  Muon tomography aims at deriving the density structure of geological bodies
from their screening attenuation produced on the natural cosmic muons flux.
Because of their open-sky exposure, muons telescopes are subject to noise
fluxes with large intensities relative to the tiny flux of interest. A
recognized source of noise flux comes from fake tracks caused by particles that
fortuitously trigger the telescope detectors at the same time. Such a flux may
be reduced by using multiple-detector telescopes so that fortuitous events
become very unlikely. In the present study, we report on a different type of
noise flux caused by upward-going muons crossing the detectors from the rear
side. We describe field experiments on La Soufri\'ere of Guadeloupe and Mount
Etna, and give details on the high-resolution clocking system and the
statistical procedure necessary to detect upward-going muons. We analyse
several data sets acquired either in calibration or in volcano tomography
situation. All data sets are shown clearly biased by upward-going noise flux
whose intensity may amount to 50% of the measured total flux in given
directions. Biases produced on density radiographies by this kind of flux are
quantified and correction procedures are detailed. Examples for La Soufri\'ere
and Mount Etna are given.

Instrumentation and Detectors;Instrumentation and Methods for Astrophysics;Geophysics