Imaging in cluttered acoustic waveguides

Abstract

We consider an inverse problem for the acoustic scalar wave equation in a cluttered waveguide. The problem is to find the location of sources or scatterers, given measurements of the pressure at a remote array of transducers. The sound speed in the waveguide fluctuates rapidly due to the presence of small inhomogeneities. These fluctuations, not known in detail, are viewed as clutter and modeled as a random process. We consider the regime of weak fluctuations, O(ε), whose effect on the wave-field accumulates after long propagation distances, O(1/ε 2). This recorded field is backpropagated using the homogeneous Green's function to search points where an image is formed. The multiple scattering due to clutter may lead to significant loss of coherence in the data, which in turn can cause instability and loss of resolution in the images. Parameters such as frequency band, depth of the waveguide, number of modes and aperture play a major role in the resolution and stability of the resulting images.