Synthesis of multicomponent quasi-P and converted quasi-P-S seismograms for intersecting fracture systems

Dynamic ray shooting with interpolation is an economical way of computing a pproximate Green's functions in 3-D heterogeneous anisotropic media. The am plitudes, traveltimes, and polarizations of the reflected rays arriving at the surface are interpolated to synthesize three-component seismograms at t he desired recording points. The algorithm is applied to investigate kinema tic quasi-P-wave propagation and converted quasi-P-S-wave splitting variati ons produced in reflections from the bottom of a layer containing two sets of intersecting dry vertical fractures as a function of the angle between t he fracture sets and of the intensity of fracturing. An analytical expressi on is derived for the stiffness constant C-16 that extends Hudson's second- order scattering theory to include tetragonal-2 symmetry systems. At any offset, the amount of splitting in nonorthogonal (orthorhombic symme try) intersecting fracture sets is larger than in orthogonal (tetragonal-1 symmetry) systems, and it increases nonlinearly as a function of the intens ity of fracturing as offset increases. Such effects should be visible in fi eld data, provided that the dominant frequency is sufficiently high and the offset is sufficiently large. The amount of shear-wave splitting at vertical incidence increases nonlinea rly as a function of the intensity of fracturing and increases nonlinearly from zero in the transition from tetragonal-1 anisotropy through orthorhomb ic to horizontal transverse isotropy; the latter corresponds to the two cra ck systems degenerating to one. The zero shear-wave splitting corresponds t o a singularity, at which the vertical velocities of the two quasi-shear wa ves converge to a single value that is both predicted theoretically and ill ustrated numerically. For the particular case of vertical fractures, there is no P-to-S conversio n of vertically propagating (zero-offset) waves. If the fractures are not v ertical, the normal incidence P-to-S reflection coefficient is not zero and thus is a potential diagnostic of fracture orientation.