In order to reveal the structural properties at small scale within a geological unit apparently homogeneous at large scale, we explore the stochastic components of petrophysical measurements recorded in a borehole drilled through the Cretaceous siliclastic units of the South-eastern Basin of France. First, we analyse the instantaneous fluctuations of gamma ray log measurements searching for scaling laws in its power spectrum. Power spectra indicate a scaling behaviour with average exponent beta a values mostly falling in the range 1