanmar and Haiti flood, Abruzzo earthquake, ice monitoring (reduction of the glaciers, Wilkins Ice Shelf disintegration), multi-temporal acquisition for agriculture monitoring, interferometry, landslides monitoring, maritime surveillance and security, rapid mapping. The results reveal the strong contribution of the X-band SAR and the importance of satellite constellation to get fast response and short revisit time.. A preview of the images acquired as from August 2008 is available on the COSMO-SkyMed web site.

Table . 1

 . . COSMO-SkyMed acquisition modes characteristics.

		SPOTLIGHT	STRIPMAP	PING-PONG	SCANSAR WR	SCANSAR HR
	Resolution [m]	1 x 1	3 x 3 -5 x 5	15 x 15	30 x 30	100 x 100
	Swath [km]	10 x 10	40 x 40	30 x 30	100 x 100	200 x 200
	Possible	Single.	Single.	Alternating polarisation:	Single.	Single.
	Polarisation [T/R]	Selectable among HH or HV or VH or VV	Selectable among HH or HV or VH or VV	2 polarisations selectable among HH, VV, VH and HV	Selectable among HH or HV or VH or VV	Selectable among HH or HV or VH or VV
	Incidence Angles [deg]		25-50 (nominal) -20-59,5 (extended)

Table . 2

 . . Time performances of the CSK constellation -Worst Case.

		2 sat.	3 sat.	Full Constellation
	Response Time	90 h	85 h	72 h
	Revisit time	37 h	35.5 h	12 h

Table . 3

 . . Time performances of the CSK constellation -Average values.

		M a n u s c r i p
	A c c e p t e d
		2 sat.	3 sat.	Full Constellation
	Response Time	40 h	38 h	37.5 h
	Revisit time	5 h	3 h	2 h

Table . 1

 . . COSMO-SkyMed acquisition modes characteristics.

		SPOTLIGHT	STRIPMAP	PING-PONG	SCANSAR WR	SCANSAR HR
	Resolution [m]	1 x 1	3 x 3 -5 x 5	15 x 15	30 x 30	100 x 100
	Swath [km]	10 x 10	40 x 40	30 x 30	100 x 100	200 x 200
	Possible Polarisation [T/R]	Single. Selectable among HH or HV or VH or VV	Single. Selectable among HH or HV or VH or VV	Alternating polarisation: 2 polarisations selectable among HH, VV, VH and HV	Single. Selectable among HH or HV or VH or VV	Single. Selectable among HH or HV or VH or VV
	Incidence Angles [deg]		25-50 (nominal) -20-59,5 (extended)

Table . 1. COSMO-SkyMed acquisition modes characteristics.

 .


M S Bos
email: mbos@ciimar.up.pt

L Bastos

R M S Fernandes

Most GPS time-series exhibit a seasonal signal that can have an amplitude of a few millimetres. This seasonal signal can be removed by fitting an extra sinusoidal signal with a period of one year to the GPS data during the estimation of the linear trend.

A c c e p t e d M a n u s c r i p t

The influence of seasonal signals on the estimation of the tectonic motion in short continuous GPS time-series However, [START_REF] Blewitt | Effect of annual signals on geodetic velocity[END_REF] showed that including an annual signal in the estimation process still can give a larger linear trend error than the trend error estimated from data from which the annual signal has been removed by other means. They assumed that the GPS data only contained white noise and we extend their result to the case of power-law plus white noise which is known to exist in most GPS observations. For the GPS stations CASC, LAGO, PDEL and TETN the difference in trend error between having or not having an annual signal in the data is around ten times larger when a power-law plus white noise model is used instead of a pure white noise model.

Preprint submitted to Journal of Geodynamics July 24, 2009

A c c e p t e d M a n u s c r i p t

Next, our methodology can be used to estimate for any station how much the accuracy of the linear trend will improve when one tries to subtract the annual signal from the GPS time-series by using a physical model.

Finally, we demonstrate that for short time-series the trend error is more influenced by the fact that the noise properties also need to be estimated from the data. This causes on average an underestimation of the trend error.

Key words: GPS, time-series, noise

Introduction

The time-series analysis of daily GPS positions to estimate the secular motion of discrete points due to plate tectonics, has become a routine operation. Examples are the routinely processing of the European Permanent Network of EUREF [START_REF] Bruyninx | The EUREF Permanent Network; a multidisciplinary[END_REF], and the daily processing carried out at the Scripps Orbit and Permanent Array Center [START_REF] Prawirodirdjo | Instantaneous global plate motion model from 12 years of continuous GPS observations[END_REF]. At both initiatives hundreds of permanent GPS stations are analysed in a semi-automatic manner.

Mostly a linear plate motion, also called a linear trend, is assumed. In addition, the fact that these daily GPS observations are correlated in time is nowadays usually taken into account. This results in a larger uncertainty of the estimated linear trend compared to the formal error of uncorrelated observations [START_REF] Johnson | Monument motion and measurements of crustal velocities[END_REF].

It has been observed that most GPS position time-series exhibit an annual signal with an amplitude of a few millimetres (e.g., [START_REF] Dong | Anatomy of apparent seasonal variations from GPS-derived site position time series[END_REF]. For 27 GPS stations located over Iberia, taken from the WEGENER's GEOdynamic Although the causes are not yet completely understood, the most likely explanations are a combination of atmospheric loading (e.g., [START_REF] Van Dam | Predictions of crustal deformation and of geoid and sea-level variability caused by oceanic and atmospheric loading[END_REF]), hydrological loading (e.g., van Dam et al., 2001), and thermal expansion of the GPS stations (e.g., [START_REF] Romagnoli | Influence of soil consolidation and thermal A c c e p t e d M a n u s c r i p t expansion effects on height and gravity variations[END_REF]. [START_REF] Blewitt | Effect of annual signals on geodetic velocity[END_REF] demonstrated that an annual signal within the data deteriorates the accuracy of the estimated linear trend in time-series with an observation time span of a few years, even when this annual signal is taken into account during the estimation process.

They also showed that the presence of an annual signal has no influence on the accuracy of the linear trend when the observation period is around 1.5, 2.5, 3.5 and 4.5 years. At these specific observation periods there is no correlation between the annual signal and the linear trend. For longer observation spans the correlation between the annual signal and the linear trend can be neglected.

However, their results are based on the assumption of having white noise in the GPS observations while we already mentioned that it is nowadays accepted that GPS noise is correlated in time. In this research we investigate how temporal correlated noise alters the conclusions of [START_REF] Blewitt | Effect of annual signals on geodetic velocity[END_REF]. In addition, since we also have to estimate the parameters of the noise that is present within the data, we investigate how our imperfect knowledge of their properties influences the estimated trend error.

A c c e p t e d M a n u s c r i p t

Theory

Let us assume that we have a data set of N daily GPS positions which we designate by the vector x. These could be positions in East, North or Up direction. Since each direction is analysed separately, we only describe the procedure in one component. To these data we fit a linear trend that represents the tectonic motion and an arbitrary offset using Weighted Least-Squares. The design matrix is simply:

H =         1 t 0 1 t 1 . . . . . . 1 t N -1         with t 0 = 0, t 1 = 1, . . . (1)
To include an annual signal in the design matrix, we need to modify it as follows:

H =         1 t 0 cos(ω a t 0 ) sin(ω a t 0 )
1 t 1 cos(ω a t 1 ) sin(ω a t 1 ) . . . . . .

1 t N cos(ω a t N ) sin(ω a t N )         (2)
where ω a is the angular velocity of the annual signal.

If we also assume that we know the covariance matrix of the noise that is present within the signal, designated by C, then the covariance matrix of the estimated parameters θ is [START_REF] Kay | Fundamentals of Statistical Signal Processing: Estimation Theory[END_REF]:

Cov( θ) = H T C -1 H -1 (3)
Eq. (3) does not account for modelling errors. If for example the data would contain a quadratic signal (the tectonic plate is accelerating) while we A c c e p t e d M a n u s c r i p t don't account for it in our design matrix, then the fit between the model and observations would be worse that it could be. This normally results in larger values in the covariance matrix C, which is estimated from the misfit between model and observations. As a result, the uncertainty of the estimated parameters is larger than it could be. The better we model the signal, the better is the accuracy of the estimated parameters.

On the other hand, if we try to fit a too complex model to the data with many parameters there is the risk that the accuracy of the estimated parameters decreases. This happens when there is a large correlation between the different parameters which complicates their separation.

The separation of different signals within the data is also less accurate when the noise is correlated in time. If the noise is not correlated in time then it is called white noise, otherwise it is called coloured noise. When the spectrum of the noise is of the form 1/f α , where f is the frequency, one speaks about power-law noise. The parameter α is called the spectral index. [START_REF] Caporali | Average strain rate in the Italian crust inferred from a permanent GPS network -I. Statistical analysis of the time-series of permanent GPS stations[END_REF] and [START_REF] Williams | Error analysis of continuous GPS position time series[END_REF], among others, have shown that the noise in GPS data can be well described as the sum of white and power-law noise.

As a result, the covariance matrix of the noise can be written as (Williams, 2003b):

C = σ 2 w I + σ 2 pl E(α) (4)
where σ 2 w and σ 2 pl are the variances of the white and power-law noise. I is the unit matrix and E represents the covariances due to the power-law noise and depends on the spectral index α.

A c c e p t e d M a n u s c r i p t

Observations

To illustrate the effects related to analysing short time-series we used GPS data from four stations of which two are in Portuguese Mainland: CASC and LAGO. The other stations are PDEL, Ponta Delgada in the Azores, and TETN which is situated in the north of Morocco. The first three timeseries have an observation span of longer than nine years while TETN only has 2.4 years of continuous GPS observations. Only the last station can be considered to be a short time-series but we will use the longer time-series to validate our results.

Data have been processed using JPL's GIPSY software package [START_REF] Webb | An introduction to GIPSY/OASIS-II[END_REF], following the precise point positioning strategy which resulted in time-series of daily coordinate solutions. These time-series were afterwards converted to the ITRF2005 reference frame [START_REF] Altamimi | ITRF2005: A new release of the International Terrestrial Reference Frame based on time series of station positions and Earth Orientation Parameters[END_REF] and filtered to remove outliers. Offsets were estimated at epochs when the GPS receiver or antenna were replaced.

For CASC, the time-series of the North component is presented in Fig. 1. The power spectral density of the differences between observations and the fitted model, is given in Fig. 2. In this last figure also the estimated power-law plus white noise model has been plotted which fits well to the observed power spectral density. The plots of the position time-series and power spectral density for the other stations and components look similar.

INSERT FIGURE 1 HERE. INSERT FIGURE 2 HERE.

The values of the estimated trend and its associated error for these timeseries were estimated using the Maximum Likelihood Estimation method 6 A c c e p t e d M a n u s c r i p t [START_REF] Mao | Noise in GPS coordinate time series[END_REF]Williams, 2003b;[START_REF] Langbein | Noise in two-color electronic distance meter measurements revisited[END_REF] and are presented in Table 1. One can see that the East component is always less accurate than the North component. This table also contains the estimated values of the white plus power-law noise model discussed in section 2. We also listed the value of the standard deviation σ w when only white noise is assumed to exist in the GPS observations.

INSERT TABLE 1 HERE.

The uncertainty of the linear trend was computed using Eq. ( 3) as function of the observation span. For the covariance matrix C we used two models: the power-law plus white noise model and a pure white noise model.

The values for both noise models were taken from Table 1. In addition, we performed the computations with and without estimating the annual signal in the design matrices, see Eqs. ( 1) and ( 2). The results for the North component of CASC are plotted in Fig. 3. It shows that the trend error for data with power-law plus white noise is larger than when only white noise is, wrongly, assumed to be present in the data. This was already observed by [START_REF] Mao | Noise in GPS coordinate time series[END_REF] who stated that the difference can vary by a factor of 5-11.

INSERT FIGURE 3 HERE.

The trend error for the white noise model in Fig. 3 corresponds to Fig. 4 of [START_REF] Blewitt | Effect of annual signals on geodetic velocity[END_REF] although our values are almost three times smaller because we used a value for σ w of 2.36 mm (last column Table 1) instead of 4 mm that was used by Blewitt and Lavellée. Fig. 3 shows that the predicted trend error is larger when an annual signal is included in the design matrix. To see this effect more clearly, we A c c e p t e d M a n u s c r i p t computed the difference between the errors associated with the two different design matrices. The results are plotted in Fig. 4 and show that for powerlaw plus white noise the difference is around ten times larger compared to pure white noise. The same result was obtained at the other stations for both the East and North component.

INSERT FIGURE 4 HERE.

This figure demonstrates that having an annual signal in your data produces larger uncertainties in your trend value compared to the situation of having no annual signal in your data. Estimating an additional annual signal in your estimation process does therefore not completely eliminate its effect on the linear trend.

For the pure white noise model we can see minimum influence of the annual signal on the trend error at observation spans of integer plus a half year intervals [START_REF] Blewitt | Effect of annual signals on geodetic velocity[END_REF]. However, for power-law plus white noise, which is found in most GPS time-series, we find minimal influence closer to integer plus a quarter year intervals.

Influence of estimating the noise

To predict the trend error in short time-series, we have until now assumed that we know the values of the power-law plus white noise model within the GPS time-series. However, this is normally not the case and we must estimate these parameter values from the data.

To investigate the influence of estimating the noise properties from the data we have cut up the CASC time-series in non-overlapping segments of equal lengths. By analysing each segment separately, we obtained informa-8 A c c e p t e d M a n u s c r i p t tion about the spread in the predicted trend error for short time-series. The results for the North component have been plotted as black dots in Fig. 5 where the segment lengths was varied between two and six years. The large trend error of 2.4 mm/year for an observation span of two years in one of the segments of the CASC time-series has been caused by the fact that it contains a gap of 150 days.

The predicted trend error using the power-law plus white noise properties of Table 1 is represented by the solid black line (see also Fig. 3).

To get a better idea of the spread in the predicted trend error one can expect when analysing short GPS time-series, we performed a Monte Carlo simulation. For each observation span we computed and analysed 100 synthetic time-series that contained the same power-law plus white noise properties as is listed in Table 1 for CASC, North component. Afterwards, we computed for each observation span the mean and standard deviation of the predicted trend error. The area between ±1 standard deviation around the mean has been plotted as a grey area in Fig. 5.

INSERT FIGURE 5 HERE.

The Monte Carlo results in Fig. 5 show that the predicted trend error is on average underestimated for short time-series [START_REF] Williams | Error analysis of continuous GPS position time series[END_REF]. That is, the estimated trend values in the Monte Carlo simulation vary more than one would expect from these predicted trend errors. This underestimation caused by the fact that some of the power-law noise is considered to be part of the linear trend by the MLE method which results in smaller residuals. This influence of estimating the noise properties from the data has a larger effect on the trend error than having an annual signal in the GPS

9

A c c e p t e d M a n u s c r i p t observations. It is therefore more effective to try to improve our knowledge of the noise within GPS observations than to improve our knowledge about what is causing the annuals signal when one is interested in the linear trend.

To reduce the spread in the predicted trend error we note from Table 1 that the value of the spectral index lies between 1.1 and 1.5. Furthermore, the value of σ w is roughly three times that of σ pl . If we assume that we can keep the value of α and the ratio σ w /σ pl fixed, the covariance matrix can be written as [START_REF] Williams | CATS: GPS coordinate time series analysis software[END_REF]:

C = σ 2 J (5)
Another argument for using this simplified model for the covariance was given by [START_REF] Bos | Fast error analysis of continuous GPS observations[END_REF] who showed that power-law noise has a larger influence than white noise on the linear trend.

Having fixed the structure of our noise model, we only need to estimate the scale factor σ 2 to determine the covariance matrix C. Before doing so, it is convenient to define the following parameter vector β = (θ, σ 2 ).

The logarithm of the probability density function is (Williams, 2003b):

ln p(x| β) = - 1 2 [N ln 2π + ln det(C)+ (x -Hθ) T C -1 (x -Hθ) (6)
For any unbiased estimator, the variance of the estimated parameters is given by the Cramer-Rao lower bound [START_REF] Kay | Fundamentals of Statistical Signal Processing: Estimation Theory[END_REF]:

Var(β i ) ≥ I(β) -1 ii (7)
where I(β) is the Fisher information matrix. The latter is defined by:

I(β) = -E ∂ ln 2 p(x| β) ∂β 2 (8)
A c c e p t e d M a n u s c r i p t

The E operator represents the expected value. After computing the various derivatives of Eq. ( 6), we obtain the following expression for the variance in the estimated values of σ 2 :

Var(σ 2 ) = 2σ 4 N (9)
Here we replaced the inequality sign of Eq. ( 7) with an equal sign because we used the Maximum Likelihood Estimation (MLE) method to estimate its value. MLE is asymptotically efficient and approaches the Cramer-Rao lower bound when the sample size becomes large [START_REF] Kay | Fundamentals of Statistical Signal Processing: Estimation Theory[END_REF]. Using Eq. ( 5), we can write the variance of the variance of θ as:

Cov( θ) = 2σ 4 N H T J -1 H -1 (10)
Instead of having one uncertainty for the trend error, say σ t , we now have a range of trend errors because the value of σ not exactly known. This causes a varying predicted trend error:

σ t 1 ± 2 N ≈ σ t ± σ t 2 2 N (11)
The last term represents the standard deviation in the predicted trend error itself.

We repeated the analysis of the CASC time-series but now we set the values α = 1.3 and σ pl /σ w = 3.3. Only σ pl was estimated which corresponds to the noise model of Eq. 5. The results are plotted in Fig. 6.

INSERT FIGURE 6 HERE.

The Monte Carlo results, the grey area, show that the spread in the predicted trend error is much smaller compared to those plotted in Fig. 5. This

A c c e p t e d M a n u s c r i p t spread agrees well with the one predicted by Eq. ( 11). In addition, they are unbiased. The spread in the predicted trend error for the CASC segments has also decreased although the variations are still significantly larger than one would expect from the Monte Carlo simulations. The assumption that the noise properties are constant over time seems therefore questionable. The reason why the noise properties vary over time is unknown and deserves further investigation. One possible explanation could be the existence of small offsets which have not been detected but are altering the noise properties (Williams, 2003a).

Conclusions

Under equal noise conditions, the accuracy of the estimated linear trend is worse in GPS time-series that have a seasonal signal compared to those which have not, even when an annual signal is included in the estimation process. We have shown in Fig 4 that for realistic GPS time-series with power-law plus white noise this difference in trend error is larger than for the situation when only white noise is assumed to exist in the data as was done by [START_REF] Blewitt | Effect of annual signals on geodetic velocity[END_REF].

Our results can be used to estimate how much the accuracy of the linear trend will improve when one tries to reduce the annual signal in short GPS time-series by, for example, subtracting atmospheric and hydrological loading values.

We have also demonstrated that for short time-series the trend error is significantly influenced by the fact that the noise properties also need to be estimated from the data. This causes a variation in the predicted trend A c c e p t e d M a n u s c r i p t

error that is larger than the effect of having an additional annual signal in the estimation process. It is therefore more effective to try to improve our knowledge of the noise within GPS observations than to improve our knowledge about what is causing the annuals signal when one is interested in the linear trend.

Our Monte Carlo simulation confirmed the result of [START_REF] Williams | Error analysis of continuous GPS position time series[END_REF] that the trend error is on average underestimated for short time-series.

Finally we have shown that when the noise model can be simplified to a simple scaling of a priori known covariance matrix, Eq. 5, the underestimation of the trend error and the spread in the predicted trend error is significantly reduced. For this simple noise model we derived Eq. ( 11) that provides the uncertainty in the predicted trend error.

  East component and 2 mm in the vertical component.

Figure 1 :Figure 2 :Figure 3 :Figure 4 :Figure 5 :Figure 6 :

 123456 Figure 1: The upper panel shows the North component of the GPS position time-series at CASC. The lower panel shows the same data set after subtraction of a linear trend and a yearly signal.

Table 1 :

 1 The values of the estimated trend with its associated error for the North and East component. For each station the time span of the observation is given in years. Also listed are the estimated standard deviations of the power-law and white noise present in the data, σ pl and σ w , and the spectral index α of the power-law noise. The last column contains the value of σ w when only white noise is assumed to exist within the data. An annual signal was included in the estimation process.

	Station	∆T	Comp. trend ± std	α	σ pl	σ w only σ w
		(years)		(mm/year)		(mm) (mm)	(mm)
	CASC	12.3	E	17.5 ±0.6 1.4	1.06	2.85	3.81
			N	16.7 ±0.3 1.3	0.61	2.01	2.36
	LAGO	9.6	E	17.1 ±0.8 1.5	0.84	2.83	3.70
			N	17.0 ±0.3 1.4	0.53	1.60	2.06
	PDEL	9.4	E	12.2 ±0.7 1.4	1.03	2.92	3.92
			N	16.8 ±0.3 1.1	1.16	2.45	3.38
	TETN	2.4	E	13.7 ±2.0 1.1	2.06	3.05	4.51
			N	16.3 ±0.8 1.1	0.92	2.05	3.02


Philippe Vernant
email: pvernant@um2.fr

Abdelali Fadil
email: abdelali.fadil@upf.pf

Taoufik Mourabit
email: tmourabit@menara.ma

Driss Ouazar
email: ouazar@emi.ac.ma

Achraf Koulali

Jose Martin Davila
email: mdavila@roa.es

Real Jorge Garate

Simon Mcclusky

Robert Reilinger
email: reilinge@erl.mit.edu

Geodetic constraints on active tectonics of the Western Mediterranean: Implications for the kinematics and dynamics of the Nubia-Eurasia plate boundary zone

published or not. The documents may come   L'archive ouverte pluridisciplinaire

A c c e p t e d M a n u s c r i p t 2 1.5 mm/yr, 95% confidence level. North of the Atlas Mountains, the GPS velocities indicate Nubia motion with respect to Eurasia, but also a component of motion normal to the direction of Nubia-Eurasia motion, consisting of southward translation of the Rif Mountains in N Morocco at rates exceeding 5 mm/yr. This southward motion appears to be directly related to Miocene opening of the Alboran Sea. The Betic mountain system north of the Alboran Sea is characterized by WNW motion with respect to Eurasia at ~ 1 -2 mm/yr, paralleling Nubia-Eurasia relative motion. In addition, sites located in the Betics north of the southerly moving Rif Mountains also indicate a component of southerly motion with respect to Eurasia. We interpret this as indicating that deformation associated with Nubia-Eurasia plate motion extends into the southern Betics, but also that the Betic system may be affected by the same processes that are causing southward motion of the Rif Mountains south of the Alboran Sea. Kinematic modeling indicates that plate boundary geometries that include a boundary through the straits of Gibraltar are most compatible with the component of motion in the direction of relative plate motion, but that two additional blocks (Alboran-Rif block, Betic Mountain block), independent of both Nubia and Eurasia are needed to account for the motions of the Rif and Betic mountains normal to the direction of relative plate motion. We speculate that the southward motions of the Alboran-Rif and Betic blocks may be related to mantle flow, possibly induced by southward rollback of the subducted Nubian plate beneath the Alboran Sea and Rif Mountains.

Introduction

The tectonic evolution of the western Mediterranean has been dominated by the long history of Nubia-Eurasia plate convergence associated with subduction of the Neotethys A c c e p t e d M a n u s c r i p t 3 oceanic lithosphere (e.g., [START_REF] Dercourt | Geological evolution of the Tethys belt from the Atlantic to the Pamirs since the Lias[END_REF]. The current-day tectonic structure of the zone of plate interaction is complex, involving back-thrust mountain ranges on the north (Betics) and south (Rif) sides of the collision zone and an intervening, deep basin (Alboran) reflecting active extension and subsidence (Figure 1). Such juxtaposition of compression and extension is observed along some subduction zones and appears to be associated with retreat (or rollback) of the subducting slab (e.g., Le [START_REF] Le Pichon | The Hellenic arc and trench system: A key to the neotectonic evolution of the eastern Mediterranean area[END_REF]Angelier, 1979, Royden, 1993). However, in the W Mediterranean the evidence for active subduction is equivocal (e.g., [START_REF] Seber | Geophysical evidence for lithospheric delamination beneath the Alboran Sea and Rif-Betic mountains[END_REF][START_REF] Gutscher | Evidence for active subduction beneath Gibraltar[END_REF][START_REF] Faccenna | Lateral slab deformation and the origin of the western Mediterranean arcs[END_REF].

Geodetic observations have revealed a highly unexpected pattern of deformation within the W Mediterranean zone of plate interaction, indicating southward motion of the Rif Mountains in N Morocco relative to the Nubian plate interior [START_REF] Fadil | Active tectonics of the western Mediterranean: GPS evidence for roll back of a delaminated subcontinental slab beneath the Rif Mountains, Morocco[END_REF]. These well-defined, anomalous motions appear to be incompatible with crustal interactions (i.e., extrusion tectonics) and, we suggest, more likely reflect active, sub-crustal processes, possibly associated with subduction and/or mantle delamination within the zone of convergence between Nubia and Iberia [START_REF] Seber | Geophysical evidence for lithospheric delamination beneath the Alboran Sea and Rif-Betic mountains[END_REF][START_REF] Gutscher | Evidence for active subduction beneath Gibraltar[END_REF][START_REF] Fadil | Active tectonics of the western Mediterranean: GPS evidence for roll back of a delaminated subcontinental slab beneath the Rif Mountains, Morocco[END_REF]. In this paper, we incorporate new observations to update the GPS velocities in Morocco, and we combine these with GPS measurements from southern Spain, and Spanish enclaves in N Africa, to develop an internally consistent velocity field for the W Mediterranean region. We use this improved velocity field to constrain block models of the Nubia-Eurasia plate boundary deformation zone and we discuss the implications of these observations for the dynamics of Nubia-Eurasia plate interactions. In the western Mediterranean, the Alboran domain is caught between North Africa and Iberia at the westernmost limit of the Alpine mountain belt (Figure 1). During the Cenozoic, the Alboran domain, along with the Atlas Mountains, grew thicker in this convergent setting [START_REF] Chalouan | The Alpine Rif Belt (Morocco); a case of mountain building in a subduction-subduction-transform fault triple junction[END_REF][START_REF] Platt | Extensional collapse of thickened continental lithosphere; a working hypothesis for the Alboran Sea and Gibraltar Arc[END_REF]. Later during the Miocene, the Alboran domain stretched and subsided below sea level, accumulating more than 7 km of sediment (Watts et al., 1993).

Present-day tectonic processes occur within the context of ongoing, ~NW-SE oblique convergence between Africa and Iberia around the Strait of Gibraltar (4.3 ± 0.5 mm/yr at an azimuth of 116 ± 6° from GPS, Figure 2a (McClusky et al., 2003)). However, the location, or existence, of a discrete Africa-Eurasia plate boundary is equivocal (Figure 1). Geomorphologic studies of active faulting demonstrate recent tectonic activity in the Rif [START_REF] Morel | Goringe-Alboran-Tell tectonic zone; a transpression system along the Africa-Eurasia plate boundary[END_REF] and the Atlas Mountains [START_REF] Gomez | Active tectonism in the intracontinental middle Atlas Mountains of Morocco; synchronous crustal 16 shortening extension[END_REF][START_REF] Meghraoui | Coastal tectonics across the South Atlas thrust front and the Agadir active zone[END_REF][START_REF] Gomez | Role of the Atlas Mountains (Northwest Africa) within the African-Eurasian plate-boundary zone[END_REF], and suggest that most of the present-day convergence is accommodated in the Rif-Betic-Alboran region.

Ideas to explain the striking N-S topographical symmetry of the Alboran Sea and surrounding mountain belts, as well as the apparently synchronous subsidence of the Alboran Sea and uplift of the Betic and Rif mountains during the Neogene and Quaternary are still widely debated. Current tectonic models for the Alboran domain include four broad categories of hypotheses: (1) backarc extension driven by the A c c e p t e d M a n u s c r i p t 5 westward rollback of an eastward subducting slab of oceanic lithosphere [START_REF] Royden | Evolution of retreating subduction boundaries formed during continental collision: Tectonics[END_REF][START_REF] Lonergan | Origin of the Betic-Rif mountain belt: Tectonics[END_REF][START_REF] Gutscher | Evidence for active subduction beneath Gibraltar[END_REF]; (2) break-off of a subducting lithospheric slab [START_REF] Blanco | The P-wave velocity structure of the mantle below the Iberian Peninsula: Evidence for subducted lithosphere below southern Spain[END_REF]; (3) crustal extrusion due to forces transmitted across the Eurasia-Africa plate boundary [START_REF] Rebai | Modern tectonic stress field in the Mediterranean region; evidence for variation in stress directions at different scales[END_REF][START_REF] Morel | Goringe-Alboran-Tell tectonic zone; a transpression system along the Africa-Eurasia plate boundary[END_REF]; and (4) delamination and convective removal of the lithospheric mantle root beneath the collisional orogen [START_REF] Platt | Extensional collapse of thickened continental lithosphere; a working hypothesis for the Alboran Sea and Gibraltar Arc[END_REF][START_REF] Seber | Geophysical evidence for lithospheric delamination beneath the Alboran Sea and Rif-Betic mountains[END_REF]Calvert et al., 2000a;Calvert et al., 2000b). Testing these hypotheses with the present-day deformation field is a principal objective of this study.

GPS Velocities and Data Processing

The GPS network used in this study includes 31 GPS survey points (SGPS) observed for different time intervals between 1999 and 2007, and 15 continuous GPS stations (CGPS, Fig. 2a). We analyze the GPS data using the GAMIT/GLOBK software [START_REF] Herring | GLOBK: Global Kalman filter VLBI and GPS analysis program[END_REF][START_REF] King | Documentation for the GAMIT analysis software[END_REF] in a two-step approach [START_REF] Mcclusky | GPS constraints on plate kinematics and dynamics in the eastern Mediterranean and Caucasus[END_REF]. The GPS solution is realized in the ITRF2005 global reference frame, and rotated into a Eurasia and Africa reference frame using 23 and 12 stations respectively. The mean values of the residuals for the eastern and the northern components of the 23 Eurasian sites and 12 African sites are -0.16 mm/yr, 0.15 mm/yr, -0.29 mm/yr and 0 mm/yr respectively, the standard deviation being 0.61 mm/yr, 0.71 mm/yr, 0.42 mm/yr and 0.45 mm/yr. Therefore no significant residuals remain in the reference frame computation, and as shown in Africa reference frames are given in Table 1.

Figure 2a shows GPS velocities in a Nubian-fixed reference frame, and Figure 2b, the same solution relative to Eurasia. One-sigma uncertainties for survey sites are mostly < 0.7 mm/yr, and < 0.4 mm/yr for long-operating CGPS stations. GPS velocities at sites located south of the Rif Mountains and north of the High Atlas (SALA, KBGA, HEBR, DEBD, BMTR) are consistent with the motion of Nubia at the 1-sigma confidence interval (Figure 2a; Table 1), implying deformation rates of less than 0.7 mm/yr within the High Atlas Mountains. Uncertainties on these survey sites are too large to detect active shortening. However, the two CGPS sites south of the Rif Mountains and north of the Atlas system (RABT, IFRN) that have more tightly constrained velocities both show significant SSE velocities with respect to Nubia (1.0 ± 0.2 and 1.7 ± 0.3, respectively) that may be due to shortening across the Atlas Mountain system, with a substantial component of shortening in the Middle Atlas. These estimates are within the range of geological rates that constrain shortening to about 1 to 2 mm/yr across the entire Atlas mountain system [START_REF] Meghraoui | Coastal tectonics across the South Atlas thrust front and the Agadir active zone[END_REF][START_REF] Gomez | Role of the Atlas Mountains (Northwest Africa) within the African-Eurasian plate-boundary zone[END_REF].

The anomalous motions of the central

Kinematics of the Nubia-Iberia Interplate Deformation Zone

To illustrate better deformation in the plate boundary zone and the relation to hypothesized plate boundaries, in Figure 4 we plot the components of the GPS velocities normal and parallel to two profiles striking N20°E, roughly perpendicular to the direction of Eurasia-Africa relative motion (~N110°E) (see profile locations on Figure 2a). For the western profile, the velocity component in the direction of Eurasia-Africa motion (i.e., normal to the strike of the profile) clearly shows the relative plate motion (Figure 4a), and A c c e p t e d M a n u s c r i p t 8 no significant motion normal to the direction of relative plate motion (Figure 4b). We use an elastic block model [START_REF] Mccaffrey | Crustal block rotations and plate coupling[END_REF], to investigate the consistency of the observed pattern of motion with the three hypothesized plate boundaries illustrated in Figure 1. The width of the deformation zone across block boundaries depends on the assumed faultlocking depth. We use a locking depth of 15 km for all faults, in agreement with the maximum depth of the seismicity [START_REF] Calvert | An integrated geophysical investigation of recent seismicity in the Al-Hoceima region of North Morocco[END_REF][START_REF] Stich | Moment tensor solutions for small and moderate earthquakes in the Ibero-Maghreb region[END_REF]. Model results for the three plate boundary geometries are shown in Figures 4a, 4b, 4d, and4e. For the westernmost profile (Profile 1) the GPS results are inconsistent with the plate boundary located south of the Rif [START_REF] Bird | An updated digital model of plate boundaries[END_REF] or north of Gibraltar in the Betic Cordillera [START_REF] Gutscher | What Caused the Great Lisbon Earthquake?[END_REF]. The best fit is for models where the boundary passes through the Gibraltar Strait [START_REF] Klitgord | Plate kinematics of the central Atlantic[END_REF]. The models predict no significant motion normal to the direction of relative plate motion (N20°E), consistent with the GPS observations, indicating that the westernmost segment of the plate boundary is consistent with simple, elastic plate interactions.

The second, more eastern profile crosses the central Rif, Alboran Sea and Betic Mountains (see location on Figure 2a). As for the western profile, Eurasia/Africa relative motion is apparent (Figure 4d), but the component of velocity normal to the direction of relative plate motion shows anomalous deformation in the Alboran/Rif, and to a lesser extent in the Betics (Figure 4e). None of the proposed plate boundary geometries can account for this motion. Expanding on the models of [START_REF] Fadil | Active tectonics of the western Mediterranean: GPS evidence for roll back of a delaminated subcontinental slab beneath the Rif Mountains, Morocco[END_REF], we investigate kinematic models including a central Alboran-Rif block and a Betic block (Figure 5).

Most of the block boundaries are consistent with mapped fault zones, or seismic

A c c e p t e d M a n u s c r i p t 9 lineaments. The western and southern boundaries of the Alboran-Rif block are well constrained by the GPS velocities. However, no regional right lateral strike slip faults are reported where we locate the western Rif block boundary. We assign a 15 km locking depth to all block boundaries. Although block models are very useful to identify large quasi-rigid blocks or plates, they have inherent limitations for smaller blocks. Indeed, the width of the interseismic transient elastic strain on one side of a fault in the block model is approximately 3 locking depths [START_REF] Savage | Geodetic determination of relative plate motion in Central California[END_REF]. Therefore if the width of a block is less than 6 locking depths, the entire block will deform elastically during the interseismic interval of the seismic cycle making it difficult to identify coherently moving areas (i.e., blocks). Furthermore, it is impossible to unambiguously separate transient elastic strain from permanent geologic deformation for small blocks. This is the case of all the blocks defined in this study. Therefore one should be careful with the fault slip rates given in Figure 5, they are upper bounds since they assume all observed strain is elastic, and depend on how the deformation is accommodated within the regions evidenced by our kinematic analysis.

The southern Alboran-Rif block boundary corresponds to mapped Quaternary thrust faults along the southern edge of the Rif [START_REF] Moratti | The 1755 "Meknes" earthquake (Morocco): Field data and geodynamic implications[END_REF]. The northern and eastern boundaries of the Rif block are poorly constrained by the GPS results. We have chosen to locate the eastern boundary along the NS trend of the 1994 and 2004 Al Hoceima earthquakes, and the seismically active Alboran Ridge, consistent with most other interpretations (Figure 1). We also include a separate block representing the Betic 5) are roughly consistent with rates reported from studies of active faults in the Rif [START_REF] Morel | Goringe-Alboran-Tell tectonic zone; a transpression system along the Africa-Eurasia plate boundary[END_REF], as well as with the sense of motion indicated by the 1994 and 2004

Al-Hoceima earthquakes [START_REF] Calvert | An integrated geophysical investigation of recent seismicity in the Al-Hoceima region of North Morocco[END_REF][START_REF] Stich | Moment tensor solutions for small and moderate earthquakes in the Ibero-Maghreb region[END_REF][START_REF] Tahayt | Present-day movements of tectonic blocks in the western Mediterranean from GPS measurements 1999-2005[END_REF]. Furthermore, the N-S width of the deep Alboran Basin is roughly 120 km. Assuming that the GPS extension rate across the basin (roughly 4 mm/yr between stable Nubia and Eurasia, see Figure 4d) has been constant in time, the basin would be formed in about 30 Ma, in good agreement with geological estimates for the beginning of extension at 27 Ma [START_REF] Platt | Early Miocene high-temperature metamorphism and rapid exhumation in the Betic Cordillera (Spain); evidence from U-Pb zircon ages: Earth Planet[END_REF]. The southward motion of the Betic block decreases the extension rate confined to the Alboran Sea (from ~4 to ~3 mm/yr, Figure 4e), possibly implying that extension has spread North into the Betics sometime after initial extension The general agreement between GPS and geologic indicators of neotectonic deformation suggests that the GPS results depict those geodynamic processes responsible for the geologic evolution of the Betic-Alboran Sea-Rif Mountain system, providing quantitative constraints on models for the evolution of this segment of the Africa-Eurasia plate boundary. The occurrence of extension on fault segments within the zone of Nubia-Iberia plate convergence (i.e., northern Betics, some of the western and eastern boundaries of the Rif block, see Figure 5) appears inconsistent with extrusion models that involve compressive forces transmitted across plate boundaries. Southward motion of the Betic Mountains also appears to be inconsistent with extrusion models since the zone of maximum compresion within the collision zone would be expected to lie south of the Betic system. West-directed roll back of an east dipping subducted slab beneath Gibraltar also appears inconsistent with the SE motion of GPS sites in northwestern Morocco since this model predicts westward motion of the Gibraltar region relative to Africa [START_REF] Gutscher | What Caused the Great Lisbon Earthquake?[END_REF]).

An alternate geodynamic model for the western Mediterranean proposes that the subcontinental part of the lithosphere under the Alboran domain has been removed by active delamination (e.g., [START_REF] Seber | Geophysical evidence for lithospheric delamination beneath the Alboran Sea and Rif-Betic mountains[END_REF], Calvert et al., 2000). As pointed out by Platt The observed, southward directed motion of the central Rif, roughly normal to the direction of Africa-Eurasia relative plate motion, and to some extent of the Betic system, supports the hypothesis that subcrustal process are controlling the opening of the Alboran Sea and adjacent shortening in the Rif [START_REF] Fadil | Active tectonics of the western Mediterranean: GPS evidence for roll back of a delaminated subcontinental slab beneath the Rif Mountains, Morocco[END_REF]. Based principally on the GPS results, the asymmetric deformation around the Alboran Sea appears to be more indicative of a component of southward-directed slab roll back and associated N-S back arc opening than with simple symmetric delamination confined to the Alboran Sea region. The direction of roll back corresponds to the direction of motion of the inferred Alboran-Rif block (SSW relative to Nubia). Because the Rif-Alboran-Betic region is continental in character [START_REF] Platt | Extensional collapse of thickened continental lithosphere; a working hypothesis for the Alboran Sea and Gibraltar Arc[END_REF], the present-day slab is probably the mantle part of the continental lithosphere, which has become detached from the crust and is rolling back to the south, possibly due to the pull of the old slab [START_REF] Faccenna | Lateral slab deformation and the origin of the western Mediterranean arcs[END_REF]. These considerations support the hypothesis that neotectonic deformation in the western Mediterranean, including juxtaposed extension of the Alboran Sea and uplift of the surrounding mountain ranges, results from dynamic processes in the upper mantle associated with continued convergence of the Nubian and Eurasian plates. [START_REF] Fadil | Active tectonics of the western Mediterranean: GPS evidence for roll back of a delaminated subcontinental slab beneath the Rif Mountains, Morocco[END_REF], we extend GPS coverage to the southern Iberia region, and show that significant displacements occur in the Betic mountain system. We further demonstrate that, while simple elastic plate interactions can account for observed Nubia-Eurasia relative plate motion in the direction of relative plate motion, the observed component of motion normal to this direction requires more complex plate interactions. We argue on the basis of the observed GPS velocities and regional tectonics that neither extrusion tectonics nor simple vertical delamination can easily account for this deformation. We suggest that the kinematics of the region are most simply associate with slab roll-back toward the SSW and back arc opening in the Alboran Basin, superimposed on Eurasia-Nubia differential motion. As the region is now an intra-continental domain, the present-day slab is probably part of the Moroccan lithospheric mantle that has been pulled down and is now delaminating, the zone of delamination being somewhere along the Moroccan Mediterranean shore. The slab must be narrow since the lateral extent of the southward motion is only 150-200 km, making it a challenge to image with seismological methods.

Figure Captions

Table 1. GPS velocities in an Africa-fixed and Eurasia-fixed reference frame (as determined in this study), 1-sigma uncertainties (σ), and correlation between the east and north components of velocity (RHO). Sites used to estimate Euler vectors are identified as * = Nubia, + = Eurasia. [START_REF] Klitgord | Plate kinematics of the central Atlantic[END_REF], green [START_REF] Bird | An updated digital model of plate boundaries[END_REF], and blue [START_REF] Gutscher | What Caused the Great Lisbon Earthquake?[END_REF]. Crustal earthquake focal mechanisms are from Harvard catalog (magnitudes 5-6.5, 1976 -2008). Seismicity is from National Earthquake Information Center catalog crustal earthquakes with magnitudes from 3 to 6.5 (1976 -2008). MA = Middle Atlas; Alb-Alboran Sea. 2a). a and d: Component of velocities and 1-sigma uncertainties along the direction of plate motion (normal to profile). b and e: Component of velocities and 1-sigma uncertainties normal to the direction of plate motion (i.e., parallel to profiles). The interseismic deformation predicted by elastic block models is shown for the three main hypothesized plate boundaries (Red= [START_REF] Klitgord | Plate kinematics of the central Atlantic[END_REF]Green= Bird, 2003;Blue= Gutscher, 2004, see Figure 1 for geometry). The pink line is for a model with a central Rif block (see Figure 4 for geometry). c and f: Topography and interpretative cross section along profiles 1 and 2. CC= continental crust, LM= lithospheric mantle, OC= Ocean crust, LVA= low velocity, high attenuation seismic anomaly (Calvert et al., 2000).

Figure

  of the residuals are lower than 1mm/yr. Site velocities in both the Eurasia and

  Rif Mountains in northern Morocco are apparent in the Nubian-fixed velocity map shown in Figure 2a. The central Rif Mountains are moving SSW as defined by 9 survey sites and the continuous station in Tetouan (TETN). Southwest motion of the Rif is largest in the northern and central Rif (5.4 ± 1.5 mm/yr) where topography is highest and decreases to the south, terminating near the northern A c c e p t e d M a n u s c r i p t 7 boundary of the Atlas system. The western boundary of the southward moving Rif zone appears to be located near station TETN, and the eastern boundary near the Al Hoceima seismic zone. Motions in southern Spain north of the Alboran Sea are best illustrated by the Eurasiafixed velocity map shown in Figure 2b. Sites located near the Betic Mountains (ALME, GRAN, MALA, ALGE, SFEB) show well-defined westward motions with respect to Eurasia (~2 mm/yr). Sites COBA and LAGO further north show similar, although slower westward motions (~ 1 mm/yr). Motion of the Betics with respect to Eurasia has a similar orientation to Nubia-Eurasia motion, but with reduced rates, and those sites in the Betics located north of the southward moving central Rif zone (ALME, GRAN, MALA) also show a southerly component of motion relative to Eurasia. These motions imply transtension in the Betics that is consistent with WSW-ENE extension pointed out by Martínez-Martínez et al. (2006) on the base of earthquake focal mechanisms and active faults.

  Figure 5 are a combination of previously proposed boundaries, finding support from, and

  Basin. Martínez-Martínez et al. (2006) point out that the mode of presentday extension in the Betic system must have remained substantially the same over the last ~15 Myr, supporting our contention that the GPS motions reflect those processes responsible for the geologic evolution of the W Mediterranean region.

  (2003), simple delamination would produce a radially symmetric pattern of surface deformation (i.e., northward transport of the Betic Mountains). The GPS data indicate that the Betics are, at least at the present time, moving with a southward component of motion relative to Africa (Figure2b), inconsistent with radially symmetric deformation predicted by active, vertical delamination models.

  GPS velocity field traversing the Nubia-Eurasia plate boundary in the westernmost Mediterranean and use it to estimate active deformation. We constrain crustal shortening in the High Atlas to ≤ 1 mm/yr, and across the entire Atlas system to ≤ 1.5 mm/yr (95%), and show that the principal deformation associated with Nubia-Eurasia interaction occurs in the Betic-Rif-Alboran domain. With 14 new sites (AION, ALGE, BOYA, CACE, MELI, GRSF, GRAN, MALA, TANT, CRDB, COBA, KTMA, CHEF, CSTL) compared to the earlier velocity field reported by

  .B.,Platt, J., and Buhl, P., 1993, Tectonic evolution of the Alboran Sea: BasinResearch, v. 5,

Figure 1 .

 1 Figure 1. Seismotectonic and topographic/bathymetric (SRTM30 PLUS) map of the

Figure 2a .

 2a Figure 2a. GPS site velocities with respect to Nubia and 95% confidence ellipses. Heavy

Figure 2b .

 2b Figure 2b. GPS site velocities with respect to Eurasia and 95% confidence ellipses.

Figure 3 .

 3 Figure 3. East and North component of the residuals in our Africa reference frame for

Figure 4 .

 4 Figure 4. Profiles 1 and 2 (see Figure 2a). a and d: Component of velocities and 1-sigma

Figure 5 .

 5 Figure 5. Map showing elastic block model for the Africa-Eurasia plate boundary in the

Figure 1 A

 1 Figure 1

  Figure 2a

  Figure 2b

  Figure 3

  Figure 4

  Figure 5

Table 1 :

 1

			Africa-fixed	Eurasia-fixed
	long. (°E)	lat. (°N)	E Vel. (mm/yr)	N Vel (mm/yr)	E Vel (mm/yr)	N Vel (mm/yr)	E σ (mm/yr)	N σ (mm/yr)	RHO	Site
	359.662	39.481	4.75	-3.82	0.56	-0.76	0.54	0.54	0.044	VALE
	359.519	38.339	3.66	-2.45	-0.45	0.59	0.49	0.50	0.053	ALAC
	358.315	55.213	4.39	-7.52	-0.81	-4.60	1.40	1.45	0.011	MORP
	357.967	33.986	-0.49	-0.39	-4.31	2.50	0.74	0.74	0.024	BMTR
	357.541	36.853	2.74	-3.51	-1.32	-0.67	0.54	0.54	0.051	ALME
	357.467	34.588	-0.04	-1.03	-3.92	1.80	0.91	0.92	0.028	AION
	357.061	35.290	0.19	-1.60	-3.76	1.19	0.73	0.73	0.031	MELI
	356.966	35.940	1.61	3.54	-2.40	6.32	1.30	1.30	0.045	ALBO
	356.945	33.919	0.08	-0.81	-3.76	1.97	0.63	0.64	0.033	DEBD
	356.603	34.216	-0.39	-1.46	-4.27	1.28	1.13	1.07	0.020	GRSF
	356.405	37.190	1.78	-3.92	-2.34	-1.20	0.55	0.56	0.051	GRAN
	356.202	43.472	4.81	-1.98	0.23	0.72	1.54	1.55	0.027	CANT
	355.816	34.432	0.10	-1.80	-3.82	0.86	0.62	0.63	0.039	MSLA
	355.699	35.081	-1.29	-3.05	-5.26	-0.40	1.08	1.08	0.020	BBFH
	355.606	36.726	3.05	-4.15	-1.05	-1.51	0.96	0.97	0.022	MALA
	355.465	32.255	-0.18	-0.14	-3.93	2.49	0.62	0.63	0.053	RIC0
	355.404	34.565	-3.35	-4.27	-7.28	-1.65	1.11	1.10	0.023	TANT
	355.366	32.769	-0.41	0.42	-4.20	3.03	0.74	0.75	0.034	MBLD
	355.359	37.841	3.25	-2.70	-0.95	-0.09	0.47	0.47	0.073	CRDB
	355.279	37.916	3.29	-2.69	-0.92	-0.09	0.47	0.47	0.073	COBA
	355.198	34.987	-2.77	-2.44	-6.75	0.15	0.87	0.88	0.022	KTMA
	354.931	34.485	-0.84	-3.96	-4.78	-1.39	1.20	1.21	0.024	BOYA
	354.892	33.540	0.63	-1.75	-3.23	0.81	0.24	0.27	0.278	IFRN
	354.869	33.333	0.19	-0.46	-3.66	2.10	0.74	0.75	0.032	HEBR
	354.845	35.395	-1.23	-2.89	-5.25	-0.33	0.76	0.76	0.032	LAOU
	354.734	35.173	-2.06	-3.25	-6.06	-0.71	1.05	1.06	0.036	CHEF
	354.683	35.891	0.66	-1.82	-3.40	0.71	0.91	0.90	0.044	CEUP
	354.637	35.562	0.17	-2.25	-3.87	0.28	0.25	0.32	0.213	TETN
	354.566	36.121	1.53	-1.63	-2.56	0.89	0.91	0.89	0.042	ALGE
	354.469	34.158	-1.06	-1.72	-4.99	0.80	0.72	0.73	0.035	ZAGO
	354.461	34.850	-1.51	-2.23	-5.49	0.29	0.79	0.79	0.029	OUZS
	354.042	35.351	0.59	-0.82	-3.45	1.65	0.72	0.73	0.035	TNIN

Table 1 A

 1

	353.794	36.464	2.22	-1.60	-2.50	0.85	0.48	0.42	0.085	SFER
	353.658	39.479	4.44	-1.78	0.08	0.65	0.61	0.61	0.041	CACE
	353.468	38.123	3.58	-2.64	-0.69	-0.23	0.58	0.59	0.057	CSTL
	353.384	31.934	-0.19	-0.62	-3.96	1.78	0.61	0.62	0.057	AZIL
	353.146	33.998	0.33	-0.91	-3.62	1.47	0.23	0.22	0.365	RABT
	353.110 353.080 351.982 351.601 351.411 351.381 351.332 350.581 350.119 20.810 344.367 13.552 9.672 354.760	32.834 33.958 31.665 43.364 41.106 33.162 37.099 38.693 -40.349 -32.380 27.764 -1.632 0.354 6.871	-0.31 1.48 -0.65 9.13 4.93 -0.25 2.96 4.62 0.29 -0.49 0.22 -0.97 -0.84 -0.15	-0.28 -0.62 -0.66 -2.63 -2.11 -0.21 -1.45 -1.60 0.07 0.12 0.28 0.72 -0.03 -0.15	-4.16 -2.47 -4.43 4.42 0.38 -4.16 -1.28 0.24 3.86 1.30 -3.32 -1.46 -1.49 M 2.09 1.74 1.59 -0.42 0.07 1.98 0.73 0.50 2.11 5.09 1.69 a n u s c r i p t 0.64 0.63 0.053 KBGA 0.56 0.57 0.051 RRMT 0.61 0.62 0.053 MARO 0.51 0.51 0.053 ACOR 0.58 0.58 0.044 GAIA 0.63 0.63 0.044 SALA 0.52 0.52 0.066 LAGO 0.49 0.49 0.075 CASC 0.29 0.37 0.299 GOUG* 0.27 0.35 0.108 SUTH* 0.19 0.25 0.578 MAS1* 5.09 0.81 0.73 0.026 MSKU* 4.00 0.27 0.35 0.209 NKLG* -1.49 2.40 0.36 0.30 0.261 YKRO*
	27.687	-25.890	0.25	0.11	1.31	5.57	0.15	0.34	0.088	HRAO*
	28.311 354.102 350.898 355.813 357.997 12.879 5.810 4.359 15.493 36.759	-15.426 30.415 30.053 31.549 33.031 49.144 52.178 50.798 47.067 c c e p t e d -0.04 0.64 0.33 -0.53 -0.06 -4.15 -0.27 -0.80 -3.93 -0.58 -0.19 -4.25 -0.39 -0.72 -4.14 4.35 -4.06 0.18 4.85 -3.10 0.15 4.52 -3.99 -0.18 4.99 -3.91 1.07 55.699 2.96 -5.77 0.29	6.13 2.42 1.33 2.47 2.17 0.25 0.56 -0.47 0.63 0.19	0.65 0.61 0.62 0.62 0.61 0.12 0.18 0.23 0.12 1.53	0.69 0.62 0.63 0.63 0.62 0.10 0.18 0.15 0.10 1.87	0.011 0.058 0.060 0.055 0.047 0.282 0.119 0.134 0.322 -0.001	ZAMB* ZARA* BAHA* ERFD* TNDR* WTZR+ KOSG+ BRUS+ GRAZ+ ZWEN+
	355.750	40.429	4.47	-2.77	0.09	-0.12	0.27	0.44	0.115	MADR+
	356.048	40.444	4.68	-2.15	0.31	0.53	0.22	0.15	0.391	VILL+
	21.032	52.097	3.62	-4.75	-0.18	0.23	0.13	0.09	0.092	JOZE+
	6.921	43.755	4.86	-3.23	0.68	0.54	0.16	0.14	0.338	GRAS+
	7.465	46.877	4.86	-3.22	0.52	0.61	0.15	0.11	0.348	ZIMM+
	13.066	52.379	4.23	-4.43	-0.08	-0.10	0.43	0.42	0.011	POTS+
	17.073	52.277	4.12	-4.66	0.06	0.00	0.18	0.10	0.091	BOR1+
					2

Acknowledgements

We thank UNAVCO for providing equipment and technical support for the surveys in Morocco, and for assistance with establishing and maintaining the continuous GPS station in Rabat. We are grateful to Rob McCaffrey for providing his DEFNODE code, and for assistance with implementation and to C. Facenna and an anonymous reviewer for their helpful reviews. This research was supported in part by NSF Grant EAR-0408728 to MIT, ACOGE_RISTE grant CGL2006-10311-C03-02 and TOPOIBERIA, grantCSD2006-00041 to ROA.