SEISMIC ANISOTROPY OF FRACTURED ROCK

A simple method for including the effects of geologically realistic fr actures on the seismic propagation through fractured rocks can be obta ined by writing the effective compliance tenser of the fractured rock as the sum of the compliance tenser of the unfractured background rock and the compliance tensors for each set of parallel fractures or alig ned fractures. The compliance tenser of each fracture set is derivable from a second rank fracture compliance tenser. For a rotationally sym metric set of fractures, the fracture compliance tenser depends on onl y two fracture compliances, one controlling fracture compliance normal , the other, tangential, to the plane of the fractures. The stiffness tenser, which is more useful in the consideration of elastic wave prop agation through rocks, can then be obtained by inversion. The componen ts of the excess fracture compliance tenser represent the maximum amou nt of information that can be obtained from seismic data. If the backg round rock is isotropic and the normal and shear compliance of each fr acture are equal, although different from those of other fractures, th e effective elastic behavior of the fractured rock is orthorhombic for any orientation distribution of fractures. A comparison of the theory with recent ultrasonic experiments on a simulated fractured medium sh ows near equality of the normal and shear compliance for the case of a ir-filled fractures.