Converted wave AVO inversion for average velocity ratio and shear wave reflection coefficient

2008 ◽  
Vol 5 (1) ◽  
pp. 35-43 ◽  
Author(s):  
Xiucheng Wei ◽  
Tiansheng Chen ◽  
Yuxin Ji
Keyword(s):  
Reflection Coefficient ◽  
Shear Wave ◽  
Average Velocity ◽  
Wave Reflection ◽  
Velocity Ratio ◽  
Converted Wave ◽  
Avo Inversion

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.

Waveform‐based AVO inversion and AVO prediction‐error

Geophysics ◽  
1996 ◽  
Vol 61 (6) ◽  
pp. 1575-1588 ◽  
Author(s):  
James L. Simmons ◽  
Milo M. Backus
Keyword(s):  
Reflection Coefficient ◽  
Thin Layer ◽  
Shear Wave ◽  
Prediction Error ◽  
Wave Reflection ◽  
A Priori ◽  
Normal Incidence ◽  
Strong Increase ◽  
Time Range ◽  
Zoeppritz Equations

A practical approach to linear prestack seismic inversion in the context of a locally 1-D earth is employed to use amplitude variation with offset (AVO) information for the direct detection in hydrocarbons. The inversion is based on the three‐term linearized approximation to the Zoeppritz equations. The normal‐incidence compressional‐wave reflection coefficient [Formula: see text] models the background reflectivity in the absence of hydrocarbons and incorporates the mudrock curve and Gardner’s equation. Prediction‐error parameters, [Formula: see text] and [Formula: see text], represent perturbations in the normal‐incidence shear‐wave reflection coefficient and the density contribution to the normal incidence reflectivity, respectively, from that predicted by the mudrock curve and Gardner’s equation. This prediction‐error approach can detect hydrocarbons in the absence of an overall increase in AVO, and in the absence of bright spots, as expected in theory. Linear inversion is applied to a portion of a young, Tertiary, shallow‐marine data set that contains known hydrocarbon accumulations. Prestack data are in the form of angle stack, or constant offset‐to‐depth ratio, gathers. Prestack synthetic seismograms are obtained by primaries‐only ray tracing using the linearized approximation to the Zoeppritz equations to model the reflection amplitudes. Where the a priori assumptions hold, the data are reproduced with a single parameter [Formula: see text]. Hydrocarbons are detected as low impedance relative to the surrounding shales and the downdip brine‐filled reservoir on [Formula: see text], also as positive perturbations (opposite polarity relative to [Formula: see text]) on [Formula: see text] and [Formula: see text]. The maximum perturbation in [Formula: see text] from the normal‐incidence shear‐wave reflection coefficient predicted by the a priori assumptions is 0.08. Hydrocarbon detection is achieved, although the overall seismic response of a gas‐filled thin layer shows a decrease in amplitude with offset (angle). The angle‐stack data (70 prestack ensembles, 0.504–1.936 s time range) are reproduced with a data residual that is 7 dB down. Reflectivity‐based prestack seismograms properly model a gas/water contact as a strong increase in AVO and a gas‐filled thin layer as a decrease in AVO.

Frequency-dependent spherical-wave nonlinear AVO inversion in elastic media

2020 ◽  
Vol 223 (2) ◽  
pp. 765-776
Author(s):  
Guangsen Cheng ◽  
Xingyao Yin ◽  
Zhaoyun Zong
Keyword(s):  
Reflection Coefficient ◽  
Wave Reflection ◽  
Fresnel Zone ◽  
Spherical Wave ◽  
Inversion Method ◽  
Elastic Media ◽  
Amplitude Variation With Offset ◽  
Avo Inversion ◽  
Well Location ◽  
The Stability

SUMMARY The plane-wave reflection coefficient (PRC) plays a remarkable role in conventional amplitude variation with offset (AVO) analysis and inversion. Compared with the widely exploited PRC that breaks down at the near- and supercritical incidence angles, the spherical-wave reflection coefficient (SRC) can overcome the influence of wide-angle reflection and give an accurate description of the actual seismic wave reflection phenomenon based on spherical-wave fronts. However, SRC is not widely used in AVO inversion due to its nonlinearity and computational complexity. In our study, the characteristics of frequency–depth-dependent monochromatic SRC are discussed and a novel three-parameter SRC is derived. Compared with the conventional six-parameter SRC, the novel three-parameter SRC improves the stability of spherical-wave AVO inversion. In addition, the concept of SRC within the Fresnel zone is proposed, and the accuracy of SRC within the Fresnel zone in the deep subsurface is tested. Finally, a nonlinear spherical-wave AVO inversion method for elastic media is proposed, which can make full use of all frequency components of wavelet. The robustness of the proposed method is verified by the application on synthetic seismogram with white Gaussian noise. The feasibility and practicability of this method are verified by comparing the spherical-wave AVO inversion results with the filtered well logs at the known well location.

Variation of P-wave reflectivity with offset and azimuth in anisotropic media

Geophysics ◽  
1998 ◽  
Vol 63 (3) ◽  
pp. 935-947 ◽  
Author(s):  
Andreas Rüger
Keyword(s):  
Reflection Coefficient ◽  
Shear Wave ◽  
Wave Reflection ◽  
Symmetry Plane ◽  
Anisotropic Media ◽  
Shear Wave Splitting ◽  
P Wave ◽  
Reflection Coefficients ◽  
Wave Splitting ◽  
Splitting Parameter

P-wave amplitudes may be sensitive even to relatively weak anisotropy of rock mass. Recent results on symmetry‐plane P-wave reflection coefficients in azimuthally anisotropic media are extended to observations at arbitrary azimuth, large incidence angles, and lower symmetry systems. The approximate P-wave reflection coefficient in transversely isotropic media with a horizontal axis of symmetry (HTI) (typical for a system of parallel vertical cracks embedded in an isotropic matrix) shows that the amplitude versus offset (AVO) gradient varies as a function of the squared cosine of the azimuthal angle. This change can be inverted for the symmetry‐plane directions and a combination of the shear‐wave splitting parameter γ and the anisotropy coefficient [Formula: see text]. The reflection coefficient study is also extended to media of orthorhombic symmetry that are believed to be more realistic models of fractured reservoirs. The study shows the orthorhombic and HTI reflection coefficients are very similar and the azimuthal variation in the orthorhombic P-wave reflection response is a function of the shear‐wave splitting parameter γ and two anisotropy parameters describing P-wave anisotropy for near‐vertical propagation in the symmetry planes. The simple relationships between the reflection amplitudes and anisotropic coefficients given here can be regarded as helpful rules of thumb in quickly evaluating the importance of anisotropy in a particular play, integrating results of NMO and shear‐wave‐splitting analyses, planning data acquisition, and guiding more advanced numerical amplitude‐inversion procedures.

scholarly journals A novel expression of the spherical-wave reflection coefficient at a plane interface

2017 ◽  
Vol 211 (2) ◽  
pp. 700-717 ◽  
Author(s):  
Jingnan Li ◽  
Shangxu Wang ◽  
Yonghui Tao ◽  
Chunhui Dong ◽  
Genyang Tang
Keyword(s):  
Reflection Coefficient ◽  
Complex Plane ◽  
Wave Reflection ◽  
Incidence Angle ◽  
Velocity Ratio ◽  
Spherical Wave ◽  
Density Ratio ◽  
Plane Interface ◽  
Analytical Equation ◽  
Wave Number

Abstract The spherical-wave reflection coefficient (SRC) describes the reflection strength when seismic waves emanating from a point source impinge on an interface. In this study, the SRC at a plane interface between two infinite half-spaces is investigated. We derive an analytical equation of the SRC when kR → 0 (k is the wave number and R is the wave propagation distance). It only depends on the density ratio; it is independent of the velocity ratio and incidence angle. On the other hand, we find that the SRCs at different kR lie along an elliptical curve on the complex plane (the complex plane is a geometric representation of the complex numbers established by the real axis and perpendicular imaginary axis). Based on this feature, we construct a new analytical equation for the reflected spherical wave with high accuracy, which is applicable to both small and large kR. Using the elliptical distribution of the SRCs for a series of frequencies recorded at only one spatial location, the density and velocity ratios can be extracted. This study complements the spherical-wave reflection theory and provides a new basis for acoustic parameters inversion, particularly density inversion.

Long-offset AVO inversion of PP reflections from plane interfaces using effective reflection coefficients

Geophysics ◽  
2011 ◽  
Vol 76 (6) ◽  
pp. C65-C79 ◽  
Author(s):  
Lyubov Skopintseva ◽  
Milana Ayzenberg ◽  
Martin Landrø ◽  
Tatyana Nefedkina ◽  
Arkady M. Aizenberg
Keyword(s):  
Reflection Coefficient ◽  
Plane Wave ◽  
Seismic Waves ◽  
Wave Reflection ◽  
Point Sources ◽  
Model Parameters ◽  
Reflection Coefficients ◽  
Avo Inversion ◽  
Long Offset ◽  
Head Waves

A conventional amplitude variation with offset (AVO) inversion is based on geometrical seismics which exploit plane-wave reflection coefficients to describe the reflection phenomenon. Widely exploited linearizations of plane-wave coefficients are mostly valid at pre-critical offsets for media with almost flat and weak-contrast interfaces. Existing linearizations do not account for the seismic frequency range by ignoring the frequency content of the wavelet, which is a strong assumption. Plane-wave reflection coefficients do not fully describe the reflection of seismic waves at near-critical and post-critical offsets, because reflected seismic waves are typically generated by point sources. We propose an improved approach to AVO inversion, which is based on effective reflection coefficients (ERCs). ERCs generalize plane-wave coefficients for seismic waves generated by point sources and therefore more accurately describe near-critical and post-critical reflections where head waves are generated. Moreover, they are frequency-dependent and incorporate the local curvatures of the wavefront and the reflecting interface. In our study, we neglect the effect of interface curvature and demonstrate the advantages of our approach on synthetic data for a simple model with a plane interface separating two isotropic half-spaces. A comparison of the inversion results obtained with our approach and the results from an AVO inversion method based on the exact plane-wave reflection coefficient suggests that our method is superior, in particular for long-offset ranges which extend to and beyond the critical angle. We thus propose that long offsets can be successfully exploited in an AVO inversion under the correct assumption about the reflection coefficient. Such long-offset AVO inversion shows the potential of outperforming a conventional moderate-offset AVO inversion in the accuracy of estimated model parameters.

ESTIMATION FORMULAS FOR WAVE REFLECTION COEFFICIENT OF LONG-PERIOD WAVE ABSORBING MOUND STRUCTURES

2019 ◽  
Vol 75 (2) ◽  
pp. I_787-I_792
Author(s):  
Jun MITSUI ◽  
Iwao HASEGAWA ◽  
Masashi TANAKA ◽  
Akira MATSUMOTO
Keyword(s):  
Reflection Coefficient ◽  
Wave Reflection ◽  
Long Period ◽  
Period Wave
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