We use numerical simulations to calculate the elastic properties of layered and fractured rocks using ultrasonic, borehole acoustics, and static measurements. The difference between static and dynamic properties vary with layer thickness, irregularities in the layer boundaries, and the location and orientation of the fractures in cores. For periodically layered medium, we compare the elastic properties of formations with horizontal boundaries to wavy (low amplitude perturbation) and undulating (high amplitude perturbation) boundaries. The wavy layered medium is approximated using a vertically transversely isotropic model. However, when the amplitude of perturbation increases, the elastic properties depend on the angle between the wave propagation and the boundary of layers. For fractured media, we show that while dynamic properties are independent of the fracture location in the sample, static measurements depend on the distance between the fracture and strain gauges. Moreover, the elastic properties vary with fracture orientation and decrease for fracture inclination between 30 and 45 degrees.
Geomechanical properties of reservoir rocks are estimated using static and dynamic measurements and are used for geosteering, drilling, and hydraulic fracture applications (Yale, 1994). In anisotropic rocks, the measured static and dynamic elastic properties are different because of thin layers, fractures, and heterogeneities that are present in the rock (Massaro et al., 2017; Fjær, 2019).
While static measurements more accurately represent rock behavior in response to large strains (and stresses) (Yale, 1994), they are performed on a limited number of cores (Sakhaee-Pour and Li, 2019). When cores are not available, acoustic logs are used to obtain dynamic elastic properties of formations continuously along the wellbore. Static properties are then inferred from empirical correlations between static and dynamic measurements.
For example, Slota-Valim, 2015 showed that there exists a linear correlation between the static and dynamic elastic properties of the Lower Paleozoic shale formation. Massaro et al., 2017 showed that the Young Modulus (E) Edynamic > Estatic for the Vaca Mureta shale formation and that E and the stiffness coefficients (Cij) measured using static and dynamic measurements are correlated using linear functions.