Novel finite-element-based subsurface imaging algorithms

Through an unconventional use of the finite-element method, we have developed a new class of wave equation-based subsurface imaging algorithms. These methods, which are based on the recently developed arbitrarily wide-angle wave equations (AWWE) [M.N. Guddati, Arbitrarily wide-angle wave equations for complex media, Comput. Methods Appl. Mech. Eng. 195(1–3), 63–93], employ the finite-element concepts not just to solve, but to derive the governing equations of the imaging problem. The authors have successfully applied the AWWE imaging algorithms to both acoustic and elastic media. These implementations of AWWE imaging algorithms are discussed here, and the role of finite elements in their derivation is depicted. The stability of the AWWE imaging methods is analytically studied, and their accuracy is shown through numerical impulse responses. Finally, the effectiveness of the methods is illustrated using various synthetic problems for both acoustic and elastic media.