##  SURVEY, ALIGNMENT, AND GEODESY (WBS 1.1.6)

### Introduction

For a long baseline neutrino experiment, properly aligning the neutrino
beam to hit the far detector 735 km away is clearly important. Actually,
as shown in **Figure 4.6-1**, the NuMI beam, for low neutrino energies,
is several kilometers wide and modern geodetic survey techniques,
especially the Global Positioning System (GPS) satellites, make hitting
the far detector relatively straightforward. For the NuMI beamline, the
physics-driven alignment goals from the MINOS experiment require that
the neutrino beam center must be within 100 meters of the far detector.

![](media/image1.wmf){width="3.717361111111111in"
height="4.811111111111111in"}

**Figure 4.6-** Transverse distribution of the NuMI low energy tune
neutrino beam at the far detector as a function of energy. Note that at
low neutrino energy the beam is several kilometers wide

**4.6.2 System Description: Determining the Line from Fermilab to
Soudan**

The relative positions of Fermilab and Soudan on the surface are
determined by making simultaneous measurements using the Global
Positioning System (GPS) satellites. Simultaneous GPS data at both
Fermilab and Soudan were recorded in April 1999 as shown in **Table
4.6-1**. The data was analyzed at Fermilab and, independently, by the
National Geodetic Survey (NGS). The agreement between the NGS result and
two methods of analysis at Fermilab was excellent. The Fermilab to
Soudan vector, averaged over the period of the observations used, is
known to better than 1 cm horizontally and 6 cm vertically, well within
requirements. The differential earth tide effect between Fermilab and
Soudan is approximately the same as this uncertainty.

Included in **Table 4.6-1** are the results from two less precise
measurements also using professional GPS receivers, which agree to
better than 1 meter, and a later result using an amateur hand held
receiver. All four results are within the 12-meter tolerance goal for
this measurement. Accuracy of a differential GPS measurement is
increased by including CORS (Continuously Observed Reference Station)
data in the analysis (**Figure 4.6-2**), simultaneous observations from
both positions, and using the precise satellite positions calculated by
NGS from the CORS data.

  ------ -------------- ---------- --------- ---------- ----------- -----------
  Year   Receiver       Measure    Include   Simulta-   Precision   Deviation

                        time       CORS      neous      Satellite   from 1999

                        (hour)                          Positions   (meter)

  1999   Professional   26         Yes       Yes        Yes         

  1998   Professional   6          No        Yes        No          0.231

  1994   Professional   1          No        No         No          0.785

  2000   Hand held      \<1        No        No         No          10.140
  ------ -------------- ---------- --------- ---------- ----------- -----------

  ------ ----- --- --------- ---- ---- ---------- ------------ ------------ ------------- ------------ ----------------
  Year             Azimuth             Vertical   Distance     north        east          up           \|(δn,δe,δu)\|

                                                  (meter)      (meter)      (meter)       (meter)      (meter)

  1999   336   5   52.383    -3   17   17.882     735273.058   671108.532   -297424.016   -42175.390   

  1998             -0.033              -0.008     -0.196       -0.229       -0.029        -0.018       0.231

  1994             -0.007              0.001      -0.785       -0.725       0.296         0.049        0.785

  2000             0.654               2.278      5.608        6.487        -0.330        7.787        10.140
  ------ ----- --- --------- ---- ---- ---------- ------------ ------------ ------------- ------------ ----------------

**Table 4.6-1.** Relative position of the SHAFT monument on the surface
at Soudan as measured from Fermilab surface monument 66589 by GPS.
Results are given in the Local Geodetic Coordinate System (reference
SHAFT). The values for the most accurate measurement are given on the
first line, followed by the differences (other -- best) of the three
additional measurements relative to the best one. The professional
receivers used were Trimble 4000 SSi's; the hand held receiver was a
Garmin GPS III+ (Best Buy \~\$350).

![](media/image2.png){width="6.5in"
height="5.666666666666667in"}**Figure 4.6-2** CORS (Continuously
Observed Reference Station) network. GPS data are recorded for over 100
accurately known locations in the United States, including 4 in
Wisconsin. (Source: National Geodetic Survey www page:
<http://www.ngs.noaa.gov/CORS/Maps.html>

The position of the 27^th^ level at the bottom of the Soudan Mine,
relative to the surface, is determined using inertial survey. An
inertial survey unit and operator were rented from the University of
Calgary during the April 1999 GPS trip to Soudan. The inertial survey
unit used (Honeywell Laseref III IMU) contains a triad of accelerometers
and optical gyroscopes to measure force and angular velocity. The
accelerometers are double integrated to yield position change along each
of the 3 axes. Internal consistency of the several inertial survey runs
indicated a 0.7 m per coordinate precision for the surface to bottom of
the mine measurement, many times better than the 12 m goal. As shown in
**Table 4.6-2,** these measurements agreed to better than 4 m per
coordinate with the old mine values for the 27^th^ level relative to the
surface.

  ------------------------------- ------------ ------------ -------------
                                  east         north        up

                                  meter        meter        meter

                                                            

  1999 INS values                 -15.2        148.2        -710.1

  INS-old mine #\'s               -0.2         3.7          -3.4
  ------------------------------- ------------ ------------ -------------

**Table 4.6-2**. Inertial Survey (INS) measurement from the surface to
level 27 at Soudan. The average of the 4 INS runs made on April 20, 1999
is given, together with the change of these measurements from the old
mine values.

Conventional survey techniques are used to determine the position of the
MINOS far detector relative to the bottom of the shaft at Soudan.
**Table 4.6-3** gives the position of monuments in the MINOS cavern and
the nominal detector axis and edges in the Cartesian Local Geodetic
Coordinate System (LGCS) relative to the surface monument called "SHAFT"
(which was used in the surface GPS measurement above). **Table 4.6-4**
gives the same points in the Cartesian beam coordinate system, with
origin at the nominal detector center, Y axis along the neutrino beam
direction, and X axis horizontal.

POINT X(+EAST) Y(+NORTH) Z(+UP)

NAME (Meter) (Meter) (Meter)

BRASS_1 37.3668 10.8767 -709.1782

BRASS_2 32.5269 20.5614 -709.1638

BRASS_3 24.9370 35.7484 -709.1476

BRASS_4 17.9893 49.6496 -709.1606

BRASS_5 3.3012 79.0429 -709.1639

CP_E11 27.1329 39.8453 -705.0098

CP_E14 24.6850 44.7639 -705.0327

CP_E17 22.2376 49.6672 -705.0330

CP_E2 34.2510 25.6183 -705.0434

CP_E5 31.7950 30.5282 -705.0347

CP_E8 29.3449 35.4377 -705.0233

CP_W11 19.5038 36.0554 -705.0210

CP_W14 17.0549 40.9669 -705.0257

CP_W17 14.6069 45.8628 -705.0210

CP_W2 26.6014 21.8538 -705.0311

CP_W5 24.1563 26.7486 -705.0431

CP_W8 21.7098 31.6510 -705.0386

EI_01 34.1657 23.6082 -709.2540

EI_035 31.8929 28.1608 -709.2580

EI_065 29.5962 32.7045 -709.2534

EI_10 27.2189 37.4801 -709.2451

EI_125 24.9455 42.0243 -709.2487

EI_155 22.6748 46.5704 -709.2416

EI_18 20.5332 50.8897 -709.2587

EO_01 37.0840 23.7565 -709.2491

EO_09 29.9725 38.0342 -709.2452

EO_19 21.3997 54.7230 -709.2630

PP1 8.2536 51.7757 -707.5768

PP2 4.2885 59.6857 -707.5483

PP3 1.1212 66.0377 -707.5610

VULCAN_E 31.7687 30.2899 -707.0321

VULCAN_W 24.2997 26.7597 -706.8035

WBE_1 17.6527 55.4088 -709.2568

WBE_1_5 16.7981 60.6413 -709.2508

WBE_2 13.3126 64.1350 -709.2516

WBE_2_5 11.7837 70.7375 -709.2529

WBE_3 8.2340 74.4346 -709.2519

WBW_1 10.6467 51.9149 -709.2533

WBW_1_5 7.8540 55.7006 -709.2597

WBW_1_7 7.2439 59.4027 -709.2612

WBW_2 6.2549 60.6034 -709.2562

WBW_2_2 5.2874 63.5825 -709.2643

WBW_2_5 2.4974 66.3988 -709.2517

WBW_3 1.1941 70.8040 -709.2534

WI_01 28.3010 20.6410 -709.2532

WI_035 26.0234 25.2087 -709.2504

WI_065 23.7625 29.7489 -709.2521

WI_10 21.3667 34.5228 -709.2503

WI_125 19.1039 39.0775 -709.2530

WI_155 16.8175 43.6237 -709.2527

WI_18 14.6497 47.9674 -709.2615

WO_01 26.9941 18.7946 -709.2483

WO_09 19.8536 32.9234 -709.2434

WO_185 12.3356 47.9075 -709.2598

DetCtr_dsgn 24.4433 35.7132 -704.5203

DetCtr_meas 24.3847 35.8303 -704.5203

dcs_origin 31.3726 21.8483 -704.5203

FD_ds_axis 17.3968 49.8124 -704.5203

FD_us_right 34.9506 23.6365 -704.5203

FD_us_left 27.7946 20.0601 -704.5203

FD_us_top 31.3726 21.8483 -700.5203

FD_us_bot 31.3726 21.8483 -708.5203

FD_us_t,r 34.9506 23.6365 -700.5203

**Table 4.6-3**. Far Cavern Monuments and Detector Points in the Local
Geodetic coordinate system, reference point Shaft Monument, with the X
axis East, Y axis North, Z axis up, to make a right handed orthogonal
system.

POINT NAME X(+\"West\") Y(+\"Up\") Z(+\"North\")

(Meter) (Meter) (Meter)

BRASS_1 -0.3794 -3.0428 -28.3462

BRASS_2 -0.4095 -3.6472 -17.5364

BRASS_3 -0.4565 -4.6014 -0.5853

BRASS_4 -0.4992 -5.5025 14.9291

BRASS_5 -0.5917 -7.3838 47.7340

CP_E11 -4.2597 -0.6231 2.3193

CP_E14 -4.2841 -0.9599 7.8030

CP_E17 -4.3020 -1.2735 13.2742

CP_E2 -4.2228 0.2526 -13.5649

CP_E5 -4.2360 -0.0525 -8.0835

CP_E8 -4.2543 -0.3547 -2.6049

CP_W11 4.2588 -0.6368 2.3626

CP_W14 4.2385 -0.9551 7.8415

CP_W17 4.2244 -1.2633 13.3066

CP_W2 4.3026 0.2605 -13.4884

CP_W5 4.2864 -0.0642 -8.0265

CP_W8 4.2681 -0.3728 -2.5563

EI_01 -3.2430 -3.8507 -15.5599

EI_035 -3.2593 -4.1455 -10.4801

EI_065 -3.2502 -4.4319 -5.3970

EI_10 -3.2733 -4.7285 -0.0707

EI_125 -3.2853 -5.0225 5.0019

EI_155 -3.3005 -5.3058 10.0756

EI_18 -3.3291 -5.5984 14.8878

EO_01 -5.9165 -3.7784 -16.7371

EO_09 -5.9821 -4.6861 -0.8124

EO_19 -5.8262 -5.7762 17.9173

PP1 7.2417 -4.2800 21.2850

PP2 7.2279 -4.7573 30.1203

PP3 7.2018 -5.1756 37.2058

VULCAN_E -4.1054 -2.0351 -8.3983

VULCAN_W 4.1533 -1.8186 -8.1816

WBE_1 -2.7874 -5.9013 20.2109

WBE_1_5 -4.3762 -6.1844 25.2611

WBE_2 -2.8332 -6.4531 29.9410

WBE_2_5 -4.4354 -6.8308 36.5153

WBE_3 -2.9265 -7.1097 41.4054

WBW_1 5.0414 -5.8994 20.2393

WBW_1_5 5.8343 -6.1708 24.8684

WBW_1_7 4.7151 -6.3770 28.4437

WBW_2 5.0588 -6.4587 29.9586

WBW_2_2 4.5839 -6.6437 33.0491

WBW_2_5 5.8101 -6.8466 36.8136

WBW_3 4.9941 -7.1067 41.3270

WI_01 3.3296 -3.8491 -15.5740

WI_035 3.3108 -4.1380 -10.4782

WI_065 3.2895 -4.4296 -5.4146

WI_10 3.2836 -4.7331 -0.0819

WI_125 3.2575 -5.0264 4.9954

WI_155 3.2563 -5.3170 10.0758

WI_18 3.2401 -5.6032 14.9219

WO_01 5.3270 -3.7835 -16.6339

WO_09 5.3542 -4.6834 -0.8288

WO_185 5.3342 -5.6579 15.9071

DetCtr_dsgn 0.0003 0.0075 -0.1307

DetCtr_meas 0.0000 0.0000 0.0000

dcs_origin 0.0431 0.8934 -15.6053

FD_ds_axis -0.0432 -0.8934 15.6054

FD_us_right -3.9568 0.8940 -15.6163

FD_us_left 4.0431 0.8927 -15.5944

FD_us_top 0.0431 4.8868 -15.3767

FD_us_bot 0.0431 -3.1001 -15.8340

FD_us_t,r -3.9568 4.8875 -15.3877

**Table 4.6-4**. Far Cavern Monuments and Detector Points. In the "Beam"
coordinate system with the Z-axis along the beam direction, X-axis
horizontal, beam left, and Y-axis to make a right handed orthogonal
system.

The line from Fermilab to Soudan is transferred from the surface at
Fermilab to underground using conventional survey techniques. The most
difficult parameter is the azimuth (horizontal angle). **Table 4.6-5**
shows the two methods we are using to determine underground azimuth and
the offset (horizontal deviation from the ideal beam line) resulting
from the expected angular error at several distances. A gyro-theodolite
is a precision theodolite combined with an accurate gyrocompass. One
accurate to 15 microradians has been loaned to Fermilab by SLAC and has
been in use on NuMI since mid 2001. Both mechanical and optical plumbing
is being used down the sight risers and shafts constructed at Fermilab.

  ---------------------- --------------- ------------ -------- -------- ------- --------
  Transferring Azimuth   Fermilab                                               
                         Surface to                                             
                         Tunnels                                                

                                                                                

  Method:                                Accuracy at:                           

                         distance \>     84 m         460 m             1040 m  735 km

                         Accuracy        Downstream   Mid               MINOS   Soudan
                                                      Decay                     

                         (milliradian)   Target Hall  Tunnel            near    far det
                                                      Vent              det     

                                                                                

  Best Gyro              0.015           1.3 mm       7 mm              16 mm   11 m

  Widely Separated Plumb 0.012           1.0 mm       6 mm              12 mm   9 m
  Bobs                                                                          
  ---------------------- --------------- ------------ -------- -------- ------- --------

### Table 4.6-5 The two methods being used to determine underground azimuth and the offset (horizontal deviation from the ideal beam line) resulting from the expected angular error at several distances {#table-4.6-5-the-two-methods-being-used-to-determine-underground-azimuth-and-the-offset-horizontal-deviation-from-the-ideal-beam-line-resulting-from-the-expected-angular-error-at-several-distances .unnumbered}

**4.6*.*3 System Description***:* **Beamline Element Accuracy
Requirements**

The PBEAM_WMC Monte Carlo was used to calculate the effect of
misalignments of each beamline element on the determination of the far
detector spectrum (without oscillations) from the measured near detector
spectrum. PBEAM is first run with all beam elements at their nominal
values and positions (\"on axis\"). A parameter is selected to
investigate and its position is varied from its nominal value. For
example, in the Monte Carlo the first focussing horn is moved 4 mm
transverse to the beam axis (\"Horn 1 X shift of 4 mm\"), and the
resulting spectra at both near and far detectors are calculated.

The ratio R~far~ , obtained by dividing the far detector flux with the
beamline element displaced by the far detector flux with the beamline
element on axis, is shown in **Figure 4.6-3a**. A dashed line has been
drawn for a flux ratio of 1.0, which would be the result if there were
no change in the flux. **Figure 4.6-3b** is a similar graph for the near
detector. The ratio of these ratios (far ratio to near ratio, RR) is
shown in **Figure 4.6-3c**. It is easy to pick out the largest
fractional difference (in the interval 1 to 10 GeV), which occurs near 5
GeV. Beam element misalignments breaking the
![](media/image3.wmf){width="4.707638888888889in"
height="6.1in"}azimuthal symmetry of the neutrino beam, such as this
horn 1 X shift, are measurable in the near detector.

**Fig 4.6-3** Effect of a 4 mm offset of horn 1 on (top) the far
detector flux, (middle) near detector at 316.6 m beyond the end of the
decay pipe, (bottom) far over near ratio(RR). These results are for the
low energy beam configuration.

![](media/image4.wmf){width="6.3in"
height="4.210416666666666in"}**Figure 4.6-4** displays RR-1 for several
horn 1 X shifts. These all start at RR-1=0 at low energy, but have been
offset by multiples of 10% to clearly display the several curves on a
single graph. To obtain sufficient statistical precision from the Monte
Carlo in a reasonable time, X shifts much larger than the expected
alignment tolerance of 0.35 mm have been calculated. At each peak and
valley shown in **Figure 4.6-4**, the data are fit to the formula
RR-1=Ax^p^. This formula forces the required result of RR=1 at x=0, i.e.
no effect on the spectrum if there is no misalignment. The value of RR
at the expected alignment tolerance is calculated using the parameters A
and p determined by the fit.

**Fig 4.6-4** Curves of RR-1 for several horn 1 X shifts. These all
start at RR-1=0 at low energy, but have been offset by multiples of 10%
to clearly display the several curves on a single graph. These results
are for the low energy beam configuration.

This analysis is repeated for all beam element misalignments shown in
**Table 4.6-6**. A similar table is prepared for each 1 GeV neutrino
energy interval and, to be conservative, lists the largest deviation of
RR found for any neutrino energy up to the table value. The overall
effect on RR is found by adding the individual element terms in
quadrature. The table takes into account that most misalignments can
occur in two transverse planes.

In the table, angle parameters are expressed by a single linear
distance; the downstream end of the device is displaced by this amount
and the upstream end is displaced by an equal amount in the opposite
direction. These two displacements are what are actually measured by the
surveyors. The length of the device, in meters, is given in square
brackets after the description.

![](media/image5.wmf){width="6.513888888888889in"
height="6.138888888888889in"}

**Table 4.6-6** The expected percentage error in RR from each
misalignment at 8 GeV neutrino energy. These results are for the low
energy beam configuration

This result is plotted in **Figure 4.6-5** as a function of neutrino
energy. Also shown is the statistical error from a two-year run. The
MINOS physics requirement is that the error due to neutrino beam
misalignments be comfortably below the 2 year run statistical error, and
**Figure 4.6-5** shows this to be the case for the low energy beam.

![](media/image6.wmf)

**Figure 4.6-5** The expected percentage error in RR from all
misalignments listed in **Table 4.6-6**. Also shown is the statistical
error for a two-year run. These results are for the low energy beam
configuration

**4.6.4 System Description:** **Construction QA**

Fermilab surveyors are providing NuMI tunnels and halls quality
assurance. Most of the decay tunnel was excavated using a 21.5-foot
diameter Tunnel Boring Machine (TBM). **Figure 4.6-6** shows the
vertical and horizontal deviations of the center of the TBM decay tunnel
from the specified line from Fermilab to Soudan. Measurement of the
completed tunnel by both the SA Healy (civil subcontractor) and Fermilab
surveyors are shown. Agreement with the design is excellent; most
vertical and horizontal centers are within 2 inches. No attempt was made
by the two groups of surveyors to measure at the same station
(horizontal distance along the tunnel), so local tunnel variations could
explain part of the differences between the measurements. The agreement
for horizontal is worse than vertical; this is likely conformation that
azimuth is the most difficult parameter to transfer underground. The
Fermilab surveyors used the 15 microradian gyro-theodolite (0.36 inch in
2000 feet), while the SA Healy surveyors used a less precise 100
microradian instrument (2.4 inch in 2000 feet).

![](media/image7.wmf)

![](media/image8.wmf)

**FIgure 4.6-6** The vertical and horizontal deviations of the "as
built" center of the TBM decay tunnel from the specification.
Measurements of the completed tunnel by both the SA Healy (civil
subcontractor) and Fermilab surveyors are shown.