Probing non-standard interaction of neutrinos with Ice Cube and Deep Core

We consider effects of the Non-Standard Interactions (NSI) on oscillations of the high energy atmospheric neutrinos. The v(mu)-oscillograms are constructed and their dependence on the NSI strength parameters epsilon(alpha beta) studied. We computed the zenith angle distributions of the v(mu)-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 vertical bar epsilon(mu T)vertical bar less than or similar to 6 x 10(-3) and vertical bar epsilon mu mu - epsilon tau tau vertical bar x 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.