Elastic dispersion and attenuation anisotropy of clay in shales

ABSTRACT Anisotropic shales are an important component of sedimentary basins and exhibit seismic velocity and attenuation that vary with frequency and direction of wave propagation. A micromechanical model of the clay phase in shales provides insight into the frequency variation of velocity, attenuation, and the real and imaginary parts of the complex elastic moduli. This model consists of domains of aligned anisotropic clay platelets each surrounded by a softer viscoelastic interparticle medium representing clay-bound water, contacts between clay particles, and electrochemical and frictional interactions between platelets. With axis x3 perpendicular to the aligned platelets, the in-plane complex moduli C11*,C12*,C66* of a domain display little dispersion for small platelet aspect ratios, whereas the out-of-plane moduli C33*,C13*,C55* are significantly dispersive, with the real parts all increasing with frequency. As the aspect ratio increases, all moduli become significantly dispersive. The off-diagonal modulus C13* may exhibit negative dispersion at sufficiently high aspect ratios. Thomsen anisotropy parameters ε, γ, and δ are significantly dispersive. Although ε and γ are positive at all frequencies, the sign of δ may change as the aspect ratio and frequency vary. This sensitivity may help explain why the sign of δ may be different for different shales and why ultrasonic measurements of δ often give positive values, whereas low-frequency measurements sometimes give negative values.