Collaborative Research: Novel Microlocal-Analysis and Domain-Decomposition Based Fast Algorithms for Elastic Wave Modeling and Inversion in Variable Media

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Wave propagation is an important phenomenon in many science and engineering disciplines. Computational wave propagation has become a fundamental, vigorously growing technology in diverse disciplines, ranging from radar, sonar, seismic imaging, medical imaging, submarine detection, stealth technology, remote sensing and electronics to microscopy and nanotechnology. These applications are important in particular for the petroleum industry, medical imaging, and material sciences. One of the most challenging problems in computational wave propagation is how to carry out large-scale high frequency wave propagation efficiently and accurately. The investigators in this project will develop novel, fast algorithms for high frequency elastic wave propagation and inversion. In particular, they will focus on techniques including microlocal-analysis and domain-decomposition based fast Huygens sweeping methods and fast multiscale Gaussian beam methods to tackle this long-standing challenge. Graduate students will be involved and receive interdisciplinary training. The project is motivated by science and engineering applications, and it will foster innovations in several theoretical and computational aspects. The goal is to develop efficient and accurate Hadamard-Babich expansion based fast Huygens sweeping methods and multiscale Gaussian wavepacket transform based fast multiscale Gaussian beams for elastic wave propagation in variable media in the high frequency regime and in the presence of caustics. Several avenues of research will be pusrued. First, the proposed new methods will address the challenges in large-scale high-frequency elastic wave modeling and inversion in the presence of caustics. Second, advances will be made in developing novel Hadamard-Babich expansion, domain decomposition, and butterfly-algorithm based fast Huygens sweeping methods for partial differential equation-based Eulerian geometrical optics and computational wave propagation. Both the Hadamard-Babich expansion and domain-decomposition based fast Huygens sweeping method and the fast multiscale Gaussian beam method are capable of producing uniform asymptotic solutions beyond caustics for wave propagation in the high-frequency regime. Third, the new methods will provide efficient tools not used before for many elastic wave-related applications in inhomogeneous media, such as seismic imaging and inversion, and medical imaging and inversion.This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria.