Modeling, evaluation, and asymptotic analysis of attenuation anisotropy

Abstract

Seismic attenuation is sensitive to the physical properties of the subsurface, which makes attenuation analysis a useful tool for reservoir characterization. In this thesis, I present algorithms for estimating directionally dependent attenuation coefficients and perform asymptotic and numerical analysis of wave propagation in attenuative anisotropic media. First, I introduce a methodology to estimate the S-wave interval attenuation coefficient by extending the layer-stripping method of Behura and Tsvankin (2009) to mode-converted (PS) waves. Kinematic reconstruction of pure shear (SS) events in the target layer and the overburden is performed by combining velocity-independent layer stripping with the PP+PS=SS method. Then, application of the spectral-ratio method and the dynamic version of velocity-independent layer stripping to the constructed SS reflections yields the S-wave interval attenuation coefficient in the target layer. The attenuation coefficient estimated for a range of source-receiver offsets can be inverted for the interval attenuation-anisotropy parameters. The method is tested on synthetic data generated with the anisotropic reflectivity method for layered VTI (transversely isotropic with a vertical symmetry axis) media and vertical symmetry planes of orthorhombic media. Then, I analyze a cross-hole data set generated by perforation shots set off in a horizontal borehole to induce hydraulic fracturing in a tight gas reservoir. The spectral-ratio method is applied to pairs of traces to set up a system of equations for directionally-dependent effective attenuation. Although the inversion provides clear evidence of attenuation anisotropy, the narrow range of propagation directions impairs the accuracy of anisotropy analysis. The observed variations of the attenuation coefficient between different perforation stages appear to be related to changes in the medium due to hydraulic fracturing and stimulation. Important insights into point-source radiation in attenuative anisotropic media can be gained by applying asymptotic methods. I derive the asymptotic Green's function in homogeneous, attenuative, arbitrarily anisotropic media using the steepest-descent method. The saddle-point condition helps describe the behavior of the far field slowness and group-velocity vectors and evaluate the inhomogeneity angle (the angle between the real and imaginary parts of the slowness vector). The results from the asymptotic analysis are compared with those from the ray-perturbation method for P-waves in TI media. Finally, I address the problem of efficient viscoelastic modeling in heterogeneous anisotropic media. The Kirchhoff scattering integral is employed to generate reflected P-waves, with the required Green's functions computed by summation of Gaussian beams. The influence of attenuation on the Gaussian beams is incorporated using ray-perturbation theory. The method is applied to generate synthetic data from a highly attenuative VTI medium above a horizontal reflector and a structurally complex acoustic model with a salt body.