1. Models of the Earth distribute U- and Th masses mainly between the continental crust and the lower mantle.
As has already been discussed here a number of detectors stationed at appropriate geographical sites can separate the crust and mantle contributions.
Adopted from F.Mantovani, L. Carmignani, G. Fiorentini, M. Lissia
Phys. Rev. D69, (2004)

2. G. Domogatsky, V. Kopeikin, L. Mikaelyan, V. Sinev
Can Radiogenic Heat Sources inside the Earth be located by their Anti Neutrino incoming Directions?
G. Domogatsky, V. Kopeikin, L. Mikaelyan, V. Sinev

3. Here we analyze directional separation of e signals arriving from the crust and the lower mantle with only one detector.
Crust
Upper mantle
Lower mantle
Geoneutrinos from the Crust and the Lower Mantle enter the detector from different directions.
Liquid core
Hard core

4. NEUTRON DETECTION
We consider CH2 ,  = 0.8 g/cm3
Liquid Scintillation Detector and
e + p => e+ + n
Geoneutrino detection reaction.
The Geoneutrino signature is delayed coincidence between the positron and neutron signals.

5. Positron energy released, MeV
Positron spectrum boosted by two 511 keV annihilation quanta is shown below:
90Sr-90Y
calibration source
Counts per MeV
U+Th Th
Positron energy released, MeV

6. Parallel geoneutrino beam (along Z-axis)
NEUTRINO DIRECTIONS
 Parallel geoneutrino beam (along Z-axis)
 This geometry was studied earlier at CHOOZ with reactor antineutrinos.
 1) Neutron initial direction is strongly correlated with the incoming e direction.
En = 2.5 MeV
qmax  26º pe
qen pn pn

7. Angular distribution of reaction (1) neutrons relative to the incident geoneutrino direction weighted with the reaction cross section
8000
4000
cos qnn = 0.967
cos qnn

8. 2). In first few collisions with scintillator atoms the memory is partially conserved and neutron is displaced from the reaction point in + Z directions. After collisions the memory is lost and neutrons slow down and diffuse symmetrically around the displaced center.
N=1
N=3
Z, cm
<Z>=0.66 cm
<Z>=1.32 cm
N=5
N=8
Z, cm
<Z>=1.58 cm
<Z>=1.72 cm
X, cm
X, cm

9. CONCLUSIONS
We present a first attempt to analyze directions of a multidirectional low energy flux. In this attempt only two geoneutrino sources have been taken into account: the continental crust and lower mantle.
We haven’t analyzed perturbations due to possible fluctuations of U and Th concentrations in the detector’s immediate vicinity.
 Clearly more work is needed to come to more accurate results.

10. At this preliminary stage of analysis we can summarize the results as follows:
 Present understanding of radiogenic sources and their distribution in the Earth’s reservoirs is based on a shaky ground of cosmogenical and geochemical arguments with an obvious deficit of direct experimental evidence
 Information obtained with one 30-kton target mass detector using directional separation of incoming geoneutrino flux is useful but limited: it can give only some indications against the orthodox Earth’s model predictions, or can provide it’s rough confirmation.
 More definite information can be obtained only with ~ 4 times larger detector

11. < Renx > = < Reny > 0  /N1/2 ,
Later neutrons diffuse and are captured symmetrically around the displaced center. For parallel e beam the average neutron displacement is calculated as:
dz = 1.72 cm
now we find:
< Renx > = < Reny > 0  /N1/2 ,
< Renz > = 1.72  /N1/2,
 N is the number of detected reaction (1) events and  is vector R component’s Gaussian dispersion.
Dispersion   20 cm is considerably larger than the displacement dZ = 1.7 cm and thus e statistics (N) should be sufficiently large.

12. ASSUMING NOW N = 2500 and  = 20cm (as in the CHOOZ experiment) we get:
  dZ = 1.7  04 cm
 Thus neutron displacement can be found at 4 st. deviation level (which is exactly the CHOOZ result).

13. Geoneutrinos from the lower mantle
We generate 105 MC events and find the average displacement dLM:
dLM = 1.20 cm

14. With ~30 kton target mass 4000 geoevents can be accumulated in 5 years of data taking.
 N = 4000 is considered here as maximally thinkable events sample.
dLM = 1.20 cm  20 / 40001/2 = 1.2  0.32

15. GEONEUTRONOS from the CRUST dCr = < Renz >  0.29 cm  /N1/2
Here we consider hypothetical case where continental crust source forms a uniform 6000 km diameter and 40 km thick circular region centered around the geoneutrino detector
The vertical component of the flux is small here and the neutron displacement is also small:
dCr = < Renz >  0.29 cm  /N1/2

16. dLM+Cr = LM dLM + (1 – LM)dCr  /N1/2,
e from the Crust and the Lower Mantle
The average displacement of neutron cloud in the vertical direction is given by the expression:
 dLM+Cr = LM dLM + (1 – LM)dCr  /N1/2,
where dLM = 1.2 cm, dCr = 0.29cm and LM = FLM / (FLM + FCr) is the lower mantle fraction in the total geoneutrino incoming flux; N = 4000, the maximal achievable events sample considered here,
/N1/2 = 0.32 cm.

17. 1.5 1
0.5
dz, cm
aLM
Vertical displacement of neutron cloud dLM +Cr vs relative contribution LM of lower mantle to the total (crust + lower mantle) geoneutrino flux (solid line). Shaded is the (68% CL) uncertainty region, the dark gray area between vertical lines represents model’ prediction for detector installed in BNO.

18. One can see that separation method considered here is not very sensitive. Only sufficiently large displacements dLM+Cr, larger than 1 cm if found, can indicate contradiction to the predictions of the orthodox Earth’s model. In case experiment favours lower displacements, and thus indicates low contribution of the mantle geoneutrino flux, the dominant role of the crust geoneutrinos predicted by the model can roughly be confirmed.
Only with much larger number of collected events (N ~ 2104 ) and therefore with much larger detector more definite conclusions could be obtained.

19. P.S. Detector calibrations
Detection of small displacements discussed above requires adequate calibration procedures.
 While usual method, based on inserting neutron- and gamma sources into the fiducial volume can and should be exploited, the use of sufficiently more strong source is highly desirable.

20. We propose for calibration purposes a movable
~ 1 MCi 90Sr-90Y antineutrino source.
90Sr (T1/2 = 28.6 yr) decays to the ground state of 90Y(Emax = 2.28 MeV, T1/2 = 64h).
If installed at the distance of 30 m from the 30 kton detector center, the source can generate about 2105 events of reaction (1) per year.

21. ~ 200 000 Two circumstances make this source attractive:
First, it will irradiate the detector with flux of known intensity, known energy spectrum in the geoneutrino energy range and of known angular structure
90Sr-90Y
calibration source
Counts per MeV
At a distance of 30 m there will be ~
events/(year·30 kt) Th
U+Th
Positron energy released, MeV

22. and, second, the sources are produced commercially and used to supply heat for Radioisotope Thermoelectric Generators (RTGs)
We note that proposed calibration method could also be used in other low energy experiments employing large liquid scintillation detectors.

23. For each neutrino event positron and neutron capture positions are reconstructed and positron –neutron vector ReNi is found:
  ReNi.= RNi – Rei
The Reconstruction procedure is based on light and (or) time signals from PMTs.
Neutrino direction is found be neutron displacement in the e direction
Information of neutrino incoming directions is derived from vector ReNi. analysis.