151 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
Selective imaging of extended reflectors in a two-dimensional waveguide
We consider the problem of selective imaging extended reflectors in waveguides using the response matrix of the scattered field obtained with an active array. Selective imaging amounts to being able to focus at the edges of a reflector which typically give raise to weaker echoes than those coming from its main body. To this end, we propose a selective imaging method that uses projections on low rank
subspaces of a weighted modal projection of the array response matrix, . We analyze
theoretically our imaging method for a simplified model problem where the scatterer is a vertical one-dimensional perfect reflector. In this case, we show that the
rank of equals the size of the reflector devided by the cross-range array resolution which is for an array spanning the whole depth of the waveguide. We also derive analytic expressions for the singular vectors of which allows us to show how selective imaging can be achieved. Our numerical simulations are in very good
agreement with the theory and illustrate the robustness of our imaging functional for reflectors of various shapes
Simulation of seismic response in a city-like environment
We study the seismic response of idealized 2D cities, constituted by non
equally-spaced, non equally-sized homogenized blocks anchored in a soft layer
overlying a hard half space. The blocks and soft layer are occupied by
dissipative media. To simulate such response, we use an approximation of the
viscoelastic modulus by a low-order rational function of frequency and
incorporate this approximation into a first-order-in-time scheme. Our results
display spatially-variable, strong, long-duration responses inside the blocks
and on the ground, which qualitatively match the responses observed in some
earthquake-prone cities of Mexico, France, the USA, etc.Comment: 22 pages, 8 figures, submitted to SDE
Signal to noise ratio analysis in virtual source array imaging
We consider correlation-based imaging of a reflector located on one side of a passive array where
the medium is homogeneous. On the other side of the array the illumination by remote impulsive sources
goes through a strongly scattering medium. It has been shown in [J. Garnier and G. Papanicolaou, Inverse Problems 28 (2012), 075002] that
migrating the cross correlations of the passive array gives an image whose resolution is as good as if
the array was active and the array response matrix was that of a homogeneous medium.
In this paper we study the signal to noise ratio of the image as a function of statistical properties of the
strongly scattering medium, the signal bandwidth and the source and passive receiver array characteristics.
Using a Kronecker model for the strongly scattering medium we show that image resolution is as
expected and that the signal to noise ratio can be computed in an essentially explicit way. We
show with direct numerical simulations using full wave propagation solvers in random media that
the theoretical predictions based on the Kronecker model are accurate
Synthetic aperture imaging with intensity-only data
We consider imaging the reflectivity of scatterers from intensity-only data
recorded by a single moving transducer that both emits and receives signals,
forming a synthetic aperture. By exploiting frequency illumination diversity,
we obtain multiple intensity measurements at each location, from which we
determine field cross-correlations using an appropriate phase controlled
illumination strategy and the inner product polarization identity. The field
cross-correlations obtained this way do not, however, provide all the missing
phase information because they are determined up to a phase that depends on the
receiver's location. The main result of this paper is an algorithm with which
we recover the field cross-correlations up to a single phase that is common to
all the data measured over the synthetic aperture, so all the data are
synchronized. Thus, we can image coherently with data over all frequencies and
measurement locations as if full phase information was recorded
Signal to Noise Ratio estimation in passive correlation-based imaging
We consider imaging with passive arrays of sensors using as illumination
ambient noise sources. The first step for imaging under such circumstances is
the computation of the cross correlations of the recorded signals, which have
attracted a lot of attention recently because of their numerous applications
in seismic imaging, volcano monitoring, and petroleum prospecting. Here, we
use these cross correlations for imaging reflectors with travel-time
migration. While the resolution of the image obtained this way has been
studied in detail, an analysis of the signal-to-noise ratio (SNR) is
presented in this paper along with numerical simulations that support the
theoretical results. It is shown that the SNR of the image inherits the SNR
of the computed cross correlations and therefore it is proportional to the
square root of the bandwidth of the noise sources times the recording
time. Moreover, the SNR of the image is proportional to the array size. This
means that the image can be stabilized by increasing the size of the array
when the recorded signals are not of long duration, which is important in
applications such as non-destructive testing
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