Istituto Nazionale di Ricerca Metrologica

Transcription

1 Istituto Nazionale di Ricerca Metrologica G. D Agostino, S. Desogus, A. Germak, C. Origlia and D. Quagliotti ABSOLUTE MEASUREMENTS OF THE FREE-FALL ACCELERATION g IN THE REPUBLIC OF PANAMA T.R. 111 March 2008 TECHNICAL REPORT I.N.RI.M. 1

2 ABSTRACT The work hereafter described was carried out on January and February 2008 by the Istituto Nazionale di Ricerca Metrologica (INRIM) of Turin (Italy) in the framework of a cooperation with the Centro Nacional de Metrologia de Panama (CENAMEP AIP) and the Istituto Geográfico Nacional Tommy Guardia (IGNTG). The project consists of the measurements of the free-fall acceleration g in twelve sites in the Republic of Panama. Gravity measurements were performed with the transportable absolute gravimeter IMGC-02. 2

3 CAPTIONS INDEX ABSTRACT...2 CAPTIONS INDEX...3 TABLES and FIGURE INDEX INTRODUCTION THE IMGC ABSOLUTE GRAVIMETER Measurement method Apparatus MEASUREMENT UNCERTAINTY Instrumental uncertainty of the IMGC-02 absolute gravimeter Influence factors characteristic of the observation site EXPERIMENTAL RESULTS Panama City CENAMEP AIP El Valle Calobre Tonosí Colon Santa Fe Yaviza Panama City IGNTG Tolé Changuinola Boquete Coiba REFERENCES TABLES and FIGURE INDEX Figure 1. Picture of the new absolute gravimeter IMGC Figure 2.1. Schematic layout of the IMGC-02 Absolute Gravimeter... 9 Figure 2.2. GravisoftM manager front panel Figure 2.3. GravisoftPP post-processing front panel Table 3.1. Instrumental uncertainty of the IMGC-02 absolute gravimeter Figure 4.1 Location of the measurement sites in the Republic of Panama Table 4.1. Location of the measurement sites in the Republic of Panama Figure 4.2 Pictures of the INRIM, CENAM AIP and IGNTG teams Figure Pictures of the observation station in Panama City - CENAMEP AIP Large Mass Lab. 19 Figure Satellite images of the observation station in Panama City CENAMEP AIP - Large Mass Lab Figure Pictures of the IMGC-02 at the observation station in Panama City CENAMEP AIP - Large Mass Lab Figure Plane of the building in Panama City CENAMEP AIP- Large mass lab at the time of measurements a), and as foreseen after the restructuration b) (scheduled in spring 2008) Table Experimental results in Panama City - CENAMEP AIP Large Mass Lab Table Apparatus setup Panama City CENAMEP AIP Large Mass Lab Figure Time series (rejected-red, accepted-white) (a), Data sets (average of 20 launches) (b), trajectory residuals (one launch-red, average-white) (c) in Panama City - CENAMEP AIP Large Mass Lab Figure Density frequency graphs (1) and normal probability graphs (2) of the g value (a), gradient (b) and friction coefficient (c) measured in Panama City - CENAMEP AIP Large Mass Lab Figure Ambient temperature (a), local barometric pressure (b) and launch chamber pressure (c) acquired at each launch and applied tide corrections (d) in Panama City CENAMEP AIP Large Mass Lab Figure Position of the bridge-laying (tackle) in Panama City CENAMEP AIP - Large Mass Lab during the measurements Table Measurement uncertainty in Panama City CENAMEP AIP Large Mass Lab

4 Figure Pictures of the observation station in El Valle Figure Satellite images of the observation station in El Valle Figure Pictures of the IMGC-02 at the observation station in El Valle Figure Plane of the building in El ValleTable Experimental results in El Valle Table Experimental results in El Valle Table Apparatus setup El Valle Figure Time series (rejected-red, accepted-white) (a), Data sets (average of 50 launches) (b), trajectory residuals (one launch-red, average-white) (c) in El Valle Figure Density frequency graphs (1) and normal probability graphs (2) of the g value (a), gradient (b) and friction coefficient (c) measured in El Valle Figure Ambient temp. (a), local barometric pressure (b) and launch chamber pressure (c) acquired at each launch and applied tide corrections (d) in El Valle Table Measurement uncertainty in El Valle Figure Pictures of the observation station in Calobre Figure Satellite images of the observation station in Calobre Figure Pictures of the IMGC-02 at the observation station in Calobre Figure Plane of the building in Calobre Table Experimental results in Calobre Table Experimental results in Calobre Table Apparatus setup Calobre Figure Time series (rejected-red, accepted-white) (a), Data sets (average of 30 launches) (b), trajectory residuals (one launch-red, average-white) (c) in Calobre Figure Density frequency graphs (1) and normal probability graphs (2) of the g value (a), gradient (b) and friction coefficient (c) measured in Calobre Figure Ambient temperature (a), local barometric pressure (b) and launch chamber pressure (c) acquired at each launch and applied tide corrections (d) in Calobre Table Measurement uncertainty in Calobre Figure Pictures of the observation station in Tonosí Figure Satellite images of the observation station in Tonosí Figure Pictures of the IMGC-02 at the observation station in Tonosí Figure Plane of the building in TonosíTable Experimental results in Tonosí Table Experimental results in Tonosí Table Apparatus setup Tonosí Figure Time series (rejected-red, accepted-white) (a), Data sets (average of 30 launches) (b), trajectory residuals (one launch-red, average-white) (c) in Tonosí Figure Density frequency graphs (1) and normal probability graphs (2) of the g value (a), gradient (b) and friction coefficient (c) measured in Tonosí Figure Ambient temperature (a), local barometric pressure (b) and launch chamber pressure (c) acquired at each launch and applied tide corrections (d) in Tonosí Table Measurement uncertainty in Tonosí Figure Pictures of the observation station in Colon Figure Satellite images of the observation station in Colon Figure Pictures of the IMGC-02 at the observation station in Colon Figure Plane of the building in Colon Table Experimental results in Colon Table Experimental results in Colon Table Apparatus setup Colon Figure Time series (rejected-red, accepted-white) (a), Data sets (average of 80 launches) (b), trajectory residuals (one launch-red, average-white) (c) in Colon Figure Density frequency graphs (1) and normal probability graphs (2) of the g value (a), gradient (b) and friction coefficient (c) measured in Colon Figure Ambient temperature (a), local barometric pressure (b) and launch chamber pressure (c) acquired at each launch and applied tide corrections (d) in Colon Table Measurement uncertainty in Colon Figure Pictures of the observation station in Santa Fe Figure Satellite images of the observation station in Santa Fe Figure Pictures of the IMGC-02 at the observation station in Santa Fe Figure Plane of the building in Santa FeTable Experimental results in Santa Fe Table Experimental results in Santa Fe

5 Table Apparatus setup Santa Fe Figure Time series (rejected-red, accepted-white) (a), Data sets (average of 30 launches) (b), trajectory residuals (one launch-red, average-white) (c) in Santa Fe Figure Density frequency graphs (1) and normal probability graphs (2) of the g value (a), gradient (b) and friction coefficient (c) measured in Santa Fe Figure Ambient temp. (a), local barometric pressure (b) and launch chamber pressure (c) acquired at each launch and applied tide corrections (d) in Santa Fe Table Measurement uncertainty in Santa Fe Figure Pictures of the observation station in Yaviza Figure Satellite images of the observation station in Yaviza Figure Pictures of the IMGC-02 at the observation station in Yaviza Figure Plane of the building in YavizaTable Experimental results in Yaviza Table Experimental results in Yaviza Table Apparatus setup Yaviza Figure Time series (rejected-red, accepted-white) (a), Data sets (average of 50 launches) (b), trajectory residuals (one launch-red, average-white) (c) in Yaviza Figure Density frequency graphs (1) and normal probability graphs (2) of the g value (a), gradient (b) and friction coefficient (c) measured in Yaviza Figure Ambient temperature see the paragraph remarks (a), local barometric pressure (b) and launch chamber pressure (c) acquired at each launch and applied tide corrections (d) in Yaviza Table Measurement uncertainty in Yaviza Figure Pictures of the observation station in Panama City - IGNTG CORS Figure Satellite images of the observation station in Panama City - IGNTG CORS Figure Pictures of the IMGC-02 at the observation station in Panama City - IGNTG CORS Figure Plane of the building station in Panama City - IGNTG CORS Table Experimental results station in Panama City - IGNTG CORS Table Experimental results station in Panama City - IGNTG CORS Table Apparatus setup Panama City - IGNTG CORS Figure Time series (rejected-red, accepted-white) (a), Data sets (average of 30 launches) (b), trajectory residuals (one launch-red, average-white) (c) in Panama City - IGNTG CORS Figure Density frequency graphs (1) and normal probability graphs (2) of the g value (a), gradient (b) and friction coefficient (c) measured in Panama City - IGNTG CORS Figure Ambient temperature see the paragraph remarks (a), local barometric pressure (b) and launch chamber pressure (c) acquired at each launch and applied tide corrections (d) in Panama City - IGNTG CORS Table Measurement uncertainty in Panama City - IGNTG CORS Figure Pictures of the observation station in Tolé Figure Satellite images of the observation station in Tolé Figure Pictures of the IMGC-02 at the observation station in Tolé Figure Plane of the building station in Tolé Table Experimental results station in Tolé Table Experimental results station in Tolé Table Apparatus setup in Tolé Figure Time series (rejected-red, accepted-white) (a), Data sets (average of 35 launches) (b), trajectory residuals (one launch-red, average-white) (c) in Tolé Figure Density frequency graphs (1) and normal probability graphs (2) of the g value (a), gradient (b) and friction coefficient (c) measured in Tolé Figure Ambient temperature see the paragraph remarks (a), local barometric pressure (b) and launch chamber pressure (c) acquired at each launch and applied tide corrections (d) in Tolé Table Measurement uncertainty in Tolé Figure Pictures of the observation station in Changuinola Figure Satellite images of the observation station in Changuinola Figure Pictures of the IMGC-02 at the observation station in Changuinola Figure Plane of the building station in Changuinola Table Experimental results station in Changuinola Table Experimental results station in Changuinola Table Apparatus setup in Changuinola

6 Figure Time series (rejected-red, accepted-white) (a), Data sets (average of 35 launches) (b), trajectory residuals (one launch-red, average-white) (c) in Changuinola Figure Density frequency graphs (1) and normal probability graphs (2) of the g value (a), gradient (b) and friction coefficient (c) measured in Changuinola Figure Ambient temperature see the paragraph remarks (a), local barometric pressure (b) and launch chamber pressure (c) acquired at each launch and applied tide corrections (d) in Changuinola Table Measurement uncertainty in Changuinola Figure Pictures of the observation station in Boquete Figure Satellite images of the observation station in Boquete Figure Pictures of the IMGC-02 at the observation station in Boquete Figure Plane of the building station in Boquete Table Experimental results station in Boquete Table Apparatus setup in Boquete Figure Time series (rejected-red, accepted-white) (a), Data sets (average of 35 launches) (b), trajectory residuals (one launch-red, average-white) (c) in Boquete Figure Density frequency graphs (1) and normal probability graphs (2) of the g value (a), gradient (b) and friction coefficient (c) measured in Boquete Figure Ambient temperature see the paragraph remarks (a), local barometric pressure (b) and launch chamber pressure (c) acquired at each launch and applied tide corrections (d) in Boquete125 Table Measurement uncertainty in Boquete Figure Pictures of the observation station in Coiba Figure Satellite images of the observation station in Coiba Figure Pictures of the IMGC-02 at the observation station in Coiba Figure Plane of the building station in Coiba Table Experimental results station in Coiba Table Apparatus setup in Coiba Figure Time series (rejected-red, accepted-white) (a), Data sets (average of 25 launches) (b), trajectory residuals (one launch-red, average-white) (c) in Coiba Figure Density frequency graphs (1) and normal probability graphs (2) of the g value (a), gradient (b) and friction coefficient (c) measured in Coiba Figure Ambient temperature see the paragraph remarks (a), local barometric pressure (b) and launch chamber pressure (c) acquired at each launch and applied tide corrections (d) in Coiba Table Measurement uncertainty in Coiba

7 1 INTRODUCTION The measurement of the free-fall acceleration, g, has been performed with the new gravimeter IMGC-02. The apparatus (fig.1) is developed by INRIM /1/, and derives from that one previously realized in collaboration with the Bureau International des Poids et Mesures in Sèvres (BIPM) /2/. Several improvements characterize the IMGC-02, among them there is the automation of the instrument which allows to perform the measurement during the night, when the disturbance due to the environmental noise is minimum. All the measurement sessions have been recorded and stored in data files for post-processing. If necessary, these files are delivered for future revision or checking. The software used is the GravisoftM 1.5 and GravisoftPP 1.5, developed and tested by INRIM. Figure 1. Picture of the new absolute gravimeter IMGC-02 7

8 2 THE IMGC ABSOLUTE GRAVIMETER 2.1 MEASUREMENT METHOD The free-fall acceleration g is measured by tracking the vertical trajectory of a test-body subjected to the gravitational acceleration. The IMGC-02 adopts the symmetric rise and falling method, where both the rising and falling trajectories of the test-body are recorded. The raw datum consists in an array where each element represents the time correspondent to the passage of the test-body through equally spaced levels (or stations). A model function derived from the equation of motion is fitted to the raw datum in a least-squares adjustment. One of the parameters of the model is the acceleration experienced by the test-body during its flight. A measurement session consists of about 2000 launches. To assure the evaluated measurement uncertainty, the g value is obtained by averaging those launches which fulfill accepting criteria. 2.2 APPARATUS A schematic layout of the apparatus is showed in fig The basic parts of the instrument are a Mach-Zehnder interferometer /3/ and a long-period (about 20 s) seismometer. The wavelength of a iodine stabilised He-Ne laser is used as the length standard. The inertial mass of a seismometer supports a cube-corner reflector, which is the reference mirror of the interferometer. The moving mirror of the interferometer is also a cube-corner retro-reflector and is directly subjected to the free falling motion. It is thrown vertically upwards by means of a launch pad in a vacuum chamber ( Pa). Interference fringes emerging from the interferometer are detected by a photomultiplier. The output signal is sampled by a high-speed waveform digitizer synchronized to a Rb oscillator, used as the time standard. Equally spaced stations are selected by counting a constant integer number of interference fringes (at present 1024); in particular consecutive stations are separated by a distance d = 1024 /2, being the wavelength of the laser radiation. The so called local fit method is used to time the interference signal /4/. In particular the time is computed by fitting the equation model of the interference of monochromatic waves to the interference fringe correspondent to the selected station. The space-time coordinates are processed in a least-squares algorithm, where a suitable model function is fitted to the trajectory. Each throw gives an estimate of the g value. A personal computer manages the instrument. The pad launch is triggered only if the system is found to be ready. In particular the software checks the pad launch state (loaded or unloaded) and the laser state (locked or unlocked). Environmental parameters such as the local barometric pressure and the temperature are acquired and stored for each launch. 8

9 seismometer interferometer photo-detector frame laser launch chamber computer electronics Figure 2.1. Schematic layout of the IMGC-02 Absolute Gravimeter The software used includes (i) the manager GravisoftM 1.5 (fig. 2.2) for driving the instrument and storing the measurement data and (ii) the post-processing GravisoftPP 1.5 (fig. 2.3) for elaborating the data-files. These programs were developed and tested on the LabVIEW8.2 platform. Geophysical corrections are applied: (i) the Earth tides and Ocean loading are computed with the T-SOFT, version 2007, developed at the Royal Observatory of Belgium, (ii) the polar motion correction is computed starting from the daily pole coordinates x and y (rad) obtained from the International Earth Rotation Service (IERS). The gravitational acceleration is normalized to a nominal pressure, taking into account a -8 barometric factor f B = m s -2 mbar -1, as recommended by the IAG 1983 resolution n.9. Instrumental corrections are also applied: (i) the diffraction correction and the (ii) laser beam verticality. The g value associated to every measurement session is calculated as the average of n measurements and it is referred to a specific height from the floor. The measurement expanded uncertainty is evaluated according to the method of combination of uncertainties as suggested by the ISO GUM guide /5/. 9

10 Figure 2.2. GravisoftM manager front panel Figure 2.3. GravisoftPP post-processing front panel 10

11 3 MEASUREMENT UNCERTAINTY The uncertainty associated to the g measurement is evaluated by combining the contributions of uncertainty of the IMGC-02 absolute gravimeter, called the instrumental uncertainties to the contribution of uncertainty depending on the observation site. Uncertainty tables, related to each observation site, are attached to the experimental results below described. 3.1 INSTRUMENTAL UNCERTAINTY OF THE IMGC-02 ABSOLUTE GRAVIMETER Influence factors which are characteristic of the instrument are: vacuum level, non-uniform magnetic field, temperature gradient, electrostatic attraction, mass distribution, laser beam verticality, air gap modulation, length and time standards, retro-reflector balancing, radiation pressure and reference height. A detailed description of these phenomena concerning the present IMGC-02 absolute gravimeter can be found in /1/. Tab. 3.1 reports the quantitative assessment of the effect of every disturbing factor. The expanded uncertainty at the 95% confidence level (coverage factor k = 2.10 and 19 degrees of freedom) is estimated to be U = m s INFLUENCE FACTORS CHARACTERISTIC OF THE OBSERVATION SITE The measurement uncertainty results from the combination of the instrument uncertainty with influence factors that are dependent from the observation site: Coriolis force, floor recoil and geophysical effects, such as local barometric pressure, gravity tides, ocean loading and polar motion. A detailed description of these phenomena concerning the present IMGC-02 absolute gravimeter can also be found in /1/ and are summarised in the following sub-chapter CORIOLIS FORCE An object which is moving relative to the earth with a velocity v, is subjected to the Coriolis acceleration 2 E v, due to the earth s angular rotational velocity E ( rad s -1 ). A freely falling body with a velocity vector v E W in the East-West direction is therefore subjected to a Coriolis acceleration with a vertical component a c which points in the up direction if the vector points in the East direction, towards down direction if the vector points in the West direction. It follows that the test-body experiences the vertical component of the Coriolis acceleration, according to: a c 2 E ve W sin(90 ) where is the latitude of the observation site. An estimation of this effect for each site (latitude) is done and included in the uncertainty table. 11

12 Table 3.1. Instrumental uncertainty of the IMGC-02 absolute gravimeter Influence parameters, Type A, Type B, Value Unit u x i or a i i s i a i g Type of distribution Equivalent variance Sensitivity coefficients Contribution to the variance Equivalent Degrees of standard freedom, i uncertainty Drag effect negligible Outgassing effect negligible Non-uniform magnetic field effect negligible Temperature gradient effect m s -2 ±1.5E E-09 U 1.1E E E E-09 Effect for Electrostatic negligible Mass distribution effect m s -2 ±5.0E E-09 rectangular 8.3E E E E-09 Laser beam verticality correction 6.6E-09 m s -2 ±2.1E E E-09 rectangular 1.5E E E E-09 Air gap modulation effect negligible Laser effect m s E E E E E E-09 Index of refraction effect negligible Beam divergence correction 1.03E-07 m s E E E E E E E-08 Beam share effect unknown unknown Clock effect m s E E-09 rectangular 3.6E E E E-09 Finges timing effect negligible Finite value of speed of light effect negligible Retroreflector balancing 0.0E+00 m ±1.0E E-04 rectangular 3.3E E E E-08 Radiation Pressure effect negligible Reference height 5.0E-01 m ±5.0E E-04 rectangular 8.3E E E E-10 Corr. 1.10E-07 m s -2 Variance 1.5E-15-4 m 2 s Combined standard uncertainty, u Degrees of freedom, eff (Welch-Satterthwaite formula) Confidence level, p Coverage factor, k (calculated with t-student) Expanded uncertainty, U = ku Relative expanded uncertainty, U rel = U/g 3.8E-08 m s % E-08 m s E-09 12

13 3.2.2 FLOOR RECOIL The inertial mass of the seismometer is used as a reference point during the trajectory tracking. The natural oscillations due to the ground motion are smoothed and damped according to the seismometer transfer function. From a theoretical point of view, supposing that the ground vibrations are random and uncorrelated with the launch of the test-body, the bias of the average g value should tend to zero. Only the data scattering should be affected by the ground vibrations. Experimental tests carried out at INRIM laboratory confirmed that the recoil effect is considered negligible. Another issue linked to the floor recoil are tilts and translations of the interferometer base. The IMGC-02 interferometer design is insensitive to translations and rotations of the optical block containing the beam splitter and pick-off mirrors. The relevant effect is assessed to be negligible GEOPHYSICAL EFFECTS The measured gravity values are also affected by geophysical effects, such as gravity tide, ocean loading, gravity attraction and loading due to atmospheric pressure variation and change in the centrifugal acceleration due to polar motion. The raw gravity records contain these environmental signals in addition to the experimental noise. The assessment of this noise can be performed only after removing the geophysical effects. Although the theoretical background is beyond the aim of this work, hereafter the information concerning the calculations of the corrections is reported LOCAL BAROMETRIC PRESSURE Local air pressure variations affect absolute gravity measurements. A portion of the total mass attraction of the earth is due to atmosphere. As the pressure at the surface increases, the integrated mass above the observation point also increases due to the average density. It follows an upward force which decreases the local gravity value. Another consequence of higher pressure is an increased load on the surface which causes a depression in the crust. As a consequence the g value increases. Between the two competing effects, the strong one is the mass attraction which is about 12 times larger than the depression in the crust. A local barometric pressure increasing makes the gravity value decreasing. As recommended by the IAG 1983 resolution n.9, the barometric factor is defined as f B = 0.30 Gal mbar -1. Moreover, the measured gravity is referred to a nominal pressure following correction: g pr f B Po Pn P n by applying the where P o is the observed atmospheric pressure. The nominal pressure at the site is defined as: P n h m

14 where P is introduced in mbar and h, the topographic elevation, in m. n m The barometer adopted is the Druck DPI 280. The calibration of this device, performed on the range mbar showed a fractional accuracy of If frequent calibration is performed, the residual uncertainty assigned after the correction is therefore negligible (0.03 Gal) GRAVITY TIDE AND OCEAN LOADING Gravity tide includes the body earth tide and attraction-loading effects from ocean tide. In particular the first one is mainly due to the external influence of the sun and moon. The latter one is a consequence of the first, because the effect of luni-solar tide is a variation of the height of the oceans twice daily. The redistribution of the ocean s surface affects the value of gravity measured at a particular site. It has to be underlined that the effect is stronger and not perfectly known at seaside, especially in an observation site with a high altitude. The gravity tide corrections can be computed either through calculation based on models or by fitting gravimetric measured data, normally acquired by means of relative gravimeters. To generate the tide corrections, the IMGC-02 is currently using the software T-SOFT version 2007, developed by the Observatoire de Belgique, based on the ETGTAB software written by late Prof. H.-G Wenzel, Geodetic Institute, Karlsruhe University. This program computes body tidal parameters and generates time series of body tides starting from the geographic coordinates of the observation point. The tidal parameters are amplitude and phase of defined waves. Parameters of the ocean loading are calculated with the Schwiderski model computed by OLMPP (Scherneck) Onsala Space Observatory ( In literature it is reported that mean typical uncertainties after correction are respectively 0.3 Gal and 0.2 Gal for body earth tide and ocean loading POLAR MOTION The rotation of the earth around its pole generates a centrifugal force which deforms the earth into an ellipsoid. Any changes in the rotation rate or the location of the rotation pole affect the amplitude and the direction of the centrifugal force. The gravitational acceleration comprises the centrifugal force, therefore the above mentioned changes directly affects the measured g value. The surface of the earth is also deformed by variations in the centrifugal force. It follows that also the earth s potential energy and the position of the observation point respect to the centre if the earth changes. Wahr discussed this subject and suggested the so called polar motion correction: g pm 2 E a 2 sin cos x cos y sin The correction is given in m s -2. E is the earth s angular rotational velocity, a = m is the equatorial radius (semi-major axis) of the reference ellipsoid, and are respectively the geodetic latitude and longitude of the observation station. The 14

15 daily pole coordinates x and y are obtained from the International Earth Rotation Service (IERS) at the web-site: The uncertainty of polar motion, after the correction, is considered negligible SCATTERING OF MEASUREMENTS This effect is estimated with the experimental standard deviation of the mean g value. It is strongly depended on the ground vibrations and floor recoil. 15

16 4 EXPERIMENTAL RESULTS The CENAMEP AIP and the IGNTG identified twelve sites (fig. 4.1 and table 4.1). Figure 4.1 Location of the measurement sites in the Republic of Panama 16

17 Table 4.1. Location of the measurement sites in the Republic of Panama City Location Long. / Lat. / H. / m Date Panama CENAMEP AIP /01/19-20 El Valle Cuartel de Bomberos /01/26-27 Calobre Municipio /01/27-28 Tonosí ANAM /01/29-30 Colon ACP /02/01-02 Santa Fe MOP /02/07-08 Yaviza Escuela /02/08-10 Panama IGNTG /02/12-13 Tolé MOP /02/13-15 Changuinola MOP /02/16-17 Boquete Escuela /02/18-19 Coiba ANAM /02/21-22 The measurements was carried out by the INRIM team with the extremely friendly and useful support of the CENAM AIP and IGNTG teams (fig. 4.2). Figure 4.2 Pictures of the INRIM, CENAM AIP and IGNTG teams 17

18 4.1 PANAMA CITY CENAMEP AIP The observation station of Panama City - CENAMEP AIP is located at the Large Mass Laboratory of the CENAMEP AIP, 215 building of the Ciudad del Saber, fig and The measurements was carried out on January The position of the measurement point (fig ) referred to the room is showed on the plan of the building, fig The orientation of the instrument is showed by the red triangle where the black square represents the laser body. The instrument processed and stored 1988 trajectories. The measured data are filtered by applying rejecting criteria. The most critical factor is the visibility variation of the interference signal during the trajectory, which highlights an horizontal motion of the test-body. The effect due to the Coriolis force and the beam share are minimized by rejecting those launches with a decrease of visibility bigger that 10%. Outliers are found by applying the Chauvenet criterion to the estimating parameters such as the vertical gradient, the friction of residual air and to the estimated g value. The final g value is obtained by averaging 318 trajectories. Tab reports the most important experimental results. Other information concerning the apparatus setup is reported in tab The time series of the post-processed trajectories, data sets (each correspondent to the average of 20 launches) and trajectory residuals are reported in fig The apparatus experienced an oscillation of about ± m s -2. The averaged trajectory residuals after the measurement session are within m. The graphs reported in fig represents the density frequency histograms and normal probability graphs of the g value, gradient and friction coefficient of the measurement session. The 2 test rejects the null hypothesis, i.e. the normal distribution, with a 20% risk error. Fig reports ambient temperature, local barometric pressure and launch chamber pressure acquired at each launch and the applied tide corrections. The measurement uncertainty is summarized in tab It includes the instrumental uncertainty reported in tab

19 Ciudad del Saber - Entrance CENAMEP - Entrance CENAMEP - Court Large Mass Laboratory - Entrance Figure Pictures of the observation station in Panama City - CENAMEP AIP Large Mass Lab 19

20 Figure Satellite images of the observation station in Panama City CENAMEP AIP - Large Mass Lab 20

21 Figure Pictures of the IMGC-02 at the observation station in Panama City CENAMEP AIP - Large Mass Lab 1,3 m 2,2 m Large Mass Laboratory a) b) Figure Plane of the building in Panama City CENAMEP AIP- Large mass lab at the time of measurements a), and as foreseen after the restructuration b) (scheduled in spring 2008) 21

22 Table Experimental results in Panama City - CENAMEP AIP Large Mass Lab Observation Station: Panama City CENAMEP AIP Large Mass Lab Observation start (data and time in UTC) 2008/01/20 00:31:22 Observation stop (data and time in UTC) 2008/01/20 19:59:13 Geodetic longitude = Geodetic latitude = Topographic elevation H T = 21 m Nominal pressure at the observation site P N = mbar Pole coordinates in IERS system x = , y = Measurement parameters Total measurement time T m = h Measurement rate m r = 132 h -1 Measurement drift m d = m s -2 h Total processed and stored throws n ps = 1988 Temperature range T = ( ) C Local barometric pressure (mean) P = 1008 mbar 2 test (80% confidence level) 2 max = 25.9; 2 min = 10.8; 2 exp = 10.5 Corrections Laser beam verticality correction g bv = m s -2 Laser beam divergence correction g bd = m s -2 Polar motion correction g pm = m s -2 Tide and ocean loading correction (mean) g tol = m s -2 Local barometric pressure correction (mean) g bp = m s -2 Results corrected mean g value g mv = m s -2 Reference height h ref = m Number of throws accepted for the average n = 318 Experimental standard deviation s g = m s -2 Experimental standard deviation of the mean value s gm = m s -2 Measurement combined uncertainty u gm = m s -2 Measurement expanded uncertainty (p = 95%, = 31, k = 2.04) U gm = m s -2 Vertical gradient = unknown Table Apparatus setup Panama City CENAMEP AIP Large Mass Lab Instrument orientation See fig Fitting Model Laser mod. & ground vibr. (19 Hz) Fringe visibility threshold f vt = 10% Measurements each set n ma = 20 Waveform digitizer sampling frequency S f = 50 MHz Laser wavelength l = m Clock frequency f c = Hz Vertical gradient input = s -2 Rise station number n rs = 350 Leaved upper stations n sl = 2 Laser modulation frequency f lm = Hz 22

23 Figure Time series (rejected-red, accepted-white) (a), Data sets (average of 20 launches) (b), trajectory residuals (one launch-red, average-white) (c) in Panama City - CENAMEP AIP Large Mass Lab 23

24 Figure Density frequency graphs (1) and normal probability graphs (2) of the g value (a), gradient (b) and friction coefficient (c) measured in Panama City - CENAMEP AIP Large Mass Lab 24

25 Figure Ambient temperature (a), local barometric pressure (b) and launch chamber pressure (c) acquired at each launch and applied tide corrections (d) in Panama City CENAMEP AIP Large Mass Lab 25

26 REMARKS After the measurement session the interferometer was found aligned as well as at the beginning. There is not reason for suspecting a thermal drift of the apparatus. The trajectory was reconstructed with the model that takes into account the laser modulation and the vibration of the inertial system. The best result was obtained by removing the 2 upper stations from the fit. The average of the trajectory residuals shows that the floor is very stiff and the low scattering of the data highlights that the observation site is very quite. The sinusoidal trend of the time series is probably due to the effect of the large variation of the level of the Pacific Ocean. The prediction of the ocean loading used by the IMGC-02 is based on a model that doesn t take into account this phenomenon. The best solution could be to acquire continuously the gravity data with a relative gravimeter and to use the results to compute the tidal parameters used to predict the tides. Nevertheless the measurement of the free-fall acceleration is considered to be correct within the evaluated uncertainty. A bridge-laying (tackle) is located in the laboratory. Since its mass can modify the gravitational field in the laboratory, its position must be noted and, in case of repetition of measurements (also with relative gravimeters), it should be located in the same position as shown in fig Figure Position of the bridge-laying (tackle) in Panama City CENAMEP AIP - Large Mass Lab during the measurements 26

27 Table Measurement uncertainty in Panama City CENAMEP AIP Large Mass Lab Influence parameters, x i Value Unit ui or a i Type A, s i Type B, a i g Type of distribution Equivalent variance Sensitivity coefficients Contribution to the variance Degrees of freedom, i Equivalent standard uncertainty u i 4 (y)/ i Instrument uncertainty m s E E E E E E E-31 Coriolis effect m s E E-08 rectangular 4.3E E E E E-32 Floor recoil effect negligible Barometric pressure correction 7.5E-09 m s E E E-09 rectangular 3.3E E E E E-35 Tide correction 3.3E-07 m s E E E E E E E E-36 Ocean loading correction m s E E E E E E E-36 Polar motion correction -1.6E-08 m s -3 negligible -1.6E-08 Standard deviation of the mean value m s E E E E E E E-35 Corr. 3.2E-07 m s -2-4 Variance 2.0E-15 m 2 s Combined standard uncertainty, u Degrees of freedom, eff (Welch-Satterthwaite formula) 4.5E-08 m s Confidence level, p Coverage factor, k (calculated with t-student) Expanded uncertainty, U = ku Relative expanded uncertainty, U rel = U/g 95% E-08 m s E-09 27

28 4.2 EL VALLE The observation station of El Valle is located at the Cuartel de Bomberos Jose Ma. Tesada, fig and The measurements was carried out on January The position of the measurement point (fig ) referred to the room is showed on the plan of the building, fig The orientation of the instrument is showed by the red triangle where the black square represents the laser body. The instrument processed and stored 1092 trajectories. The measured data are filtered by applying rejecting criteria. The most critical factor is the visibility variation of the interference signal during the trajectory, which highlights an horizontal motion of the test-body. The effect due to the Coriolis force and the beam share are minimized by rejecting those launches with a decrease of visibility bigger that 40%. Outliers are found by applying the Chauvenet criterion to the estimating parameters such as the vertical gradient, the friction of residual air and to the estimated g value. The final g value is obtained by averaging 695 trajectories. Tab reports the most important experimental results. Other information concerning the apparatus setup is reported in tab The time series of the post-processed trajectories, data sets (each correspondent to the average of 50 launches) and trajectory residuals are reported in fig The apparatus experienced an oscillation of about ± m s -2. The averaged trajectory residuals after the measurement session are within m. The graphs reported in fig represents the density frequency histograms and normal probability graphs of the g value, gradient and friction coefficient of the measurement session. The 2 test doesn t rejects the null hypothesis, i.e. the normal distribution, with a 20% risk error. Fig reports ambient temperature, local barometric pressure and launch chamber pressure acquired at each launch and the applied tide corrections. The measurement uncertainty is summarized in tab It includes the instrumental uncertainty reported in tab

29 Cuartel de Bomberos Jose Ma. Tesada - Cuartel de Bomberos Jose Ma. Tesada - Door Figure Pictures of the observation station in El Valle 29

30 Figure Satellite images of the observation station in El Valle 30

31 Figure Pictures of the IMGC-02 at the observation station in El Valle Figure Plane of the building in El Valle 31

32 Table Experimental results in El Valle Observation Station: El Valle Observation start (data and time in UTC) 2008/01/26 00:55:08 Observation stop (data and time in UTC) 2008/01/27 12:35:47 Geodetic longitude = Geodetic latitude = Topographic elevation H T = 586 m Nominal pressure at the observation site P N = mbar Pole coordinates in IERS system x = , y = Measurement parameters Total measurement time T m = h Measurement rate m r = 52 h -1 Measurement drift m d = m s -2 h Total processed and stored throws n ps = 1092 Temperature range T = ( ) C Local barometric pressure (mean) P = mbar 2 test (80% confidence level) 2 max = 36.7; 2 min = 18.1; 2 exp = 32.6 Corrections Laser beam verticality correction g bv = m s -2 Laser beam divergence correction g bd = m s -2 Polar motion correction g pm = m s -2 Tide and ocean loading correction (mean) g tol = m s -2 Local barometric pressure correction (mean) g bp = m s -2 Results corrected mean g value g mv = m s -2 Reference height h ref = m Number of throws accepted for the average n = 695 Experimental standard deviation s g = m s -2 Experimental standard deviation of the mean value s gm = m s -2 Measurement combined uncertainty u gm = m s -2 Measurement expanded uncertainty (p = 95%, = 254, k = 1.97) U gm = m s -2 Vertical gradient = unknown Table Apparatus setup El Valle Instrument orientation See fig Fitting Model Laser modul. & ground vibr. (18.9 Hz) Fringe visibility threshold f vt = 40% Measurements each set n ma = 50 Waveform digitizer sampling frequency S f = 50 MHz Laser wavelength l = m Clock frequency f c = Hz Vertical gradient input = s -2 Rise station number n rs = 350 Leaved upper stations n sl = 80 Laser modulation frequency f lm = Hz 32

33 Figure Time series (rejected-red, accepted-white) (a), Data sets (average of 50 launches) (b), trajectory residuals (one launch-red, average-white) (c) in El Valle 33

34 Figure Density frequency graphs (1) and normal probability graphs (2) of the g value (a), gradient (b) and friction coefficient (c) measured in El Valle 34

35 Figure Ambient temp. (a), local barometric pressure (b) and launch chamber pressure (c) acquired at each launch and applied tide corrections (d) in El Valle 35

36 REMARKS After the measurement session the interferometer was found aligned as well as at the beginning. There is not reason for suspecting a thermal drift of the apparatus. The trajectory was reconstructed with the model that takes into account the laser modulation and the vibration of the inertial system. The best result was obtained by removing the 80 upper stations from the fit. The average of the trajectory residuals shows that the floor is sufficiently stiff but the scattering of the data highlights that the observation site is very noisy. The very windy days probably influenced the measurements due to the inducted the vibrations to the ground floor of the site. Nevertheless the measurement of the free-fall acceleration is considered to be correct within the evaluated uncertainty. 36

37 Table Measurement uncertainty in El Valle Influence parameters, Value Unit u i or a i Type A, x i s i Type B, a i g Type of distribution Equivalent variance Sensitivity coefficients Contribution to the variance Degrees of freedom, i Equivalent standard uncertainty Instrument uncertainty m s E E E E E E-08 Coriolis effect m s E E-08 rectangular 1.7E E E E-08 Floor recoil effect negligible Barometric pressure correction 7.1E-09 m s E E E-09 rectangular 3.3E E E E-09 Tide correction 3.0E-07 m s E E E E E E E-09 Ocean loading correction m s E E E E E E-09 Polar motion correction -1.6E-08 m s -3 negligible -1.6E-08 Standard deviation of the mean value m s E E E E E E-08 Corr. 2.9E-07 m s -2 Variance 1.1E-14 m 2 s -4 Combined standard unc ertainty, u Degrees of freedom, eff (Welch-Satterthwaite formula) 1.1E-07 m s Confidence level, p Coverage factor, k ( cal culated with t-student) 95% 1.97 Expanded uncertaint y, U = ku 2.1E-07 m s -2 Relative expanded uncertainty, U rel = U/g 2.1E-08 37

38 4.3 CALOBRE The observation station of Calobre is located in a building of the Municipio, fig and The measurements was carried out on January The position of the measurement point (fig ) referred to the room is showed on the plan of the building, fig The orientation of the instrument is showed by the red triangle where the black square represents the laser body. The instrument processed and stored 702 trajectories. The measured data are filtered by applying rejecting criteria. The most critical factor is the visibility variation of the interference signal during the trajectory, which highlights an horizontal motion of the test-body. The effect due to the Coriolis force and the beam share are minimized by rejecting those launches with a decrease of visibility bigger that 20%. Outliers are found by applying the Chauvenet criterion to the estimating parameters such as the vertical gradient, the friction of residual air and to the estimated g value. The final g value is obtained by averaging 146 trajectories. Tab reports the most important experimental results. Other information concerning the apparatus setup is reported in tab The time series of the post-processed trajectories, data sets (each correspondent to the average of 30 launches) and trajectory residuals are reported in fig The apparatus experienced an oscillation of about ± m s -2. The averaged trajectory residuals after the measurement session are within m. The graphs reported in fig represents the density frequency histograms and normal probability graphs of the g value, gradient and friction coefficient of the measurement session. The 2 test doesn t rejects the null hypothesis, i.e. the normal distribution, with a 20% risk error. Fig reports ambient temperature, local barometric pressure and launch chamber pressure acquired at each launch and the applied tide corrections. The measurement uncertainty is summarized in tab It includes the instrumental uncertainty reported in tab

39 Calobre - Municipio - Front entrance Calobre - Municipio - Back entrance and Calobre - Municipio - Site building Calobre - Municipio - Site building entrance Figure Pictures of the observation station in Calobre 39

40 Figure Satellite images of the observation station in Calobre 40

41 Figure Pictures of the IMGC-02 at the observation station in Calobre Figure Plane of the building in Calobre 41

42 Table Experimental results in Calobre Observation Station: Calobre Observation start (data and time in UTC) 2008/01/27 23:02:43 Observation stop (data and time in UTC) 2008/01/28 23:30:30 Geodetic longitude = Geodetic latitude = Topographic elevation H T = 126 m Nominal pressure at the observation site P N = mbar Pole coordinates in IERS system x = , y = Measurement parameters Total measurement time T m = h Measurement rate m r = 53 h -1 Measurement drift m d = m s -2 h Total processed and stored throws n ps = 702 Temperature range T = ( ) C Local barometric pressure (mean) P = mbar 2 test (80% confidence level) 2 max = 19.8; 2 min = 7.0; 2 exp = 19.7 Corrections Laser beam verticality correction g bv = m s -2 Laser beam divergence correction g bd = m s -2 Polar motion correction g pm = m s -2 Tide and ocean loading correction (mean) g tol = m s -2 Local barometric pressure correction (mean) g bp = m s -2 Results corrected mean g value g mv = m s -2 Reference height h ref = m Number of throws accepted for the average n = 146 Experimental standard deviation s g = m s -2 Experimental standard deviation of the mean value s gm = m s -2 Measurement combined uncertainty u gm = m s -2 Measurement expanded uncertainty (p = 95%, = 42, k = 2.02) U gm = m s -2 Vertical gradient = unknown Table Apparatus setup Calobre Instrument orientation See fig Fitting Model Laser mod. & ground vibr. (16.8 Hz) Fringe visibility threshold f vt = 20% Measurements each set n ma = 30 Waveform digitizer sampling frequency S f = 50 MHz Laser wavelength l = m Clock frequency f c = Hz Vertical gradient input = s -2 Rise station number n rs = 350 Leaved upper stations n sl = 2 Laser modulation frequency f lm = Hz 42

43 Figure Time series (rejected-red, accepted-white) (a), Data sets (average of 30 launches) (b), trajectory residuals (one launch-red, average-white) (c) in Calobre 43

44 Figure Density frequency graphs (1) and normal probability graphs (2) of the g value (a), gradient (b) and friction coefficient (c) measured in Calobre 44

45 Figure Ambient temperature (a), local barometric pressure (b) and launch chamber pressure (c) acquired at each launch and applied tide corrections (d) in Calobre 45

46 REMARKS After the measurement session the interferometer was found aligned as well as at the beginning. There is not reason for suspecting a thermal drift of the apparatus. The trajectory was reconstructed with the model that takes into account the laser modulation and the vibration of the inertial system. The best result was obtained by removing the 2 upper stations from the fit. The average of the trajectory residuals shows that the floor is stiff and the low scattering of the data highlights that the observation site is quite. The measurement during the day was affected by the noise coming from the near road. The measurement of the free-fall acceleration is considered to be correct within the evaluated uncertainty. 46

47 Table Measurement uncertainty in Calobre Influence parameters, Value Unit u i or a i Type A, x i s i Type B, a i g Type of distribution Equivalent variance Sensitivity coefficients Contribution to the variance Degrees of freedom, i Equivalent standard uncertainty Instrument uncertainty m s E E E E E E-08 Coriolis effect m s E E-08 rectangular 7.3E E E E-08 Floor recoil effect negligible Barometric pressure correction 2.8E-09 m s E E E-09 rectangular 3.3E E E E-09 Tide correction 1.3E-07 m s E E E E E E E-09 Ocean loading correction m s E E E E E E-09 Polar motion correction -1.6E-08 m s -3 negligible -1.6E-08 Standard deviation of the mean value m s E E E E E E-08 Corr. 1.2E-07 m s -2 Variance 2.7E-15 m 2 s -4 Combined standard unc ertainty, u Degrees of freedom, eff (Welch-Satterthwaite formula) 5.2E-08 m s Confidence level, p Coverage factor, k ( cal culated with t-student) 95% 2.02 Expanded uncertaint y, U = ku 1.0E-07 m s -2 Relative expanded uncertainty, U rel = U/g 1.1E-08 47

48 4.4 TONOSÍ The observation station of Tonosí is located in a room of the Autoritad Nacional del Ambiente (ANAM), fig and The measurements was carried out on January The position of the measurement point (fig ) referred to the room is showed on the plan of the building, fig The orientation of the instrument is showed by the red triangle where the black square represents the laser body. The instrument processed and stored 770 trajectories. The measured data are filtered by applying rejecting criteria. The most critical factor is the visibility variation of the interference signal during the trajectory, which highlights an horizontal motion of the test-body. The effect due to the Coriolis force and the beam share are minimized by rejecting those launches with a decrease of visibility bigger that 10%. Outliers are found by applying the Chauvenet criterion to the estimating parameters such as the vertical gradient, the friction of residual air and to the estimated g value. The final g value is obtained by averaging 193 trajectories. Tab reports the most important experimental results. Other information concerning the apparatus setup is reported in tab The time series of the post-processed trajectories, data sets (each correspondent to the average of 30 launches) and trajectory residuals are reported in fig The apparatus experienced an oscillation of about ± m s -2. The averaged trajectory residuals after the measurement session are within m. The graphs reported in fig represents the density frequency histograms and normal probability graphs of the g value, gradient and friction coefficient of the measurement session. The 2 test doesn t rejects the null hypothesis, i.e. the normal distribution, with a 20% risk error. Fig reports ambient temperature, local barometric pressure and launch chamber pressure acquired at each launch and the applied tide corrections. The measurement uncertainty is summarized in tab It includes the instrumental uncertainty reported in tab

49 Tonosí ANAM - Entrance Tonosí ANAM - Court Tonosí ANAM - Door Figure Pictures of the observation station in Tonosí 49

50 Figure Satellite images of the observation station in Tonosí 50

51 Figure Pictures of the IMGC-02 at the observation station in Tonosí Figure Plane of the building in Tonosí 51

52 Table Experimental results in Tonosí Observation Station: Tonosí Observation start (data and time in UTC) 2008/01/29 23:56:23 Observation stop (data and time in UTC) 2008/01/30 20:57:12 Geodetic longitude = Geodetic latitude = Topographic elevation H T = 17 m Nominal pressure at the observation site P N = mbar Pole coordinates in IERS system x = , y = Measurement parameters Total measurement time T m = 21.0 h Measurement rate m r = 51 h -1 Measurement drift m d = m s -2 h Total processed and stored throws n ps = 770 Temperature range T = ( ) C Local barometric pressure (mean) P = mbar 2 test (80% confidence level) 2 max = 21.1; 2 min = 7.8; 2 exp = 12.7 Corrections Laser beam verticality correction g bv = m s -2 Laser beam divergence correction g bd = m s -2 Polar motion correction g pm = m s -2 Tide and ocean loading correction (mean) g tol = m s -2 Local barometric pressure correction (mean) g bp = m s -2 Results corrected mean g value g mv = m s -2 Reference height h ref = m Number of throws accepted for the average n = 193 Experimental standard deviation s g = m s -2 Experimental standard deviation of the mean value s gm = m s -2 Measurement combined uncertainty u gm = m s -2 Measurement expanded uncertainty (p = 95%, = 37, k = 2.03) U gm = m s -2 Vertical gradient = unknown Table Apparatus setup Tonosí Instrument orientation See fig Fitting Model Laser mod. & ground vibr. (18.6 Hz) Fringe visibility threshold f vt = 20% Measurements each set n ma = 30 Waveform digitizer sampling frequency S f = 50 MHz Laser wavelength l = m Clock frequency f c = Hz Vertical gradient input = s -2 Rise station number n rs = 350 Leaved upper stations n sl = 90 Laser modulation frequency f lm = Hz 52

53 Figure Time series (rejected-red, accepted-white) (a), Data sets (average of 30 launches) (b), trajectory residuals (one launch-red, average-white) (c) in Tonosí 53

54 Figure Density frequency graphs (1) and normal probability graphs (2) of the g value (a), gradient (b) and friction coefficient (c) measured in Tonosí 54

55 Figure Ambient temperature (a), local barometric pressure (b) and launch chamber pressure (c) acquired at each launch and applied tide corrections (d) in Tonosí 55

56 REMARKS After the measurement session the interferometer was found aligned as well as at the beginning. There is not reason for suspecting a thermal drift of the apparatus. The trajectory was reconstructed with the model that takes into account the laser modulation and the vibration of the inertial system. The best result was obtained by removing the 90 upper stations from the fit. The average of the trajectory residuals shows that the floor is quite stiff and the low scattering of the data highlights that the observation site is quite. The measurement of the free-fall acceleration is considered to be correct within the evaluated uncertainty. 56

57 Table Measurement uncertainty in Tonosí Influence parameters, Value Unit u i or a i Type A, x i s i Type B, a i g Type of distribution Equivalent variance Sensitivity coefficients Contribution to the variance Degrees of freedom, i Equivalent standard uncertainty Instrument uncertainty m s E E E E E E-08 Coriolis effect m s E E-08 rectangular 7.4E E E E-08 Floor recoil effect negligible Barometric pressure correction -2.0E-09 m s E E E-09 rectangular 3.3E E E E-09 Tide correction 1.7E-07 m s E E E E E E E-09 Ocean loading correction m s E E E E E E-09 Polar motion correction -1.5E-08 m s -3 negligible -1.5E-08 Standard deviation of the mean value m s E E E E E E-08 Corr. 1.6E-07 m s -2 Variance 2.5E-15 m 2 s -4 Combined standard uncertainty, u Degrees of freedom, eff (Welch-Satterthwaite formula) 5.0E-08 m s Confidence level, p Coverage factor, k (calculated with t-student) 95% 2.03 Expanded uncertainty, U = ku Relative expanded uncertainty, U rel = U/g 1.0E-07 m s E-08 57

58 4.5 COLON The observation station of Colon is located at ACP, fig and The measurements was carried out on 1-2 February The position of the measurement point (fig ) referred to the room is showed on the plan of the building, fig The orientation of the instrument is showed by the red triangle where the black square represents the laser body. The instrument processed and stored 1412 trajectories. The measured data are filtered by applying rejecting criteria. The most critical factor is the visibility variation of the interference signal during the trajectory, which highlights an horizontal motion of the test-body. The effect due to the Coriolis force and the beam share are minimized by rejecting those launches with a decrease of visibility bigger that 40%. Outliers are found by applying the Chauvenet criterion to the estimating parameters such as the vertical gradient, the friction of residual air and to the estimated g value. The final g value is obtained by averaging 547 trajectories. Tab reports the most important experimental results. Other information concerning the apparatus setup is reported in tab The time series of the post-processed trajectories, data sets (each correspondent to the average of 80 launches) and trajectory residuals are reported in fig The apparatus experienced an oscillation of about ± m s -2. The averaged trajectory residuals after the measurement session are within m. The graphs reported in fig represents the density frequency histograms and normal probability graphs of the g value, gradient and friction coefficient of the measurement session. The 2 test rejects the null hypothesis, i.e. the normal distribution, with a 20% risk error. Fig reports ambient temperature, local barometric pressure and launch chamber pressure acquired at each launch and the applied tide corrections. The measurement uncertainty is summarized in tab It includes the instrumental uncertainty reported in tab

59 Colon ACP - Entrance Colon ACP Front court Colon ACP Back court Colon ACP - Door Figure Pictures of the observation station in Colon 59

60 Figure Satellite images of the observation station in Colon 60

61 Figure Pictures of the IMGC-02 at the observation station in Colon Figure Plane of the building in Colon 61

62 Table Experimental results in Colon Observation Station: Colon Observation start (data and time in UTC) 2008/02/01 04:38:53 Observation stop (data and time in UTC) 2008/02/02 15:12:49 Geodetic longitude = Geodetic latitude = Topographic elevation H T = 2 m Nominal pressure at the observation site P N = mbar Pole coordinates in IERS system x = , y = Measurement parameters Total measurement time T m = h Measurement rate m r = 51 h -1 Measurement drift m d = m s -2 h Total processed and stored throws n ps = 1412 Temperature range T = ( ) C Local barometric pressure (mean) P = mbar 2 test (80% confidence level) 2 max = 33.2; 2 min = 15.6; 2 exp = 38.9 Corrections Laser beam verticality correction g bv = m s -2 Laser beam divergence correction g bd = m s -2 Polar motion correction g pm = m s -2 Tide and ocean loading correction (mean) g tol = m s -2 Local barometric pressure correction (mean) g bp = m s -2 Results corrected mean g value g mv = m s -2 Reference height h ref = m Number of throws accepted for the average n = 547 Experimental standard deviation s g = m s -2 Experimental standard deviation of the mean value s gm = m s -2 Measurement combined uncertainty u gm = m s -2 Measurement expanded uncertainty (p = 95%, = 62, k = 2.00) U gm = m s -2 Vertical gradient = unknown Table Apparatus setup Colon Instrument orientation See fig Fitting Model Laser modulation Fringe visibility threshold f vt = 40% Measurements each set n ma = 80 Waveform digitizer sampling frequency S f = 50 MHz Laser wavelength l = m Clock frequency f c = Hz Vertical gradient input = s -2 Rise station number n rs = 350 Leaved upper stations n sl = 2 Laser modulation frequency f lm = Hz 62

63 Figure Time series (rejected-red, accepted-white) (a), Data sets (average of 80 launches) (b), trajectory residuals (one launch-red, average-white) (c) in Colon 63

64 Figure Density frequency graphs (1) and normal probability graphs (2) of the g value (a), gradient (b) and friction coefficient (c) measured in Colon 64

65 Figure Ambient temperature (a), local barometric pressure (b) and launch chamber pressure (c) acquired at each launch and applied tide corrections (d) in Colon 65

66 REMARKS After the measurement session the interferometer was found aligned as well as at the beginning. There is not reason for suspecting a thermal drift of the apparatus. The trajectory was reconstructed with the model that takes into account the laser modulation. The best result was obtained by removing the 2 upper stations from the fit. The average of the trajectory residuals shows that the floor is stiff but the scattering of the data highlights that the observation site is significantly noisy. Probably the passage of the boats through the Panama canal inducted the vibrations to the ground floor of the site. Nevertheless the measurement of the free-fall acceleration is considered to be correct within the evaluated uncertainty. 66

67 Table Measurement uncertainty in Colon Influence parameters, Value Unit u i or a i Type A, x i s i Type B, a i g Type of distribution Equivalent variance Sensitivity coefficients Contribution to the variance Degrees of freedom, i Equivalent standard uncertainty Instrument uncertainty m s E E E E E E-08 Coriolis effect m s E E-08 rectangular 1.7E E E E-08 Floor recoil effect negligible Barometric pressure correction 4.0E-09 m s E E E-09 rectangular 3.3E E E E-09 Tide correction 1.4E-07 m s E E E E E E E-09 Ocean loading correction m s E E E E E E-09 Polar motion correction -1.8E-08 m s -3 negligible -1.8E-08 Standard deviation of the mean value m s E E E E E E-08 Corr. 1.3E-07 m s -2 Variance 5.2E-15 m 2 s -4 Combined standard unc ertainty, u Degrees of freedom, eff (Welch-Satterthwaite formula) 7.2E-08 m s Confidence level, p Coverage factor, k ( cal culated with t-student) 95% 2.00 Expanded uncertaint y, U = ku 1.4E-07 m s -2 Relative expanded uncertainty, U rel = U/g 1.5E-08 67

68 4.6 SANTA FE The observation station of Santa Fe is located at the MOP (Ministerio de Obras Publicas), fig and The measurements were carried out on 7-8 February The position of the measurement point (fig ) referred to the room is showed on the plan of the building, fig The orientation of the instrument is showed by the red triangle where the black square represents the laser body. The instrument processed and stored 992 trajectories. The measured data are filtered by applying rejecting criteria. The most critical factor is the visibility variation of the interference signal during the trajectory, which highlights an horizontal motion of the test-body. The effect due to the Coriolis force and the beam share are minimized by rejecting those launches with a decrease of visibility bigger that 20%. Outliers are found by applying the Chauvenet criterion to the estimating parameters such as the vertical gradient, the friction of residual air and to the estimated g value. The final g value is obtained by averaging 223 trajectories. Tab reports the most important experimental results. Other information concerning the apparatus setup is reported in tab The time series of the post-processed trajectories, data sets (each correspondent to the average of 30 launches) and trajectory residuals are reported in fig The apparatus experienced an oscillation of about ± m s -2. The averaged trajectory residuals after the measurement session are within m. The graphs reported in fig represents the density frequency histograms and normal probability graphs of the g value, gradient and friction coefficient of the measurement session. The 2 test doesn t rejects the null hypothesis, i.e. the normal distribution, with a 20% risk error. Fig reports ambient temperature, local barometric pressure and launch chamber pressure acquired at each launch and the applied tide corrections. The measurement uncertainty is summarized in tab It includes the instrumental uncertainty reported in tab

69 Santa Fe MOP - Entrance Santa Fe MOP - Court Santa Fe MOP - Door Figure Pictures of the observation station in Santa Fe 69

70 Figure Satellite images of the observation station in Santa Fe 70

71 Figure Pictures of the IMGC-02 at the observation station in Santa Fe Figure Plane of the building in Santa Fe 71

72 Table Experimental results in Santa Fe Observation Station: Santa Fe Observation start (data and time in UTC) 2008/02/07 03:41:53 Observation stop (data and time in UTC) 2008/02/08 13:36:04 Geodetic longitude = Geodetic latitude = Topographic elevation H T = 19 m Nominal pressure at the observation site P N = mbar Pole coordinates in IERS system x = , y = Measurement parameters Total measurement time T m = h Measurement rate m r = 50 h -1 Measurement drift m d = m s -2 h Total processed and stored throws n ps = 992 Temperature range T = ( ) C Local barometric pressure (mean) P = mbar 2 test (80% confidence level) 2 max = 22.3; 2 min = 8.5; 2 exp = 15.7 Corrections Laser beam verticality correction g bv = m s -2 Laser beam divergence correction g bd = m s -2 Polar motion correction g pm = m s -2 Tide and ocean loading correction (mean) g tol = m s -2 Local barometric pressure correction (mean) g bp = m s -2 Results corrected mean g value g mv = m s -2 Reference height h ref = m Number of throws accepted for the average n = 223 Experimental standard deviation s g = m s -2 Experimental standard deviation of the mean value s gm = m s -2 Measurement combined uncertainty u gm = m s -2 Measurement expanded uncertainty (p = 95%, = 41, k = 2.02) U gm = m s -2 Vertical gradient = unknown Table Apparatus setup Santa Fe Instrument orientation See fig Fitting Model Laser modul. & ground vibr. (19.0 Hz) Fringe visibility threshold f vt = 20% Measurements each set n ma = 30 Waveform digitizer sampling frequency S f = 50 MHz Laser wavelength l = m Clock frequency f c = Hz Vertical gradient input = s -2 Rise station number n rs = 350 Leaved upper stations n sl = 90 Laser modulation frequency f lm = Hz 72

73 Figure Time series (rejected-red, accepted-white) (a), Data sets (average of 30 launches) (b), trajectory residuals (one launch-red, average-white) (c) in Santa Fe 73

74 Figure Density frequency graphs (1) and normal probability graphs (2) of the g value (a), gradient (b) and friction coefficient (c) measured in Santa Fe 74

75 Figure Ambient temp. (a), local barometric pressure (b) and launch chamber pressure (c) acquired at each launch and applied tide corrections (d) in Santa Fe 75

76 REMARKS A misalignment of the interferometer was observed once during the continuous running of the apparatus: the relevant data were not processed. For the remaining time the interferometer was found aligned as well as at the beginning. The trajectory was reconstructed with the model that takes into account the laser modulation and the vibration of the inertial system. The best result was obtained by removing the 90 upper stations from the fit. The average of the trajectory residuals shows that the floor is sufficiently stiff and the low scattering of the data highlights that the observation site is quite. The measurement of the free-fall acceleration is considered to be correct within the evaluated uncertainty. 76

77 Table Measurement uncertainty in Santa Fe Influence parameters, Value Unit u i or a i Type A, x i s i Type B, a i g Type of distribution Equivalent variance Sensitivity coefficients Contribution to the variance Degrees of freedom, i Equivalent standard uncertainty Instrument uncertainty m s E E E E E E-08 Coriolis effect m s E E-08 rectangular 7.3E E E E-08 Floor recoil effect negligible Barometric pressure correction -6.0E-09 m s E E E-09 rectangular 3.3E E E E-09 Tide correction 4.8E-07 m s E E E E E E E-09 Ocean loading correction m s E E E E E E-09 Polar motion correction -1.8E-08 m s -3 negligible -1.8E-08 Standard deviation of the mean value m s E E E E E E-08 Corr. 4.6E-07 m s -2 Variance 2.6E-15 m 2 s -4 Combined standard unc ertainty, u Degrees of freedom, eff (Welch-Satterthwaite formula) 5.1E-08 m s Confidence level, p Coverage factor, k ( cal culated with t-student) 95% 2.02 Expanded uncertaint y, U = ku 1.0E-07 m s -2 Relative expanded uncertainty, U rel = U/g 1.1E-08 77

78 4.7 YAVIZA The observation station of Santa Fe is located at the escuela Jose' del Carmen Mejia, fig and The measurements were carried out on 8-10 February The position of the measurement point (fig ) referred to the room is showed on the plan of the building, fig The orientation of the instrument is showed by the red triangle where the black square represents the laser body. The instrument processed and stored 1563 trajectories. The measured data are filtered by applying rejecting criteria. The most critical factor is the visibility variation of the interference signal during the trajectory, which highlights an horizontal motion of the test-body. The effect due to the Coriolis force and the beam share are minimized by rejecting those launches with a decrease of visibility bigger that 10%. Outliers are found by applying the Chauvenet criterion to the estimating parameters such as the vertical gradient, the friction of residual air and to the estimated g value. The final g value is obtained by averaging 292 trajectories. Tab reports the most important experimental results. Other information concerning the apparatus setup is reported in tab The time series of the post-processed trajectories, data sets (each correspondent to the average of 50 launches) and trajectory residuals are reported in fig The apparatus experienced an oscillation of about ± m s -2. The averaged trajectory residuals after the measurement session are within m. The graphs reported in fig represents the density frequency histograms and normal probability graphs of the g value, gradient and friction coefficient of the measurement session. The 2 test doesn t rejects the null hypothesis, i.e. the normal distribution, with a 20% risk error. Fig reports ambient temperature, local barometric pressure and launch chamber pressure acquired at each launch and the applied tide corrections. The measurement uncertainty is summarized in tab It includes the instrumental uncertainty reported in tab

79 Yaviza escuela Yaviza escuela Court Yaviza escuela Court Yaviza escuela Door Figure Pictures of the observation station in Yaviza 79

80 Figure Satellite images of the observation station in Yaviza 80

81 Figure Pictures of the IMGC-02 at the observation station in Yaviza Figure Plane of the building in Yaviza 81

82 Table Experimental results in Yaviza Observation Station: Yaviza Observation start (data and time in UTC) 2008/02/08 23:31:04 Observation stop (data and time in UTC) 2008/02/10 13:12:03 Geodetic longitude = Geodetic latitude = Topographic elevation H T = 64 m Nominal pressure at the observation site P N = mbar Pole coordinates in IERS system x = , y = Measurement parameters Total measurement time T m = h Measurement rate m r = 50 h -1 Measurement drift m d = m s -2 h Total processed and stored throws n ps = 1562 Temperature range T = ( ) C Local barometric pressure (mean) P = mbar 2 test (80% confidence level) 2 max = 26.0; 2 min = 10.9; 2 exp = 14.9 Corrections Laser beam verticality correction g bv = m s -2 Laser beam divergence correction g bd = m s -2 Polar motion correction g pm = m s -2 Tide and ocean loading correction (mean) g tol = m s -2 Local barometric pressure correction (mean) g bp = m s -2 Results corrected mean g value g mv = m s -2 Reference height h ref = m Number of throws accepted for the average n = 292 Experimental standard deviation s g = m s -2 Experimental standard deviation of the mean value s gm = m s -2 Measurement combined uncertainty u gm = m s -2 Measurement expanded uncertainty (p = 95%, = 45, k = 2.01) U gm = m s -2 Vertical gradient = unknown Table Apparatus setup Yaviza Instrument orientation See fig Fitting Model Laser modulation Fringe visibility threshold f vt = 10% Measurements each set n ma = 50 Waveform digitizer sampling frequency S f = 50 MHz Laser wavelength l = m Clock frequency f c = Hz Vertical gradient input = s -2 Rise station number n rs = 350 Leaved upper stations n sl = 2 Laser modulation frequency f lm = Hz 82

83 Figure Time series (rejected-red, accepted-white) (a), Data sets (average of 50 launches) (b), trajectory residuals (one launch-red, average-white) (c) in Yaviza 83

84 Figure Density frequency graphs (1) and normal probability graphs (2) of the g value (a), gradient (b) and friction coefficient (c) measured in Yaviza 84

85 Figure Ambient temperature see the paragraph remarks (a), local barometric pressure (b) and launch chamber pressure (c) acquired at each launch and applied tide corrections (d) in Yaviza 85

86 REMARKS After the measurement session the interferometer was found aligned as well as at the beginning. There is not reason for suspecting a thermal drift of the apparatus. The trajectory was reconstructed with the model that takes into account the laser modulation. The best result was obtained by removing the 2 upper stations from the fit. The average of the trajectory residuals shows that the floor is not sufficiently stiff but the low scattering of the data highlights that the observation site is quite. Observe that the acquisition of the ambient temperature was affected by error at the beginning of the measurement. The sensor was repaired at the 600 th launch (fig a). The measurement of the free-fall acceleration is considered to be correct within the evaluated uncertainty. 86

87 Table Measurement uncertainty in Yaviza Influence parameters, Value Unit u i or a i Type A, x i s i Type B, a i g Type of distribution Equivalent variance Sensitivity coefficients Contribution to the variance Degrees of freedom, i Equivalent standard uncertainty Instrument uncertainty m s E E E E E E-08 Coriolis effect m s E E-08 rectangular 4.3E E E E-08 Floor recoil effect negligible Barometric pressure correction 8.0E-09 m s E E E-09 rectangular 3.3E E E E-09 Tide correction 4.2E-07 m s E E E E E E E-09 Ocean loading correction m s E E E E E E-09 Polar motion correction -1.7E-08 m s -3 negligible -1.7E-08 Standard deviation of the mean value m s E E E E E E-08 Corr. 4.1E-07 m s -2 Variance 2.5E-15 m 2 s -4 Combined standard unc ertainty, u Degrees of freedom, eff (Welch-Satterthwaite formula) 5.0E-08 m s Confidence level, p Coverage factor, k ( cal culated with t-student) 95% 2.01 Expanded uncertaint y, U = ku 1.0E-07 m s -2 Relative expanded uncertainty, U rel = U/g 1.0E-08 87

88 4.8 PANAMA CITY IGNTG The observation station of Panama City Tommy Guardia is located at the building Continuous Operation Reference System (CORS), fig and The measurements were carried out on February The position of the measurement point (fig ) referred to the room is showed on the plan of the building, fig The orientation of the instrument is showed by the red triangle where the black square represents the laser body. The instrument processed and stored 634 trajectories. The measured data are filtered by applying rejecting criteria. The most critical factor is the visibility variation of the interference signal during the trajectory, which highlights an horizontal motion of the test-body. The effect due to the Coriolis force and the beam share are minimized by rejecting those launches with a decrease of visibility bigger that 20%. Outliers are found by applying the Chauvenet criterion to the estimating parameters such as the vertical gradient, the friction of residual air and to the estimated g value. The final g value is obtained by averaging 177 trajectories. Tab reports the most important experimental results. Other information concerning the apparatus setup is reported in tab The time series of the post-processed trajectories, data sets (each correspondent to the average of 30 launches) and trajectory residuals are reported in fig The apparatus experienced an oscillation of about ± m s -2. The averaged trajectory residuals after the measurement session are within m. The graphs reported in fig represents the density frequency histograms and normal probability graphs of the g value, gradient and friction coefficient of the measurement session. The 2 test rejects the null hypothesis, i.e. the normal distribution, with a 20% risk error. Fig reports ambient temperature, local barometric pressure and launch chamber pressure acquired at each launch and the applied tide corrections. The measurement uncertainty is summarized in tab It includes the instrumental uncertainty reported in tab

89 Tommy Guradia CORS - Entrance Tommy Guradia CORS - Court Tommy Guradia CORS - Door Figure Pictures of the observation station in Panama City - IGNTG CORS 89

90 Figure Satellite images of the observation station in Panama City - IGNTG CORS 90

91 Figure Pictures of the IMGC-02 at the observation station in Panama City - IGNTG CORS Figure Plane of the building station in Panama City - IGNTG CORS 91

92 Table Experimental results station in Panama City - IGNTG CORS Observation Station: Panama City - Tommy Guardia CORS Observation start (data and time in UTC) 2008/02/12 00:27:41 Observation stop (data and time in UTC) 2008/02/13 04:38:36 Geodetic longitude = Geodetic latitude Topographic elevation = H T = 25 m Nominal pressure at the observation site P N = mbar Pole coordinates in IERS system x = , y = Measurement parameters Total measurement time T m = h Measurement rate m r = 51 h -1 Measurement drift m d = m s -2 h Total processed and stored throws n ps = 634 Temperature range T = ( ) C Local barometric pressure (mean) P = mbar 2 test (80% confidence level) 2 max = 21.0; 2 min = 7.8; 2 exp = 27.6 Corrections Laser beam verticality correction g bv = m s -2 Laser beam divergence correction g bd = m s -2 Polar motion correction g pm = m s -2 Tide and ocean loading correction (mean) g tol = m s -2 Local barometric pressure correction (mean) g bp = m s -2 Results corrected mean g value g mv = m s -2 Reference height h ref = m Number of throws accepted for the average n = 177 Experimental standard deviation s g = m s -2 Experimental standard deviation of the mean value s gm = m s -2 Measurement combined uncertainty u gm = m s -2 Measurement expanded uncertainty (p = 95%, = 77, k = 1.99) U gm = m s -2 Vertical gradient = unknown Table Apparatus setup Panama City - IGNTG CORS Instrument orientation See fig Fitting Model Laser mod. & ground vibr. (18.9 Hz) Fringe visibility threshold f vt = 20% Measurements each set n ma = 30 Waveform digitizer sampling frequency S f = 50 MHz Laser wavelength l = m Clock frequency f c = Hz Vertical gradient input = s -2 Rise station number n rs = 350 Leaved upper stations n sl = 2 Laser modulation frequency f lm = Hz 92

93 Figure Time series (rejected-red, accepted-white) (a), Data sets (average of 30 launches) (b), trajectory residuals (one launch-red, average-white) (c) in Panama City - IGNTG CORS 93

94 Figure Density frequency graphs (1) and normal probability graphs (2) of the g value (a), gradient (b) and friction coefficient (c) measured in Panama City - IGNTG CORS 94

95 Figure Ambient temperature see the paragraph remarks (a), local barometric pressure (b) and launch chamber pressure (c) acquired at each launch and applied tide corrections (d) in Panama City - IGNTG CORS 95

96 REMARKS A misalignment of the interferometer was observed two times during the continuous running of the apparatus: the relevant data were not processed. For the remaining time the interferometer was found aligned as well as at the beginning. The trajectory was reconstructed with the model that takes into account the laser modulation and the vibration of the inertial system. The best result was obtained by removing the 90 upper stations from the fit. The average of the trajectory residuals shows that the floor is stiff but the scattering of the data highlights that the observation site is noisy. Probably the vehicles in transit on the nearby roads inducted the vibrations to the ground floor of the site. The measurement of the free-fall acceleration is considered to be correct within the evaluated uncertainty. 96

97 Table Measurement uncertainty in Panama City - IGNTG CORS Influence parameters, Value Unit u i or a i Type A, x i s i Type B, a i g Type of distribution Equivalent variance Sensitivity coefficients Contribution to the variance Degrees of freedom, i Equivalent standard uncertainty Instrument uncertainty m s E E E E E E-08 Coriolis effect m s E E-08 rectangular 7.3E E E E-08 Floor recoil effect negligible Barometric pressure correction -1.3E-08 m s E E E-08 rectangular 3.3E E E E-09 Tide correction 2.1E-07 m s E E E E E E E-09 Ocean loading correction m s E E E E E E-09 Polar motion correction -2.0E-08 m s -3 negligible -2.0E-08 Standard deviation of the mean value m s E E E E E E-08 Corr. 1.7E-07 m s -2 Variance 3.7E-15 m 2 s -4 Combined standard unc ertainty, u Degrees of freedom, eff (Welch-Satterthwaite formula) 6.1E-08 m s Confidence level, p Coverage factor, k ( cal culated with t-student) 95% 1.99 Expanded uncertaint y, U = ku 1.2E-07 m s -2 Relative expanded uncertainty, U rel = U/g 1.2E-08 97

98 4.9 TOLÉ The observation station of Tolé is located at the MOP (Ministerio de Obras Publicas), fig and The measurements were carried out on February The position of the measurement point (fig ) referred to the room is showed on the plan of the building, fig The orientation of the instrument is showed by the red triangle where the black square represents the laser body. The instrument processed and stored 1041 trajectories. The measured data are filtered by applying rejecting criteria. The most critical factor is the visibility variation of the interference signal during the trajectory, which highlights an horizontal motion of the test-body. The effect due to the Coriolis force and the beam share are minimized by rejecting those launches with a decrease of visibility bigger that 10%. Outliers are found by applying the Chauvenet criterion to the estimating parameters such as the vertical gradient, the friction of residual air and to the estimated g value. The final g value is obtained by averaging 139 trajectories. Tab reports the most important experimental results. Other information concerning the apparatus setup is reported in tab The time series of the post-processed trajectories, data sets (each correspondent to the average of 35 launches) and trajectory residuals are reported in fig The apparatus experienced an oscillation of about ± m s -2. The averaged trajectory residuals after the measurement session are within m. The graphs reported in fig represents the density frequency histograms and normal probability graphs of the g value, gradient and friction coefficient of the measurement session. The 2 test doesn t rejects the null hypothesis, i.e. the normal distribution, with a 20% risk error. Fig reports ambient temperature, local barometric pressure and launch chamber pressure acquired at each launch and the applied tide corrections. The measurement uncertainty is summarized in tab It includes the instrumental uncertainty reported in tab

99 Tolé MOP - Entrance Tolé MOP - Court Tolé MOP - Door Figure Pictures of the observation station in Tolé 99

100 Figure Satellite images of the observation station in Tolé 100

101 Figure Pictures of the IMGC-02 at the observation station in Tolé Figure Plane of the building station in Tolé 101

102 Table Experimental results station in Tolé Observation Station: Tolé Observation start (data and time in UTC) 2008/02/13 23:56:57 Observation stop (data and time in UTC) 2008/02/15 13:06:24 Geodetic longitude = Geodetic latitude = Topographic elevation H T = 315 m Nominal pressure at the observation site P N = mbar Pole coordinates in IERS system x = , y = Measurement parameters Total measurement time T m = h Measurement rate m r = 53 h -1 Measurement drift m d = m s -2 h Total processed and stored throws n ps = 1041 Temperature range T = ( ) C Local barometric pressure (mean) P = mbar 2 test (80% confidence level) 2 max = 18.5; 2 min = 6.3; 2 exp = 14.1 Corrections Laser beam verticality correction g bv = m s -2 Laser beam divergence correction g bd = m s -2 Polar motion correction g pm = m s -2 Tide and ocean loading correction (mean) g tol = m s -2 Local barometric pressure correction (mean) g bp = m s -2 Results corrected mean g value g mv = m s -2 Reference height h ref = m Number of throws accepted for the average n = 139 Experimental standard deviation s g = m s -2 Experimental standard deviation of the mean value s gm = m s -2 Measurement combined uncertainty u gm = m s -2 Measurement expanded uncertainty (p = 95%, = 36, k = 2.03) U gm = m s -2 Vertical gradient = unknown Table Apparatus setup in Tolé Instrument orientation See fig Fitting Model Laser modulation Fringe visibility threshold f vt = 10% Measurements each set n ma = 35 Waveform digitizer sampling frequency S f = 50 MHz Laser wavelength l = m Clock frequency f c = Hz Vertical gradient input = s -2 Rise station number n rs = 350 Leaved upper stations n sl = 2 Laser modulation frequency f lm = Hz 102

103 Figure Time series (rejected-red, accepted-white) (a), Data sets (average of 35 launches) (b), trajectory residuals (one launch-red, average-white) (c) in Tolé 103

104 Figure Density frequency graphs (1) and normal probability graphs (2) of the g value (a), gradient (b) and friction coefficient (c) measured in Tolé 104

105 Figure Ambient temperature see the paragraph remarks (a), local barometric pressure (b) and launch chamber pressure (c) acquired at each launch and applied tide corrections (d) in Tolé 105

106 REMARKS A misalignment of the interferometer was observed once during the continuous running of the apparatus: the relevant data were not processed. For the remaining time the interferometer was found aligned as well as at the beginning. The trajectory was reconstructed with the model that takes into account the laser modulation. The best result was obtained by removing the 2 upper stations from the fit. The average of the trajectory residuals shows that the floor is not sufficiently stiff but the scattering of the data highlights that the observation site is quite. The measurement drift (fig a) can be accepted. The measurement of the free-fall acceleration is considered to be correct within the evaluated uncertainty. 106

107 Table Measurement uncertainty in Tolé Influence parameters, Value Unit u i or a i Type A, x i s i Type B, a i g Type of distribution Equivalent variance Sensitivity coefficients Contribution to the variance Degrees of freedom, i Equivalent standard uncertainty Instrument uncertainty m s E E E E E E-08 Coriolis effect m s E E-08 rectangular 4.3E E E E-08 Floor recoil effect negligible Barometric pressure correction 6.0E-09 m s E E E-09 rectangular 3.3E E E E-09 Tide correction 1.1E-07 m s E E E E E E E-09 Ocean loading correction m s E E E E E E-09 Polar motion correction -1.9E-08 m s -3 negligible -1.9E-08 Standard deviation of the mean value m s E E E E E E-08 Corr. 9.2E-08 m s -2 Variance 2.2E-15 m 2 s -4 Combined standard unc ertainty, u Degrees of freedom, eff (Welch-Satterthwaite formula) 4.7E-08 m s Confidence level, p Coverage factor, k ( cal culated with t-student) 95% 2.03 Expanded uncertaint y, U = ku 9.5E-08 m s -2 Relative expanded uncertainty, U rel = U/g 9.7E

108 4.10 CHANGUINOLA The observation station of Changuinola is located at the MOP (Ministerio de Obras Publicas), fig and The measurements were carried out on February The position of the measurement point (fig ) referred to the room is showed on the plan of the building, fig The orientation of the instrument is showed by the red triangle where the black square represents the laser body. The instrument processed and stored 569 trajectories. The measured data are filtered by applying rejecting criteria. The most critical factor is the visibility variation of the interference signal during the trajectory, which highlights an horizontal motion of the test-body. The effect due to the Coriolis force and the beam share are minimized by rejecting those launches with a decrease of visibility bigger that 20%. Outliers are found by applying the Chauvenet criterion to the estimating parameters such as the vertical gradient, the friction of residual air and to the estimated g value. The final g value is obtained by averaging 137 trajectories. Tab reports the most important experimental results. Other information concerning the apparatus setup is reported in tab The time series of the post-processed trajectories, data sets (each correspondent to the average of 35 launches) and trajectory residuals are reported in fig The apparatus experienced an oscillation of about ± m s -2. The averaged trajectory residuals after the measurement session are within m. The graphs reported in fig represents the density frequency histograms and normal probability graphs of the g value, gradient and friction coefficient of the measurement session. The 2 test doesn t rejects the null hypothesis, i.e. the normal distribution, with a 20% risk error. Fig reports ambient temperature, local barometric pressure and launch chamber pressure acquired at each launch and the applied tide corrections. The measurement uncertainty is summarized in tab It includes the instrumental uncertainty reported in tab

109 Changuinola MOP - Entrance Changuinola MOP - Court Changuinola MOP - Door Figure Pictures of the observation station in Changuinola 109

110 Figure Satellite images of the observation station in Changuinola 110

111 Figure Pictures of the IMGC-02 at the observation station in Changuinola Figure Plane of the building station in Changuinola 111

112 Table Experimental results station in Changuinola Observation Station: Changuinola Observation start (data and time in UTC) 2008/02/16 03:14:16 Observation stop (data and time in UTC) 2008/02/17 11:26:35 Geodetic longitude = Geodetic latitude = Topographic elevation H T = 8 m Nominal pressure at the observation site P N = mbar Pole coordinates in IERS system x = , y = Measurement parameters Total measurement time T m = h Measurement rate m r = 52 h -1 Measurement drift m d = m s -2 h Total processed and stored throws n ps = 569 Temperature range T = ( ) C Local barometric pressure (mean) P = mbar 2 test (80% confidence level) 2 max = 18.5; 2 min = 6.3; 2 exp = 14.3 Corrections Laser beam verticality correction g bv = m s -2 Laser beam divergence correction g bd = m s -2 Polar motion correction g pm = m s -2 Tide and ocean loading correction (mean) g tol = m s -2 Local barometric pressure correction (mean) g bp = m s -2 Results corrected mean g value g mv = m s -2 Reference height h ref = m Number of throws accepted for the average n = 137 Experimental standard deviation s g = m s -2 Experimental standard deviation of the mean value s gm = m s -2 Measurement combined uncertainty u gm = m s -2 Measurement expanded uncertainty (p = 95%, = 39, k = 2.02) U gm = m s -2 Vertical gradient = unknown Table Apparatus setup in Changuinola Instrument orientation See fig Fitting Model Laser mod. & ground vibration (19.4 Hz) Fringe visibility threshold f vt = 20% Measurements each set n ma = 35 Waveform digitizer sampling frequency S f = 50 MHz Laser wavelength l = m Clock frequency f c = Hz Vertical gradient input = s -2 Rise station number n rs = 350 Leaved upper stations n sl = 2 Laser modulation frequency f lm = Hz 112

113 Figure Time series (rejected-red, accepted-white) (a), Data sets (average of 35 launches) (b), trajectory residuals (one launch-red, average-white) (c) in Changuinola 113

114 Figure Density frequency graphs (1) and normal probability graphs (2) of the g value (a), gradient (b) and friction coefficient (c) measured in Changuinola 114

115 Figure Ambient temperature see the paragraph remarks (a), local barometric pressure (b) and launch chamber pressure (c) acquired at each launch and applied tide corrections (d) in Changuinola 115

116 REMARKS A misalignment of the interferometer was observed twice during the continuous running of the apparatus: the relevant data were not processed. For the remaining time the interferometer was found aligned as well as at the beginning. The trajectory was reconstructed with the model that takes into account the laser modulation and the ground vibration. The best result was obtained by removing the 2 upper stations from the fit. The average of the trajectory residuals shows that the floor is stiff and the scattering of the data highlights that the observation site is quite. The measurement of the free-fall acceleration is considered to be correct within the evaluated uncertainty. 116

117 Table Measurement uncertainty in Changuinola Influence parameters, Value Unit u i or a i Type A, x i s i Type B, a i g Type of distribution Equivalent variance Sensitivity coefficients Contribution to the variance Degrees of freedom, i Equivalent standard uncertainty Instrument uncertainty m s E E E E E E-08 Coriolis effect m s E E-08 rectangular 7.3E E E E-08 Floor recoil effect negligible Barometric pressure correction -4.0E-09 m s E E E-09 rectangular 3.3E E E E-09 Tide correction 2.5E-07 m s E E E E E E E-09 Ocean loading correction m s E E E E E E-09 Polar motion correction -2.2E-08 m s -3 negligible -2.2E-08 Standard deviation of the mean value m s E E E E E E-08 Corr. 2.3E-07 m s -2 Variance 2.6E-15 m 2 s -4 Combined standard unc ertainty, u Degrees of freedom, eff (Welch-Satterthwaite formula) 5.1E-08 m s Confidence level, p Coverage factor, k ( cal culated with t-student) 95% 2.02 Expanded uncertaint y, U = ku 1.0E-07 m s -2 Relative expanded uncertainty, U rel = U/g 1.0E

118 4.11 BOQUETE The observation station of Boquete is located at the escuela Josefa Montero de Vasquez, fig and The measurements were carried out on February The position of the measurement point (fig ) referred to the room is showed on the plan of the building, fig The orientation of the instrument is showed by the red triangle where the black square represents the laser body. The instrument processed and stored 1323 trajectories. The measured data are filtered by applying rejecting criteria. The most critical factor is the visibility variation of the interference signal during the trajectory, which highlights an horizontal motion of the test-body. The effect due to the Coriolis force and the beam share are minimized by rejecting those launches with a decrease of visibility bigger that 10%. Outliers are found by applying the Chauvenet criterion to the estimating parameters such as the vertical gradient, the friction of residual air and to the estimated g value. The final g value is obtained by averaging 139 trajectories. Tab reports the most important experimental results. Other information concerning the apparatus setup is reported in tab The time series of the post-processed trajectories, data sets (each correspondent to the average of 50 launches) and trajectory residuals are reported in fig The apparatus experienced an oscillation of about ± m s-2. The averaged trajectory residuals after the measurement session are within m. The graphs reported in fig represents the density frequency histograms and normal probability graphs of the g value, gradient and friction coefficient of the measurement session. The 2 test rejects the null hypothesis, i.e. the normal distribution, with a 20% risk error. Fig reports ambient temperature, local barometric pressure and launch chamber pressure acquired at each launch and the applied tide corrections. The measurement uncertainty is summarized in tab It includes the instrumental uncertainty reported in tab

119 Boquete esquela Entrance Boquete esquela Court Boquete esquela Door Figure Pictures of the observation station in Boquete 119

120 Figure Satellite images of the observation station in Boquete 120

121 Figure Pictures of the IMGC-02 at the observation station in Boquete Figure Plane of the building station in Boquete 121

122 Table Experimental results station in Boquete Observation Station: Boquete Observation start (data and time in UTC) 2008/02/18 02:27:32 Observation stop (data and time in UTC) 2008/02/19 11:11:08 Geodetic longitude = Geodetic latitude = Topographic elevation H T = 1084 m Nominal pressure at the observation site P N = mbar Pole coordinates in IERS system x = , y = Measurement parameters Total measurement time T m = h Measurement rate m r = 50 h -1 Measurement drift m d = m s -2 h Total processed and stored throws n ps = 1323 Temperature range T = ( ) C Local barometric pressure (mean) P = mbar 2 test (80% confidence level) 2 max = 23.5; 2 min = 9.3; 2 exp = 26.4 Corrections Laser beam verticality correction g bv = m s -2 Laser beam divergence correction g bd = m s -2 Polar motion correction g pm = m s -2 Tide and ocean loading correction (mean) g tol = m s -2 Local barometric pressure correction (mean) g bp = m s -2 Results corrected mean g value g mv = m s -2 Reference height h ref = m Number of throws accepted for the average n = 232 Experimental standard deviation s g = m s -2 Experimental standard deviation of the mean value s gm = m s -2 Measurement combined uncertainty u gm = m s -2 Measurement expanded uncertainty (p = 95%, = 34, k = 2.03) U gm = m s -2 Vertical gradient = unknown Table Apparatus setup in Boquete Instrument orientation See fig Fitting Model Laser modulation Fringe visibility threshold f vt = 10% Measurements each set n ma = 50 Waveform digitizer sampling frequency S f = 50 MHz Laser wavelength l = m Clock frequency f c = Hz Vertical gradient input = s -2 Rise station number n rs = 350 Leaved upper stations n sl = 2 Laser modulation frequency f lm = Hz 122

123 Figure Time series (rejected-red, accepted-white) (a), Data sets (average of 35 launches) (b), trajectory residuals (one launch-red, average-white) (c) in Boquete 123

124 Figure Density frequency graphs (1) and normal probability graphs (2) of the g value (a), gradient (b) and friction coefficient (c) measured in Boquete 124

125 Figure Ambient temperature see the paragraph remarks (a), local barometric pressure (b) and launch chamber pressure (c) acquired at each launch and applied tide corrections (d) in Boquete 125

126 REMARKS A misalignment of the interferometer was observed once during the continuous running of the apparatus: the relevant data were not processed. For the remaining time the interferometer was found aligned as well as at the beginning. The trajectory was reconstructed with the model that takes into account the laser modulation. The best result was obtained by removing the 2 upper stations from the fit. The average of the trajectory residuals shows that the floor is quite stiff and the scattering of the data highlights that the observation site is quite. The measurement of the free-fall acceleration is considered to be correct within the evaluated uncertainty. 126

127 Table Measurement uncertainty in Boquete Influence parameters, Value Unit u i or a i Type A, x i s i Type B, a i g Type of distribution Equivalent variance Sensitivity coefficients Contribution to the variance Degrees of freedom, i Equivalent standard uncertainty Instrument uncertainty m s E E E E E E-08 Coriolis effect m s E E-08 rectangular 4.3E E E E-08 Floor recoil effect negligible Barometric pressure correction 1.2E-08 m s E E E-08 rectangular 3.3E E E E-09 Tide correction 3.6E-07 m s E E E E E E E-09 Ocean loading correction m s E E E E E E-09 Polar motion correction -2.0E-08 m s -3 negligible -2.0E-08 Standard deviation of the mean value m s E E E E E E-08 Corr. 3.6E-07 m s -2 Variance 2.1E-15 m 2 s -4 Combined standard unc ertainty, u Degrees of freedom, eff (Welch-Satterthwaite formula) 4.6E-08 m s Confidence level, p Coverage factor, k ( cal culated with t-student) 95% 2.03 Expanded uncertaint y, U = ku 9.4E-08 m s -2 Relative expanded uncertainty, U rel = U/g 9.6E

128 4.12 COIBA The observation station of Coiba is located at the Centro des visitantes of the the Autoritad Nacional del Ambiente (ANAM), fig and The measurements were carried out on February The position of the measurement point (fig ) referred to the room is showed on the plan of the building, fig The orientation of the instrument is showed by the red triangle where the black square represents the laser body. The instrument processed and stored 170 trajectories. The measured data are filtered by applying rejecting criteria. The most critical factor is the visibility variation of the interference signal during the trajectory, which highlights an horizontal motion of the test-body. The effect due to the Coriolis force and the beam share are minimized by rejecting those launches with a decrease of visibility bigger that 40%. Outliers are found by applying the Chauvenet criterion to the estimating parameters such as the vertical gradient, the friction of residual air and to the estimated g value. The final g value is obtained by averaging 76 trajectories. Tab reports the most important experimental results. Other information concerning the apparatus setup is reported in tab The time series of the post-processed trajectories, data sets (each correspondent to the average of 25 launches) and trajectory residuals are reported in fig The apparatus experienced an oscillation of about ± m s -2. The averaged trajectory residuals after the measurement session are within m. The graphs reported in fig represents the density frequency histograms and normal probability graphs of the g value, gradient and friction coefficient of the measurement session. The 2 test doesn t rejects the null hypothesis, i.e. the normal distribution, with a 20% risk error. Fig reports ambient temperature, local barometric pressure and launch chamber pressure acquired at each launch and the applied tide corrections. The measurement uncertainty is summarized in tab It includes the instrumental uncertainty reported in tab

129 Coiba ANAM - Entrance Coiba ANAM - Court Coiba ANAM - Door Figure Pictures of the observation station in Coiba 126

130 Figure Satellite images of the observation station in Coiba 127

131 Figure Pictures of the IMGC-02 at the observation station in Coiba Figure Plane of the building station in Coiba 128

132 Table Experimental results station in Coiba Observation Station: Coiba Observation start (data and time in UTC) 2008/02/21 20:04:13 Observation stop (data and time in UTC) 2008/02/22 00:50:05 Geodetic longitude = Geodetic latitude = Topographic elevation H T = 2 m Nominal pressure at the observation site P N = mbar Pole coordinates in IERS system x = , y = Measurement parameters Total measurement time T m = 4.76 h Measurement rate m r = 43 h -1 Measurement drift m d = m s -2 h Total processed and stored throws n ps = 170 Temperature range T = ( ) C Local barometric pressure (mean) P = mbar 2 test (80% confidence level) 2 max = 14.7; 2 min = 4.1; 2 exp = 7.8 Corrections Laser beam verticality correction g bv = m s -2 Laser beam divergence correction g bd = m s -2 Polar motion correction g pm = m s -2 Tide and ocean loading correction (mean) g tol = m s -2 Local barometric pressure correction (mean) g bp = m s -2 Results corrected mean g value g mv = m s -2 Reference height h ref = m Number of throws accepted for the average n = 76 Experimental standard deviation s g = m s -2 Experimental standard deviation of the mean value s gm = m s -2 Measurement combined uncertainty u gm = m s -2 Measurement expanded uncertainty (p = 95%, = 46, k = 2.01) U gm = m s -2 Vertical gradient = unknown Table Apparatus setup in Coiba Instrument orientation See fig Fitting Model Laser mod. & ground vibr. (14.2 Hz) Fringe visibility threshold f vt = 40% Measurements each set n ma = 25 Waveform digitizer sampling frequency S f = 50 MHz Laser wavelength l = m Clock frequency f c = Hz Vertical gradient input = s -2 Rise station number n rs = 350 Leaved upper stations n sl = 2 Laser modulation frequency f lm = Hz 129

133 Figure Time series (rejected-red, accepted-white) (a), Data sets (average of 25 launches) (b), trajectory residuals (one launch-red, average-white) (c) in Coiba 130