Shot-profile true amplitude crosscorrelation imaging condition

Geophysics ◽  
2013 ◽  
Vol 78 (4) ◽  
pp. S221-S231 ◽  
Author(s):  
B. Arntsen ◽  
A. Kritski ◽  
B. Ursin ◽  
L. Amundsen
Keyword(s):  
Reflection Coefficient ◽  
Time Lag ◽  
Reflection Coefficients ◽  
Damping Factor ◽  
Simple Modification ◽  
Imaging Condition ◽  
Correct Angle ◽  
Zero Time ◽  
Amplitude Versus ◽  
Stable Result

The U/D imaging condition for shot profile migration can be used to estimate the angle dependent reflection coefficient, but is difficult to implement numerically because of the spectral division involved. Most techniques for stabilizing the division require a damping factor which might be difficult to estimate and which also introduces bias into the final result. A stable result can be achieved by approximating the imaging condition with a crosscorrelation of the up- and downgoing wavefields at zero time lag, but this will lead to incorrect amplitude-versus-angle (AVA) behavior of the estimated reflection coefficient. We use a simple model for wave propagation of primary reflections in the wavenumber frequency domain and invert the model with respect to the reflection coefficient. By using the properties of wavefield extrapolators it can then be shown that the reflection coefficients can be estimated by crosscorrelation of the upgoing wavefield and a downgoing wavefield where the initial wavefield is the inverse of the wavefield generated by a point source. The new imaging condition gives the correct AVA behavior for horizontal reflectors. For dipping reflectors it is shown that a postmigration correction factor can be used to recover the correct angle behavior of the reflection coefficient. The new imaging condition is numerically stable, does not involve damping factors, is simple to implement numerically, and is a simple modification of the classical crosscorrelation imaging condition. Numerical examples confirm the correct AVA behavior of the new imaging condition.

scholarly journals Time-shift imaging condition in seismic migration

Geophysics ◽  
2006 ◽  
Vol 71 (6) ◽  
pp. S209-S217 ◽  
Author(s):  
Paul Sava ◽  
Sergey Fomel
Keyword(s):  
Time Lag ◽  
Synthetic Data ◽  
Complex Salt ◽  
Time Shift ◽  
Reverse Time ◽  
Data Set ◽  
Imaging Condition ◽  
Space And Time ◽  
Wavefield Extrapolation ◽  
Zero Time

Seismic imaging based on single-scattering approximation is in the analysis of the match between the source and receiver wavefields at every image location. Wavefields at depth are functions of space and time and are reconstructed from surface data either by integral methods (Kirchhoff migration) or by differential methods (reverse-time or wavefield extrapolation migration). Different methods can be used to analyze wavefield matching, of which crosscorrelation is a popular option. Implementation of a simple imaging condition requires time crosscorrelation of source and receiver wavefields, followed by extraction of the zero time lag. A generalized imaging condition operates by crosscorrelation in both space and time, followed by image extraction at zero time lag. Images at different spatial crosscorrelation lags are indicators of imaging accuracy and are also used for image-angle decomposition. In this paper, we introduce an alternative prestack imaging condition in which we preserve multiple lags of the time crosscorrelation. Prestack images are described as functions of time shifts as opposed to space shifts between source and receiver wavefields. This imaging condition is applicable to migration by Kirchhoff, wavefield extrapolation, or reverse-time techniques. The transformation allows construction of common-image gathers presented as functions of either time shift or reflection angle at every location in space. Inaccurate migration velocity is revealed by angle-domain common-image gathers with nonflat events. Computational experiments using a synthetic data set from a complex salt model demonstrate the main features of the method.

PP-wave reflection coefficients in weakly anisotropic elastic media

Geophysics ◽  
1998 ◽  
Vol 63 (6) ◽  
pp. 2129-2141 ◽  
Author(s):  
Václav Vavryuk ◽  
Ivan Peník
Keyword(s):  
Reflection Coefficient ◽  
Approximate Formula ◽  
Wave Reflection ◽  
Transversely Isotropic ◽  
Reflection Coefficients ◽  
Transversely Isotropic Media ◽  
Isotropic Media ◽  
Pp Wave ◽  
Axis Of Symmetry ◽  
Amplitude Versus

Approximate PP-wave reflection coefficients for weak contrast interfaces separating elastic, weakly transversely isotropic media have been derived recently by several authors. Application of these coefficients is limited because the axis of symmetry of transversely isotropic media must be either perpendicular or parallel to the reflector. In this paper, we remove this limitation by deriving a formula for the PP-wave reflection coefficient for weak contrast interfaces separating two weakly but arbitrarily anisotropic media. The formula is obtained by applying the first‐order perturbation theory. The approximate coefficient consists of a sum of the PP-wave reflection coefficient for a weak contrast interface separating two background isotropic half‐spaces and a perturbation attributable to the deviation of anisotropic half‐spaces from their isotropic backgrounds. The coefficient depends linearly on differences of weak anisotropy parameters across the interface. This simplifies studies of sensitivity of such coefficients to the parameters of the surrounding structure, which represent a basic part of the amplitude‐versus‐offset (AVO) or amplitude‐versus‐azimuth (AVA) analysis. The reflection coefficient is reciprocal. In the same way, the formula for the PP-wave transmission coefficient can be derived. The generalization of the procedure presented for the derivation of coefficients of converted waves is also possible although slightly more complicated. Dependence of the reflection coefficient on the angle of incidence is expressed in terms of three factors, as in isotropic media. The first factor alone describes normal incidence reflection. The second yields the low‐order angular variations. All three factors describe the coefficient in the whole region, in which the approximate formula is valid. In symmetry planes of weakly anisotropic media of higher symmetry, the approximate formula reduces to the formulas presented by other authors. The accuracy of the approximate formula for the PP reflection coefficient is illustrated on the model with an interface separating an isotropic half‐space from a half‐space filled by a transversely isotropic material with a horizontal axis of symmetry. The results show a very good fit with results of the exact formula, even in cases of strong anisotropy and strong velocity contrast.

Imaging conditions for prestack reverse-time migration

Geophysics ◽  
2008 ◽  
Vol 73 (3) ◽  
pp. S81-S89 ◽  
Author(s):  
Sandip Chattopadhyay ◽  
George A. McMechan
Keyword(s):  
Amplitude Ratio ◽  
Reflection Coefficients ◽  
Reverse Time ◽  
Reverse Time Migration ◽  
Imaging Condition ◽  
Angle Dependence ◽  
Time Migration ◽  
Dependence Scale ◽  
Correct Angle ◽  
Imaging Conditions

Numerical implementations of six imaging conditions for prestack reverse-time migration show widely differing ability to provide accurate, angle-dependent estimates of reflection coefficients. Evaluation is in the context of a simple, one-interface acoustic model. Only reflection coefficients estimated by normalization of a crosscorrelation image by source illumination or by receiver-/source-wavefield amplitude ratio have the correct angle dependence, scale factor, and sign and the required (dimensionless) units; thus, these are the preferred imaging-condition algorithms. To obtain accurate image amplitudes, source- and receiver-wavefield extrapolations must be able to accurately reconstruct their respective wavefields at the target reflector.

scholarly journals An Estimate of Reflection Coefficients for Rabbit Heart Capillaries

1964 ◽  
Vol 47 (4) ◽  
pp. 667-677 ◽  
Author(s):  
Fernando Vargas ◽  
John A. Johnson
Keyword(s):  
Weight Change ◽  
Rabbit Heart ◽  
Ringer Solution ◽  
Reflection Coefficients ◽  
Test Substance ◽  
Time Rate ◽  
Loss Of Weight ◽  
Test Molecule ◽  
Zero Time ◽  
Heart Capillaries

Isolated perfused rabbit hearts have been used to determine the reflection coefficients, σ, of the heart capillaries to certain lipoid-insoluble substances. This was done by initially perfusing the heart with a Ringer solution containing no test molecule and then suddenly switching to a solution which differed from the original only by containing a small amount of test substance. This produced a loss of weight of the heart which was continuously recorded as a function of time. Taking the "zero" time rate of weight change and using an equation given by Kedem and Katchalsky reflection coefficients for urea, sucrose, raffinose, and inulin were obtained. These turned out to be 0.1, 0.3, 0.38, and 0.69 respectively. Using the approach of Durbin and Solomon equivalent pore radii were estimated to be about 35 Angstroms.

scholarly journals Visuomotor integration is associated with zero time-lag synchronization among cortical areas

Nature ◽  
1997 ◽  
Vol 385 (6612) ◽  
pp. 157-161 ◽  
Author(s):  
Pieter R. Roelfsema ◽  
Andreas K. Engel ◽  
Peter König ◽  
Wolf Singer
Keyword(s):  
Time Lag ◽  
Lag Synchronization ◽  
Visuomotor Integration ◽  
Cortical Areas ◽  
Zero Time

LOOP ANTENNA WITH A SEMICONDUCTOR ELEMENT

2021 ◽  
Author(s):  
П.А. ТИТОВЕЦ ◽  
А.И. САТТАРОВА ◽  
А.А. ПИЩЕРКОВ ◽  
Н.С. БЕКУШЕВ
Keyword(s):  
Laser Radiation ◽  
Reflection Coefficient ◽  
Copper Foil ◽  
Loop Antenna ◽  
Laser Source ◽  
Reflection Coefficients ◽  
Building Element ◽  
External Contour ◽  
In Series ◽  
Loop Antennas

Представлены результаты исследований рамочной антенны, в которой подстроечным элементом является фоторезистор, управляемый лазерным излучением. Показано, что использование фоторезистора как элемента внешнего контура рамочной антенны, включенного последовательно, позволяет изменять согласование рамочной антенны с помощью внешнего лазерного источника. Представлены результаты исследований характеристик коэффициента передачи рамочных антенн, состоящих из медной фольги на диэлектрической основе и полупроводникового элемента. Установлено, что при изменении интенсивности лазерного излучения, падающего на полупроводниковый элемент-фоторезистор, изменяется коэффициент отражения рамочной антенны. В диапазоне от 10 МГц до 18ГГц получены зависимости коэффициентов отражения (Su)рамочных антенн с полупроводниковым элементом. Проведено сравнение рамочной антенны и рамочной антенны с фоторезистором. The results of an experiment with a loop antenna, in which the building element is a photoresistor controlled by laser radiation, are presented. It is shown that the use of a photoresistor as an element of the external contour of a loop antenna connected in series makes it possible to change the matching of the loop antenna due to an external laser source. The results of studies of the characteristics of the transmission coefficient of loop antennas consisting of a dielectric copper foil and a semiconductor element are presented. It was found that when the intensity of the laser radiation incident on the semiconductor element-photoresistor changes, the reflection coefficient of the frame antenna changes. In the range of 10 MHz-18 GHz, the dependences of the reflection coefficients (S11) of loop antennas with a semiconductor element are obtained. A comparison is made between a loop antenna and a loop antenna with a photoresistor.

Measurement of osmotic reflection coefficient for small molecules in cat hindlimbs

1989 ◽  
Vol 256 (1) ◽  
pp. H282-H290 ◽  
Author(s):  
M. B. Wolf ◽  
P. D. Watson
Keyword(s):  
Skeletal Muscle ◽  
Reflection Coefficient ◽  
Small Molecules ◽  
Osmotic Pressure ◽  
Maximum Rate ◽  
Reflection Coefficients ◽  
Flow Rates ◽  
Perfusate Flow ◽  
Arterial Inflow ◽  
Osmotic Reflection Coefficient

Capillary osmotic reflection coefficients (sigma) for NaCl, urea, sucrose, and raffinose were measured in the isolated, perfused cat hindlimb using the osmotic transient technique. sigma were determined from the ratio of the maximum rate of transcapillary absorption [delta Jv(max)] to the increase in the osmotic pressure (25-35 mosmol/kg H2O) in the arterial inflow (delta pi a) produced by adding one of the molecules to an albumin-electrolyte perfusate containing isoproterenol (greater than 10(-7) M). delta Jv (max) was determined from organ weight and delta pi a from perfusate osmolalities. For each molecule, the delta Jv(max)/delta pi a ratio increased monotonically with perfusate flow rates (Q) to Q greater than 100 ml.min-1.100 g-1. This ratio was independent of the size of the delta pi a. Apparent sigma values were calculated by dividing these ratios by the capillary hydraulic capacity determined in other studies. At low Q, apparent sigma was comparable to the approximately 0.1 values found by others in skeletal muscle. At the highest Q, apparent sigma for these molecules were at least 0.5. These data are consistent with at least 50% of transcapillary water flow moving through a water-exclusive pathway.

Protein osmotic pressure gradients and microvascular reflection coefficients

1997 ◽  
Vol 273 (2) ◽  
pp. H997-H1002 ◽  
Author(s):  
R. E. Drake ◽  
S. Dhother ◽  
R. A. Teague ◽  
J. C. Gabel
Keyword(s):  
Reflection Coefficient ◽  
Pressure Gradient ◽  
Osmotic Pressure ◽  
Reflection Coefficients ◽  
Pressure Gradients ◽  
Fluid Filtration ◽  
The Mean ◽  
Osmotic Reflection Coefficient ◽  
New Equation ◽  
Osmotic Pressure Gradient

Microvascular membranes are heteroporous, so the mean osmotic reflection coefficient for a microvascular membrane (sigma d) is a function of the reflection coefficient for each pore. Investigators have derived equations for sigma d based on the assumption that the protein osmotic pressure gradient across the membrane (delta II) does not vary from pore to pore. However, for most microvascular membranes, delta II probably does vary from pore to pore. In this study, we derived a new equation for sigma d. According to our equation, pore-to-pore differences in delta II increase the effect of small pores and decrease the effect of large pores on the overall membrane osmotic reflection coefficient. Thus sigma d for a heteroporous membrane may be much higher than previously derived equations indicate. Furthermore, pore-to-pore delta II differences increase the effect of plasma protein osmotic pressure to oppose microvascular fluid filtration.

Boundary conditions for the numerical solution of wave propagation problems

Geophysics ◽  
1978 ◽  
Vol 43 (6) ◽  
pp. 1099-1110 ◽  
Author(s):  
Albert C. Reynolds
Keyword(s):  
Wave Propagation ◽  
Reflection Coefficient ◽  
Finite Difference ◽  
Boundary Conditions ◽  
Numerical Solution ◽  
Neumann Boundary ◽  
Synthetic Seismograms ◽  
Neumann Boundary Conditions ◽  
Numerical Calculations ◽  
Reflection Coefficients

Many finite difference models in use for generating synthetic seismograms produce unwanted reflections from the edges of the model due to the use of Dirichlet or Neumann boundary conditions. In this paper we develop boundary conditions which greatly reduce this edge reflection. A reflection coefficient analysis is given which indicates that, for the specified boundary conditions, smaller reflection coefficients than those obtained for Dirichlet or Neumann boundary conditions are obtained. Numerical calculations support this conclusion.

scholarly journals Study of superradiance in the Lambert-W potential barrier

2019 ◽  
Vol 34 (16) ◽  
pp. 1950087 ◽  
Author(s):  
Luis Puente ◽  
Carlos Cocha ◽  
Clara Rojas
Keyword(s):  
Reflection Coefficient ◽  
Potential Barrier ◽  
Gordon Equation ◽  
Reflection Coefficients ◽  
Hyperbolic Tangent ◽  
Step Potential ◽  
Transmission And Reflection Coefficients ◽  
Klein Gordon ◽  
Klein Gordon Equation ◽  
Transmission And Reflection

We present a new potential barrier that presents the phenomenon of superradiance when the reflection coefficient [Formula: see text] is greater than one. We calculated the transmission and reflection coefficients for three different regions. The results are compared with those obtained for the hyperbolic tangent potential barrier and the step potential barrier. We also present the solution of the Klein–Gordon equation with the Lambert-[Formula: see text] potential barrier in terms of the Heun Confluent functions.

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