Migration/inversion: think image point coordinates, process in acquisition surface coordinates

We present a first-principle method for quantitative modeling of optical energy flow and dissipation in thin-film (TF) light-emitting diodes (LEDs) based on highly general Green's function method. Unlike conventional models, the presented model simultaneously accounts for interference, near-field effects, and internal absorption in determining the radiance generated by a LED. We show that these effects have a profound influence on the efficiency of LEDs and strongly affect the light extraction efficiency (LEE) and the internal quantum efficiency. According to our results, the LEE of an InGaN-GaN TF-LED with untextured surfaces and typical active region (AR) thickness on the order of 10 nm is 67% while a LED with a thin AR exhibits only a LEE of 29%. Based on the numerical results, we discuss the factors that affect the overall efficiency and design considerations to optimize the structure of thin-film LEDs.

Xα-SW estimation of the degree of localization of 3d and 2p states in transition metal oxides

A computationally efficient model for fracture propagation and fluid flow in naturally fractured reservoirs

Many geophysical processes can be formulated in terms of the Green's functions of the wave equation. A process such as pre-stack Kirchhoff migration requires the estimation of the Green's function for every surface (source or receiver) location. The cost of calculating and storing the full Green's function is often prohibitive. Calculating one Green's function involves solving the full two-way wave equation for an impulsive source at each surface location. The storage required for the full Green's function is very large, the Green's function has an extra dimension, depth, compared to surface seismic data.

A novel, general Green's function technique for elastic spin-dependent\ntransport calculations is presented, which (i) scales linearly with system size\nand (ii) allows straightforward application to general tight-binding\nHamiltonians (spd in the present work). The method is applied to studies of\nconductance and giant magnetoresistance (GMR) of magnetic multilayers in CPP\n(current perpendicular to planes) geometry in the limit of large coherence\nlength. The magnetic materials considered are Co and Ni, with various\nnon-magnetic materials from the 3d, 4d, and 5d transition metal series.\nRealistic tight-binding models for them have been constructed with the use of\ndensity functional calculations. We have identified three qualitatively\ndifferent cases which depend on whether or not the bands (densities of states)\nof a non-magnetic metal (i) form an almost perfect match with one of spin\nsub-bands of the magnetic metal (as in Cu/Co spin valves); (ii) have almost\npure sp character at the Fermi level (e.g. Ag); (iii) have almost pure d\ncharacter at the Fermi energy (e.g. Pd, Pt). The key parameters which give rise\nto a large GMR ratio turn out to be (i) a strong spin polarization of the\nmagnetic metal, (ii) a large energy offset between the conduction band of the\nnon-magnetic metal and one of spin sub-bands of the magnetic metal, and (iii)\nstrong interband scattering in one of spin sub-bands of a magnetic metal. The\npresent results show that GMR oscillates with variation of the thickness of\neither non-magnetic or magnetic layers, as observed experimentally.\n

We apply the GGF (Generalized Green Function) method on a ferromagnet with magnetic impurities. In order to minimize the numerical calculations, we use Ising ferromagnet model. We are interested in temperatures around the phase transition in a ferromagnet, were Ising model gives real results which are often used in the literature. Investigations of a domain around the phase transition of a ferromagnet with impurities with the GGF method show that the phase transition is made on lower temperatures than in the case of ideal ferromagnet. In the point of phase transition, the derivative with respect to temperature of the ordering parameter is infinite as in ideal ferromagnet, bat this parameter does not vanish, it has a turning point.© (2000) COPYRIGHT SPIE--The International Society for Optical Engineering. Downloading of the abstract is permitted for personal use only.

Gaussian beams have been shown in some cases to provide smoother leading order asymptotic expansions of the solution of wave equations than classical ray theory provides. They do this through complex‐valued traveltime functions that describe the propagating wave in a tube around some central ray. Quadratic exponential decay orthogonal to the central ray arising from the imaginary part of the traveltime provides a "skin depth" to the ray tube. Gaussian beams also have complex‐valued amplitudes that avoid the vanishing ray Jacobians of classical ray theory in the neighborhood of caustics. By contrast, classical ray theory requires an extension to more general waveforms (Airy functions, for example) to describe the wavefield in the neighborhood of a caustic. Gaussian beam representations are influenced by the neighborhood of the ray through the sum over wavefields on nearby rays, whereas classical ray‐theory produces a solution that depends only on the medium heterogeneity along a single ray, up to second derivatives of those functions. Further, no special tracking of a KMAH index is necessary for the phase shift through caustics to be effected by the sum/integral over Gaussian beams. This note presents a hierarchy of ray methods starting from classical ray theory, followed by dynamic ray tracing and modeling in ray‐centered coordinates with real traveltime and amplitude and then with complex traveltime and amplitude leading to Gaussian beams. We introduce a sample application of the representations of wavefields—the Green's function—for source point and beam fan initial point coincident and non‐coincident. Thereafter, we show how these wavefield representations can be used in seismic migration/inversion (M/I) for the common‐shot configuration

Imaging is a field of mathematics and physics that aims to retrieve information about the internal structure of an object that can only be accessed on its boundary. Many imaging methods are based on the following principle: a source outside of the object emits a wave. The wave propagates through the object. Wherever the physical structure of the object changes, scattered waves are induced. These scattered waves are measured by receivers outside of the object, and these scattered data are used to invert for the interior composition of the medium under investigation. The Marchenko integral was originally introduced for one-dimensional inverse scattering problems in the context of quantum mechanics. It can be related to Green's functions and so-called focusing functions - fields that produce a focus when injected into a medium from a single side. About ten years ago, the Marchenko integral was extended to two and three dimensions. This paved the way for, e.g., the elimination of imaging artefacts due to multiple scattering and Green's function retrieval for virtual source locations. However, many questions about the full potential as well as the accuracy of the Marchenko equation in two and three dimensions remain unanswered. In this thesis we present a new derivation for the multidimensional Marchenko integral. Our derivation is based on a generalised framework for wavefield focusing and circumvents the limiting assumptions of the previous extension. As we use partial differential equations rather than integral equations to define focusing functions, it allows for new physical insights. For instance, our approach indicates that it is possible to model Marchenko-type focusing functions with a conventional wave equation. Ultimately, this enables us to study Marchenko-type focusing in different 2D and 3D media and learn about the accuracy of the concept. We present a straightforward modelling approach for 1D as well as a least-squares modelling approach for 2D and 3D. The latter suggests that the Marchenko integral might be inherently approximative in multiple dimensions. We also discuss Green's function retrieval with our newly derived Marchenko integral, i.e. without wavefield decomposition. This method allows for estimating Green's functions for virtual sources inside of the medium. While it requires single-sided scattering data and an estimate of the first arrival of the desired Green's function there is no need to have an actual source or receiver inside of the medium. Our results demonstrate that we can retrieve good estimates of the full-spectrum Green's functions, involving evanescent and refracted waves, which were believed to not be retrievable with the previously derived Marchenko integral. Ultimately, we discuss imaging with these Marchenko-based Green's functions. Being able to include measurements for virtual sources inside of the medium allows for a natural linearisation of the imaging problem. Thus, we use the Marchenko integral to linearise state-of-the-art imaging approaches, similar to full waveform inversion or least-squares reverse time migration, and estimate the scattering potential. Our Marchenko-based linearisation accounts for all orders of scattering and performs slightly better than a single-scattering approximation.

In this paper, we present general analytical formulas of the full-wave spectral domain Green's functions for arbitrarily multilayered dielectric media. The Green's functions are two scalar potentials created by a horizontal dipole, corresponding two electromagnetic modes, transverse magnetic and transverse electric modes to the normal direction of the layer plane. The analytical formulas in spectral domain have simple form and are applicable to arbitrary number of the dielectric layers. The derivation of the formulas employs a technique developed for the derivation of the electrostatic Green's function in multilayered media. The Green's functions used in the spectral domain approach are also presented.

General time-dependent Green's functions of line forces in a two-dimensional, anisotropic, elastic, and infinite solid

ABSTRACTLeast‐squares reverse time migration is often formulated as an iterative updating process, where estimating the gradient of the misfit function is necessary. Traditional time domain shot‐profile least‐squares reverse time migration is computationally expensive because computing the gradient involves solving the two‐way wave equation several times in every iteration. To reduce the computational cost of least‐squares reverse time migration, we propose a double‐plane‐wave least‐squares reverse time migration method based on a misfit function for frequency‐domain double‐plane‐wave data. In double‐plane‐wave least‐squares reverse time migration, the gradient is computed by multiplying frequency‐domain plane‐wave Green's functions with the corresponding double‐plane‐wave data residual. Because the number of plane‐wave Green's functions used for migration is relatively small, they can be pre‐computed and stored in a computer's discs or memory. We can use the pre‐computed plane‐wave Green's functions to obtain the gradient without solving the two‐way wave equation in each iteration. Therefore, the migration efficiency is significantly improved. In addition, we study the effects of using sparse frequency sampling and sparse plane‐wave sampling on the proposed method. We can achieve images with correct reflector amplitudes and reasonable resolution using relatively sparse frequency sampling and plane‐wave sampling, which are larger than that determined by the Nyquist theorem. The well‐known wrap‐around artefacts and linear artefacts generated due to under‐sampling frequency and plane wave can be suppressed during iterations in cases where the sampling rates are not excessively large. Moreover, implementing the proposed method with sparse frequency sampling and sparse plane‐wave sampling further improves the computational efficiency. We test the proposed double‐plane‐wave least‐squares reverse time migration on synthetic models to show the practicality of the method.

The theory for skeletonized least squares wave equation migration (LSM) is presented. The key idea is, for an assumed velocity model, the source‐side Green's function and the geophone‐side Green's function are computed by a numerical solution of the wave equation. Only the early‐arrivals of these Green's functions are saved and skeletonized to form the migration Green's function (MGF) by convolution. Then the migration image is obtained by a dot product between the recorded shot gathers and the MGF for every trial image point. The key to an efficient implementation of iterative LSM is that at each conjugate gradient iteration, the MGF is reused and no new finitedifference (FD) simulations are needed to get the updated migration image. It is believed that this procedure combined with phase‐encoded multi‐source technology will allow for the efficient computation of wave equation LSM images in less time than that of conventional reverse time migration (RTM).

We address in a recent gauge model of unparticles the issues that are important for consistency of a gauge theory, i.e., unitarity and the Ward identity of the physical amplitudes. We find that non-integrable singularities arise in physical quantities like the cross section and the decay rate from the gauge interactions of unparticles. We also show that the Ward identity is violated due to the lack of a dispersion relation for charged unparticles although the Ward–Takahashi identity for general Green functions is incorporated in the model. A previous observation that the contribution of the unparticle (with scaling dimension d) to the gauge boson self-energy is a factor (2−d) of the particle’s self-energy has been extended to the Green function of triple gauge bosons. This (2−d) rule may be generally true for Green functions for any number of points of the gauge bosons. This implies that the model would be trivial even as one that mimics certain dynamical effects on gauge bosons in which unparticles serve as an interpolating field.

An accurate earth model is key to any successful depth imaging effort. Full waveform inversion is an advanced velocity model building process which uses the full two way wave equation. Existing methods use a ray tracing approach to distribute velocity errors within the model. In this presentation, we will show examples of seismic data processed with the latest technology, including earth model building with full waveform inversion. Introduction The industry has moved to using two-way wave equation migrations(commonly known as reverse time migration), especially in areas of complex geology such as the salt bodies in the Gulf of Mexico and offshore Brazil. The velocity model, including velocity anisotropy, is key to any depth migration effort. The natural next step is to use the two-way wave equation for velocity model building. One of the most advanced tools for velocity model building using the two-way wave equation is Full Waveform Inversion(FWI). Full-waveform inversion uses computer intensive forward modeling of the seismic measurement combined with residual wavefield back propagation to iterate to a final velocity model, which can provide greater detail than tomographic ray tracing approaches. Velocity inversion using full waveform inversion has been used on a number of projects around the world including the GOM, Brazil and the North Sea.

In this paper the time domain scattering problem of a stratified dissipative half‐space excited by a point source is considered. Both the direct and inverse scattering problem are treated. The dissipative wave equation is reduced to an equation in one spatial dimension by spatial Fourier series and a Hankel transform. The transformed wave equation is then solved by a combination of a time domain wave‐splitting technique and a Green function technique. The Green functions represent the internal fields inside the stratified medium. The splitting is expressed in terms of a Neumann operator K which has an explicit expression as a convolution integral with a Bessel function kernel. Based upon this wave splitting, Green functions can be defined and a set of first order partial differential equations for Green functions are derived. The equations are well suited for a numerical treatment and a number of numerical examples for both the direct and inverse problems are presented. A brief discussion of the invariant imbedding method applied to the direct and inverse scattering problem is also given. It is shown that one‐sided reflection data are sufficient to reconstruct the phase velocity and the dissipation coefficient simultaneously by using two different values of the Hankel transform parameter.