A ray perturbation method for the acoustic attenuating transversely isotropic eikonal equation

Abstract

Modeling complex-valued traveltimes is helpful for developing attenuation-associated techniques for seismic data processing. Transverse isotropy can explain the directional variation of velocity- and attenuation-anisotropy of long-wavelength seismic waves in many sedimentary rocks. The acoustic attenuating transversely isotropic eikonal equation can be used to accurately calculate P-wave complex-valued traveltimes under such a geological condition. However, no ray tracing system for this eikonal equation can be found in the literature until now. We present a ray perturbation method to solve this eikonal equation. Unlike all existing ray perturbation methods, our newly proposed method does not perturb the exact ray tracing system but splits the acoustic attenuating transversely isotropic eikonal equation into a nonlinear partial differential equation and a first-order partial differential equation. These two partial differential equations can be solved by the method of characteristics. This gives rise to two sets of ray tracing equations for the real and imaginary parts ofthe complex-valued traveltimes, respectively. Both sets of ray tracing equations share the same ray path, which allows us to merge them into a complete ray tracing system for the complex-valued traveltimes. Numerical examples are used to demonstrate the high accuracy of the newly proposed ray tracing system, analyze the complex-valued traveltimes of divingP-waves, and compare the modeled complex-valued traveltimes with those extracted from constant-Q viscoelastic waveforms.