Deposits of clastic carbonate-dominated (calciclastic) sedimentary slope systems in the rock record have been identified mostly as linearly-consistent carbonate apron deposits, even though most ancient clastic carbonate slope deposits fit the submarine fan systems better. Calciclastic submarine fans are consequently rarely described and are poorly understood. Subsequently, very little is known especially in mud-dominated calciclastic submarine fan systems. Presented in this study are a sedimentological core and petrographic characterisation of samples from eleven boreholes from the Lower Carboniferous of Bowland Basin (Northwest England) that reveals a >250 m thick calciturbidite complex deposited in a calciclastic submarine fan setting. Seven facies are recognised from core and thin section characterisation and are grouped into three carbonate turbidite sequences. They include: 1) Calciturbidites, comprising mostly of highto low-density, wavy-laminated bioclast-rich facies; 2) low-density densite mudstones which are characterised by planar laminated and unlaminated muddominated facies; and 3) Calcidebrites which are muddy or hyper-concentrated debrisflow deposits occurring as poorly-sorted, chaotic, mud-supported floatstones. These

Phd by thesis

Introduction.- The Helmholtz Equation.- Direct Acoustic Obstacle Scattering.- III-Posed Problems.- Inverse Acoustic Obstacle Scattering.- The Maxwell Equations.- Inverse Electromagnetic Obstacle Scattering.- Acoustic Waves in an Inhomogeneous Medium.- Electromagnetic Waves in an Inhomogeneous Medium.- The Inverse Medium Problem.-References.- Index

Inverse Acoustic and Electromagnetic Scattering Theory

This paper deals with the fractional Sobolev spaces W s;p . We analyze the relations among some of their possible denitions and their role in the trace theory. We prove continuous and compact embeddings, investigating the problem of the extension domains and other regularity results. Most of the results we present here are probably well known to the experts, but we believe that our proofs are original and we do not make use of any interpolation techniques nor pass through the theory of Besov spaces. We also present some counterexamples in non-Lipschitz domains.

/pdf/hitchhiker-s-guide-to-the-fractional-sobolev-spaces-irm2sao95g.pdf

Hitchhiker's guide to the fractional Sobolev spaces

We present a review of methods for the forward and inverse problems in optical tomography. We limit ourselves to the highly scattering case found in applications in medical imaging, and to the problem of absorption and scattering reconstruction. We discuss the derivation of the diffusion approximation and other simplifications of the full transport problem. We develop sensitivity relations in both the continuous and discrete case with special concentration on the use of the finite element method. A classification of algorithms is presented, and some suggestions for open problems to be addressed in future research are made.

https://iopscience.iop.org/article/10.1088/0266-5611/15/2/022/pdf

Optical tomography in medical imaging

The package REGULARIZATION TOOLS consists of 54 Matlab routines for analysis and solution of discrete ill-posed problems, i.e., systems of linear equations whose coefficient matrix has the properties that its condition number is very large, and its singular values decay gradually to zero. Such problems typically arise in connection with discretization of Fredholm integral equations of the first kind, and similar ill-posed problems. Some form of regularization is always required in order to compute a stabilized solution to discrete ill-posed problems. The purpose of REGULARIZATION TOOLS is to provide the user with easy-to-use routines, based on numerical robust and efficient algorithms, for doing experiments with regularization of discrete ill-posed problems. By means of this package, the user can experiment with different regularization strategies, compare them, and draw conclusions from these experiments that would otherwise require a major programming effert. For discrete ill-posed problems, which are indeed difficult to treat numerically, such an approach is certainly superior to a single black-box routine. This paper describes the underlying theory gives an overview of the package; a complete manual is also available.

/pdf/regularization-tools-a-matlab-package-for-analysis-and-3c2tydm07j.pdf

REGULARIZATION TOOLS: A Matlab package for analysis and solution of discrete ill-posed problems

Preface to the Classics Edition Preface Symbols 1. The Riesz-Fredholm theory for compact operators 2. Regularity properties of surface potentials 3. Boundary-value problems for the scalar Helmholtz equation 4. Boundary-value problems for the time-harmonic Maxwell equations and the vector Helmholtz equation 5. Low frequency behavior of solutions to boundary-value problems in scattering theory 6. The inverse scattering problem: exact data 7. Improperly posed problems and compact families 8. The determination of the shape of an obstacle from inexact far-field data 9. Optimal control problems in radiation and scattering theory References Index.

Integral equation methods in scattering theory

This paper is concerned with the development of an inversion scheme for two-dimensional inverse scattering problems in the resonance region which does not use nonlinear optimization methods and is relatively independent of the geometry and physical properties of the scatterer It is assumed that the far field pattern corresponding to observation angle and plane waves incident at angle is known for all  From this information, the support of the scattering obstacle is obtained by solving the integral equation where k is the wavenumber and is on a rectangular grid containing the scatterer The support is found by noting that is unbounded as approaches the boundary of the scattering object from inside the scatterer Numerical examples are given showing the practicality of this method

https://iopscience.iop.org/article/10.1088/0266-5611/12/4/003/pdf

A simple method for solving inverse scattering problems in the resonance region

A major problem in the use of ultrasound or microwaves for purposes of nondestructive testing or medical imaging is the computational complexity of solving the inverse scattering problem that arises in such applications. This is due to the fact that in order to achieve satisfactory resolution and sufficient penetration of the wave into the material it is often necessary to use frequencies in the resonance region. In this case the inverse scattering problem is not only improperly posed but also nonlinear and even in the case of two dimensions the time needed to solve such problems can be prohibitive. To date the time consuming nature of the problem has mainly been dealt with by the introduction of various innovative schemes that avoid the use of volume integral equations and instead rely on finite difference or finite element methods (cf. [5], [8]). However, for large scale problems (for example those involving imaging of the human body) the problem of computational complexity remains a serious problem for any practitioner. In this paper we would like to propose a different approach to this problem that, although still in its infancy, has the promise of providing rapid solutions to a number of inverse scattering problems of practical significance.

qualitative-methods-in-inverse-scattering-theory

We survey the linear sampling method for solving the inverse scattering problem for time-harmonic electromagnetic waves at fixed frequency. We consider scattering by an obstacle as well as scattering by an inhomogeneous medium both in and . Included in our discussion is the use of regularization methods for ill-posed problems and numerical examples in both two and three dimensions.

https://iopscience.iop.org/article/10.1088/0266-5611/19/6/057/pdf

David Colton

Papers

Inverse Acoustic and Electromagnetic Scattering Theory

Integral equation methods in scattering theory

A simple method for solving inverse scattering problems in the resonance region

qualitative-methods-in-inverse-scattering-theory

The linear sampling method in inverse electromagnetic scattering theory