4.1. Bounds on the energy spectrum
The basic operational system of neutrino telescopes is an array of strings with photo-multiplier tubes (PMTs) distributed throughout a natural Cerenkov medium such as ice or water. The largest pilot experiments (~ 0.1 km in size) are: the now defunct DUMAND (Deep Underwater Muon and Neutrino Detector) experiment  in the deep sea near Hawaii, the underwater experiment in Lake Baikal , and AMANDA (Antarctic Muon And Neutrino Detector Array)  in the South Pole ice. Next generation neutrino telescopes aim towards an active volume in the range of 1 km3 of water. Projects under construction or in the proposal stage are: two deep sea experiments in the Mediterranean, the French ANTARES (Astronomy with a Neutrino telescope Abyss environment RESearch)  and NESTOR (Neutrino Experiment SouthwesT Of GReece ), and ICECUBE , a scaled up version of the AMANDA detector.
The traditional technique to observe cosmic neutrinos is to look for muons (along with a visible hadronic shower if the is of sufficient energy) generated via charged-current interactions, (µ, µ) N (µ-, µ+) + anything, in the rock below the detector. The Cerenkov light emitted by these muons is picked up by the PMTs, and is used for track reconstruction. The muon energy threshold is typically in the range of 10 - 100 GeV. However, besides the desired extraterrestrial neutrinos, below ~ 103 GeV there is a significant background of leptons (produced by CRs interacting in the atmosphere) [476, 477] and so the task of developing diagnostics for neutrino sources becomes complicated. With rising energy ( 106 GeV) the three neutrino flavors can be identified .
The spectacular neutrino fireworks (in the 10 MeV range) from supernova 1987A constitute the only extragalactic source so far observed [479, 480]. The Fréjus , Baikal , MACRO , and AMANDA  collaborations reported no excess of neutrinos above the expected atmospheric background, enabling significant limts to be set on the diffuse neutrino flux. (39) These limits are shown in Fig. 9.
Figure 9. The horizontal solid lines indicate current 90% CL upper limits on the neutrino fluxes E-2 as reported by the EAS-TOP , DUMAND , Baikal , MACRO , AMANDA , and RICE [490, 491] collaborations. The * - * - * lines indicate model independent bounds on the neutrino flux from AGASA + Fly's Eye data  (95% CL), Frejus , GLUE [390, 493], and FORTE searches in the Greenland ice sheet . The horizontal thick dotted line indicates the expected 90% CL sensitivity of IceCube in 1 yr of operation . Also shown (non-horizontal thick dotted lines) are the projected sensitivities of PAO (1 yr running) , EUSO (1 yr running)  and ANITA (45 days running)  corresponding to 1 event per decade. The region between the falling dashed-dotted lines indicates the flux of atmospheric neutrinos.
Upward going neutrinos with energies 108 GeV are typically blocked by the Earth. This shadowing severely restricts the high energy event rates in underground detectors. However, neutrinos may also induce extensive air showers, so current and future air shower experiments might also function as neutrino detectors. The neutrino interaction length is far larger than the Earth's atmospheric depth, which is only 0.36 km water equivalent (kmwe) even when traversed horizontally. Neutrinos therefore shower uniformly at all atmospheric depths. As a result, the most promising signal of neutrino-induced cascades are quasi-horizontal showers initiated deep in the atmosphere. For showers with large enough zenith angles, the likelihood of interaction is maximized and the background from hadronic cosmic rays is eliminated, since the latter shower high in the atmosphere. These -showers will appear as hadronic vertical showers, with large electromagnetic components, curved fronts (a radius of curvature of a few km), and signals well spread over time (on the order of microseconds).
The event rate for quasi-horizontal deep showers from ultra-high energy neutrinos is 
where the sum is over all neutrino species i = e, e, µ, µ, , , and all final states X. NA = 6.022 × 1023 is Avogadro's number, and di / dEi is the source flux of neutrino species i, as usual denotes the cross section, and is the exposure measured in cm3 w.e. sr time. The Fly's Eye and the AGASA Collaborations have searched for quasi-horizontal showers that are deeply-penetrating, with depth at shower maximum Xmax > 2500 g/cm2 (see e.g. [498, 499]). There is only 1 event that unambiguously passes this cut with 1.72 events expected from hadronic background, implying an upper bound of 3.5 events at 95%CL from neutrino fluxes. Note that if the number of events integrated over energy is bounded by 3.5, then the same limit is certainly applicable bin by bin in energy. Thus, using Eq. (70) one obtains
at 95% CL for some energy interval . Here, the sum over X takes into account charge and neutral current processes. In a logarithmic interval where a single power law approximation
is valid, a straightforward calculation shows that
where = ( + 1) / 2 and <A> denotes the quantity A evaluated at the center of the logarithmic interval. The parameter = 0.363 + - , where 0.363 is the power law index of the SM neutrino cross sections  and and - are the power law indices (in the interval ) of the exposure and flux di / dEi, respectively. Since sinh / > 1, a conservative bound may be obtained from Eqs. (71) and (73):
By taking = 1 as a likely interval in which the single power law behavior is valid (this corresponds to one e-folding of energy), and setting <Ei d i / dEi> = 1/6 <E d / dE> ( total neutrino flux) from Eq. (74) it is straightforward to obtain 95%CL upper limits on the neutrino flux. The limits are shown in Fig. 9.
These bounds will be improved in the near future. In particular, each site of PAO will observe ~ 15 km3we sr of target mass around 1019 eV . Moreover, the study of radio pulses from electromagnetic showers created by neutrino interactions in ice would provide an increase in the effective area up to 104 km2. A prototype of this technique is the Radio Ice Cerenkov Experiment (RICE) . Similar concepts are used by the Goldstone Lunar ultrahigh energy neutrino Experiment (GLUE), (40) the ANtartic Impulse Transient Array (ANITA), (41) and the Fast On-orbit Recording of Transient Events (FORTE). (42) Existing limits on -fluxes from RICE, GLUE and FORTE, as well as the projected sensitivities of forthcoming experiments are collected in Fig. 9.
39 The Frejus experiment, located in an underground laboratory, measured the energy of muons produced by neutrino interactions in the rock above the detector. The detector itself comprised a calorimeter made from a vertical sandwich of over 900 iron slabs interspersed with flash chambers. Geiger tubes embedded in the structure provided the trigger . The extensive air shower array on top of the Gran Sasso Laboratory (EAS-TOP)  and MACRO  used similar techniques. Back.
40 This experiment observes microwave Cerenkov pulses from electromagnetic showers induced by neutrinos interacting in the Moon's rim  Back.
41 A balloon-borne payload that will circle the continent of Antartica at 35,000 meters, scanning the vast expanses of ice for telltale pulses of radio emission generated by the neutrino collisions [http://www.ps.uci.edu/~anita/]. Back.
42 The FORTE satellite records bursts of electromagnetic waves arising from near the Earth's surface in the radio frequency range 30 to 300 MHz with a dual polarization antena . Back.