Seismic characterization of multiple fracture sets: Does orthotropy suffice?

As geophysicists rely increasingly on effective media theories to characterize naturally fractured reservoirs, they become more and more interested in evaluating the accuracy of different theories, estimating their limits of applicability, and assessing their usefulness for practice. With this in mind, we compare two popular seismological theories of Hudson and Schoenberg with the theory of Kachanov developed in the context of mechanics of materials. By performing finite-element simulations of effective media for models that contain several sets of nonintersecting, circular, vertical fractures embedded in otherwise isotropic host rock, we examine the accuracy of these theories. Our numeric study reveals that predictions of both the first- and second-order Hudson's theories are typically inferior to those of others. especially when the fractures are dry. While, on average, the theories of Schoenberg and Kachanov fit finite-element computations with comparable accuracy, the latter appears to be more useful for fracture characterization. The reason is that it correctly predicts the proximity of crack-induced anisotropy to orthotropy, whereas the other theories do not. Kachanov's results not only yield approximate effective orthotropy regardless of the number of fracture sets, their crack densities, and orientations, but they also lead to a substantially reduced number of independent parameters that govern the effective stiffnesses. This number is only four for dry cracks, compared to nine required for general orthorhombic media. These four quantities can be chosen as two Lame constants of the isotropic background and two principal crack densities. If fractures are filled with a compressible fluid, the number of independent parameters increases. After numeric verification of the accuracy of crack-induced orthotropy, we invert the NMO ellipses and zero-offset traveltimes of P-waves and two split shear waves for the parameters characterizing multiple fracture sets. Our inversion reveals the fracture parameters that can be unainbiguously estimated from multiazimuth, multicomponent surface reflection data.