Innovative Butterfly-Compressed Microlocal Hadamard-Babich Integrators for Large-Scale High-Frequency Wave Modeling and Inversion in Variable Media

Michigan State University, East Lansing MI

Investigators

Abstract

This project develops and implements innovative fast algorithms for large-scale wave modeling and inversion. Waves are ubiquitous, for example, wireless signals are communicated in the form of electromagnetic waves, and ultrasound CT imaging is based on propagation of acoustic waves. In fact, wave simulation is a fundamental, growing technology in a variety of disciplines ranging from synthetic aperture radar, sonar, geophysical resources exploration, medical imaging, submarine detection, remote sensing and electronics to microscopy and nanotechnology. Developing fast algorithms for these fields and applications will serve the national interest very well in many aspects, such as advancing national health by providing fast algorithms for medical imaging and advancing national energy security by helping the U.S. petroleum industry maintain its edge in oil and gas exploration. One of the most challenging problems in computational wave propagation is how to carry out large-scale high frequency wave simulation efficiently and accurately, and the investigator will develop new fast butterfly-compressed integrator to address this crucial objective. To expand the educational impacts, the project will integrate the scientific discoveries with a series of short courses so that graduate students can be trained on the latest scientific tools. Interdisciplinary hands-on training will be developed for both undergraduate and graduate students, with an emphasis on increasing the diversity and participation of under-represented groups of students for STEM education. The project will design novel fast butterfly-compressed microlocal Hadamard-Babich (HB) integrators for large-scale high-frequency acoustic, electromagnetic, and elastic wave modeling and inversion motivated by industrial and military applications. The targeted problems for this scientific computing project are large-scale wave modeling and inverse problems with big data sets. The aimed model equations include high-frequency Helmholtz equations, Maxwell's equations, and elastic wave equations in inhomogeneous media in the presence of caustics. This project will foster breakthrough innovations in at least three theoretical and computational aspects. First, the new butterfly-compressed HB integrators will meet significant scientific challenges in large-scale high-frequency wave modeling and inversion in the presence of caustics. Second, significant advances will be made in developing novel butterfly compression and HB integrators for PDE-based Eulerian microlocal analysis and computational wave propagation. The new fast HB integrator is capable of producing uniform asymptotic solutions beyond caustics. Third, new butterfly-compressed HB integrators will provide efficient tools for many wave-related applications in inhomogeneous media, such as seismic imaging and inversion. New butterfly-compressed microlocal HB integrators will be developed for the first time for these applications. The new methodology generated by the project will have broad impacts on multiple scientific fields in both mathematics and engineering applications and will significantly improve the simulation capacities of large-scale wave propagation. 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.