The influence of reflection coefficient statistics on the seismic method: scattering and the minimum detectable reflection coefficient

1993 ◽  
Vol 440 (1909) ◽  
pp. 221-240 ◽  
Keyword(s):  
Reflection Coefficient ◽  
Seismic Reflection ◽  
Target Strength ◽  
Scattered Signal ◽  
Reflection Coefficients ◽  
Signal To Noise ◽  
Statistical Parameters ◽  
Conservation Of Energy ◽  
Scattered Energy ◽  
Short Period

Propagation of seismic reflection energy through layered media is discussed in terms of one-dimensional elastic scattering and the effect of a layered overburden on the detectability of the underlying target horizons is investigated. In a previous paper, using Walden & Hosken’s statistical models of real reflection series, Q -like attenuation laws were derived for the two-way transmission. Considerable use was made of the O’Doherty and Anstey relation between the amplitude spectrum of the two-way transmission and the energy spectrum of the reflection coefficients. With reference to the seismic reflection bandwidth, in general the equivalent Q is seen to increase with frequency, except over an intermediate band of frequencies where it often decreases with frequency. Also, the minimum phase wavelet predicted by the theory was shown to model adequately the first pulse of the two-way transmission waveform, carrying the greater part of the energy, and the lag of the first peak was approximately described in terms of the statistical parameters of the reflection coefficients in the overburden. The spectrum of the back-scattered energy can be determined from the conservation of energy into and out of the overburden and is seen to be complementary to the forward scattered signal and thus it can also be described in term s of the Walden and Hosken statistical parameters. The back-scattered energy can be divided into two components: (i) the primary reflections from within the overburden together with their associated short period multiples and (ii) the long period internal multiple noise which may arrive at the same time as the reflections from the underlying target horizons, obscuring them . The ratio of forward-scattered signal to back-scattered noise is a function of frequency and travel time through the overburden and it sets a fundamental signal-to-noise ratio for the section. An approximate expression is derived for the signal-to-noise peak power ratio which we use to determine both a natural cut-off frequency above which the noise dominates over signal from a given target strength, and α min , the minimum reflection coefficient detectable below the overburden. α min is seen to depend on the statistical properties of the overburden and can usually be decreased by decreasing the high and low-cut frequencies of the seismic bandwidth. There is thus a trade-off between detectability level and resolution.

The influence of reflection coefficient statistics on the seismic method: scattering attenuation and transmission wavelets

1992 ◽  
Vol 439 (1905) ◽  
pp. 1-23 ◽  
Keyword(s):  
Reflection Coefficient ◽  
Seismic Energy ◽  
Reflection Coefficients ◽  
Mean Square ◽  
Statistical Parameters ◽  
Seismic Surveys ◽  
Reflection Seismic ◽  
Starting Point ◽  
Sonic Logs ◽  
Scattered Component

The propagation through layered media of seismic energy from reflection seismic surveys is discussed in terms of one dimensional elastic scattering. The effect of a layered overburden on the detectability of the underlying target horizons is investigated. The required signal from the target reflectors arises from the two-way forward-scattered component whereas the internal multiple noise (which tends to obscure the target reflections) arises from the back-scattered component. The starting point of the investigation is the O’Doherty-Anstey relation for the two-way transmission response. In this paper, using statistical models of real reflection series, we derive Q -like attenuation laws for the two-way transmission. Most real sequences of reflection coefficients have spectra which rise with frequency in the seismic band and this leads to signal attenuation which only approximates to that of a 'constant Q ’ type over small bands of frequency. The implications of the theory are checked for two very different types of overburden, one being a repetitive type of sedimentary sequence with a large mean square reflection coefficient and the other a non-repetitive sequence with a small mean square reflection coefficient, against synthetic seismograms derived from real sonic logs. The minimum phase wavelet predicted by the theory is shown to model adequately the first pulse of the two-way transmission waveform, carrying the greater part of the energy, and the lag of the first peak is given approximately in terms of the statistical parameters of the reflection coefficients in the overburden.

scholarly journals Second-Order Approximation of the Seismic Reflection Coefficient in Thin Interbeds

Energies ◽  
2020 ◽  
Vol 13 (6) ◽  
pp. 1465 ◽  
Author(s):  
Zhen Yang ◽  
Jun Lu
Keyword(s):  
Theoretical Model ◽  
Reflection Coefficient ◽  
Seismic Reflection ◽  
Transmission Loss ◽  
Order Approximation ◽  
Compressional Wave ◽  
Second Order ◽  
Reflection Coefficients ◽  
Second Order Approximation ◽  
Approximate Equations

As most of the lithostratigraphic reservoirs in China are thin interbeds, the study of seismic responses in thin interbeds is an integral part of lithologic reservoir exploration. However, at present, the research on seismic reflection coefficients of thin interbeds in exploration seismology is still weak, which leads to the lack of theoretical basis for the subsequent interpretation of amplitude variation with offset (AVO) related to thin interbed. To solve this problem, in this paper, we proposed second-order approximate equations of the seismic reflection coefficients in thin-bed and thin-interbed layers. Under the assumption of a small impedance contrast in layered media, we made a second-order approximation with a more evident physical meaning to the reflection coefficient calculation method proposed by Kennett. Then, based on the test of the single thin-layer theoretical model, it was confirmed that the second-order approximation equation of the PP-wave (reflected compressional wave) is accurate at incident angles less than 30°, and that of the PS-wave (converted shear wave) is accurate at wider incident angles. Finally, based on the single-thin-bed equations, the approximate equations of seismic reflection coefficients in thin interbeds were established, the validity of which was verified by the theoretical model. Our equations will be applicable to the calculation of PP- and PS-wave reflection coefficients in thin interbeds where internal multiples are difficult to suppress and transmission loss is hard to accurately compensate. This lays a theoretical foundation for improving the seismic prediction accuracy of lithologic reservoirs.

LONG-PERIOD SURFACE-RELATED MULTIPLE SUPPRESSION IN 2D MARINE SEISMIC DATA USING PREDICTIVE DECONVOLUTION AND COMBINATION OF SURFACE-RELATED MULTIPLE ELIMINATION AND PARABOLIC RADON FILTERING

2021 ◽  
Author(s):  
Pimpawee Sittipan ◽  
Pisanu Wongpornchai
Keyword(s):  
Seismic Data ◽  
Seismic Reflection ◽  
Petroleum Reservoirs ◽  
The United States ◽  
Multiple Reflections ◽  
Long Period ◽  
Predictive Deconvolution ◽  
Short Period ◽  
Marine Seismic ◽  
Multiple Elimination

Some of the important petroleum reservoirs accumulate beneath the seas and oceans. Marine seismic reflection method is the most efficient method and is widely used in the petroleum industry to map and interpret the potential of petroleum reservoirs. Multiple reflections are a particular problem in marine seismic reflection investigation, as they often obscure the target reflectors in seismic profiles. Multiple reflections can be categorized by considering the shallowest interface on which the bounces take place into two types: internal multiples and surface-related multiples. Besides, the multiples can be categorized on the interfaces where the bounces take place, a difference between long-period and short-period multiples can be considered. The long-period surface-related multiples on 2D marine seismic data of the East Coast of the United States-Southern Atlantic Margin were focused on this research. The seismic profile demonstrates the effectiveness of the results from predictive deconvolution and the combination of surface-related multiple eliminations (SRME) and parabolic Radon filtering. First, predictive deconvolution applied on conventional processing is the method of multiple suppression. The other, SRME is a model-based and data-driven surface-related multiple elimination method which does not need any assumptions. And the last, parabolic Radon filtering is a moveout-based method for residual multiple reflections based on velocity discrimination between primary and multiple reflections, thus velocity model and normal-moveout correction are required for this method. The predictive deconvolution is ineffective for long-period surface-related multiple removals. However, the combination of SRME and parabolic Radon filtering can attenuate almost long-period surface-related multiple reflections and provide a high-quality seismic images of marine seismic data.

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.

Linearized amplitude variation with offset (AVO) inversion with supercritical angles

Geophysics ◽  
2006 ◽  
Vol 71 (5) ◽  
pp. E49-E55 ◽  
Author(s):  
Jonathan E. Downton ◽  
Charles Ursenbach
Keyword(s):  
Reflection Coefficient ◽  
Critical Angle ◽  
Waveform Inversion ◽  
Phase Variation ◽  
Reflection Coefficients ◽  
Amplitude Variation ◽  
Amplitude Variation With Offset ◽  
Zoeppritz Equations ◽  
Avo Inversion ◽  
Angle Data

Contrary to popular belief, a linearized approximation of the Zoeppritz equations may be used to estimate the reflection coefficient for angles of incidence up to and beyond the critical angle. These supercritical reflection coefficients are complex, implying a phase variation with offset in addition to amplitude variation with offset (AVO). This linearized approximation is then used as the basis for an AVO waveform inversion. By incorporating this new approximation, wider offset and angle data may be incorporated in the AVO inversion, helping to stabilize the problem and leading to more accurate estimates of reflectivity, including density reflectivity.

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