Novel Methods for Acoustic and Elastic Wave-Based Subsurface Imaging

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Title: Novel Methods for Acoustic and Elastic Wave-Based Subsurface Imaging
Author: Heidari, Amir Homayoun
Advisors: M. Shamimur Rahman, Committee Member
C. C. David Tung, Committee Member
Murthy N. Guddati, Committee Chair
Richard Y. Kim, Committee Member
Abstract: Novel, accurate and computationally efficient methods for wave-based subsurface imaging in acoustic and elastic media are developed. The methods are based on Arbitrarily Wide-Angle Wave Equations (AWWE), which are highly-accurate space-domain one-way wave equations, formulated in terms of displacement components. Main contributions of this research are as follows. (I) Acoustic-AWWE Imaging, a new time-domain migration technique that is highly accurate for imaging steep dips in heterogeneous media. Similar in form to conventional 15° equation, the acoustic AWWE is implemented using an efficient double-marching explicit finite-difference scheme. Its accuracy and efficiency is studied both analytically and through numerical experiments. The method is able to achieve highly accurate images with only a few times the computational cost of the conventional low-order methods. (II) A new class of highly-accurate Absorbing Boundary Conditions (ABCs) for modeling and imaging with high-order one-way wave equations and parabolic equations. These ABCs, are developed using special imaginary-length finite elements. They effectively absorb the incident wave front and generate artifact-free images with as few as three absorbing layers. They are essential tools in imaging in truncated domains and underwater acoustics. (III) Elastic-AWWE imaging: The first high-order space-domain displacement-based elastic imaging method is developed in this research. The method, which is applicable to complex elastic media, is implemented using a unique downward continuation technique. At each depth step, a half-space is attached to the physical layer to simulate one-way propagation. The half-space is effectively approximated using special imaginary-length finite elements. The method is eventually implemented in frequency-space domain using a finite difference method. Numerical instabilities due to improper mapping of complex wave modes are suppressed by rotating the AWWE parameters in complex wavenumber plane thus adjusting its mapping properties. Effectiveness of the method is illustrated through analytical studies and numerical experiments in homogeneous and heterogeneous elastic media.
Date: 2005-04-29
Degree: PhD
Discipline: Civil Engineering

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