the problem of a complete recrystallization of micrit to form sparit cement in carbonate succession which alternate with recrystallized siliclatic cement in succession of carbonat facies?
the presence of sparit calcite is as stated Mr. Tamborrino a normal recrystallisation (transformation) of micrite to spartie or also, the precipitation of sparite within voids.
for the silice cement, its presence can be caused by of water saturation with silice (derived from organism with siliceous test like sponges etc).
Micrite typically comprises very fine-grained metastable aragonite or high-Mg calcite. Neomorphism refers to the replacement of these metastable grains to more stable coarsely crystalline calcite in the form of micro-/pseudo-spar (Folk 1965, 1974; Bathurst 1975). Crucially no carbonate is gained or lost in this process and former matrix porosity may be converted into intercrystalline porosity between spar crystals (Lucia and Loucks, 2013).
One process of neomorphism may be the effect of meteoric diagenesis, which aggressively dissolves metastable minerals such as the aragonite/high-Mg calcite in micrite. In the low ionic strength of the meteoric pore waters that bathe the rock there is little competition for lattice sites so larger equant micro-/pseudo-spar crystals develop under slow continual growth (Folk, 1974).
See:
Bathurst, R.G.C., 1975. Carbonate sediments and their diagenesis.
Folk, R.L., 1965. The natural history of crystalline calcium carbonates; effect of magnesium content and salinity. J. Sed. Res., v. 44, no. 1, p. 40-53.
Folk, R.L. 1974. The natural history of crystalline calcium carbonate: Effect of magnesium content and salinity. Journal of Sedimentary Petrology, 44, 40-53
Lucia, F. J. and Loucks, R. G. 2013. Micropores in carbonate mud: Early development and petrophysics. Gulf Coast Association of Geological Societies Journal, 2, 1-10