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 ...

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