Effects of attenuation and anisotropy on reflection amplitude versus offset

Geophysics ◽  
1998 ◽  
Vol 63 (5) ◽  
pp. 1652-1658 ◽  
Author(s):  
José M. Carcione ◽  
Hans B. Helle ◽  
Tong Zhao
Keyword(s):  
Symmetry Axis ◽  
Transversely Isotropic ◽  
Critical Distance ◽  
Reflection Coefficients ◽  
Amplitude Variation With Offset ◽  
Reflection Amplitude ◽  
Amplitude Versus Offset ◽  
Viscoelastic Wave ◽  
Lossy Media ◽  
Amplitude Versus

To investigate the effects that attenuation and anisotropy have on reflection coefficients, we consider a homogeneous and viscoelastic wave incident on an interface between two transversely isotropic and lossy media with the symmetry axis perpendicular to the interface. Analysis of P P and P S reflection coefficients shows that anisotropy should be taken into account in amplitude variation with offset (AVO) studies involving shales. Different anisotropic characteristics may reverse the reflection trend and substantially influence the position of the critical angle versus offset. The analysis of a shale‐chalk interface indicates that when the critical distance is close to the near offsets, the AVO response is substantially affected by the presence of dissipation. In a second example, we compute reflection coefficients and synthetic seismograms for a limestone/black shale interface with different rheological properties of the underlying shale. This case shows reversal of the reflection trend with increasing offset and compensation between the anisotropic and anelastic effects.

Three‐parameter AVO crossplotting in anisotropic media

Geophysics ◽  
2001 ◽  
Vol 66 (5) ◽  
pp. 1359-1363 ◽  
Author(s):  
He Chen ◽  
John P. Castagna ◽  
Raymon L. Brown ◽  
Antonio C. B. Ramos
Keyword(s):  
Real World ◽  
Transversely Isotropic ◽  
Reflection Coefficients ◽  
Anisotropic Behavior ◽  
Amplitude Versus Offset ◽  
Transversely Isotropic Media ◽  
Interpretation Errors ◽  
Isotropic Media ◽  
Empirical Corrections ◽  
Amplitude Versus

Amplitude versus offset (AVO) interpretation can be facilitated by crossplotting AVO intercept (A), gradient (B), and curvature (C) terms. However, anisotropy, which exists in the real world, usually complicates AVO analysis. Recognizing anisotropic behavior on AVO crossplots can help avoid AVO interpretation errors. Using a modification to a three‐term (A, B, and C) approximation to the exact anisotropic reflection coefficients for transversely isotropic media, we find that anisotropy has a nonlinear effect on an A versus C crossplot yet causes slope changes and differing intercepts on A versus B or C crossplots. Empirical corrections that result in more accurate crossplot interpretation are introduced for specific circumstances.

Geometrical spreading in a layered transversely isotropic medium with vertical symmetry axis

Geophysics ◽  
2003 ◽  
Vol 68 (6) ◽  
pp. 2082-2091 ◽  
Author(s):  
Bjørn Ursin ◽  
Ketil Hokstad
Keyword(s):  
Ray Tracing ◽  
Seismic Data ◽  
Symmetry Axis ◽  
Transversely Isotropic ◽  
Analytical Approximation ◽  
Geometrical Spreading ◽  
S Wave ◽  
Weak Anisotropy ◽  
P Waves ◽  
Amplitude Versus

Compensation for geometrical spreading is important in prestack Kirchhoff migration and in amplitude versus offset/amplitude versus angle (AVO/AVA) analysis of seismic data. We present equations for the relative geometrical spreading of reflected and transmitted P‐ and S‐wave in horizontally layered transversely isotropic media with vertical symmetry axis (VTI). We show that relatively simple expressions are obtained when the geometrical spreading is expressed in terms of group velocities. In weakly anisotropic media, we obtain simple expressions also in terms of phase velocities. Also, we derive analytical equations for geometrical spreading based on the nonhyperbolic traveltime formula of Tsvankin and Thomsen, such that the geometrical spreading can be expressed in terms of the parameters used in time processing of seismic data. Comparison with numerical ray tracing demonstrates that the weak anisotropy approximation to geometrical spreading is accurate for P‐waves. It is less accurate for SV‐waves, but has qualitatively the correct form. For P waves, the nonhyperbolic equation for geometrical spreading compares favorably with ray‐tracing results for offset‐depth ratios less than five. For SV‐waves, the analytical approximation is accurate only at small offsets, and breaks down at offset‐depth ratios less than unity. The numerical results are in agreement with the range of validity for the nonhyperbolic traveltime equations.

scholarly journals QVOA Techniques for Estimation of Fracture Directions

2018 ◽  
Vol 2018 ◽  
pp. 1-11
Author(s):  
Vladimir Sabinin
Keyword(s):  
Quality Factor ◽  
Symmetry Axis ◽  
Factor Versus ◽  
Synthetic Data ◽  
Computational Techniques ◽  
High Quality ◽  
Amplitude Versus Offset ◽  
Target Layer ◽  
Analysis Quality ◽  
Amplitude Versus

Some new computational techniques are suggested for estimating symmetry axis azimuth of fractures in the viscoelastic anisotropic target layer in the framework of QVOA analysis (Quality factor Versus Offset and Azimuth). The different QVOA techniques are compared using synthetic viscoelastic surface reflected data with and without noise. I calculated errors for these techniques which depend on different sets of azimuths and intervals of offsets. Superiority of the high-order “enhanced general” and “cubic” techniques is shown. The high-quality QVOA techniques are compared with one of the high-quality AVOA techniques (Amplitude Versus Offset and Azimuth) in the synthetic data with noise and attenuation. Results are comparable.

scholarly journals Analysis of fluid substitution in a porous and fractured medium

Geophysics ◽  
2011 ◽  
Vol 76 (3) ◽  
pp. WA157-WA166 ◽  
Author(s):  
Samik Sil ◽  
Mrinal K. Sen ◽  
Boris Gurevich
Keyword(s):  
Water Saturation ◽  
Transversely Isotropic ◽  
P Wave ◽  
Reflection Coefficients ◽  
Fluid Substitution ◽  
Fracture Density ◽  
Maximum Increase ◽  
Amplitude Variation With Offset ◽  
Fractured Medium ◽  
Medium Change

To improve quantitative interpretation of seismic data, we analyze the effect of fluid substitution in a porous and fractured medium on elastic properties and reflection coefficients. This analysis uses closed-form expressions suitable for fluid substitution in transversely isotropic media with a horizontal symmetry axis (HTI). For the HTI medium, the effect of changing porosity and water saturation on (1) P-wave moduli, (2) horizontal and vertical velocities, (3) anisotropic parameters, and (4) reflection coefficients are examined. The effects of fracture density on these four parameters are also studied. For the model used in this study, a 35% increase in porosity lowers the value of P-wave moduli by maximum of 45%. Consistent with the reduction in P-wave moduli, P-wave velocities also decrease by maximum of 17% with a similar increment in porosity. The reduction is always larger for the horizontal P-wave modulus than for the vertical one and is nearly independent of fracture density. The magnitude of the anisotropic parameters of the fractured medium also changes with increased porosity depending on the changes in the value of P-wave moduli. The reflection coefficients at an interface of the fractured medium with an isotropic medium change in accordance with the above observations and lead to an increase in anisotropic amplitude variation with offset (AVO) gradient with porosity. Additionally, we observe a maximum increase in P-wave modulus and velocity by 30% and 8%, respectively, with a 100% increase in water saturation. Water saturation also changes the anisotropic parameters and reflection coefficients. Increase in water saturation considerably increases the magnitude of the anisotropic AVO gradient irrespective of fracture density. From this study, we conclude that porosity and water saturation have a significant impact on the four studied parameters and the impacts are seismically detectable.

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.

Multiazimuthal modeling and inversion of qP reflection coefficients in fractured media

Geophysics ◽  
1999 ◽  
Vol 64 (4) ◽  
pp. 1143-1152 ◽  
Author(s):  
Ivan A. Simões‐Filho ◽  
Fernando A. Neves ◽  
Júlio S. Tinen ◽  
João S. Protázio ◽  
Jessé C. Costa
Keyword(s):  
Isotropic Medium ◽  
Model Space ◽  
Transversely Isotropic ◽  
Reservoir Rock ◽  
Reflection Coefficients ◽  
Fracture Density ◽  
Amplitude Variation ◽  
Amplitude Variation With Offset ◽  
The Difference ◽  
And Inversion

We present a method for the exact modeling and inversion of multiazimuthal qP-wave reflection coefficients at an interface separating two anisotropic media. This procedure can be used for media with at least one of its planes of symmetry parallel to the interface (i.e., monoclinic or higher symmetries). To illustrate the method, we compute qP-wave reflection coefficients at an interface separating an isotropic medium (representing a seal rock) from a transversely isotropic medium (representing a reservoir rock with vertical aligned fractures). Forward modeling shows that the difference in the offset of the critical angles for different azimuths is proportional to the fracture density: the higher the fracture density, the larger the difference. In the second part of the paper, we use a global optimization technique (genetic algorithm) to invert wide‐angle amplitude variation with offset (AVO) synthetic data. The model space consists of mass density and five elastic parameters of a transversely isotropic medium with a horizontal symmetry axis (HTI medium), which, to the first order, represents the fractured reservoir rock. For this model, we find that the configuration of three azimuths of data acquisition is the minimum number of acquisition planes needed to invert amplitude variation with offset/amplitude variation with azimuth (AVO/AVA) data. Further, there is a need for incidence angles up to 40°; a more narrow range of angles can lead to models that fit the data perfectly only up to the “maximum” incidence angle. We assume that the velocities and density of the isotropic rock are known, but use no prior information on the values of the model space parameters of the fractured rock except for reasonable velocity values in crustal rocks and constraints of elastic stability of solid media. After inversion for the model space parameters, we compute statistics of the 30 best models and likelihood functions, which provide information on the nonuniqueness and quality of the AVO/AVA inverse problem.

The effects of transverse isotropy on reflection amplitude versus offset

Geophysics ◽  
1987 ◽  
Vol 52 (4) ◽  
pp. 564-567 ◽  
Author(s):  
J. Wright
Keyword(s):  
Wave Velocity ◽  
Transverse Isotropy ◽  
Transversely Isotropic ◽  
P Wave ◽  
S Wave ◽  
Reflection Amplitude ◽  
Amplitude Versus Offset ◽  
Transversely Isotropic Media ◽  
P Wave Velocity ◽  
Isotropic Media

Studies have shown that elastic properties of materials such as shale and chalk are anisotropic. With the increasing emphasis on extraction of lithology and fluid content from changes in reflection amplitude with shot‐to‐group offset, one needs to know the effects of anisotropy on reflectivity. Since anisotropy means that velocity depends upon the direction of propagation, this angular dependence of velocity is expected to influence reflectivity changes with offset. These effects might be particularly evident in deltaic sand‐shale sequences since measurements have shown that the P-wave velocity of shales in the horizontal direction can be 20 percent higher than the vertical P-wave velocity. To investigate this behavior, a computer program was written to find the P- and S-wave reflectivities at an interface between two transversely isotropic media with the axis of symmetry perpendicular to the interface. Models for shale‐chalk and shale‐sand P-wave reflectivities were analyzed.

True‐amplitude transformation to zero offset of data from curved reflectors

Geophysics ◽  
1999 ◽  
Vol 64 (1) ◽  
pp. 112-129 ◽  
Author(s):  
Norman Bleistein ◽  
Jack Cohen ◽  
Herman Jaramillo
Keyword(s):  
General Context ◽  
Reflection Coefficients ◽  
Geometrical Spreading ◽  
Curvature Effects ◽  
Multiplicative Factor ◽  
Amplitude Factor ◽  
Amplitude Versus Offset ◽  
Zero Offset ◽  
The Cost ◽  
Amplitude Versus

Transformation to zero offset (TZO), alternatively known as migration to zero offset (MZO), or the combination of normal moveout and dip moveout (NMO/DMO), is a process that transforms data collected at finite offset between source and receiver to a pseudozero offset trace. The kinematic validity of NMO/DMO processing has been well established. The TZO integral operators proposed here differ from their NMO/DMO counterparts by a simple amplitude factor. (The form of the operator depends on how the input and output variables are chosen from among the combinations of midpoint or wavenumber with time or frequency.) With this modification in place, the dynamical validity for planar reflectors of the proposed TZO operators of this paper have been established in earlier studies. This means that the traveltime and geometrical spreading terms of the finite offset data are transformed to their counterparts for zero offset data, while the finite offset reflection coefficient is preserved. The main purpose of this study is to show that dynamical validity of the TZO operator extends to the case of curved reflectors in the 2.5-D limit. Thus, at the cost of a simple additional multiplicative factor in any standard NMO/DMO operator to produce the corresponding TZO operator, the amplitude factor attributed to curvature effects in finite offset data is transformed by this TZO processing to the corresponding curvature factor for zero offset data. This problem has also been addressed in a more general context by Tygel and associates. However, in the generality, some of the specifics and interpretations of the simpler problem are lost. Thus, we see some value in presenting this analysis where one can carry out all calculations explicitly and see specific quantities that are more familiar and accessible to users of DMO. Furthermore, in this paper, we show how processing of the input data with a second TZO operator allows for the extraction of the cosine of the preserved specular angle, a necessary piece of information for amplitude versus angle (AVA) analysis. We then discuss the possibility of using the output of our processing formalism at multiple offsets to create a table of angularly dependent reflection coefficients and attendant incidence angles as a function of offset. This is the basis of a proposed amplitude versus offset/amplitude versus angle (AVO/AVA) analysis of the pseudozero offset traces. Finally, we describe the modifications of Hale DMO and Gardner/Forel DMO to obtain true amplitude output equivalent to ours and also how to extract the cosine of the specular angle for these forms of DMO. This last does not depend on true amplitude processing, but only on processing two DMO operators with slightly different kernels and then taking the quotient of their peak amplitudes.

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