On: “Reflection of spherical seismic waves in elastic layered media” by P. M. Krail and H. Brysk (GEOPHYSICS, June 1983, p. 655–664).

Geophysics ◽  
1984 ◽  
Vol 49 (5) ◽  
pp. 588-589
Author(s):  
Stephen H. Danbom ◽  
S. Norman Domenico
Keyword(s):  
Seismic Waves ◽  
Spherical Wave ◽  
Petroleum Exploration ◽  
Radius Of Curvature ◽  
Model Parameters ◽  
Angle Of Incidence ◽  
Reflection Amplitude ◽  
Half Wavelength ◽  
Bright Spots ◽  
Amplitude Versus

This paper develops the wavefront curvature correction for the plane‐wave Zoeppritz coefficients. The authors imply that seismic reflection amplitude versus angle of incidence does not enhance detection of pore‐fluid‐caused amplitude anomalies (“bright spots”) as proposed in the scientific literature by Backus et al (1982), Ostrander (1982), and Stolt (1981). We believe certain parts of this discussion are incorrect. Points of disagreement are as follows. (1) The model parameters associated with Figure 6 (especially the values for the brine‐filled sandstone) are unrealistic and are not taken from Domenico (1977) as the authors have indicated. (2) The conclusion “… it is clear that the CMP gather by itself fails as a gas indicator” based on Figure 6 is incorrect. (3) A reflecting spherical wave having a radius of curvature equal to approximately one‐half wavelength (kr = 3) requires a shallow reflector unreasonable for petroleum exploration.

Reflection of spherical seismic waves in elastic layered media

Geophysics ◽  
1983 ◽  
Vol 48 (6) ◽  
pp. 655-664 ◽  
Author(s):  
Paul M. Krail ◽  
Henry Brysk
Keyword(s):  
Plane Wave ◽  
Seismic Waves ◽  
Plane Waves ◽  
Spherical Wave ◽  
Bright Spot ◽  
Angle Of Incidence ◽  
Complicated Manner ◽  
Plane Wave Incident ◽  
Wave Limit ◽  
The Impact

The solution of the elastic wave equation for a plane wave incident on a plane interface has been known since the turn of the century. For reflections from reasonably shallow beds, however, it is necessary to treat the incident wave as spherical rather than plane. The formalism for expressing spherical wavefronts as contour integrals over plane waves goes back to Sommerfeld (1909) and Weyl (1919). Brekhovskikh (1960) performed a steepest descent evaluation of the integrals to attain analytic results in the acoustic case. We have extended his approach to elastic waves to obtain spherical‐wave Zoeppritz coefficients. We illustrate the impact of the curvature correction parametrically (as the velocity and density contrasts and Poisson’s ratios are varied). In particular, we examine conditions appropriate to “bright spot” analysis; expectedly, the situation becomes less simple than in the plane‐wave limit. The curvature‐corrected Zoeppritz coefficients vary more strongly (and in a more complicated manner) with the angle of incidence than do the original ones. The determination of material properties (velocities and densities) from the reflection coefficients is feasible in principle, with exacting prestack processing and interpretation. For orientation, we outline the procedure for the simple case of a separated single source and detector pair over a multilayered horizontal earth.

scholarly journals Computational Method for Wavefront Sensing Based on Transport-Of-Intensity Equation

Photonics ◽  
2021 ◽  
Vol 8 (6) ◽  
pp. 177
Author(s):  
Iliya Gritsenko ◽  
Michael Kovalev ◽  
George Krasin ◽  
Matvey Konoplyov ◽  
Nikita Stsepuro
Keyword(s):  
A Priori ◽  
Spherical Wave ◽  
Computational Method ◽  
Optical Systems ◽  
Radius Of Curvature ◽  
Imaging Method ◽  
Wavefront Sensing ◽  
Phase Imaging ◽  
Transport Of Intensity Equation ◽  
Priori Information

Recently the transport-of-intensity equation as a phase imaging method turned out as an effective microscopy method that does not require the use of high-resolution optical systems and a priori information about the object. In this paper we propose a mathematical model that adapts the transport-of-intensity equation for the purpose of wavefront sensing of the given light wave. The analysis of the influence of the longitudinal displacement z and the step between intensity distributions measurements on the error in determining the wavefront radius of curvature of a spherical wave is carried out. The proposed method is compared with the traditional Shack–Hartmann method and the method based on computer-generated Fourier holograms. Numerical simulation showed that the proposed method allows measurement of the wavefront radius of curvature with radius of 40 mm and with accuracy of ~200 μm.

Incomplete AVO near salt structures

Geophysics ◽  
1992 ◽  
Vol 57 (4) ◽  
pp. 543-553 ◽  
Author(s):  
Christopher P. Ross
Keyword(s):  
Seismic Profiles ◽  
Spectral Modeling ◽  
Signal Degradation ◽  
Amplitude Versus Offset ◽  
Bright Spots ◽  
Close Proximity ◽  
Pseudo Spectral ◽  
Amplitude Versus ◽  
Structure Class ◽  
Made In

Amplitude versus offset (AVO) measurements for deep hydrocarbon‐bearing sands can be compromised when made in close proximity to a shallow salt piercement structure. Anomalous responses are observed, particularly on low acoustic impedance bright spots. CMP data from key seismic profiles traversing the bright spots do not show the expected Class 3 offset responses. On these CMPs, significant decrease of far trace energy is observed. CMP data from other seismic profiles off‐structure do exhibit the Class 3 offset responses, implying that structural complications may be interfering with the offset response. A synthetic AVO gather was generated using well log data, which supports the off‐structure Class 3 responses, further reinforcing the concept of structurally‐biased AVO responses. Acoustic, pseudo‐spectral modeling of the structure substantiates the misleading AVO response. Pseudo‐spectral modeling results suggest that signal degradation observed on the far offsets is caused by wavefield refraction—a shadow zone, where the known hydrocarbon‐bearing sands are not completely illuminated. Such shadow zones obscure the correct AVO response, which may have bearing on exploration and development.

Variable Angle of Incidence Spectroscopic Ellipsometric Measurement of the Franz-Keloysh Effect in Modfet Structures

1986 ◽  
Vol 77 ◽  
Author(s):  
P. G. Snyder ◽  
J. E. Oh ◽  
J. A. Woollam
Keyword(s):  
Electric Field ◽  
Bandgap Energy ◽  
Model Parameters ◽  
Angle Of Incidence ◽  
Internal Electric Field ◽  
Ellipsometric Measurement ◽  
Band Bending ◽  
Variable Angle ◽  
Two Samples ◽  
Franz Keldysh Effect

ABSTRACTIt has been shown recently that variable angle of incidence spectroscopie ellipsometry (VASE) is a sensitive technique for determining semiconductor multilayer model parameters, e.g. layer thicknesses and ternary compositions. In this paper we show that VASE is, in addition, sensitive to the Franz-Keldysh effect induced by band bending in the barrier layer of a GaAs-AlGaAs-GaAs (MODFET) structure. VASE measurements differ from electro-reflectance and photoreflectance, in that the internal heterojunction region electric field is directly probed, without the application of a modulating field. The Franz-Keldysh effect appears in the VASE spectra near the AlGaAs bandgap energy. Data for two samples, with different doping profiles, are quantitatively modeled to determine the internal electric field amplitudes.

Fault whispers: Transmission distortions on prestack seismic reflection data

Geophysics ◽  
2000 ◽  
Vol 65 (2) ◽  
pp. 377-389 ◽  
Author(s):  
Paul J. Hatchell
Keyword(s):  
Seismic Data ◽  
Seismic Waves ◽  
Shallow Gas ◽  
Seismic Reflection Data ◽  
Reflection Data ◽  
Amplitude Versus Offset ◽  
Velocity Changes ◽  
Transmission Distortions ◽  
Amplitude Versus ◽  
Buried Faults

Transmission distortions are observed on prestack seismic data at two locations in the Gulf of Mexico. These distortions produce anomalous amplitude versus offset (AVO) signatures. The locations of the distortion zones are determined using acquisition geometry and ray tracing. No obvious reflection events, such as shallow gas zones, are observed at the predicted locations of the distortion zones. Instead, the distortion zones correlate with buried faults and unconformities. It is postulated that the distortions are produced by velocity changes across buried faults and unconformities. The distortions result from an interference pattern resulting from seismic waves arriving from different sides of the faults. A simple model is developed to explain many of the characteristics of the distortion pattern.

THE ROLE OF AMPLITUDE VERSUS OFFSET TECHNOLOGY IN PROMOTING OFFSHORE PETROLEUM EXPLORATION IN AUSTRALIA

2007 ◽  
Vol 47 (1) ◽  
pp. 163 ◽  
Author(s):  
P. E. Williamson ◽  
F. Kroh
Keyword(s):  
Petroleum Exploration ◽  
Gas Field ◽  
North West ◽  
Preliminary Results ◽  
Exmouth Plateau ◽  
The North ◽  
Amplitude Versus Offset ◽  
Cable Lines ◽  
The Cost ◽  
Amplitude Versus

Amplitude versus offset (AVO) technology has proved itself useful in petroleum exploration in various parts of the world, particularly for gas exploration. To determine if modern AVO compliant processing could identify potential anomalies for exploration of open acreage offshore Australia, Geoscience Australia reprocessed parts of four publicly available long cable lines. These lines cover two 2006 acreage release areas on the Exmouth Plateau and in the Browse Basin on the North West Shelf. An earlier study has also been done on two publicly available long cable lines from Geoscience Australia’s Bremer Basin study and cover areas from the 2005 frontier acreage release on the southern margin. The preliminary results from these three reprocessing efforts produced AVO anomalies and were made publicly available to assist companies interested in assessing the acreage. The results of the studies and associated data are available from Geoscience Australia at the cost of transfer.The AVO data from the Exmouth Plateau show AVO anomalies including one that appears to be at the Jurassic level of the reservoir in the Jansz/Io supergiant gas field in adjacent acreage to the north. The AVO data from the Caswell Sub-basin of the Browse Basin show an AVO anomaly at or near the stratigraphic zone of the Brecknock South–1 gas discovery to the north. The geological settings of strata possibly relating to two AVO anomalies in the undrilled Bremer Basin are in the Early Cretaceous section, where lacustrine sandstones are known to occur. The AVO anomalies from the three studies are kilometres in length along the seismic lines.These preliminary results from Geoscience Australiaand other AVO work that has been carried out by industry show promise that AVO compliant processing has value—particularly for gas exploration offshore Australia—and that publicly available long-cable data can be suitable for AVO analysis.

Robust Empirical Time–Frequency Relations for Seismic Spectral Amplitudes, Part 1: Application to Regional S Waves in Southeastern Iran

2020 ◽  
Author(s):  
Maryam Safarshahi ◽  
Igor B. Morozov
Keyword(s):  
Seismic Waves ◽  
Joint Inversion ◽  
Vertical Component ◽  
Transverse Component ◽  
Model Parameters ◽  
S Wave ◽  
Near Surface ◽  
S Waves ◽  
Time Frequency ◽  
Frequency Independent

ABSTRACT Empirical models of geometrical-, Q-, t-star, and kappa-type attenuation of seismic waves and ground-motion prediction equations (GMPEs) are viewed as cases of a common empirical standard model describing variation of wave amplitudes with time and frequency. Compared with existing parametric and nonparametric approaches, several new features are included in this model: (1) flexible empirical parameterization with possible nonmonotonous time or distance dependencies; (2) joint inversion for time or distance and frequency dependencies, source spectra, site responses, kappas, and Q; (3) additional constraints removing spurious correlations of model parameters and data residuals with source–receiver distances and frequencies; (4) possible kappa terms for sources as well as for receivers; (5) orientation-independent horizontal- and three-component amplitudes; and (6) adaptive filtering to reduce noise effects. The approach is applied to local and regional S-wave amplitudes in southeastern Iran. Comparisons with previous studies show that conventional attenuation models often contain method-specific biases caused by limited parameterizations of frequency-independent amplitude decays and assumptions about the models, such as smoothness of amplitude variations. Without such assumptions, the frequency-independent spreading of S waves is much faster than inferred by conventional modeling. For example, transverse-component amplitudes decrease with travel time t as about t−1.8 at distances closer than 90 km and as t−2.5 beyond 115 km. The rapid amplitude decay at larger distances could be caused by scattering within the near surface. From about 90 to 115 km distances, the amplitude increases by a factor of about 3, which could be due to reflections from the Moho and within the crust. With more accurate geometrical-spreading and kappa models, the Q factor for the study area is frequency independent and exceeds 2000. The frequency-independent and Q-type attenuation for vertical-component and multicomponent amplitudes is somewhat weaker than for the horizontal components. These observations appear to be general and likely apply to other areas.

Porosity identification using amplitude variations with offset: Examples from South Sumatra

Geophysics ◽  
1989 ◽  
Vol 54 (8) ◽  
pp. 942-951 ◽  
Author(s):  
S. Chacko
Keyword(s):  
Oil And Gas ◽  
Angle Of Incidence ◽  
The South ◽  
Gas Reservoir ◽  
Amplitude Versus Offset ◽  
Variation Patterns ◽  
Reefal Facies ◽  
Highly Porous ◽  
Amplitude Versus ◽  
Good Agreement

Widespread deposition of platform and reefal carbonates of the Baturaja limestone formation occurred during the Miocene epoch in the South Sumatra basin. Although significant oil and gas deposits have been discovered in the porous facies, porosity within the Baturaja limestone has been observed to vary widely between tight platform facies and highly porous reefal facies, making predrill prediction of porosity an important exploration objective. I use amplitude‐versus‐offset seismic modeling to distinguish between porous and tight Baturaja limestone facies. Amplitude variations with offset for reflections from two Baturaja reefs in the South Sumatra basin were studied: one, a proven gas reservoir, the other, an interpreted reef that had not yet been drilled at the time of study. The seismic data were processed judiciously to preserve and enhance amplitude effects, which were then modeled using the Bortfeld approximation for reflection coefficients. A key assumption was that the [Formula: see text] ratio of limestone depends primarily on minerology rather than on porosity or pore‐fluid content. The modeling showed that porous and tight limestone facies have unique and different reflection-coefficient variation patterns with angle of incidence. Good agreement was found between observed data and the modeling results, indicating that the modeling of amplitude variations with offset can be used as a lithology discriminant. In the second case, a predrill prediction of porosity was confirmed by subsequent drilling.

Case study: The importance of gas leakage in interpreting amplitude‐versus‐offset (AVO) analysis

Geophysics ◽  
1991 ◽  
Vol 56 (11) ◽  
pp. 1886-1895 ◽  
Author(s):  
M. K. Sengupta ◽  
C. A. Rendleman
Keyword(s):  
Seismic Energy ◽  
Gas Content ◽  
Bright Spot ◽  
Seismic Section ◽  
Gas Leakage ◽  
Hydrocarbon Reservoir ◽  
Reflection Amplitude ◽  
Amplitude Versus Offset ◽  
Amplitude Anomaly ◽  
Amplitude Versus

The amplitude‐versus‐offset (AVO) method has been shown to indicate the presence of gas sands if the reflection amplitude from the seal/reservoir‐sand interface, measured in a common midpoint (CMP) gather, increases rapidly with increasing shot‐to‐geophone distance (or offset). However, in a few instances, it has been observed that the seismic reflection amplitude does not increase with offset and may even decrease if there is widespread gas leakage above the hydrocarbon reservoir causing partial gas saturation in the overburden sediments. Gas‐charged sediments are known to attenuate seismic energy. Depending on the size and shape of this gas leakage zone, there may be higher attenuation of seismic amplitudes with increasing offset. We present one such case that involves a prominent “bright‐spot” amplitude anomaly corresponding to a 56‐ft‐thick (17 m‐thick) gas sand in the Gulf of Mexico slope. The reflection amplitude for the sand top was found to decrease with increasing offset. There is also evidence of gas leakage into the sediments above the reservoir. Color amplitude displays of the seismic section show a low‐amplitude diffused zone above the bright‐spot amplitude anomaly, which suggests gas leakage. Further evidence of gas leakage can be inferred from the significant gas content (including heavier hydrocarbons) observed in the mud log. Gas leakage is also confirmed by gather modeling in which the effects of leakage‐caused attenuation are accounted for in matching the variation of seismic amplitude with offset.

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