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.

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.

Effective reflection coefficients for curved interfaces in transversely isotropic media

Geophysics ◽  
2009 ◽  
Vol 74 (5) ◽  
pp. WB33-WB53 ◽  
Author(s):  
Milana Ayzenberg ◽  
Ilya Tsvankin ◽  
Arkady Aizenberg ◽  
Bjørn Ursin
Keyword(s):  
Plane Wave ◽  
Transversely Isotropic ◽  
Reflection Coefficients ◽  
Superposition Method ◽  
Low Frequencies ◽  
Amplitude Variation With Offset ◽  
Reflection Data ◽  
Transversely Isotropic Media ◽  
Isotropic Media ◽  
The Difference

Plane-wave reflection coefficients (PWRCs) are routinely used in amplitude-variation-with-offset analysis and for generating boundary data in Kirchhoff modeling. However, the geometrical-seismics approximation based on PWRCs becomes inadequate in describing reflected wavefields at near- and postcritical incidence angles. Also, PWRCs are derived for plane interfaces and break down in the presence of significant reflector curvature. Here, we discuss effective reflection coefficients (ERCs) designed to overcome the limitations of PWRCs for multicomponent data from heterogeneous anisotropic media. We represent the reflected wavefield in the immediate vicinity of a curved interface by a generalized plane-wave decomposition, which approximately reduces to the conventional Weyl-type integral computed for an apparent source location. The ERC then is obtainedas the ratio of the reflected and incident wavefields at each point of the interface. To conduct diffraction modeling, we combine ERCs with the tip-wave superposition method (TWSM), extended to elastic media. This methodology is implemented for curved interfaces that separate an isotropic incidence half-space and a transversely isotropic (TI) medium with the symmetry axis orthogonal to the reflector. If the interface is plane, ERCs generally are close to the exact solution, sensitive to the anisotropy parameters and source-receiver geometry. Numerical tests demonstrate that the difference between ERCs and PWRCs for typical TI models can be significant, especially at low frequencies and in the postcritical domain. For curved interfaces, ERCs provide a practical approximate tool to compute the reflected wavefield. We analyze the dependence of ERCs on reflector shape and demonstrate their advantages over PWRCs in 3D diffraction modeling of PP and PS reflection data.

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.

Amplitude variation with offset inversion using acoustic-elastic local solver

Geophysics ◽  
2020 ◽  
Vol 85 (3) ◽  
pp. R251-R262 ◽  
Author(s):  
Ligia Elena Jaimes-Osorio ◽  
Alison Malcolm ◽  
Ali Gholami
Keyword(s):  
Elastic Material ◽  
Point Sources ◽  
P Wave ◽  
Reflection Coefficients ◽  
Local Domain ◽  
Amplitude Variation ◽  
Amplitude Variation With Offset ◽  
Zoeppritz Equations ◽  
Avo Inversion ◽  
Full Domain

Conventional amplitude variation with offset (AVO) inversion analysis uses the Zoeppritz equations, which are based on a plane-wave approximation. However, because real seismic data are created by point sources, wave reflections are better modeled by spherical waves than by plane waves. Indeed, spherical reflection coefficients deviate from planar reflection coefficients near the critical and postcritical angles, which implies that the Zoeppritz equations are not applicable for angles close to critical reflection in AVO analysis. Elastic finite-difference simulations provide a solution to the limitations of the Zoeppritz approximation because they can handle near- and postcritical reflections. We have used a coupled acoustic-elastic local solver that approximates the wavefield with high accuracy within a locally perturbed elastic subdomain of the acoustic full domain. Using this acoustic-elastic local solver, the local wavefield generation and inversion are much faster than performing a full-domain elastic inversion. We use this technique to model wavefields and to demonstrate that the amplitude from within the local domain can be used as a constraint in the inversion to recover elastic material properties. Then, we focus on understanding how much the amplitude and phase contribute to the reconstruction accuracy of the elastic material parameters ([Formula: see text], [Formula: see text], and [Formula: see text]). Our results suggest that the combination of amplitude and phase in the inversion helps with the convergence. Finally, we analyze elastic parameter trade-offs in AVO inversion, from which we find that to recover accurate P-wave velocities we should invert for [Formula: see text] and [Formula: see text] simultaneously with fixed density.

Quantifying the uncertainty in an AVO interpretation

Geophysics ◽  
2002 ◽  
Vol 67 (1) ◽  
pp. 117-125 ◽  
Author(s):  
Richard T. Houck
Keyword(s):  
North Sea ◽  
Seismic Data ◽  
Reflection Coefficients ◽  
Amplitude Variation ◽  
Data Set ◽  
Amplitude Variation With Offset ◽  
Full Characterization ◽  
The North ◽  
The North Sea

Lithologic interpretations of amplitude variation with offset (AVO) information are ambiguous both because different lithologies occupy overlapping ranges of elastic properties, and because angle‐dependent reflection coefficients estimated from seismic data are uncertain. This paper presents a method for quantifying and combining these two components of uncertainty to get a full characterization of the uncertainty associated with an AVO‐based lithologic interpretation. The result of this approach is a compilation of all the lithologies that are consistent with the observed AVO behavior, along with a probability of occurrence for each lithology. A 2‐D line from the North Sea illustrates how the method might be applied in practice. For any data set, the interaction between the geologic and measurement components of uncertainty may significantly affect the overall uncertainty in a lithologic interpretation.

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.

scholarly journals Effect of Rotation on Propagation of Waves in Transversely Isotropic Thermoelastic Half-Space

2014 ◽  
Vol 2014 ◽  
pp. 1-7 ◽  
Author(s):  
Raj Rani Gupta ◽  
Rajani Rani Gupta
Keyword(s):  
Boundary Conditions ◽  
Half Space ◽  
Thermal Wave ◽  
Isotropic Medium ◽  
Plane Waves ◽  
Transversely Isotropic ◽  
Reflection Coefficients ◽  
Governing Equations ◽  
Transversely Isotropic Medium ◽  
Propagation Of Waves

The present study is concerned with the effect of rotation on the propagation of plane waves in a transversely isotropic medium in the context of thermoelasticity theory of GN theory of types II and III. After solving the governing equations, three waves propagating in the medium are obtained. The fastest among them is a quasilongitudinal wave. The slowest of them is a thermal wave. The remaining is called quasitransverse wave. The prefix “quasi” refers to their polarizations being nearly, but not exactly, parallel or perpendicular to the direction of propagation. The polarizations of these three waves are not mutually orthogonal. After imposing the appropriate boundary conditions, the amplitudes of reflection coefficients have been obtained. Numerically simulated results have been plotted graphically with respect to frequency to evince the effect of rotation and anisotropy.

Azimuthal amplitude variation with offset parameterization and inversion for fracture weaknesses in tilted transversely isotropic media

Geophysics ◽  
2020 ◽  
Vol 86 (1) ◽  
pp. C1-C18
Author(s):  
Xinpeng Pan ◽  
Lin Li ◽  
Shunxin Zhou ◽  
Guangzhi Zhang ◽  
Jianxin Liu
Keyword(s):  
Tilt Angle ◽  
Stiffness Matrix ◽  
Incidence Angle ◽  
Fractured Reservoirs ◽  
Seismic Inversion ◽  
Inversion Method ◽  
Amplitude Variation ◽  
Amplitude Variation With Offset ◽  
Pp Wave ◽  
And Inversion

The characterization of fracture-induced tilted transverse isotropy (TTI) seems to be more suitable to actual scenarios of geophysical exploration for fractured reservoirs. Fracture weaknesses enable us to describe fracture-induced anisotropy. With the incident and reflected PP-wave in TTI media, we have adopted a robust method of azimuthal amplitude variation with offset (AVO) parameterization and inversion for fracture weaknesses in a fracture-induced reservoir with TTI symmetry. Combining the linear-slip model with the Bond transformation, we have derived the stiffness matrix of a dipping-fracture-induced TTI medium characterized by normal and tangential fracture weaknesses and a tilt angle. Integrating the first-order perturbations in the stiffness matrix of a TTI medium and scattering theory, we adopt a method of azimuthal AVO parameterization for PP-wave reflection coefficient for the case of a weak-contrast interface separating two homogeneous weakly anisotropic TTI layers. We then adopt an iterative inversion method by using the partially incidence-angle-stacked seismic data with different azimuths to estimate the fracture weaknesses of a TTI medium when the tilt angle is estimated based on the image well logs prior to the seismic inversion. Synthetic examples confirm that the fracture weaknesses of a TTI medium are stably estimated from the azimuthal seismic reflected amplitudes for the case of moderate noise. A field data example demonstrates that geologically reasonable results of fracture weaknesses can be determined when the tilt angle is treated as the prior information. We determine that the azimuthal AVO inversion approach provides an available tool for fracture prediction in a dipping-fracture-induced TTI reservoir.

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