scholarly journals The virtual refraction: Useful spurious energy in seismic interferometry

Geophysics ◽  
2009 ◽  
Vol 74 (3) ◽  
pp. A13-A17 ◽  
Author(s):  
Dylan Mikesell ◽  
Kasper van Wijk ◽  
Alexander Calvert ◽  
Matt Haney
Keyword(s):  
Energy Distribution ◽  
Stationary Phase ◽  
Critical Time ◽  
Seismic Interferometry ◽  
Phase Point ◽  
Wave Speeds ◽  
The Real ◽  
Spurious Wave ◽  
Established Technique ◽  
Spurious Event

Seismic interferometry is rapidly becoming an established technique to recover the Green’s function between receivers, but practical limitations in the source-energy distribution inevitably lead to spurious energy in the results. Instead of attempting to suppress all such energy, we use a spurious wave associated with the crosscorrelation of refracted energy at both receivers to infer estimates of subsurface parameters. We named this spurious event the virtual refraction. Illustrated by a numerical two-layer example, we found that the slope of the virtual refraction defines the velocity of the faster medium and that the stationary-phase point in the correlation gather provides the critical offset. With the associated critical time derived from the real shot record, this approach includes all of the necessary information to estimate wave speeds and interface depth without the need of inferences from other wave types.

Phase retrieval from spectral interferograms including a stationary-phase point

2012 ◽  
Vol 285 (24) ◽  
pp. 4733-4738 ◽  
Author(s):  
Petr Hlubina ◽  
Jacek Olszewski
Keyword(s):  
Stationary Phase ◽  
Phase Retrieval ◽  
Phase Point

Optisches Modell für die Streuung von K--Mesonen an Kernen

1957 ◽  
Vol 12 (12) ◽  
pp. 947-955 ◽  
Author(s):  
P. Mittelstaedt
Keyword(s):  
Angular Distribution ◽  
Elastic Scattering ◽  
Energy Distribution ◽  
Inelastic Scattering ◽  
Optical Potential ◽  
Optical Model ◽  
Experimental Results ◽  
The Real ◽  
Elastic And Inelastic Scattering ◽  
Plate Group

The elastic and inelastic scattering of K--Mesons by complex nuclei are described by means of a phenomenological optical model. The real and the imaginary parts of the optical potential are determined by a comparison with the experimental results of the Goettingen and of the Bern plate group from the angular distribution of the elastic scattering and also from the energy distribution of the inelastically scattered K--Mesons by means of the GoLDBERGER-method.

Geometrical considerations in the acquisition of borehole interferometric data for imaging near-vertical features: Design of field experiments

Geophysics ◽  
2013 ◽  
Vol 78 (3) ◽  
pp. K1-K10 ◽  
Author(s):  
Emma Brand ◽  
Charles Hurich ◽  
Sharon Deemer
Keyword(s):  
Stationary Phase ◽  
Field Experiments ◽  
Hard Rock ◽  
Critical Role ◽  
Seismic Profile ◽  
Dominant Frequency ◽  
Critical Parameters ◽  
Seismic Interferometry ◽  
Surface Source ◽  
Major Factors

Seismic interferometry applied to walkaway vertical seismic profile data has significant potential for imaging the steeply dipping structures often encountered in hard-rock minerals exploration. Using the interferometry process, surface shots can be redatumed to the borehole receivers resulting in virtual shot gathers. The virtual shot gathers can then be processed using a standard common midpoint (CMP) processing flow. Carrying out this procedure for a subvertical borehole results in a geometry that is optimal for imaging structures that are near vertical. Field acquisition parameters play a critical role in recovering reliable virtual source images. We evaluated the major factors that play a role in designing a field acquisition program with the objective of providing guidance to field practitioners. The major issue to be considered is insuring that correlation gathers created in the interferometry process have a stationary phase component that when summed produces events with correct timing and cancellation of nonstationary components. Consistent with previous work, the ray-tracing-based analysis identified the surface source spacing, surface source aperture, and dominant frequency as the most critical parameters. The analysis indicated that because of the high apparent velocities typically encountered in hard rock terrains, a surface source spacing of 20 m and an aperture of 1000 m will result in stationary phase components and avoid spatial alias in the correlation gathers for frequencies as high as 80 Hz. However, closer spacing of the surface sources provided more traces in the correlation gathers resulting in fewer artifacts during summation. These results were further verified by acoustic wave modeling that provided data from more complex targets that were processed through a complete interferometry and CMP flow. The analysis indicated that with care in designing field acquisition parameters, seismic interferometry is realizable within the terrain and access restrictions imposed by many mining camps.

scholarly journals Asymptotic expansion of integrals occurring in linear wave theory

1972 ◽  
Vol 7 (1) ◽  
pp. 121-130 ◽  
Author(s):  
P. van den Driessche ◽  
R.D. Braddock
Keyword(s):  
Asymptotic Expansion ◽  
Stationary Phase ◽  
Wave Theory ◽  
Linear Wave ◽  
Phase Point ◽  
One Dimensional ◽  
Special Cases ◽  
Order Of Magnitude ◽  
Leading Term ◽  
Wave Problems

The asymptotic expansion of an integral of the type , is derived in terms of the large parameter t. Functions Φ(k) and ψ(k) are assumed analytic, and ψ(k) may have zeros at a stationary phase point. The usual one dimensional stationary phase and Airy integral terms are found as special cases of a more general result. The result is used to find the leading term of the asymptotic expansion of the double integral. A particular two dimensional Φ(k) relevant to surface water wave problems is considered in detail, and the order of magnitude of the integral is shown to depend on the nature of ψ(k) at the stationary phase point.

The asymptotic theory of rapidly rotating sound fields

1992 ◽  
Vol 436 (1898) ◽  
pp. 511-526 ◽  
Keyword(s):  
Stationary Phase ◽  
Acoustic Field ◽  
Airy Function ◽  
Sound Field ◽  
Stationary Points ◽  
Simple Type ◽  
Phase Point ◽  
Sound Fields ◽  
Asymptotic Formulae ◽  
Leading Term

A rapidly rotating sound field, such as that produced by a supersonic propeller, may contain several types of diffraction pattern, each in a different region of space. This paper determines these patterns and their locations for the field around a propeller of simple type ; the method used is stationary phase analysis of a certain double integral, and leads to asymptotic formulae valid when the number of blades is not too small or the high harmonics are being investigated. Physically, the results describe propagation along rays : each stationary phase point is a ‘ loud spot ’, producing a ray which points directly at the observer; most of the noise comes from these loud spots, because extensive cancellation takes place everywhere else. At most two interior and two boundary stationary points may be present: the number and type depend on the position of the observer in relation to a cusped torus and two hyperboloids of one sheet. As these surfaces are crossed, the acoustic field changes in character. For example, when two stationary points coalesce and annihilate each other, as they do at a caustic, an Airy function describes the transition from a loud zone of rapid oscillation to a quiet zone of exponential decay; and when an interior stationary point crosses the boundary of the disc the transition region is described either by a Fresnel integral or by a generalized Airy function. Separate analyses are given for regions close to and well away from the transition surfaces, and inner and outer limits are calculated for use in the method of matched asymptotic expansions. In all cases, an overlap region is found in which the leading term s agree. The results of the paper determine completely the geometry of the acoustic field, because the different regions have boundaries at known positions and cover the whole of space.

scholarly journals Integration Of Smart Grid And Blockchain

2021 ◽  
Author(s):  
Kartikey Garg
Keyword(s):  
Smart Grid ◽  
Energy Distribution ◽  
Energy Production ◽  
Fossil Fuels ◽  
Third Parties ◽  
Conventional System ◽  
Power Generators ◽  
The Real ◽  
Security Issues ◽  
Electricity Bill

<div><div><div><p>A majority of electricity consumed by humans comes from traditional power generators, that work on a centralised framework, distributing it through wires and grids. More than 80% of this electricity comes from fossil fuels, leading to large amounts of pollution, since it is carbon intensive. The distribution methods are inefficient as much energy is lost in transmission. This leads to it being expensive for the consumer, and makes them dependent on large corporations. A large percentage of the electricity bill goes towards paying off the investment in infrastructure needed to provide it. This model is clearly not sustainable. Furthermore, it is estimated that around 1.2 billion people live without access to safe electricity. This is primarily since electricity providers don’t deem building infrastructure for a remote or economically backward location as profitable enough, since they are unlikely to pay it back. Contrary to conventional system, our proposed framework will be focused at introducing the decentralised energy distribution and consumption using Blockchain. Many prior studies have been done to decentralise the energy distribution but due to security and trust scare the systems could not be fully adopted in the real setting. We take a look into the methodologies third parties can use to counter the security issues as well. However, by integrating blockchain into the existing smart grid architecture we open up the possibility of bypassing the tiring process of renewable certification, make a localised energy production a reality and detach the consumers from the dependency of central grid. To fully assimilate this environment with the end users we also discuss about the real time platform for prosumers and consumers to trade energy. At the end, we look at the costs, consumption and other attributes of three different community microgrids simu</p></div></div></div>

scholarly journals EfficiencyBeta Batteries with Direct Energy Conversion

2018 ◽  
Vol 1 (2) ◽  
Author(s):  
Sergey V. Bulyarskiy ◽  
Ivan E. Abanin ◽  
Alexander V. Lakalin
Keyword(s):  
Energy Distribution ◽  
Energy Conversion ◽  
High Activity ◽  
Beta Decay ◽  
High Energy ◽  
Electron Hole ◽  
The Real ◽  
Direct Energy Conversion ◽  
Direct Energy ◽  
Real Value

The properties of the beta batteries are compared, which are made on the basis of the different β-isotopes with beta decay. Tritium and Ni-63 make it possible to make β-sources of high activity, without harmful associated emissions, with low self-absorption, emitting high-energy β-electrons that penetrate deep into the semiconductor and generate a large number of electron-hole pairs. The efficiency of beta batteries needs to be analyzed based on the real energy distribution of β-electrons. It makes possible to obtain the real value of the energy absorbed inside the β-source, correctly estimate the amount of self-absorption of the β-electrons and part of the β-electronsthere is a penetrate into the semiconductor, the number of electrons and holes that are generated in the semiconductor, and the magnitude of the idling voltage. Formulas for these quantities are calculated in this paper.

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