This project concerns development of models for wave propagation in heterogeneous and random media. The work aims to: (i) advance the theory of multimode and strong scattering with an emphasis on situations where the clutter does not satisfy a separation of scales assumption, in particular using the theory of rough paths; and (ii) apply this theory to the use of incoherent waves for imaging in a cluttered environment, focusing on situations where direct application of time reversal does not work, but where related techniques using wave field correlations can be applied.
Many important physical phenomena involve waves propagating through heterogeneous media, such as sound waves in the ocean, seismic waves in the earth's crust, electromagnetic waves propagating through the atmosphere, or ultrasound probing the human body. A good understanding of how waves interact with the heterogeneity is crucial in applications like wireless communication, medical imaging, reflection seismology, remote sensing, atmospheric laser beam propagation, underwater communication, nondestructive testing, fiber optics, nano-technology, seismology, helioseismology, and astronomic imaging. Many, if not most, of the applications mentioned above do not fully exploit a mathematical description of waves in random media, partly because of the complexity of this description. Yet, modern techniques such as "time reversal" have shown that medium heterogeneity can improve performance. The general objective of the proposal is to further the theory for waves in clutter, the clutter modeled as a random medium, and show how an accurate description of incoherent waves can lead to new or enhanced technologies.
