Implications of thin layers for amplitude variation with offset (AVO) studies

Geophysics ◽  
1993 ◽  
Vol 58 (8) ◽  
pp. 1200-1204 ◽  
Author(s):  
Christopher Juhlin ◽  
Roger Young
Keyword(s):  
Reflection Coefficient ◽  
Poisson’S Ratio ◽  
Thin Layers ◽  
Poisson's Ratio ◽  
Angle Of Incidence ◽  
Amplitude Variation ◽  
Seismic Reflection Data ◽  
Amplitude Variation With Offset ◽  
Rock Types ◽  
Gas Bearing

Amplitude variation with offset (AVO), or amplitude variation with angle (AVA), analyses of seismic reflection data are becoming increasingly popular in the exploration industry (Ostrander, 1984; Pichin and Mitchell, 1991; Mazzotti and Mirri, 1991) and also in scientific studies of the earth’s crust (Juhlin, 1990). In the exploration industry, AVO analyses are particularly suitable for the detection and mapping of gas zones since reservoirs often consist of shale with high Poisson’s ratio (high [Formula: see text]) overlying gas bearing sands with low Poisson’s ratio (low [Formula: see text]). If the gas sand has lower impedance than the overlying shale, the magnitude of the reflection coefficient will increase with increasing angle of incidence or offset. Other combinations of rock types will also show a similar increase in magnitude, such as shale over hard limestone, but the sign of the reflection coefficient will be positive in most of these cases. Therefore, if the polarity of the reflection can be determined to be negative and there is an increase in the absolute amplitude of the reflection with offset, then this is highly indicative of a gas bearing zone.

AVA analysis after velocity-independent DMO and imaging

Geophysics ◽  
1998 ◽  
Vol 63 (2) ◽  
pp. 686-691 ◽  
Author(s):  
Gerald H. F. Gardner ◽  
Anat Canning
Keyword(s):  
Reflection Coefficient ◽  
Peak Amplitude ◽  
Angle Of Incidence ◽  
Amplitude Variation ◽  
Amplitude Variation With Offset ◽  
The Past ◽  
Reflectivity Function ◽  
Velocity Of Propagation ◽  
Zero Offset ◽  
Amplitude Versus

A common midpoint (CMP) gather usually provides amplitude variation with offset (AVO) information by displaying the reflectivity as the peak amplitude of symmetrical deconvolved wavelets. This puts a reflection coefficient R at every offset h, giving a function R(h). But how do we link h with the angle of incidence, θ, to get the reflectivity function, R(θ)? This is necessary for amplitude versus angle-of-incidence (AVA) analysis. One purpose of this paper is to derive formulas for this linkage after velocity-independent dip-moveout (DMO), done by migrating radial sections, and prestack zero-offset migration. Related studies of amplitude-preserving DMO in the past have dealt with constant-offset DMO but have not given the connection between offset and angle of incidence after processing. The results in the present paper show that the same reflectivity function can be extracted from the imaged volume whether it is produced using radial-trace DMO plus zero-offset migration, constant-offset DMO plus zero-offset migration, or directly by prestack, common-offset migration. The data acquisition geometry for this study consists of parallel, regularly spaced, multifold lines, and the velocity of propagation is constant. Events in the data are caused by an arbitrarily oriented 3-D plane reflector with any reflectivity function. The DMO operation transforms each line of data (m, h, t), i.e., midpoint, half-offset, and time, into an (m1, k, t1) space by Stolt-migrating each radial-plane section of the data, 2h = Ut, with constant velocity U/2. Merging the (m1, k, t1) spaces for all the lines forms an (x, y, k, t1) space, where the first two coordinates are the midpoint location, the third is the new half-offset, and the fourth is the time. Normal moveout (NMO) plus 3-D zero-offset migration of the subspace (x, y, t1) for each k creates a true-amplitude imaged volume (X, Y, k, T). Each peak amplitude in the volume is a reflection coefficient linked to an angle of incidence.

Plane‐wave reflection coefficients for gas sands at nonnormal angles of incidence

Geophysics ◽  
1984 ◽  
Vol 49 (10) ◽  
pp. 1637-1648 ◽  
Author(s):  
W. J. Ostrander
Keyword(s):  
Reflection Coefficient ◽  
Poisson’S Ratio ◽  
Wave Reflection ◽  
P Wave ◽  
Poisson's Ratio ◽  
Angle Of Incidence ◽  
High Porosity ◽  
Low Velocity ◽  
Poisson's Ratios ◽  
Poisson’S Ratios

The P-wave reflection coefficient at an interface separating two media is known to vary with angle of incidence. The manner in which it varies is strongly affected by the relative values of Poisson’s ratio in the two media. For moderate angles of incidence, the relative change in reflection coefficient is particularly significant when Poisson’s ratio differs greatly between the two media. Theory and laboratory measurements indicate that high‐porosity gas sands tend to exhibit abnormally low Poisson’s ratios. Embedding these low‐velocity gas sands into sediments having “normal” Poisson’s ratios should result in an increase in reflected P-wave energy with angle of incidence. This phenomenon has been observed on conventional seismic data recorded over known gas sands.

Some effects of velocity variation on AVO and its interpretation

Geophysics ◽  
1993 ◽  
Vol 58 (9) ◽  
pp. 1297-1300 ◽  
Author(s):  
Yu Xu ◽  
G. H. F. Gardner ◽  
J. A. McDonald
Keyword(s):  
Velocity Gradient ◽  
Poisson’S Ratio ◽  
Incident Angle ◽  
Elastic Parameter ◽  
Poisson's Ratio ◽  
Velocity Variation ◽  
Elastic Parameters ◽  
Amplitude Variation ◽  
Amplitude Variation With Offset ◽  
Meaningful Relationship

In recent years interest has increased in the interpretation of the amplitude variation of reflected signals as a function of offset (AVO). A more meaningful relationship for interpreting reflection coefficients at the target horizon is amplitude variation with incident angle (AVA). The challenge is to convert from AVO to AVA. The effects of velocity variation in the overburden on amplitude variation with offset (AVO) and on the final inversion of AVO data into velocity, density, and Poisson’s ratio can be significant. Examples are given here for subsurface medium with a vertical velocity gradient range of [Formula: see text] to [Formula: see text]. When the medium is treated as homogeneous in the conversion from AVO to AVA, this velocity variation causes significant errors (about 10 percent) in both the gradient of AVA and in the normal incident reflection coefficient. Such errors produce errors of similar magnitude in the inversion of AVA data into the elastic parameters of velocity, Poisson’s ratio, and density. The errors depend on the velocity gradient, the offset range, the elastic parameter contrast across the interface, and the interface depth.

scholarly journals Estimation of the Poisson’s Rate of the Intact Rock in the Function of the Rigidity

2019 ◽  
Author(s):  
Benedek A. Lógó ◽  
Balázs Vásárhelyi
Keyword(s):  
Poisson’S Ratio ◽  
Experimental Error ◽  
Limit Equilibrium ◽  
Material Constant ◽  
Friction Angle ◽  
Intact Rock ◽  
Poisson's Ratio ◽  
Mechanical Parameters ◽  
Linear Elastic ◽  
Rock Types

Although Poisson’s ratio is one of the basic rock mechanical parameters, it is less investigated than the other parameters. It can be assumed, that this material constant depends on the rigidity of the rock, among the others. The goal of this research is to find a theoretical relationship between the rigidity of the intact rock and Poisson’s ratio. It was assumed that there is a connection between the internal friction angle (or cohesion) and rigidity of the isotropic, linear elastic material, using the Mohr-Coulomb theory. Based on these equations from different published limit equilibrium, six different equations were compared. It is published that the rigidity value is equal (within the experimental error) to the Hoek-Brown material constant (mi) which value is well-known for many different rock types. Plotting the published Poisson’s ratio in the function of the rigidity of the intact rock the optimal connection was chosen.

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.

Two-step joint PP- and PS-wave three-term amplitude-variation with offset inversion

2016 ◽  
Vol 4 (4) ◽  
pp. T613-T625 ◽  
Author(s):  
Qizhen Du ◽  
Bo Zhang ◽  
Xianjun Meng ◽  
Chengfeng Guo ◽  
Gang Chen ◽  
...  
Keyword(s):  
Reflection Coefficient ◽  
Wave Reflection ◽  
Coefficient Matrix ◽  
P Wave ◽  
Inversion Method ◽  
S Wave ◽  
Amplitude Variation ◽  
Amplitude Variation With Offset ◽  
Avo Inversion ◽  
Pp Wave

Three-term amplitude-variation with offset (AVO) inversion generally suffers from instability when there is limited prior geologic or petrophysical constraints. Two-term AVO inversion shows higher instability compared with three-term AVO inversion. However, density, which is important in the fluid-type estimation, cannot be recovered from two-term AVO inversion. To reliably predict the P- and S-waves and density, we have developed a robust two-step joint PP- and PS-wave three-term AVO-inversion method. Our inversion workflow consists of two steps. The first step is to estimate the P- and S-wave reflectivities using Stewart’s joint two-term PP- and PS-AVO inversion. The second step is to treat the P-wave reflectivity obtained from the first step as the prior constraint to remove the P-wave velocity related-term from the three-term Aki-Richards PP-wave approximated reflection coefficient equation, and then the reduced PP-wave reflection coefficient equation is combined with the PS-wave reflection coefficient equation to estimate the S-wave and density reflectivities. We determined the effectiveness of our method by first applying it to synthetic models and then to field data. We also analyzed the condition number of the coefficient matrix to illustrate the stability of the proposed method. The estimated results using proposed method are superior to those obtained from three-term AVO inversion.

On: “Long‐wave elastic anisotropy in transversely isotropic media” by J. G. Berryman, and “Seismic velocities in transversely isotropic media” by F. K. Levin (GEOPHYSICS, v. 44, May 1979, p. 896–917 and p. 918–936, respectively).

Geophysics ◽  
1981 ◽  
Vol 46 (3) ◽  
pp. 336-338 ◽  
Author(s):  
Felix M. Lyakhovitskiy
Keyword(s):  
Poisson’S Ratio ◽  
Elastic Anisotropy ◽  
Transversely Isotropic ◽  
Layered Media ◽  
Thin Layers ◽  
Poisson's Ratio ◽  
Seismic Velocities ◽  
Long Wave ◽  
Transversely Isotropic Media ◽  
Isotropic Media

Berryman and Levin made an assumption about constancy or limited variations of Poisson’s ratio in the thin layers, in their analyses of elastic anisotropy in thin‐layered media. Berryman states (p. 913): “Rare cases can occur with large variations in Poisson’s ratio.” However, on p. 911 Berryman does point out (with reference to Benzing) that range of variations of the parameter γ = VS/VP from 0.45 to 0.65 is typical of rocks. That corresponds to a range of variations of Poisson’s ratio of 0.373 to 0.134 (i.e., almost three times as much).

Factors facilitating or limiting the use of AVO for coal-bed methane

Geophysics ◽  
2006 ◽  
Vol 71 (4) ◽  
pp. C49-C56 ◽  
Author(s):  
Suping Peng ◽  
Huajing Chen ◽  
Ruizhao Yang ◽  
Yunfeng Gao ◽  
Xinping Chen
Keyword(s):  
Poisson’S Ratio ◽  
Poisson's Ratio ◽  
Coal Bed ◽  
Coal Bed Methane ◽  
Coal Seams ◽  
Amplitude Variation With Offset ◽  
Impedance Contrast ◽  
Reservoir Potential ◽  
Sweet Spots

There are similarities and differences in employing amplitude variation with offset (AVO) to explore for gas-sand reservoirs, as opposed to coal-bed methane (CBM) reservoirs. The main similarity is that large Poisson’s ratio contrasts, resulting in AVO gradient anomalies, are expected for both kinds of reservoirs. The main difference is that cleating and fracturing raise the Poisson’s ratio of a coal seam as it improves its reservoir potential for CBM, while gas always lowers the Poisson’s ratio of a sandstone reservoir. The top of gas sands usually has a negative AVO gradient, leading to a class one, two, or three anomaly depending on the impedance contrast with the overlying caprock. On the other hand, the top of a CBM reservoir has a positive AVO gradient, leading to a class four anomaly. Three environmental factors may limit the usage of AVO for CBM reservoirs: the smaller contrast in Poisson’s ratio between a CBM reservoir and its surrounding rock, variations in the caprock of a specific CBM reservoir, and the fact that CBM is not always free to collect at structurally high points in the reservoir. However, other factors work in favor of using AVO. The strikingly high reflection amplitude of coal improves signal/noise ratio and hence the reliability of AVO measurements. The relatively simple characteristics of AVO anomalies make them easy to interpret. Because faults are known to improve the quality of CBM reservoirs, faults accompanied by AVO anomalies would be especially convincing. A 3D-AVO example offered in this paper shows that AVO might be helpful to delineate methane-rich sweet spots within coal seams.

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