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If weak equivalence principle is violated then different types of neutrinoswould couple differently with gravity and that may produce a gravity inducedoscillation for the neutrinos of different flavour. We explore here thepossibility that very small violation of the principle of weak equivalence(VEP) can be probed by ultra high energy neutrinos from distant astrophysicalsources. The very long baseline length and the ultra high energies of suchneutrinos could be helpful to probe very small VEP. We consider a 4-flavourneutrino scenario (3 active + 1 sterile) with both mass-flavour and gravityinduced oscillations and compare the detection signatures for these neutrinos(muon tracks and shower events) with and without gravity induced oscillationsat a kilometer scale detector such as IceCube. We find that even very small VEP($\sim 10^{-42}$) can considerably affect the detected muon yield produced byUHE neutrinos from distant Gamma Ray Bursts (GRBs)

Effects of Violation of Equivalence Principle on UHE Neutrinos at IceCube in 4 Flavour Scenario