Behavior of elastic properties in carbonates: scale does matter

Understanding the evolution of rock physical properties with changing scale is a critical challenge when characterising spatial subsurface heterogeneities. One of the possible approaches can be using elastic wave velocities at various scales, from laboratory to field, by solely tuning the sensing wavelength to the studied media. Theoretically, in the case of a dry, isotropic, and homogeneous porous medium, at all scales of investigation, the elastic properties are not dependent on the scales of analysis (non-dispersive medium). However, as already pointed out in the literature, carbonate rocks have very heterogeneous pore networks at different scales, which may lead to different Representative Elementary Volumes (REV) with changing scales. In our work, we assume that the elastic wavelength is equal to the upper bound of the REV. In this study, we investigated marine carbonate rocks of Middle Jurassic age outcropping in the western part of France (Charentes, near Angouleme city) in four different quarries. A total of three REVs were investigated, always in dry conditions: i) the centimeter scale, acquiring P and S wave velocities (Vp, Vs) on 60 cylindrical samples of one inch-diameter using a central frequency of 500 kHz (wavelength ~ 1 cm); ii) the decimeter scale, acquiring more than 1500 measurements of Vp and Vs on outcropping carbonates with a frequency of 40 kHz (wavelength ~ 10 cm); and iii) the decameter scale acquiring seismic wave velocity measurements along a vertical profile (geophones connected to a vertical outcrop wall), where the 6 kg sledgehammer source was situated on the plateau, delivering a frequency of 100 Hz (wavelength ~ 10 m). In parallel, a thorough geological description was done at all the investigated scales, combining i) microscope-driven microstructure analysis of samples under the microscope, ii) sedimentary facies description of outcrops and iii) fracture orientation analysis on photogrammetric models of quarries. The elastic wave velocity results were interpreted considering facies and diagenetic processes of sedimentary rock fabric. At the centimeter scale (i), for a given sedimentary facies, we show a clear control of diagenesis (cementation and dissolution) on the elastic properties, in agreement with the well-documented literature. At the decimeter scale (ii), horizontal and vertical Vp-Vs data were used to construct 2D acoustic property maps (1 square meter). Two extreme behaviors can be pointed out. On the one hand, velocity data are homogeneous and anisotropic in zones showing evidence of primary stratification and lithostatic compaction. On the other hand, data are heterogeneous and isotropic in zones exhibiting significant early diagenesis heterogeneities (“hardgrounds”). These results are thus linked to facies and diagenesis heterogeneities. Finally, at the decameter scale, seismic velocities clearly show an azimuthal anisotropy, mainly controlled by the occurrence of outcropping open joints from tectonic origin. Our study tends to highlight the crucial need to always characterise sedimentary facies, diagenesis evolution and structural overprint in carbonate reservoir rocks if one wants to interpret and correctly understand the multi-scale elastic properties of carbonates.