  We propose a new test of the critical earthquake model based on the
hypothesis that precursory earthquakes are ``actors'' that create fluctuations
in the stress field which exhibit an increasing correlation length as the
critical large event becomes imminent. Our approach constitutes an attempt to
build a more physically-based cumulative function in the spirit of but
improving on the cumulative Benioff strain used in previous works documenting
the phenomenon of accelerated seismicity. Using a space and time dependent
visco-elastic Green function in a two-layer model of the Earth lithosphere, we
compute the spatio-temporal stress fluctuations induced by every earthquake
precursor and estimate, through an appropriate wavelet transform, the
contribution of each event to the correlation properties of the stress field
around the location of the main shock at different scales. Our physically-based
definition of the cumulative stress function adding up the contribution of
stress loads by all earthquakes preceding a main shock seems to be unable to
reproduce an acceleration of the cumulative stress nor an increase of the
stress correlation length similar to those observed previously for the
cumulative Benioff strain. Either earthquakes are ``witnesses'' of large scale
tectonic organization and/or the triggering Green function requires much more
than just visco-elastic stress transfers.
