We consider effects of the Non-Standard Interactions (NSI) on oscillations of the high energy atmospheric neutrinos. The ν μ -oscillograms are constructed and their dependence on the NSI strength parameters Ïμ αβ studied. We computed the zenith angle distributions of the ν μ -events in the presence of NSI in different energy regions. The distributions are confronted with the IceCube-79 (high energy sample) and the DeepCore (low energy sample) data and constraints on the strength parameters |Ïμ μτ |≠6 × 10-3 and |Ïμ μμ - Ïμ ττ | â‰3 × 10-2 (90% C.L.) have been obtained. Future measurements of the zenith angle distributions by DeepCore in several energy bins will allow to improve the bounds by factor 2-3. We discuss the signatures of NSI in the zenith angle and energy distributions of events which allow to discriminate them from the effects of sterile neutrinos. © 2013 SISSA, Trieste, Italy.20136 Gonzalez-Garcia, M., Maltoni, M., Atmospheric neutrino oscillations and new physics (2004) Phys. Rev., D70, p. 033010. , 2004PhRvD.70c3010G [hep-ph/0404085] [INSPIRE]Ohlsson, T., Status of non-standard neutrino interactions (2013) Rep. Prog. Phys., 76, p. 044201. , 044201 [ arXiv:1209.2710 ] [ INSPIRE ]Fornengo, N., Maltoni, M., Tomas, R., Valle, J., Probing neutrino nonstandard interactions with atmospheric neutrino data (2002) Phys. Rev., D65, p. 013010. , 2002PhRvD.65a3010F [hep-ph/0108043] [INSPIRE]Gonzalez-Garcia, M., Guzzo, M., Krastev, P., Nunokawa, H., Peres, O., Atmospheric neutrino observations and flavor changing interactions (1999) Phys. Rev. Lett., 82, p. 3202. , 1999PhRvL.82.3202G 10.1103/PhysRevLett.82.3202 [hep-ph/9809531] [INSPIRE]Fornengo, N., Gonzalez-Garcia, M., Valle, J., On the interpretation of the atmospheric neutrino data in terms of flavor changing neutrino interactions (2000) JHEP, 7, p. 006. , 2000JHEP.07.006F 10.1088/1126-6708/2000/07/006 [hep-ph/9906539] [INSPIRE]Lipari, P., Lusignoli, M., On exotic solutions of the atmospheric neutrino problem (1999) Phys. Rev., D60, p. 013003. , 1999PhRvD.60a3003L [hep-ph/9901350] [INSPIRE]Gonzalez-Garcia, M., Maltoni, M., Atmospheric neutrino oscillations and new physics (2004) Phys. Rev., D70, p. 033010. , 2004PhRvD.70c3010G [hep-ph/0404085] [INSPIRE]Friedland, A., Lunardini, C., Maltoni, M., Atmospheric neutrinos as probes of neutrino-matter interactions (2004) Phys. Rev., D70, p. 111301. , 2004PhRvD.70k1301F [hep-ph/0408264] [INSPIRE]Friedland, A., Lunardini, C., A Test of tau neutrino interactions with atmospheric neutrinos and K2K (2005) Phys. Rev., D72, p. 053009. , 2005PhRvD.72e3009F [hep-ph/0506143] [INSPIRE]Gonzalez-Garcia, M., Maltoni, M., Salvado, J., Testing matter effects in propagation of atmospheric and long-baseline neutrinos (2011) JHEP, 5, p. 075. , 2011JHEP.05.075G 10.1007/JHEP05(2011)075 [arXiv:1103.4365] [INSPIRE]Escrihuela, F., Tortola, M., Valle, J., Miranda, O., Global constraints on muon-neutrino non-standard interactions (2011) Phys. Rev., D83, p. 093002. , 2011PhRvD.83i3002E [arXiv:1103.1366] [INSPIRE]Gonzalez-Garcia, M., Halzen, F., Maltoni, M., Physics reach of high-energy and high-statistics IceCube atmospheric neutrino data (2005) Phys. Rev., D71, p. 093010. , 2005PhRvD.71i3010G [hep-ph/0502223] [INSPIRE]Bolanos, A., Miranda, O., Palazzo, A., Tortola, M., Valle, J., Probing non-standard neutrino-electron interactions with solar and reactor neutrinos (2009) Phys. Rev., D79, p. 113012. , 2009PhRvD.79k3012B [arXiv:0812.4417] [INSPIRE]Barranco, J., Miranda, O., Moura, C., Valle, J., Constraining non-standard neutrino-electron interactions (2008) Phys. Rev., D77, p. 093014. , 2008PhRvD.77i3014B [arXiv:0711.0698] [INSPIRE]Barranco, J., Miranda, O., Moura, C., Valle, J., Constraining non-standard interactions in νee or {{\overline{\nu}}-e}e scattering (2006) Phys. Rev., D73, p. 113001. , 2006PhRvD.73k3001B [hep-ph/0512195] [INSPIRE]Davidson, S., Pena-Garay, C., Rius, N., Santamaria, A., Present and future bounds on nonstandard neutrino interactions (2003) JHEP, 3, p. 011. , 2003JHEP.03.011D 10.1088/1126-6708/2003/03/011 [hep-ph/0302093] [INSPIRE]Biggio, C., Blennow, M., Fernandez-Martinez, E., General bounds on non-standard neutrino interactions (2009) JHEP, 8, p. 090. , 2009JHEP.08.090B 10.1088/1126-6708/2009/08/090 [arXiv:0907.0097] [INSPIRE]Mitsuka, G., Study of Non-Standard Neutrino Interactions with Atmospheric Neutrino Data in Super-Kamiokande i and II (2011) Phys. Rev., D84, p. 113008. , Super-Kamiokande collaboration 2011PhRvD.84k3008M [arXiv:1109.1889] [INSPIRE]Adamson, P., A Search for Flavor-changing Non-standard Neutrino Interactions by MINOS, , MINOS collaboration arXiv:1303.5314 [ INSPIRE ]Ohlsson, T., Zhang, H., Zhou, S., Effects of Non-standard Neutrino Interactions at PINGU, , arXiv:1303.6130 [ INSPIRE ]Dziewonski, A.M., Anderson, D.L., Preliminary reference earth model (1981) Phys. Earth Planet. Interiors, 25, p. 297. , 1981PEPI.25.297D 10.1016/0031-9201(81)90046-7 [INSPIRE]Gonzalez-Garcia, M., Maltoni, M., Salvado, J., Schwetz, T., Global fit to three neutrino mixing: Critical look at present precision (2012) JHEP, 12, p. 123. , 2012JHEP.12.123G 10.1007/JHEP12(2012)123 [arXiv:1209.3023] [INSPIRE]Akhmedov, E.K., Matter effects in oscillations of neutrinos traveling short distances in matter (2001) Phys. Lett., 503, p. 133. , 2001PhLB.503.133A [hep-ph/0011136] [INSPIRE]Yasuda, O., Vacuum mimicking phenomena in neutrino oscillations (2001) Phys. Lett., 516, p. 111. , 2001PhLB.516.111Y [hep-ph/0106232] [INSPIRE]Honda, M., Kajita, T., Kasahara, K., Midorikawa, S., Sanuki, T., Calculation of atmospheric neutrino flux using the interaction model calibrated with atmospheric muon data (2007) Phys. Rev., D75, p. 043006. , 2007PhRvD.75d3006H [astro-ph/0611418] [INSPIRE]Sajjad Athar, M., Honda, M., Kajita, T., Kasahara, K., Midorikawa, S., Atmospheric neutrino flux at INO, South Pole and Pyhásalmi (2013) Phys. Lett., 718, p. 1375. , 2013PhLB.718.1375S [arXiv:1210.5154] [INSPIRE]Abbasi, R., The Design and Performance of IceCube DeepCore (2012) Astropart. Phys., 35, p. 615. , IceCube collaboration 2012APh.35.615A 10.1016/j.astropartphys.2012.01.004 [arXiv:1109.6096] [INSPIRE]Esmaili, A., Halzen, F., Peres, O., Constraining Sterile Neutrinos with AMANDA and IceCube Atmospheric Neutrino Data (2012) JCAP, 11, p. 041. , 2012JCAP.11.041E 10.1088/1475-7516/2012/11/041 [arXiv:1206.6903] [INSPIRE]Abbasi, R., Measurement of the atmospheric neutrino energy spectrum from 100 GeV to 400 TeV with IceCube (2011) Phys. Rev., D83, p. 012001. , IceCube collaboration 2011PhRvD.83a2001A [arXiv:1010.3980] [INSPIRE]Aguilar-Arevalo, A., Evidence for neutrino oscillations from the observation of anti-neutrino(electron) appearance in a anti-neutrino(muon) beam (2001) Phys. Rev., D64, p. 112007. , LSND collaboration 2001PhRvD.64k2007A [hep-ex/0104049] [INSPIRE]Aguilar-Arevalo, A., A Combined ν μ → ν e and Oscillation Analysis of the MiniBooNe Excesses, , MiniBooNE collaboration arXiv:1207.4809 [ INSPIRE ]Giunti, C., Laveder, M., Statistical Significance of the Gallium Anomaly (2011) Phys. Rev., C83, p. 065504. , 2011PhRvC.83f5504G [arXiv:1006.3244] [INSPIRE]Mention, G., Fechner, M., Lasserre, T., Mueller, T., Lhuillier, D., The Reactor Antineutrino Anomaly (2011) Phys. Rev., D83, p. 073006. , 2011PhRvD.83g3006M [arXiv:1101.2755] [INSPIRE]Kopp, J., Machado, P.A.N., Maltoni, M., Schwetz, T., Sterile Neutrino Oscillations: The Global Picture (2013) JHEP, 5, p. 050. , 2013JHEP.05.050K 10.1007/JHEP05(2013)050 [arXiv:1303.3011] [INSPIRE]Nunokawa, H., Peres, O., Zukanovich Funchal, R., Probing the LSND mass scale and four neutrino scenarios with a neutrino telescope (2003) Phys. Lett., 562, p. 279. , 2003PhLB.562.279N [hep-ph/0302039] [INSPIRE]Choubey, S., Signature of sterile species in atmospheric neutrino data at neutrino telescopes (2007) JHEP, 12, p. 014. , 2007JHEP.12.014C 10.1088/1126-6708/2007/12/014 [arXiv:0709.1937] [INSPIRE]Razzaque, S., Smirnov, A.Y., Searches for sterile neutrinos with IceCube DeepCore (2012) Phys. Rev., D85, p. 093010. , 2012PhRvD.85i3010R [arXiv:1203.5406] [INSPIRE]Razzaque, S., Smirnov, A.Y., Searching for sterile neutrinos in ice (2011) JHEP, 7, p. 084. , 2011JHEP.07.084R 10.1007/JHEP07(2011)084 [arXiv:1104.1390] [INSPIRE]Barger, V., Gao, Y., Marfatia, D., Is there evidence for sterile neutrinos in IceCube data? (2012) Phys. Rev., D85, p. 011302. , 2012PhRvD.85a1302B [arXiv:1109.5748] [INSPIRE]Aartsen, M., Measurement of Atmospheric Neutrino Oscillations with IceCube, , IceCube collaboration arXiv:1305.3909 [ INSPIRE ]Gross, A., Atmospheric Neutrino Oscillations in IceCube, , IceCube collaboration arXiv:1301.4339 [ INSPIRE ]