14 research outputs found
Source localization in random acoustic waveguides
Mode coupling due to scattering by weak random inhomogeneities in waveguides leads to loss of coherence of wave fields at long distances of propagation. This in turn leads to serious deterioration of coherent source localization methods, such as matched field. We study with analysis and numerical simulations how such deterioration occurs and introduce a novel incoherent approach for long range source localization in random waveguides. It is based on a special form of transport theory for the incoherent fluctuations of the wave field. We study theoretically the statistical stability of the method and illustrate its performance with numerical simulations. We also show how it can be used to estimate the correlation function of the random fluctuations of the wave speed
Filtering Deterministic Layer Effects in Imaging
Sensor array imaging arises in applications such as nondestructive evaluation of materials
with ultrasonic waves, seismic exploration, and radar. The sensors probe a medium with
signals and record the resulting echoes, which are then processed to determine the location
and reflectivity of remote reflectors. These could be defects in materials such as voids,
fault lines or salt bodies in the earth, and cars, buildings, or aircraft in radar applications.
Imaging is relatively well understood when the medium through which the signals
propagate is smooth, and therefore nonscattering. But in many problems the medium is
heterogeneous, with numerous small inhomogeneities that scatter the waves. We refer to
the collection of inhomogeneities as clutter, which introduces an uncertainty in imaging
because it is unknown and impossible to estimate in detail. We model the clutter as a
random process. The array data is measured in one realization of the random medium,
and the challenge is to mitigate cumulative clutter scattering so as to obtain robust images
that are statistically stable with respect to different realizations of the inhomogeneities.
Scatterers that are not buried too deep in clutter can be imaged reliably with the coherent
interferometric (CINT) approach. But in heavy clutter the signal-to-noise ratio (SNR)
is low and CINT alone does not work. The “signal,” the echoes from the scatterers to be
imaged, is overwhelmed by the “noise,” the strong clutter reverberations. There are two
existing approaches for imaging at low SNR: The first operates under the premise that data
are incoherent so that only the intensity of the scattered field can be used. The unknown
coherent scatterers that we want to image are modeled as changes in the coefficients of
diffusion or radiative transport equations satisfied by the intensities, and the problem becomes
one of parameter estimation. Because the estimation is severely ill-posed, the results
have poor resolution, unless very good prior information is available and large arrays are
used. The second approach recognizes that if there is some residual coherence in the data,
that is, some reliable phase information is available, it is worth trying to extract it and
use it with well-posed coherent imaging methods to obtain images with better resolution.
This paper takes the latter approach and presents a first attempt at enhancing the SNR
of the array data by suppressing medium reverberations. It introduces filters, or annihilators of layer backscatter, that are designed to remove primary echoes from strong, isolated
layers in a medium with additional random layering at small, subwavelength scales. These
strong layers are called deterministic because they can be imaged from the data. However,
our goal is not to image the layers, but to suppress them and thus enhance the echoes
from compact scatterers buried deep in the medium. Surprisingly, the layer annihilators
work better than intended, in the sense that they suppress not only the echoes from the
deterministic layers, but also multiply scattered ones in the randomly layered structure.
Following the layer annihilators presented here, other filters of general, nonlayered
heavy clutter have been developed. We review these more recent developments and the
challenges of imaging in heavy clutter in the introduction in order to place the research
presented here in context. We then present in detail the layer annihilators and show with
analysis and numerical simulations how they work