Limited‐view diffraction tomography in a nonuniform background

Geophysics ◽  
1995 ◽  
Vol 60 (2) ◽  
pp. 580-588 ◽  
Author(s):  
Leiv‐J. Gelius
Keyword(s):  
Point Source ◽  
General Structure ◽  
Wave Theory ◽  
Background Model ◽  
Diffraction Tomography ◽  
Strong Resemblance ◽  
Background Wave ◽  
Homogeneous Background ◽  
Paraxial Ray ◽  
Background Models

The main problems in geophysical diffraction tomography are (1) complicated media and (2) rather limited acquisition geometries. Existing algorithms solve the limited‐view problem in an iterative manner, but are valid only for line sources and 2-D homogeneous background models. In this paper, we derive an iterative algorithm based on asymptotic wave theory that can compensate for a limited acquisition geometry. The method is valid for a 2-D nonuniform background model and point‐source illumination (i.e., a 2.5-D geometry). Paraxial ray tracing is employed to model the arbitrary background wave response, and the general structure of the algorithm has a strong resemblance to the iterative ART‐algorithm used in straight ray tomography. Our method is shown to be stable in the presence of moderate white noise and gives reasonable results, both geometrically and quantitatively, when applied to synthetic crosshole data involving a nonhomogeneous background model and limited view.

Are Social Background Models Time-Bound?

1986 ◽  
Vol 80 (3) ◽  
pp. 957-967 ◽  
Author(s):  
S. Sidney Ulmer
Keyword(s):  
Supreme Court ◽  
Social Background ◽  
Research Note ◽  
Background Model ◽  
Confounding Variable ◽  
Background Models

In this research note I seek to determine whether a significantly predicting social background model for analyzing the votes of Supreme Court justices is time-bound. I argue that an affirmative result poses serious questions for past uses of such models, none of which has controlled for the possibility that time is a confounding variable. A model that significantly predicted the votes of the justices in the Court's 1903–1968 terms was constructed. Analysis with this model for two periods—from 1903 to 1935, and from 1936 to 1968—established that the model was not timeneutral. Appropriate theoretical implications are drawn.

scholarly journals Scattered moonlight observations with X-shooter

2019 ◽  
Vol 624 ◽  
pp. A39
Author(s):  
A. Jones ◽  
S. Noll ◽  
W. Kausch ◽  
S. Unterguggenberger ◽  
C. Szyszka ◽  
...  
Keyword(s):  
Near Infrared ◽  
Current Model ◽  
Background Model ◽  
Lunar Phase ◽  
Aerosol Extinction ◽  
Coarse Particles ◽  
The Moon ◽  
Aerosol Scattering ◽  
Phase Functions ◽  
Background Models

Estimating the sky background is critical for ground-based astronomical research. In the optical, scattered moonlight dominates the sky background, when the moon is above the horizon. The most uncertain component of a scattered moonlight model is the aerosol scattering. The current, official sky background model for Cerro Paranal uses an extrapolated aerosol extinction curve. With a set of X-shooter sky observations, we have tested the current sky background model as well as determined the aerosol extinction from the ultra-violet (UV) to near-infrared (NIR). To our knowledge, this is the first time that a scattered moonlight model has been used for this purpose. These observations were taken of blank sky, during three different lunar phases, and at six different angular distances from the moon for each lunar phase. Overall, the current model does reproduce the observations for average conditions quite well. Using a set of sky background models with varying aerosol distributions to compare with the observations, we found the most likely aerosol extinction curves, phase functions, and volume densities for the three nights of observations and compare them with the current model. While there are some degeneracies in the aerosol scattering properties, the extinction curves tend to flatten towards redder wavelengths and are overall less steep compared to the extrapolated curve used in the current model. Also, the current model had significantly less coarse particles compared to the favored volume densities from the X-shooter data. Having more coarse particles affects the phase function by being more peaked at small angular distances. For the three nights of sky observations, the aerosol size distributions differed, most likely reflecting the changes in atmospheric conditions and aerosol content, which is expected. In short, the current sky background model is in fair agreement with the observations, and we have determined better aerosol extinction curves and phase functions for Cerro Paranal. Using nighttime sky observations of scattered moonlight and a set of sky background models is a new method to probe the aerosol content of the atmosphere.

Background Modeling Approach Based on Eigenspace Decomposition

2012 ◽  
Vol 157-158 ◽  
pp. 1399-1403
Author(s):  
Jian Wu Long ◽  
Xuan Jing Shen ◽  
Hai Peng Chen
Keyword(s):  
Video Sequence ◽  
Moving Objects ◽  
Principal Component ◽  
Background Model ◽  
Training Set ◽  
Training Samples ◽  
The Matrix ◽  
Eigenspace Decomposition ◽  
Svd Decomposition ◽  
Background Models

In this work principal component analysis (PCA) was adopted to construct a background model and moving objects were detected by background subtraction method. Firstly, constructed the matrix of training samples by means of converting the video sequence to vectors. Then calculated the covariance matrix C of the training set, and acquired the eigenvalues and eigenvectors of C through SVD decomposition. Next, sorted the eigenvalues and reconstructed the background model by using several image vectors which had higher cumulative contribution. Finally, comparison experiments are performed with the detection results by GMM approach. Experimental results show that the proposed method in this paper could establish background models more accurate and have better effective of object detection.

scholarly journals Elastic reflection waveform inversion with variable density

Geophysics ◽  
2019 ◽  
Vol 84 (4) ◽  
pp. R553-R567 ◽  
Author(s):  
Yuanyuan Li ◽  
Qiang Guo ◽  
Zhenchun Li ◽  
Tariq Alkhalifah
Keyword(s):  
Waveform Inversion ◽  
Variable Density ◽  
Background Model ◽  
Reverse Time ◽  
S Wave ◽  
Low Frequencies ◽  
Wave Velocities ◽  
Reflection Data ◽  
Time Migration ◽  
Background Models

Elastic full-waveform inversion (FWI) provides a better description of the subsurface information than those given by the acoustic assumption. However, it suffers from a more serious cycle-skipping problem compared with the latter. Reflection waveform inversion (RWI) is able to build a good background model, which can serve as an initial model for elastic FWI. Because, in RWI, we use the model perturbation to explicitly fit reflections, such perturbations should include density, which mainly affects the dynamics. We applied Born modeling to generate synthetic reflection data using optimized perturbations of the P- and S-wave velocities and density. The inversion for the perturbations of the P- and S-wave velocities and density is similar to elastic least-squares reverse time migration. An incorrect background model will lead to misfits mainly at the far offsets, which can be used to update the background P- and S-wave velocities along the reflection wavepath. We optimize the perturbations and background models in an alternate way. We use two synthetic examples and a field-data case to demonstrate our proposed elastic RWI algorithm. The results indicate that our elastic RWI with variable density is able to build reasonably good background models for elastic FWI with the absence of low frequencies, and it can deal with the variable density, which is required in real cases.

Generalized Projection-Slice Theorem for Fan Beam Diffraction Tomography

1985 ◽  
Vol 7 (3) ◽  
pp. 264-275 ◽  
Author(s):  
Anthony J. Devaney
Keyword(s):  
Point Source ◽  
Plane Surface ◽  
Three Dimensional ◽  
Generalized Projection ◽  
Diffraction Tomography ◽  
Slice Theorem ◽  
Measurement Plane ◽  
Ellipsoid Of Revolution ◽  
Special Case ◽  
Beam Diffraction

A generalized projection-slice theorem is derived for transmission fan beam diffraction tomography within the Born or Rytov approximations. The development is based on the use of the so-called paraxial approximation which requires that the object being probed subtend a small angle relative to the source point and to the measurement plane. Within this approximation it is shown that the transmitted field measured over a plane surface located on the opposite side of the object from the insonifying point source determines the three-dimensional spatial Fourier transform of the object profile over the surface of an ellipsoid of revolution in Fourier space. In the special case where the point source is in the far field of the object the semiaxes of the ellipsoid become equal and the surface degenerates to a sphere and the result reduces to the usual projection-slice theorem of plane beam diffraction tomography.

REAL-TIME OBJECT DETECTION USING TWO BACKGROUND MODELS UNDER SHAKING CAMERA

2009 ◽  
Vol 06 (01) ◽  
pp. 13-21 ◽  
Author(s):  
TAEHO KIM ◽  
KANG-HYUN JO
Keyword(s):  
Moving Objects ◽  
Displacement Vector ◽  
Motion Vector ◽  
Computational Cost ◽  
Image Sequence ◽  
Background Model ◽  
Experimental Result ◽  
Camera Motion ◽  
Short Period ◽  
Background Models

In this paper, we propose a novel approach to detect moving objects by two background models, multiple background model (MBM) and temporal median background (TMB), from hand-taken image sequence. For this purpose, we record image sequences by hand-held camera without tripod so every frame has variation between consecutive frames. A pixel-based background model is fragile while image sequence has variation. Therefore we calculate the camera movement using correlation between two consecutive images and it helps us to generate MBM under shaking camera. The computational cost of correlation quickly increases if image resolution increases. Hence, we use edge segments to reduce computational cost. These edge segments are gathered by Sobel operator and those are distinctive spatial features to calculate similarity between two regions, belonging to current and previous images, organized by neighbors of edge segments. Based on the similarity result, we obtain a set of best matched regions, centroids of matched regions, and displacement vectors from each pair of previous and current images. Each displacement vector in a set describes the transition of each matched region in the image pair. Using the highest density of displacement vector histogram, we choose the camera motion vector, indicates camera movement between consecutive frames. According to the camera motion vector, every pixel in a current image is related to different position pixels in a previous image. The pixel relation is used to generate MBM in this paper, unlike original MBM [Xiao, M., Han, C. and Kang, K. [2006]. Proc. Int. Conf. Information Fuscon, pp. 1–7.]. The MBM algorithm classifies the variation of pixel values in frame sequence to several clusters. Classification of varying pixel values to several clusters is similar with mixture of gaussian (MOG). Nevertheless, MBM has low cost to calculate because it does not need to estimate parameter. However, MBM is not sensitive to short period changes. Therefore, we use TMB to support MBM. The experimental result shows that proposed algorithm successfully detects moving objects using background subtraction less than 25 ms per frame when camera has 2D translation.

scholarly journals Hierarchic Superposition Revisited

10.29007/w9vg ◽  
2018 ◽  
Author(s):  
Uwe Waldmann
Keyword(s):  
Black Box ◽  
Background Model ◽  
Linear Arithmetic ◽  
Completeness Result ◽  
Standard Models ◽  
Theory Reasoning ◽  
Rational Arithmetic ◽  
Background Models ◽  
Superposition Calculus

In 1994,Bachmair, Ganzinger, and Waldmann introduced the hierarchicalsuperposition calculus as a generalization of the superpositioncalculus for black-box style theory reasoning.Their calculus works in a framework of hierarchic specifications.It tries to prove theunsatisfiability of a set of clauses with respect to interpretationsthat extend a background model such as the integers with linear arithmeticconservatively, that is, withoutidentifying distinct elements of old sorts ("confusion") and withoutadding new elements to old sorts ("junk").We show how the calculus can be improved,report on practical experiments,and present a new completeness result fornon-compact classes of background models(i.e., linear integer or rational arithmetic restricted tostandard models).

3-D crosswell transmissions: Paraxial ray solutions and reciprocity paradox

Geophysics ◽  
1995 ◽  
Vol 60 (3) ◽  
pp. 810-820 ◽  
Author(s):  
Jianguo Sun
Keyword(s):  
Seismic Waves ◽  
Fresnel Zone ◽  
Matrix Decomposition ◽  
Decomposition Theorem ◽  
Wave Theory ◽  
Transformation Matrix ◽  
Reciprocity Relation ◽  
Earth Model ◽  
Vector Calculus ◽  
Paraxial Ray

Transmission of seismic waves through a 3-D earth model is of fundamental importance in seismology. If the model consists of many layers separated by curved interfaces, the only feasible solution to the transmitted waves is the one given by the geometrical optics approximation. Transmitted rays, transmitted wavefield, and the first Fresnel zone associated with a transmission point can be expressed by four 2 × 2 constant matrices constituting the 4 × 4 linearized ray transformation matrix. Generally, the ray transformation matrix can be constructed by dynamic ray tracing. However, if the layers are homogeneous, it can be formulated in closed form by using elementary vector calculus and coordinate transformations. Using the symplecticity of the ray transformation matrix, transmissions in opposite directions can be formulated by the ray transformation matrix for only one direction, and a reciprocity relation can be established. After the decomposition theorem for the ray transformation matrix, the transmitted wavefield in a model with many curved interfaces can be computed in a cascaded way. Using the [Formula: see text]‐matrix decomposition theorem, the normalized geometrical spreading factor can be expressed by means of the area of the first Fresnel zone of a transmission point. If seismic waves propagate through a locally spherical interface, the reciprocity relation may not hold. Using ray theory, this fact is shown by formulating the transmitted wavefield with the two principal radii of curvature of the transmitted wavefront at the transmission point under consideration. Using wave theory, this fact is shown by analyzing the Debye integral with the method of stationary phase.

North Sea reservoir description: Benefits of an elastic migration/inversion applied to multicomponent vertical seismic profile data

Geophysics ◽  
1990 ◽  
Vol 55 (2) ◽  
pp. 209-217 ◽  
Author(s):  
W. B. Beydoun ◽  
M. Mendes ◽  
J. Blanco ◽  
A. Tarantola
Keyword(s):  
North Sea ◽  
Confidence Region ◽  
Seismic Profile ◽  
Background Model ◽  
Quality Data ◽  
S Wave ◽  
Ray Method ◽  
Target Zone ◽  
The North ◽  
Paraxial Ray

A linearized elastic migration/inversion (M/I) technique is applied to multicomponent offset VSP data collected in the North Sea. High‐resolution elastic images of the target zone (P- and S-wave velocities and density) are obtained from upgoing P-P and P-S wave fields. These M/I images are an approximate representation of rapid variations of subsurface parameters. Three image confidence criteria provide a measure of uncertainty in the interpretation. VSP-CDP transform maps assisted in the definition of the confidence region in M/I images. M/I was helpful in delineating the Brent reservoir, and detecting a twofault system. Preliminary interpretation indicates an increase in Poisson’s ratio at the top of the reservoir. Surface data were not able to image this target due to strong multiples at the Cretaceous base. This is the first time elastic depth images have been obtained from M/I of offset VSP field data. Generally, image artifacts depend on the following conditions: (1) good quality data with satisfactory coverage of the target zone; (2) accurate, amplitude‐preserving data preprocessing techniques for filtering out “unwanted” waves; and (3) an elastic background model which adequately represents the main subsurface features. Our M/I approach is flexible, since it can be used with single or multicomponent prestack data P-P, P-S, S-P, and S-S scattered waves simultaneously, an arbitrary acquisition geometry, and a two‐dimensional heterogeneous background model. Computational efficiency results from concentrating the inversion on a target zone and using the paraxial ray method to compute ray‐approximate Green’s functions.

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