2D Seismic Ray-Tracing of Multi-Arrivals in Viscoelastic Media for Seismic Tomography

Abstract

There are two ways for seismic wave modeling, which are the full-waveform modeling by solving the partial differential equation (PDE) of the displacement vector and the ray-tracing asymptotic approach by solving the Eikonal or ray PDE under the high-frequency assumption. The ray tracing is the fundamental part of seismic ray tomography which is a very vigorous method to image the subsurface structure of the earth. Meanwhile, the subsurface condition could be extremely heterogeneous as a result of varying density, grain, unconformity, pores, fractures, and fluids, constituting the model called viscoelastic anisotropic media (VEAM). However, the difficulty of seismic ray tracing in VEAM is the cumbersomeness and complexity of the traditional method using the complex-valued raypaths, and the biggest challenge of the ray tracing is the computation of the ray-velocity vectors for three seismic body wave modes, which are qP, qSV, and qSH in VEAM. This research bases on the real raypath instead of the complex-valued raypath and demonstrate five analytical methods, including three common methods (g-Hamiltonian, p-Hamiltonian, and explicit derivatives) and two novel methods (implicit c-derivative and g*-Hamiltonian) to compute the ray-velocity vectors for seismic ray tracing in VEAM. Through applications of these methods to various rocks, we found that only the g*-Hamiltonian method is valid for offering the ray-velocity vectors for the three body wave modes in VEAM, particularly, successfully overcomes the triplication or cusps of the qSV wavefronts in VEAM, where all other methods fail. Without the triplication or cusps, all the methods generate consistent results of the ray-velocity vectors for the three body wave modes. Furthermore, we applied the g*-Hamiltonian method to investigate the different components of the slowness vectors, such as traveltime-gradient components, homogeneous and inhomogeneous components, and their percentages of the magnitudes of the three body wave modes. The results of different rocks indicate that the magnitude ratios of the imaginary parts |𝑠 (𝐼) | to the real parts |𝑠 (𝑅) | of the slowness vectors are less than 10%, and the magnitude ratios of the inhomogeneous parts |𝑠 (⊥) | to the homogeneous parts |𝑠 (∥) | are less than 4%. If all the components of the Q-factor tensor are constant, the slowness vector becomes homogeneous (𝑠 (⊥)= 0), and the homogeneous components of the slowness vectors play a dominant role in the propagation and attenuation of seismic wave propagation in VEAM. Based on these findings, we developed two efficient and accurate methods, namely ‘homogeneous slowness-vector (HSV) approximations’ to compute the ray-velocity vectors in VEAM. The new approximations significantly reduce the runtime with high accuracies, and become applicable for seismic ray tracing for the multi-arrivals in VEAM. Finally, we have established the multi-arrival ray-tracing methodology and workflow using the g*-Hamiltonian method and the HSV approximations in heterogeneous viscoelastic TTI media.

Date of Award	Aug 2023
Original language	American English
Supervisor	Bing Zhou (Supervisor)