Modeling, imaging and waveform-inversion in attenuative anisotropic media

Seismic attenuation, which is often anisotropic, has a profound influence on wave propagation and seismic processing. In addition to application of attenuation coefficients in lithology and fluid discrimination, compensation for angle-dependent attenuation and velocity dispersion is critically important in amplitude-variation-with-offset (AVO) analysis and imaging. In this thesis, I develop a waveform-inversion (WI) methodology for attenuation estimation, as well as an attenuationcompensated time-reversal (TR) imaging algorithm, for transversely isotropic media with a vertical symmetry axis (VTI). The attenuation model is assumed to have the same symmetry as the velocity function and is described by the Thomsen-style attenuation parameters. First, the thesis introduces a time-domain finite-difference modeling technique for viscoelastic VTI media. Within the framework of the generalized standard linear solid (GSLS) model, I extend to anisotropic media the so-called “⌧ -method”, which produces a nearly constant quality-factor matrix Q ij within a specified frequency range. Then I present a system of anisotropic viscoelastic wave equations which include the memory variables that facilitate numerical implementation. Numerical examples for a range of TI models with different structural complexity confirm the accuracy of the proposed modeling scheme and illustrate the influence of attenuation and attenuation anisotropy on multicomponent wavefields. Then this wavefield propagator is employed in a waveform-inversion algorithm for attenuation analysis in heterogeneous VTI media. Model updating is performed with the conventional `2-norm objective function, and the inversion gradients for the viscoelastic parameters are derived from the adjoint-state method. Four VTI attenuation parameters for Pand SV-waves are updated simultaneously with a quasi-Newton optimization algorithm. The influence of velocity errors is mitigated by using a local-similarity technique. Transmission tests for a model with Gaussian anomalies in the VTI attenuation parameters and a reflection experiment for a modified BP TI section validate the developed WI algorithm. iii The performance of waveform inversion may be strongly influenced by the accuracy of the estimated source wavelet. To mitigate the cross-talk between the attenuation parameters and source signature, I extend source-independent waveform inversion (SIWI) to anisotropic attenuative media. The corresponding objective function evaluates the difference between two convolved data sets that include reference traces from the observed and simulated data. As illustrated by numerical examples, the proposed SIWI method can produce sufficiently accurate attenuation parameters (albeit with reduced resolution) even for a substantially distorted source wavelet. Accounting for attenuation anisotropy is essential in implementing attenuation-compensated time-reversal (TR) imaging for locating microseismic sources in unconventional shale reservoirs. TR imaging is carried out with a viscoelastic VTI propagator based on fractional Laplacians, which is designed to decouple the influence of dissipation from that of dispersion. The obtained viscoelastic equations make it possible to compensate for anisotropic attenuation and preserve time symmetry during back-propagation. The proposed Q-compensated TR imaging algorithm is tested on synthetic microseismic data from 2D VTI media. Taking attenuation anisotropy into account produces superior source images and more accurate excitation times compared to those obtained by purely elastic back-propagation or by the TR algorithm with isotropic Q-compensation.