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.

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.

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.

The Shuey-Radon transform

Geophysics ◽  
2019 ◽  
Vol 84 (3) ◽  
pp. V197-V206 ◽  
Author(s):  
Ali Gholami ◽  
Milad Farshad
Keyword(s):  
Radon Transform ◽  
Seismic Data ◽  
Matching Pursuit ◽  
Real Data ◽  
Transform Domain ◽  
Amplitude Variation ◽  
Amplitude Variation With Offset ◽  
Linear System Of Equations ◽  
Matching Pursuit Algorithm ◽  
Zero Offset

The traditional hyperbolic Radon transform (RT) decomposes seismic data into a sum of constant amplitude basis functions. This limits the performance of the transform when dealing with real data in which the reflection amplitudes include the amplitude variation with offset (AVO) variations. We adopted the Shuey-Radon transform as a combination of the RT and Shuey’s approximation of reflectivity to accurately model reflections including AVO effects. The new transform splits the seismic gather into three Radon panels: The first models the reflections at zero offset, and the other two panels add capability to model the AVO gradient and curvature. There are two main advantages of the Shuey-Radon transform over similar algorithms, which are based on a polynomial expansion of the AVO response. (1) It is able to model reflections more accurately. This leads to more focused coefficients in the transform domain and hence provides more accurate processing results. (2) Unlike polynomial-based approaches, the coefficients of the Shuey-Radon transform are directly connected to the classic AVO parameters (intercept, gradient, and curvature). Therefore, the resulting coefficients can further be used for interpretation purposes. The solution of the new transform is defined via an underdetermined linear system of equations. It is formulated as a sparsity-promoting optimization, and it is solved efficiently using an orthogonal matching pursuit algorithm. Applications to different numerical experiments indicate that the Shuey-Radon transform outperforms the polynomial and conventional RTs.

Predicting the seismic implications of salt anisotropy using numerical simulations of halite deformation

Geophysics ◽  
2000 ◽  
Vol 65 (4) ◽  
pp. 1272-1280 ◽  
Author(s):  
Daniel G. Raymer ◽  
Andréa Tommasi ◽  
J‐Michael Kendall
Keyword(s):  
Elastic Constants ◽  
Seismic Waves ◽  
Seismic Anisotropy ◽  
Numerical Models ◽  
Amplitude Variation ◽  
Amplitude Variation With Offset ◽  
The Past ◽  
Numerical Studies ◽  
Polycrystalline Aggregates ◽  
Ray Paths

In the past, the potential for seismic anisotropy in salt structures and its effect on their seismic imaging has received little attention. We consider the plausibility of salt anisotropy through linked numerical studies of salt deformation and its seismic consequences. Numerical models are used to predict lattice preferred orientations (LPOs) in halite polycrystalline aggregates subjected to axial extension and simple shear. The elastic constants for the deformed polycrystalline aggregate are then calculated. Simple models representing a salt sill and the stem of a diapir are created using these elastic constants. Ray tracing is used to investigate the effects of halite LPO on the propagation of seismic waves. The results suggest that salt anisotropy can cause significant traveltime effects and could lead to significant errors in seismic interpretation in salt environments if this anisotropy is ignored. We also investigate potential amplitude variation with offset and azimuth (AVOA) for the reflection from the top and bottom of an anisotropic salt sill. Ray paths with a shear‐wave leg within the salt display strong AVOA effects with a clear four‐fold symmetry.

Amplitude-variation-with-offset, elastic-impedence, and wave-equation synthetics — A modeling study

Geophysics ◽  
2007 ◽  
Vol 72 (1) ◽  
pp. C1-C7 ◽  
Author(s):  
Subhashis Mallick
Keyword(s):  
Wave Equation ◽  
Incidence Angle ◽  
Synthetic Data ◽  
P Wave ◽  
Equation Modeling ◽  
Parameter Estimates ◽  
Angle Of Incidence ◽  
Amplitude Variation ◽  
Amplitude Variation With Offset ◽  
Wave Modes

Amplitude-variation-with-offset (AVO) and elastic-impedance (EI) analysis use an approximate plane P-wave reflection coefficient as a function of angle of incidence. AVO and EI both can be used in a three-term or a two-term formulation. This study uses synthetic data to demonstrate that the P-wave primary reflections at large offsets can be contaminated by reflections from other wave modes that can affect the quality of three-term AVO or EI results. The coupling of P-waves and S-waves in seismic-wave propagation through finely layered media generates the interfering wave modes. A methodology such as prestack-wave-equation modeling can properly account for these coupling effects. Both AVO and EI also assume a convolutional model whose accuracy decreases as incidence angles increase. On the other hand, wave-equation modeling is based on the rigorous solution to the wave equation and is valid for any incidence angle. Because wave interference is minimal at small angles, a two-term AVO/EI analysis that restricts input from small angles is likely to give more reliable parameter estimates than a three-term analysis. A three-term AVO/EI analysis should be used with caution and should be calibrated against well data and other data before being used for quantitative analysis.

Effects of transverse isotropy on P‐wave AVO for gas sands

Geophysics ◽  
1993 ◽  
Vol 58 (6) ◽  
pp. 883-888 ◽  
Author(s):  
Ki Young Kim ◽  
Keith H. Wrolstad ◽  
Fred Aminzadeh
Keyword(s):  
Transverse Isotropy ◽  
Transversely Isotropic ◽  
P Wave ◽  
Amplitude Variation ◽  
Amplitude Variation With Offset ◽  
Velocity Anisotropy ◽  
Special Cases ◽  
Class 1 ◽  
Zero Offset ◽  
Ti Media

Velocity anisotropy should be taken into account when analyzing the amplitude variation with offset (AVO) response of gas sands encased in shales. The anisotropic effects on the AVO of gas sands in transversely isotropic (TI) media are reviewed. Reflection coefficients in TI media are computed using a planewave formula based on ray theory. We present results of modeling special cases of exploration interest having positive reflectivity, near‐zero reflectivity, and negative reflectivity. The AVO reflectivity in anisotropic media can be decomposed into two parts; one for isotropy and the other for anisotropy. Zero‐offset reflectivity and Poisson’s ratio contrast are the most significant parameters for the isotropic component while the δ difference (Δδ) between shale and gas sand is the most important factor for the anisotropic component. For typical values of Tl anisotropy in shale (positive δ and ε), both δ difference (Δδ) and ε difference (Δε) amplify AVO effects. For small angles of incidence, Δδ plays an important role in AVO while Δε dominates for large angles of incidence. For typical values of δ and ε, the effects of anisotropy in shale are: (1) a more rapid increase in AVO for Class 3 and Class 2 gas sands, (2) a more rapid decrease in AVO for Class 1 gas sands, and (3) a shift in the offset of polarity reversal for some Class 1 and Class 2 gas sands.

Three-term amplitude-variation-with-offset projections

Geophysics ◽  
2018 ◽  
Vol 83 (5) ◽  
pp. N51-N65 ◽  
Author(s):  
Vaughn Ball ◽  
Luis Tenorio ◽  
Christian Schiøtt ◽  
Michelle Thomas ◽  
J. P. Blangy
Keyword(s):  
Rock Physics ◽  
Projection Methods ◽  
Well Logs ◽  
Rock Properties ◽  
Inversion Method ◽  
Practical Implementation ◽  
Angle Of Incidence ◽  
Amplitude Variation ◽  
Amplitude Variation With Offset ◽  
Maximum Angle

A three-term (3T) amplitude-variation-with-offset projection is a weighted sum of three elastic reflectivities. Parameterization of the weighting coefficients requires two angle parameters, which we denote by the pair [Formula: see text]. Visualization of this pair is accomplished using a globe-like cartographic representation, in which longitude is [Formula: see text], and latitude is [Formula: see text]. Although the formal extension of existing two-term (2T) projection methods to 3T methods is trivial, practical implementation requires a more comprehensive inversion framework than is required in 2T projections. We distinguish between projections of true elastic reflectivities computed from well logs and reflectivities estimated from seismic data. When elastic reflectivities are computed from well logs, their projection relationships are straightforward, and they are given in a form that depends only on elastic properties. In contrast, projection relationships between reflectivities estimated from seismic may also depend on the maximum angle of incidence and the specific reflectivity inversion method used. Such complications related to projections of seismic-estimated elastic reflectivities are systematized in a 3T projection framework by choosing an unbiased reflectivity triplet as the projection basis. Other biased inversion estimates are then given exactly as 3T projections of the unbiased basis. The 3T projections of elastic reflectivities are connected to Bayesian inversion of other subsurface properties through the statistical notion of Bayesian sufficiency. The triplet of basis reflectivities is computed so that it is Bayes sufficient for all rock properties in the hierarchical seismic rock-physics model; that is, the projection basis contains all information about rock properties that is contained in the original seismic.

Inversion of the seismic AVF/AVA signatures of highly attenuative targets

Geophysics ◽  
2011 ◽  
Vol 76 (1) ◽  
pp. R1-R14 ◽  
Author(s):  
Kristopher A. Innanen
Keyword(s):  
Reflection Coefficient ◽  
Wave Velocity ◽  
P Wave ◽  
Reflection Coefficients ◽  
Angle Of Incidence ◽  
Amplitude Variation ◽  
P Wave Velocity ◽  
Amplitude Variation With Angle ◽  
Source Of Information ◽  
Two Parameter

Frequency-dependent seismic field data anomalies, appearing in association with low-[Formula: see text] targets, have, on occasion, been attributed to the presence of a strong absorptive reflection coefficient. This “absorptive reflectivity” represents a potent, and largely untapped, source of information for determining subsurface target properties. It would most likely be encountered where a predominantly elastic/nonattenuating overburden suddenly is interrupted by a highly attenuative target. Series expansions of absorptive reflection coefficients about small parameter contrasts and incidence angles can expose these anomalies to analysis, either frequency-by-frequency (amplitude variation with frequency [AVF]) or angle-by-angle (amplitude variation with angle of incidence [AVA]). Within this framework, variations in P-wave velocity and [Formula: see text] can be estimated separately through a range of direct formulas, both linear and with nonlinear corrections. The latter come to the fore when a contrast from an incidence medium [Formula: see text] (i.e., acoustic/elastic) to a target medium [Formula: see text] is encountered, in which case the linearized estimate can be in error by as much as 50%. Algorithmically, it is a differencing of the reflection coefficient across frequencies that separates [Formula: see text] variations from variations in other parameters. This holds for both two-parameter (P-wave velocity and [Formula: see text]) problems and five-parameter anelastic problems, and would appear to be a general feature of direct absorptive inversion.

Sign in / Sign up

Export Citation Format

Share Document