1. Primary Energy Reconstruction Method for Air Shower Array Experiments Samvel Ter-Antonyan and Ali Fazely

2. Inverse Problem for All-particle energy spectrum Event-by-event methodUnfolding Advantage: general formulation Solutions: a) regularized unfolding iterative algorithm [KASCADE Collaboration, Astropart.Phys. 24 (2005) 1] b) parameterization of inverse problem + + a priory spectral info. [GAMMA Collaboration, Astropart.Phys. 28 (2007) 169] Disadvantage: Pseudo solutions for elemental spectra and undefined systematic errors for unfolding algorithms (KASCADE). [S. Ter-Antonyan, Astropart.Phys. 28 (2007) 321] Advantage: simplicity Solution: analytical or numerical integration [J. Phys. G: Nucl. Part. Phys. 35 (2008) 115] Disadvantage: ? The most experiments ignore the methodic errors.

3. Energy estimator: Event-by-event analysis [GAMMA_09] This work [ICETOP_09] is ill-posed problem for F(E 0 ) due to A  H, He, … Fe Redefinition of inverse problem:  a priori:  =2.9  0.25 for 1 PeV  E 0 < 500 PeV  Let and [KASCADE-GRANDE], for ,  - constant

4. where, and | a | << 0.1 Solution for primary spectrum Spectral errors: Statistic ErrorsMethodic Errors  2%

5. Multi-parametric energy estimator for ICETOP Array: 5 i=1,…10 4, A  H, He, O, Fe min {  2 (a 1,a 2,…a 6,  (E i )| E 0,i )} CORSIKA EAS SIMULATION + ICETOP DETECTOR RESPONSE + LDF RECONSTRUCTION

6. if then Expected biases and uncertainties of primary energy Log(E 0 /GeV) GAMMA ExperimentICETOP Log(E 0 /GeV)  (Ln(E 1 /E 0 ))

7. Distribution of errors (~ Gaussian)

8. Verification of method Primary energy spectra for p, He, O, Fe from GAMMA Experiment data [GAMMA Collaboration, Astropart.Phys. 28 (2007) 169] Expected reconstructed all-particle spectrum for ICETOP

9. Expected (red symbols) all-particle spectrum for ICETOP