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17
Inverse electromagnetic scattering models for sea ice,” this issue
"... Abstract—Recent advances in forward modeling of the electromagnetic scattering properties of sea ice are presented. In particular, the principal results include the following: 1) approximate calculations of electromagnetic scattering from multilayer random media with rough interfaces, based on the ..."
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Abstract—Recent advances in forward modeling of the electromagnetic scattering properties of sea ice are presented. In particular, the principal results include the following: 1) approximate calculations of electromagnetic scattering from multilayer random media with rough interfaces, based on the distorted Born approximation and radiative transfer (RT) theory; 2) comprehensive theory of the effective complex permittivity of sea ice based on rigorous bounds in the quasistatic case and strong fluctuation theory in the weakly scattering regime; 3) rigorous analysis of the Helmholtz equation and its solutions for idealized sea ice models, which has led in the one dimensional (1D) case to nonlinear generalizations of classical theorems in Fourier analysis.
Optimal acoustic measurements
 SIAM J. Appl. Math
"... We consider the problem of obtaining information about an inaccessible halfspace from acoustic measurements made in the accessible halfspace. If the measurements are of limited precision, some scatterers will be undetectable because their scattered fields are below the precision of the measuring i ..."
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We consider the problem of obtaining information about an inaccessible halfspace from acoustic measurements made in the accessible halfspace. If the measurements are of limited precision, some scatterers will be undetectable because their scattered fields are below the precision of the measuring instrument. How can we make measurements that are optimal for detecting the presence of an object? In other words, what incident fields should we apply that will result in the biggest measurements? There are many ways to formulate this question, depending on the measuring instruments. In this paper we consider a formulation involving wavesplitting in the accessible halfspace: what downgoing wave will result in an upgoing wave of greatest energy? A closely related question arises in the case when we have a guess about the configuration of the inaccessible halfspace. What measurements should we make to determine whether our guess is accurate? In this case we compare the scattered field to the field computed from the guessed configuration. Again we look for the incident field that results in the greatest energy difference. We show that the optimal incident field can be found by an iterative process involving time reversal “mirrors”. For bandlimited incident fields and compactly supported scatterers, in the generic case this iterative process converges to a single timeharmonic field. In particular, the process automatically “tunes ” to the best frequency. This analysis provides a theoretical foundation for the frequencyshifting and pulsebroadening observed in certain computations [3] and timereversal experiments [14] [15].
A globally convergent numerical method for a Coefficient Inverse Problem with backscattering data
, 2010
"... A survey of recent results of the authors is presented. This survey is short due to space limitations. A Coefficient Inverse Problem for a hyperbolic PDE with backscattering data is considered. A globally convergent numerical method for this problem is presented. Analytical results are supported by ..."
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A survey of recent results of the authors is presented. This survey is short due to space limitations. A Coefficient Inverse Problem for a hyperbolic PDE with backscattering data is considered. A globally convergent numerical method for this problem is presented. Analytical results are supported by computational ones. 1
The inverse Robin boundary value problem in a halfspace. arXiv:1311.6947
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Recovery Of Surface Parameters From SteppedFrequency Radar Returns
"... This paper discusses a method for using the reflected signal from a steppedfrequency radar system to obtain the electrical permittivity and conductivity in a thin layer at the flat surface of a (possibly inhomogeneous) body. The method is based on a bandlimited version of geometrical optics. 1. I ..."
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This paper discusses a method for using the reflected signal from a steppedfrequency radar system to obtain the electrical permittivity and conductivity in a thin layer at the flat surface of a (possibly inhomogeneous) body. The method is based on a bandlimited version of geometrical optics. 1. INTRODUCTION. This work is motivated by the problem of remote sensing of sea ice [A]. There are several reasons for interest in this topic. First, it is hoped that remote electromagnetic measurements will provide information about the electric properties, and then it is hoped that knowledge of the electric properties can eventually be translated into information about the ice's physical properties. Knowledge of these properties would, in turn, be very useful as an aid to ship navigation and other operations in icecovered regions, such as landing planes on ice. Another reason for interest in sea ice is its importance in global climate models. Because of the remoteness of polar regions, satel...
An Inverse Boundary Value Problem for the Magnetic Schrödinger Operator on a Half Space
, 2012
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Coefficient Inverse Problems for Imaging Inhomogeneities
"... How can we differentiate between an underground stone and a land mine? We discuss a class of methods for solving such problems. This class of methods concerns globally convergent numerical methods for Coefficient Inverse Problems, unlike conventional locally convergent algorithms. Numerical results ..."
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How can we differentiate between an underground stone and a land mine? We discuss a class of methods for solving such problems. This class of methods concerns globally convergent numerical methods for Coefficient Inverse Problems, unlike conventional locally convergent algorithms. Numerical results are presented modeling imaging of the spatially distributed dielectric permittivity function in an environment where antipersonnel land mines are embedded along with stones. While these results are concerned with the first generation of globally convergent algorithms, images obtained by the most recent second generation are also presented for a generic case of imaging of the dielectric permittivity function. The mathematical apparatus is sketched only very briefly with references to corresponding publications. 1
A posteriori error estimates for the adaptivity technique for the Tikhonov functional and global convergence for a coefficient inverse problem
, 2009
"... A synthesis of a globally convergent numerical method for a coefficient inverse problem and the adaptivity technique is presented.
First, the globally convergent method provides a good approximation for the unknown coefficient. Next, this approximation is refined via the adaptivity technique.
The ..."
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A synthesis of a globally convergent numerical method for a coefficient inverse problem and the adaptivity technique is presented.
First, the globally convergent method provides a good approximation for the unknown coefficient. Next, this approximation is refined via the adaptivity technique.
The analytical effort is focused on a posteriori error estimates for the adaptivity.
A numerical test is presented.
A globally convergent numerical method and adaptivity for a hyperbolic coefficient inverse problem
, 2009
"... A globally convergent numerical method for a multidimensional Coefficient Inverse Problem for a hyperbolic equation is presented.
It is shown that this technique provides a good starting point for the socalled finite element adaptive method (adaptivity).
This leads to a natural twostage numerica ..."
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A globally convergent numerical method for a multidimensional Coefficient Inverse Problem for a hyperbolic equation is presented.
It is shown that this technique provides a good starting point for the socalled finite element adaptive method (adaptivity).
This leads to a natural twostage numerical procedure, which synthesizes both these methods.
Numerical examples are presented.