Analysis of the spectral hole in velocity versus depth resolution for reflection traveltimes with limited aperture

Geophysics ◽  
2005 ◽  
Vol 70 (3) ◽  
pp. U37-U45 ◽  
Author(s):  
Kenneth P. Bube ◽  
Robert T. Langan ◽  
Tamas Nemeth
Keyword(s):  
Taylor Expansion ◽  
Depth Resolution ◽  
Theoretical Explanation ◽  
Velocity Versus ◽  
Angle Of Incidence ◽  
Vertical Variation ◽  
Spectral Hole ◽  
Maximum Angle ◽  
Zero Offset ◽  
Horizontal Wavelength

It is difficult to resolve the ambiguity between velocity and reflector depth using reflection traveltimes when the aperture is small, as is common for deep reflectors. For velocity perturbations that are independent of the vertical variable, there is an even stronger velocity-versus-depth ambiguity at a horizontal wavelength of 2.5 times the reflector depth. We give a theoretical explanation of why this spectral hole occurs. When the maximum offset is small, there are velocity and reflector depth perturbations that cause almost cancelling traveltime perturbations; the net traveltime perturbations are second order in offset, making resolution between velocity and depth difficult at all wavelengths. But for the particular wavelength [Formula: see text] ≈ 2.565 times the reflector depth, an extra term in the Taylor expansion for traveltime near zero offset vanishes; the net traveltime perturbations are fourth order in offset. Thus velocity-versus-depth resolution degrades much sooner at this wavelength as the maximum offset gets small. We show in addition that this behavior extends to velocity perturbations that can depend on the vertical variable, and spectral holes in velocity-versus-depth resolution can appear at any horizontal wavelength. Velocity perturbations with very simple vertical variation are sufficient to create these spectral holes. This behavior is not limited to extremely small apertures; the effect of this spectral hole can be felt when the maximum angle of incidence is as large as 25°.

AVA analysis after velocity-independent DMO and imaging

Geophysics ◽  
1998 ◽  
Vol 63 (2) ◽  
pp. 686-691 ◽  
Author(s):  
Gerald H. F. Gardner ◽  
Anat Canning
Keyword(s):  
Reflection Coefficient ◽  
Peak Amplitude ◽  
Angle Of Incidence ◽  
Amplitude Variation ◽  
Amplitude Variation With Offset ◽  
The Past ◽  
Reflectivity Function ◽  
Velocity Of Propagation ◽  
Zero Offset ◽  
Amplitude Versus

A common midpoint (CMP) gather usually provides amplitude variation with offset (AVO) information by displaying the reflectivity as the peak amplitude of symmetrical deconvolved wavelets. This puts a reflection coefficient R at every offset h, giving a function R(h). But how do we link h with the angle of incidence, θ, to get the reflectivity function, R(θ)? This is necessary for amplitude versus angle-of-incidence (AVA) analysis. One purpose of this paper is to derive formulas for this linkage after velocity-independent dip-moveout (DMO), done by migrating radial sections, and prestack zero-offset migration. Related studies of amplitude-preserving DMO in the past have dealt with constant-offset DMO but have not given the connection between offset and angle of incidence after processing. The results in the present paper show that the same reflectivity function can be extracted from the imaged volume whether it is produced using radial-trace DMO plus zero-offset migration, constant-offset DMO plus zero-offset migration, or directly by prestack, common-offset migration. The data acquisition geometry for this study consists of parallel, regularly spaced, multifold lines, and the velocity of propagation is constant. Events in the data are caused by an arbitrarily oriented 3-D plane reflector with any reflectivity function. The DMO operation transforms each line of data (m, h, t), i.e., midpoint, half-offset, and time, into an (m1, k, t1) space by Stolt-migrating each radial-plane section of the data, 2h = Ut, with constant velocity U/2. Merging the (m1, k, t1) spaces for all the lines forms an (x, y, k, t1) space, where the first two coordinates are the midpoint location, the third is the new half-offset, and the fourth is the time. Normal moveout (NMO) plus 3-D zero-offset migration of the subspace (x, y, t1) for each k creates a true-amplitude imaged volume (X, Y, k, T). Each peak amplitude in the volume is a reflection coefficient linked to an angle of incidence.

scholarly journals Design of a Concentrator With a Rectangular Flat Focus and Operation With a Suspension Reactor for Experiments in the Field of Photocatalytic Water Splitting

2014 ◽  
Author(s):  
Michael Wullenkord ◽  
Christian Jung ◽  
Christian Sattler
Keyword(s):  
Water Splitting ◽  
High Performance ◽  
Performance Test ◽  
Test Facility ◽  
Angle Of Incidence ◽  
Solar Concentrator ◽  
Tracking Accuracy ◽  
Photocatalytic Water Splitting ◽  
Maximum Angle ◽  
Production Of Hydrogen

Photocatalytic water splitting is a potential route for future carbon-free production of hydrogen. However catalysts still need to be enhanced in order to reach acceptable solar-to-fuel efficiency. In the context of the project HyCats funded by the Federal Ministry of Education and Research of Germany a high performance test facility for the evaluation of the activity of photocatalysts under practical conditions was established. It mainly consists of a solar concentrator and a planar receiver reactor. A modified linear Fresnel concentrator configuration was chosen based on ray tracing simulation results and improved concerning the number of different facets and the tolerance of tracking errors. It meets the major demand of a homogeneous irradiance distribution on the surface of the reactor. The SoCRatus (Solar Concentrator with a Rectangular Flat Focus) is a 2-axis solar concentrator with a geometrical concentration ratio of 20.2 and an aperture area of 8.8 m2. The tracking accuracy is better than 0.1° respecting both the solar azimuth and altitude angle. Its 22 highly UV/Vis-reflective flat aluminum mirror facets reflect the sunlight resulting in a rectangular focus with a nominal width of 100 mm and a nominal length of 2500 mm. The reactor is placed in the focal plane at a distance of 2500 mm from the mounting plane of the facets and allows concentrated solar radiation to penetrate suspensions of water, electrolytes and photocatalyst particles flowing through it. Corresponding to a maximum angle of incidence of 36.6° the Quartz window reflects not more than 5% of the incoming radiation and assures only marginal absorption, particularly in the UV-part of the sun’s spectrum. The material of the receiver body is PTFE (polytetrafluoroethylene) providing reflection coefficients above 90% concerning wavelengths of UV-A and UV-B. The design of the reactor features two parallel reaction chambers, offering the possibility to test two separate suspensions at the same irradiation conditions. A pump transports the tempered suspension to the reactor. The geometry of the reactor inlet and outlet minimizes critical regions with inadequate flow caused by vortices. Any evolved gases are separated from the suspension in a tank together with nitrogen introduced in the piping upstream and are analyzed by micro chromatographs. Numerous devices are installed in order to control and monitor the reaction conditions. First experiments have been carried out using methanol as a sacrificial reagent.

The WARR Machine: System Design, Implementation and Data

2018 ◽  
Vol 23 (4) ◽  
pp. 469-487 ◽  
Author(s):  
Nectaria Diamanti ◽  
E. Judith Elliott ◽  
Steven R. Jackson ◽  
A. Peter Annan
Keyword(s):  
Data Storage ◽  
Survey Design ◽  
Survey Methods ◽  
Automated Analysis ◽  
Velocity Versus ◽  
Implementation Challenges ◽  
Field Deployment ◽  
Zero Offset ◽  
Ground Penetrating ◽  
And Control

In this paper, we describe a ground penetrating radar (GPR) system called the wide angle reflection and refraction (WARR) machine, outline the design and discuss the implementation challenges. WARR and the closely related common-mid-point (CMP) GPR soundings have been standard survey methods to measure velocity since GPR first existed. Earliest efforts demonstrated the variation in ice sheet velocity versus depth. Although GPR multi-offset soundings are valuable survey methods, they have seen little adoption since many systems are not bistatic. In addition, surveys most often use a single transmitter with a single receiver deployed sequentially at varying antenna separations, making data acquisition slow. Modern instrumentation with recent advances in GPR timing and control technology has enabled deployment of systems with multiple concurrent sampling receivers. This development has resulted in the ability to continuously acquire multi-offset WARR data at the same rate as two dimensional (2D) common offset reflection surveys in the past. The concomitant issues of survey design plus organizing the WARR data storage, documentation and analysis present numerous challenges. The extraction of velocity information from the large volumes of GPR WARR/CMP data demands automated analysis techniques. We have explored the use of normal move out (NMO) stacking at creating enhanced zero offset section from multi-offset data. Furthermore, we investigated the use of semblance analysis at estimating move-out velocities in order to apply in the NMO stack. These traditional seismic processing steps have proven to be less effective with GPR. These conclusions point to the differences in data character between seismic and GPR. Results of in-field deployment are used to illustrate advances to date and point the way to further advancements.

Characterization of Thin Titanium and Titanium Nitride Layers Using Sims

1998 ◽  
Vol 514 ◽  
Author(s):  
Andrei V. Li-Fatou ◽  
Mauro R. Sardela ◽  
Chunsheng Tian
Keyword(s):  
Titanium Nitride ◽  
Large Fraction ◽  
Film Surface ◽  
Depth Resolution ◽  
Angle Of Incidence ◽  
Tin Films ◽  
Analytical Technique ◽  
Nitride Layers ◽  
The Impact

ABSTRACTTitanium (Ti) and titanium nitride (TiN) films are widely used as barrier stack to prevent junction spiking. It is also an important material for an anti-reflection coating (ARC) on aluminum (Al) films to facilitate lithography processes during multilevel metallization for the manufacture of integrated circuits on silicon-based (Si) semiconductor devices. Secondary Ion Mass Spectrometry (SIMS) is proven to be very powerful analytical technique for the semiconductor materials. However, quantitative analysis of very thin structures using SIMS constitutes an ultimate challenge since a large fraction of the profile is located in the transient region where a stable concentration of primary beam species has not been established.This paper reports a SIMS technique for advanced characterization of very thin titanium and titanium nitride layers. Improvements in depth resolution were achieved by reducing the angle of incidence and the impact energy maintaining enhanced ionization yield associated with oxygen bombardment. Significant improvements in characterization of the film surface were developed by using oxygen flooding technique. Optimized oxygen pressure was used to achieve a stable ion yield due to the complete surface oxidation of titanium and titanium nitride layers during the analysis. The method was employed in the SIMS characterization of multiple Ti/TiN films deposited on silicon substrate. The example presents dramatic enhancement in depth resolution due to minimized matrix related ion yield variations at the interfaces.

Three-term amplitude-variation-with-offset projections

Geophysics ◽  
2018 ◽  
Vol 83 (5) ◽  
pp. N51-N65 ◽  
Author(s):  
Vaughn Ball ◽  
Luis Tenorio ◽  
Christian Schiøtt ◽  
Michelle Thomas ◽  
J. P. Blangy
Keyword(s):  
Rock Physics ◽  
Projection Methods ◽  
Well Logs ◽  
Rock Properties ◽  
Inversion Method ◽  
Practical Implementation ◽  
Angle Of Incidence ◽  
Amplitude Variation ◽  
Amplitude Variation With Offset ◽  
Maximum Angle

A three-term (3T) amplitude-variation-with-offset projection is a weighted sum of three elastic reflectivities. Parameterization of the weighting coefficients requires two angle parameters, which we denote by the pair [Formula: see text]. Visualization of this pair is accomplished using a globe-like cartographic representation, in which longitude is [Formula: see text], and latitude is [Formula: see text]. Although the formal extension of existing two-term (2T) projection methods to 3T methods is trivial, practical implementation requires a more comprehensive inversion framework than is required in 2T projections. We distinguish between projections of true elastic reflectivities computed from well logs and reflectivities estimated from seismic data. When elastic reflectivities are computed from well logs, their projection relationships are straightforward, and they are given in a form that depends only on elastic properties. In contrast, projection relationships between reflectivities estimated from seismic may also depend on the maximum angle of incidence and the specific reflectivity inversion method used. Such complications related to projections of seismic-estimated elastic reflectivities are systematized in a 3T projection framework by choosing an unbiased reflectivity triplet as the projection basis. Other biased inversion estimates are then given exactly as 3T projections of the unbiased basis. The 3T projections of elastic reflectivities are connected to Bayesian inversion of other subsurface properties through the statistical notion of Bayesian sufficiency. The triplet of basis reflectivities is computed so that it is Bayes sufficient for all rock properties in the hierarchical seismic rock-physics model; that is, the projection basis contains all information about rock properties that is contained in the original seismic.

Laser and Water-Jet Fiber Coupling Technology for Water-Jet Guided Laser Micromachining

2009 ◽  
Vol 69-70 ◽  
pp. 29-33 ◽  
Author(s):  
Yang Wang ◽  
Li Jun Yang ◽  
J. Tang ◽  
L. Li ◽  
Yan Bin Chen
Keyword(s):  
High Speed ◽  
Laser Energy ◽  
Laser Micromachining ◽  
Laser Wavelength ◽  
Water Jet ◽  
Angle Of Incidence ◽  
Effective Coupling ◽  
Fluid Field ◽  
Dynamical Simulation ◽  
Maximum Angle

The processing effect using water-jet guided laser micromachining technology is determined by the accurate coupling of focused laser and high speed water-jet. In order to realize the effective coupling, based on the analysis and calculation, a coupling unit with special structures was designed. The maximum angle of incidence was researched, which determined whether the total reflection occurred when laser transported in the water-jet. By the aid of fluid dynamical simulation, the coupling unit with uniform distribution of inner-cavity fluid field was designed. The attenuation of laser energy in water-jet fiber was investigated. Using appropriate laser wavelength, pulse energy and filtered and de-ionized water, energy attenuation in fiber was reduced. Experimental results showed that applying this coupling technology, perfect water-jet guided laser micromachining can be achieved.

scholarly journals Theory of interval traveltime parameter estimation in layered anisotropic media

Geophysics ◽  
2016 ◽  
Vol 81 (5) ◽  
pp. C253-C263 ◽  
Author(s):  
Yanadet Sripanich ◽  
Sergey Fomel
Keyword(s):  
Parameter Estimation ◽  
Fourth Order ◽  
Taylor Expansion ◽  
Symmetry Plane ◽  
Transversely Isotropic ◽  
Anisotropic Media ◽  
Interval Parameter ◽  
Effective Parameters ◽  
Zero Offset ◽  
Vti Media

Moveout approximations for reflection traveltimes are typically based on a truncated Taylor expansion of traveltime squared around the zero offset. The fourth-order Taylor expansion involves normal moveout velocities and quartic coefficients. We have derived general expressions for layer-stripping second- and fourth-order parameters in horizontally layered anisotropic strata and specified them for two important cases: horizontally stacked aligned orthorhombic layers and azimuthally rotated orthorhombic layers. In the first of these cases, the formula involving the out-of-symmetry-plane quartic coefficients has a simple functional form and possesses some similarity to the previously known formulas corresponding to the 2D in-symmetry-plane counterparts in vertically transversely isotropic (VTI) media. The error of approximating effective parameters by using approximate VTI formulas can be significant in comparison with the exact formulas that we have derived. We have proposed a framework for deriving Dix-type inversion formulas for interval parameter estimation from traveltime expansion coefficients in the general case and in the specific case of aligned orthorhombic layers. The averaging formulas for calculation of effective parameters and the layer-stripping formulas for interval parameter estimation are readily applicable to 3D seismic reflection processing in layered anisotropic media.

Two-term AVO inversion: Equivalences and new methods

Geophysics ◽  
2008 ◽  
Vol 73 (6) ◽  
pp. C31-C38 ◽  
Author(s):  
Charles P. Ursenbach ◽  
Robert R. Stewart
Keyword(s):  
Parameter Method ◽  
Angle Of Incidence ◽  
Amplitude Variation With Offset ◽  
New Methods ◽  
Avo Inversion ◽  
Parameter Inversion ◽  
Maximum Angle ◽  
Resource Exploration ◽  
New Formulation ◽  
Two Parameter

Most amplitude-variation-with-offset (AVO) studies use two-parameter inversion methods that are approximations of a more general three-parameter method based on the Aki-Richards approximation. Two-parameter methods are popular because the three-parameter inversion is often plagued by numerical instability. Reducing the dimensionality of the parameter space stabilizes the inversion. A variety of constraints can accomplish this, and these lead to the multiplicity of current two-parameter methods. It would be useful to understand relationships between various two-parameter methods. To this end, we derive formal expressions for inversion errors of each method. Using these expressions, conversion formulas are obtained that allow the flexibility to convert results of any two-parameter method to those of any other two-parameter method. The only requirement for the equivalence of methods is that the maximum angle of incidence be at least a few degrees less than the critical angle. In addition, error expressions result in a new formulation for a two-parameter AVO tool that combines strengths of two commonly used methods. The expressions also suggest a simple way to incorporate information from well-log calibration into legacy AVO inversions. These results should be helpful in resource exploration.

Experiments on gravity currents propagating down slopes. Part 1. The release of a fixed volume of heavy fluid from an enclosed lock into an open channel

2007 ◽  
Vol 584 ◽  
pp. 433-453 ◽  
Author(s):  
T. MAXWORTHY ◽  
R. I. NOKES
Keyword(s):  
Open Channel ◽  
Gravity Current ◽  
Gravity Currents ◽  
Velocity Versus ◽  
Heavy Fluid ◽  
Velocity Measurements ◽  
Video Images ◽  
Maximum Angle ◽  
Time Histories ◽  
Vertical Slice

Gravity currents formed by the release of heavy fluid from an enclosed lock on a sloping open channel were investigated experimentally. The experiments were conducted in a channel that had a running length of 13 lock depths, and could be inclined to a maximum angle of 17°. The release of heavy dyed salt solution from a lock with an aspect ratio (height to length) of 0.5, was examined using video images to determine the front velocity, and a particle-tracking technique was used to measure the two-dimensional velocity field in a vertical slice through the centre of the evolving current. The gravity current head velocity increased with time and downstream distance to a maximum at approximately 10 lock depths from the front of the lock. Flow visualization and the velocity measurements have shown that during the acceleration phase the head was being fed by a following current that increased its buoyancy as it propagated downstream. A modified version of the theory of P. Beghin, E. J. Hopfinger and R. E. Britter (J. Fluid Mech.vol. 107, 1981, p. 407) in which the measured increase in buoyancy was used, instead of the original assumption of constant buoyancy, gave results that agreed closely with the experimental velocity versus time histories.

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