scholarly journals Improved and isotropic resolution in tomographic diffractive microscopy combining sample and illumination rotation

Open Physics ◽  
2011 ◽  
Vol 9 (4) ◽  
Author(s):  
Stanislas Vertu ◽  
Jens Flügge ◽  
Jean-Jacques Delaunay ◽  
Olivier Haeberlé
Keyword(s):  
Frequency Domain ◽  
Born Approximation ◽  
Three Dimensions ◽  
Maximal Extension ◽  
Isotropic Resolution ◽  
First Order ◽  
Illumination Method

AbstractTomographic Diffractive Microscopy is a technique, which permits to image transparent living specimens in three dimensions without staining. It is commonly implemented in two configurations, by either rotating the sample illumination keeping the specimen fixed, or by rotating the sample using a fixed illumination. Under the first-order Born approximation, the volume of the frequency domain that can be mapped with the rotating illumination method has the shape of a “doughnut”, which exhibits a so-called “missing cone” of non-captured frequencies, responsible for the strong resolution anisotropy characteristic of transmission microscopes. When rotating the sample, the resolution is almost isotropic, but the set of captured frequencies still exhibits a missing part, the shape of which resembles that of an apple core. Furthermore, its maximal extension is reduced compared to tomography with rotating illumination. We propose various configurations for tomographic diffractive microscopy, which combine both approaches, and aim at obtaining a high and isotropic resolution. We illustrate with simulations the expected imaging performances of these configurations.

Synthetic reflection seismograms in three dimensions by a locked‐mode approximation

Geophysics ◽  
1989 ◽  
Vol 54 (3) ◽  
pp. 350-358 ◽  
Author(s):  
G. Nolet ◽  
R. Sleeman ◽  
V. Nijhof ◽  
B. L. N. Kennett
Keyword(s):  
Finite Difference ◽  
Born Approximation ◽  
Large Scale ◽  
Layered Medium ◽  
Three Dimensional ◽  
Simple Algorithm ◽  
Realistic Model ◽  
Three Dimensions ◽  
Acoustic Response ◽  
Many Sources

We present a simple algorithm for computing the acoustic response of a layered structure containing three‐dimensional (3-D) irregularities, using a locked‐mode approach and the Born approximation. The effects of anelasticity are incorporated by use of Rayleigh’s principle. The method is particularly attractive at somewhat larger offsets, but computations for near‐source offsets are stable as well, due to the introduction of anelastic damping. Calculations can be done on small minicomputers. The algorithm developed in this paper can be used to calculate the response of complicated models in three dimensions. It is more efficient than any other method whenever many sources are involved. The results are useful for modeling, as well as for generating test signals for data processing with realistic, model‐induced “noise.” Also, this approach provides an alternative to 2-D finite‐difference calculations that is efficient enough for application to large‐scale inverse problems. The method is illustrated by application to a simple 3-D structure in a layered medium.

Inversion of slingram electromagnetic induction data using a Born approximation

Geophysics ◽  
2013 ◽  
Vol 78 (4) ◽  
pp. E201-E212 ◽  
Author(s):  
Jochen Kamm ◽  
Michael Becken ◽  
Laust B. Pedersen
Keyword(s):  
Half Space ◽  
Born Approximation ◽  
High Efficiency ◽  
Three Dimensions ◽  
Background Model ◽  
Desktop Computer ◽  
Near Surface ◽  
Homogeneous Half Space ◽  
Integral Equation Formulation ◽  
Forward Operator

We present an efficient approximate inversion scheme for near-surface loop-loop EM induction data (slingram) that can be applied to obtain 2D or 3D models on a normal desktop computer. Our approach is derived from a volume integral equation formulation with an arbitrarily conductive homogeneous half-space as a background model. The measurements are not required to fulfill the low induction number condition (low frequency and conductivity). The high efficiency of the method is achieved by invoking the Born approximation around a half-space background. The Born approximation renders the forward operator linear. The choice of a homogeneous half-space yields closed form expressions for the required electromagnetic normal fields. It also yields a translationally invariant forward operator, i.e., a highly redundant Jacobian. In connection with the application of a matrix-free conjugate gradient method, this allows for very low memory requirements during the inversion, even in three dimensions. As a consequence of the Born approximation, strong conductive deviations from the background model are underestimated. Highly resistive anomalies are in principle overestimated, but at the same time difficult to resolve with induction methods. In the case of extreme contrasts, our forward model may fail in simultaneously explaining all the data collected. We applied the method to EM34 data from a profile that has been extensively studied with other electromagnetic methods and compare the results. Then, we invert three conductivity maps from the same area in a 3D inversion.

scholarly journals Can We Compare Solidarity Across Europe? What, Why, When, and How to Assess Exact and Approximate Equivalence of First- and Second-Order Factor Models

2021 ◽  
Vol 3 ◽  
Author(s):  
Vera Lomazzi
Keyword(s):  
Factor Model ◽  
Second Order ◽  
Three Dimensions ◽  
Alignment Method ◽  
Cross Sectional ◽  
Political Values ◽  
First Order ◽  
Measurement Models ◽  
European Values ◽  
Order Factor

Although measurement invariance is widely considered a precondition for meaningful cross-sectional comparisons, substantive studies have often neglected evaluating this assumption, thereby risking drawing conclusions and making theoretical generalizations based on misleading results. This study offers a theoretical overview of the key issues concerning the measurement and the comparison of socio-political values and aims to answer the questions of what must be evaluated, why, when, and how to assess measurement equivalence. This paper discusses the implications of formative and reflective approaches to the measurement of socio-political values and introduces challenges in their comparison across different countries. From this perspective, exact and approximate approaches to equivalence are described as well as their empirical translation in statistical techniques, such as the multigroup confirmatory factor analysis (MGCFA) and the frequentist alignment method. To illustrate the application of these methods, the study investigates the construct of solidarity as measured by European Values Study (EVS) and using data collected in 34 countries in the last wave of the EVS (2017–2020). The concept is captured through a battery of nine items reflecting three dimensions of solidarity: social, local, and global. Two measurement models are hypothesized: a first-order factor model, in which the three independent dimensions of solidarity are correlated, and a second-order factor model, in which solidarity is conceived according to a hierarchical principle, and the construct of solidarity is reflected in the three sub-factors. In testing the equivalence of the first-order factor model, the results of the MGCFA indicated that metric invariance was achieved. The alignment method supported approximate equivalence only when the model was reduced to two factors, excluding global solidarity. The second-order factor model fit the data of only seven countries, in which this model could be used to study solidarity as a second-order concept. However, the comparison across countries resulted not appropriate at any level of invariance. Finally, the implications of these results for further substantive research are discussed.

scholarly journals Parsimonious truncated Newton method for time-domain full waveform inversion based on Fourier-domain full-scattered-field approximation

Geophysics ◽  
2021 ◽  
pp. 1-147
Author(s):  
Peng Yong ◽  
Romain Brossier ◽  
Ludovic Métivier
Keyword(s):  
Frequency Domain ◽  
Time Domain ◽  
Cross Correlation ◽  
Waveform Inversion ◽  
Field Approximation ◽  
Second Order ◽  
Vector Product ◽  
First Order ◽  
Full Waveform ◽  
Truncated Newton

In order to exploit Hessian information in Full Waveform Inversion (FWI), the matrix-free truncated Newton method can be used. In such a method, Hessian-vector product computation is one of the major concerns due to the huge memory requirements and demanding computational cost. Using the adjoint-state method, the Hessian-vector product can be estimated by zero-lag cross-correlation of the first-order/second-order incident wavefields and the second-order/first-order adjoint wavefields. Different from the implementation in frequency-domain FWI, Hessian-vector product construction in the time domain becomes much more challenging as it is not affordable to store the entire time-dependent wavefields. The widely used wavefield recomputation strategy leads to computationally intensive tasks. We present an efficient alternative approach to computing the Hessian-vector product for time-domain FWI. In our method, discrete Fourier transform is applied to extract frequency-domain components of involved wavefields, which are used to compute wavefield cross-correlation in the frequency domain. This makes it possible to avoid reconstructing the first-order and second-order incident wavefields. In addition, a full-scattered-field approximation is proposed to efficiently simplify the second-order incident and adjoint wavefields computation, which enables us to refrain from repeatedly solving the first-order incident and adjoint equations for the second-order incident and adjoint wavefields (re)computation. With the proposed method, the computational time can be reduced by 70% and 80% in viscous media for Gauss-Newton and full-Newton Hessian-vector product construction, respectively. The effectiveness of our method is also verified in the frame of a 2D multi-parameter inversion, in which the proposed method almost reaches the same iterative convergence of the conventional time-domain implementation.

Joint inversion of seismic traveltime and frequency-domain airborne electromagnetic data for hydrocarbon exploration

Geophysics ◽  
2018 ◽  
Vol 83 (2) ◽  
pp. U9-U22 ◽  
Author(s):  
Jide Nosakare Ogunbo ◽  
Guy Marquis ◽  
Jie Zhang ◽  
Weizhong Wang
Keyword(s):  
Frequency Domain ◽  
Joint Inversion ◽  
Sedimentary Environment ◽  
Computational Cost ◽  
Velocity Model ◽  
Two Dimensions ◽  
Hydrocarbon Exploration ◽  
Three Dimensions ◽  
Data Sets ◽  
The One

Geophysical joint inversion requires the setting of a few parameters for optimum performance of the process. However, there are yet no known detailed procedures for selecting the various parameters for performing the joint inversion. Previous works on the joint inversion of electromagnetic (EM) and seismic data have reported parameter applications for data sets acquired from the same dimensional geometry (either in two dimensions or three dimensions) and few on variant geometry. But none has discussed the parameter selections for the joint inversion of methods from variant geometry (for example, a 2D seismic travel and pseudo-2D frequency-domain EM data). With the advantage of affordable computational cost and the sufficient approximation of a 1D EM model in a horizontally layered sedimentary environment, we are able to set optimum joint inversion parameters to perform structurally constrained joint 2D seismic traveltime and pseudo-2D EM data for hydrocarbon exploration. From the synthetic experiments, even in the presence of noise, we are able to prescribe the rules for optimum parameter setting for the joint inversion, including the choice of initial model and the cross-gradient weighting. We apply these rules on field data to reconstruct a more reliable subsurface velocity model than the one obtained by the traveltime inversions alone. We expect that this approach will be useful for performing joint inversion of the seismic traveltime and frequency-domain EM data for the production of hydrocarbon.

scholarly journals A NONLOCAL UNITARY VECTOR MODEL IN THREE DIMENSIONS

2011 ◽  
Vol 26 (26) ◽  
pp. 4603-4615
Author(s):  
ADEL KHOUDEIR ◽  
J. STEPHANY
Keyword(s):  
Path Integral ◽  
The Self ◽  
Three Dimensions ◽  
Vector Model ◽  
Nonlocal Model ◽  
First Order ◽  
Duality Transformations ◽  
Massive Models ◽  
Nonlocal Terms

We present a unified analysis of single excitation vector models in three dimensions. We show that there is a family of first-order master actions related by duality transformations which interpolate between the different models. We use a Hamiltonian (2+1) analysis to show the equivalence of the self-dual and topologically massive models with a covariant nonlocal model which propagates also a single massive excitation. It is shown how the nonlocal terms appears naturally in the path integral framework.

Do attractive scattering potentials concentrate particles at the origin in one, two and three dimensions? III. High energies in quantum mechanics

1983 ◽  
Vol 388 (1795) ◽  
pp. 445-456 ◽  
Keyword(s):  
Quantum Mechanics ◽  
Born Approximation ◽  
Enhancement Factor ◽  
Bessel Functions ◽  
Particle Density ◽  
Incident Beam ◽  
Three Dimensions ◽  
Incident Momentum ◽  
High Energies ◽  
Factor Α

The enhancement factor α D ≡ 1+ δα D is defined (in D dimensions) as the ratio of the particle density at the origin to the density far upstream in the incident beam. At high incident momentum p (and for regular potentials) the first Born approximation is known to be adequate in 3D and 1D, and is assumed to be adequate also in 2D; it entails δα 1 = ─δα 3 if U ( r ) in 3D equals U ( x ) in 1D when r = x . For central potentials U ( r ) with U (0) finite, previous work implies δα 3 ~ ─δα 1 ~ ─ mU (0)/ p 2 , and δα 2 = 0 to the same order h °. It is shown that if U ( r →0) ~ U (0) + r U' (0) + ..., then δα 2 ~ (2 m U' (0) h / p 3 )(π/16), the value of U (0) being irrelevant. If U ( r →0) ~ ─ C / r q , with 0 < q < 2, then δα 3 ~ ─δα 1 ~ (2 mC / h q p 2- q ) π ½ Γ(1-½ q )/2Γ(½+½ q ); and, with -1 < q < 2, δα 2 ~ (2 m C / h q p 2- q )π ½ Γ 2 (1-½ q )/2Γ(½ q )Γ(3/2-½ q ). The only mathematics needed in 3D and 1D is the standard asymptotic estimation of Fourier integrals; but in 2D one needs to develop corresponding methods for integrals where the sine or cosine has been replaced by a product J 0 Y 0 of two Bessel functions.

Inversion of airborne geophysics over the DO-27/DO-18 kimberlites — Part 2: Electromagnetics

2017 ◽  
Vol 5 (3) ◽  
pp. T313-T325 ◽  
Author(s):  
Dominique Fournier ◽  
Seogi Kang ◽  
Michael S. McMillan ◽  
Douglas W. Oldenburg
Keyword(s):  
Frequency Domain ◽  
Time Domain ◽  
Three Dimensions ◽  
Data Sets ◽  
Conductivity Model ◽  
Time Domain Data ◽  
Conductivity Structure ◽  
Lake Bottom ◽  
Geologic Interpretation ◽  
Lateral Extent

We focus on the task of finding a 3D conductivity structure for the DO-18 and DO-27 kimberlites, historically known as the Tli Kwi Cho (TKC) kimberlite complex in the Northwest Territories, Canada. Two airborne electromagnetic (EM) surveys are analyzed: a frequency-domain DIGHEM and a time-domain VTEM survey. Airborne time-domain data at TKC are particularly challenging because of the negative values that exist even at the earliest time channels. Heretofore, such data have not been inverted in three dimensions. In our analysis, we start by inverting frequency-domain data and positive VTEM data with a laterally constrained 1D inversion. This is important for assessing the noise levels associated with the data and for estimating the general conductivity structure. The analysis is then extended to a 3D inversion with our most recent optimized and parallelized inversion codes. We first address the issue about whether the conductivity anomaly is due to a shallow flat-lying conductor (associated with the lake bottom) or a vertical conductive pipe; we conclude that it is the latter. Both data sets are then cooperatively inverted to obtain a consistent 3D conductivity model for TKC that can be used for geologic interpretation. The conductivity model is then jointly interpreted with the density and magnetic susceptibility models from a previous paper. The addition of conductivity enriches the interpretation made with the potential fields in characterizing several distinct petrophysical kimberlite units. The final conductivity model also helps better define the lateral extent and upper boundary of the kimberlite pipes. This conductivity model is a crucial component of the follow-up paper in which our colleagues invert the airborne EM data to recover the time-dependent chargeability that further advances our geologic interpretation.

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