Tomographic imaging of opaque and low-contrast objects in range-independent waveguides

A feasibility study is presented for acoustic tomographic imaging of arbitrarily shaped objects in range-independent oceanic waveguides. One of the main obstacles in the efficient use of tomographic imaging is that tomographic systems usually allow for a number of different independent solutions which satisfy the same systems of equations. This adverse property of acoustic tomography is especially pronounced in underdetermined systems characterized by null spaces of tomographic matrices which relate measured data to an unknown sound-speed distribution. In fact, acoustic tomography is usually underdetermined and the null space problem becomes critical in many applications. Acoustic tomography in many instances yields blurred images precluding its efficient use for mapping underwater objects in oceanic waveguides. How to improve the resolving power of tomographic imagery in waveguides is shown. A new technique based on the sliding window approach is suggested which uses constrained traveltime inversion. The method will be tested on mapping opaque and low-contrast acoustic objects placed in range-independent waveguides. The method is fast since it does not directly invert tomographic matrices of large rank but instead carries out summation over nonzero elements of tomographic matrices. It can be proved that constrained inversion compensates for limited angular aperture recording and thus can be applied to practical problems with incomplete angular aperture. This work is limited to processing of transmitted signals. A separate study will be devoted to the analysis of reflection data.