scholarly journals Study of the influence of anisotropy parameters on reflection coefficients from a boundary between two azimuthally anisotropic media

2020 ◽  
pp. 18-29
Author(s):  
G. A. Dugarov ◽  
R. K. Bekrenev ◽  
T. V. Nefedkina
Keyword(s):  
Significant Influence ◽  
Anisotropic Media ◽  
Elastic Parameter ◽  
Media Analysis ◽  
Reflection Coefficients ◽  
Reflection Data ◽  
Hti Media ◽  
Target Layer ◽  
Anisotropy Parameters ◽  
Hti Medium

The paper considers an algorithm for calculating reflection coefficients from boundary between two HTI media. Analysis of the presence of anisotropy above and below the target boundary, as well as variations in the parameters of HTI media, was done. Interpretation of reflection data from the boundary between two HTI media with neglect of anisotropy above or below potentially leads to significant errors in estimation of symmetry axes directions, and hence fracturing orientation. Overestimation/underestimation of an elastic parameter in the overlying HTI medium could lead to a corresponding overestimation/underestimation of similar parameter in the underlying target layer in the result of AVAZ inversion. Furthermore, among the anisotropy parameters Thomsen parameter γ has most significant influence on the reflection coefficients dependences. Thus, the parameter γ could be used foremost as a result of the AVAZ inversion.

Reflection coefficients in attenuative anisotropic media

Geophysics ◽  
2009 ◽  
Vol 74 (5) ◽  
pp. WB193-WB202 ◽  
Author(s):  
Jyoti Behura ◽  
Ilya Tsvankin
Keyword(s):  
Plane Wave ◽  
Wave Reflection ◽  
Symmetry Plane ◽  
Anisotropic Media ◽  
P Wave ◽  
Substantial Contribution ◽  
Reflection Coefficients ◽  
Slowness Vector ◽  
Anisotropy Parameters ◽  
Attenuation Anisotropy

Such reservoir rocks as tar sands are characterized by significant attenuation and, in some cases, attenuation anisotropy. Most existing attenuation studies are focused on plane-wave attenuation coefficients, which determine the amplitude decay along the raypath of seismic waves. Here we study the influence of attenuation on PP- and PS-wave reflection coefficients for anisotropic media with the main emphasis on transversely isotropic models with a vertical symmetry axis (VTI). Concise analytic solutions obtained by linearizing the exact plane-wave reflection coefficients are verified by numerical modeling. To make a substantial contribution to reflection coefficients, attenuation must be strong, with the quality factor [Formula: see text] not exceeding 10. For such highly attenuative media, it is also necessary to take attenuation anisotropy into account if the magnitude of the Thomsen-styleattenuation-anisotropy parameters is relatively large. In general, the linearized reflection coefficients in attenuative media include velocity-anisotropy parameters but have almost “isotropic” dependence on attenuation. Our formalism also helps evaluate the influence of the inhomogeneity angle (the angle between the real and imaginary parts of the slowness vector) on the reflection coefficients. A nonzero inhomogeneity angle of the incident wave introduces additional terms into the PP- and PS-wave reflection coefficients, which makes conventional amplitude-variation-with-offset (AVO) analysis inadequate for strongly attenuative media. For instance, an incident P-wave with a nonzero inhomogeneity angle generates a mode-converted PS-wave at normal incidence, even if both half-spaces have a horizontal symmetry plane. The developed linearized solutions can be used in AVO inversion for highly attenuative (e.g., gas-sand and heavy-oil) reservoirs.

scholarly journals DETERMINATION OF AZIMUTHAL ANISOTROPIC MEDIA ELASTIC PARAMETERS FROM MULTIWAVE AVOA DATA BY NONLINEAR OPTIMIZATION METHOD

2019 ◽  
pp. 14-26 ◽  
Author(s):  
T. V. Nefedkina ◽  
P. A. Lykhin ◽  
G. A. Dugarov
Keyword(s):  
Signal To Noise Ratio ◽  
Anisotropic Media ◽  
Optimization Method ◽  
Parameter Estimates ◽  
Reflection Coefficients ◽  
Elastic Parameters ◽  
Ray Method ◽  
Pp Wave ◽  
Hti Medium

In this paper, we investigate optimization algorithm of joint nonlinear AVOA inversion of PP+PS reflections in anisotropic media. Algorithm is based on the exact solution for PP and PS waves reflection coefficients in anisotropic HTI medium. The PP and PS wave’s reflections from the top of the anisotropic layer are examined. We use synthetic seismograms generated by ray method for the algorithm testing. We show that joint compressional and converted wave’s inversion allows increasing the robustness of the method and the accuracy of medium-parameter estimates. Coefficients of anisotropy are determined with better accuracy if signal-to-noise ratio is bigger than 5 for PP wave and bigger than 2 for PS wave.

scholarly journals Radiation pattern analyses for seismic multi-parameter inversion of HTI anisotropic media

2019 ◽  
Author(s):  
Fengxia Gao ◽  
Yanghua Wang
Keyword(s):  
Waveform Inversion ◽  
Anisotropic Media ◽  
The Third ◽  
Seismic Waveform ◽  
Parameter Inversion ◽  
Stage Scheme ◽  
Hti Media ◽  
Transverse Isotropic ◽  
Anisotropy Parameters ◽  
Elastic Coefficients

Abstract In seismic waveform inversion, selecting an optimal multi-parameter group is a key step to derive an accurate subsurface model for characterising hydrocarbon reservoirs. There are three parameterizations for the horizontal transverse isotropic (HTI) media, and each parameterization consists of five parameters. The first parameterization (P-I) consists of two velocities and three anisotropy parameters, the second (P-II) consists of five elastic coefficients and the third (P-III) consists of five velocity parameters. The radiation patterns of these three parameterizations indicate a strong interference among five parameters. An effective inversion strategy is a two-stage scheme that first inverts for the velocities or velocity-related parameters and then inverts for all five parameters simultaneously. The inversion results clearly demonstrate that P-I is the best parameterization for seismic waveform inversion in HTI anisotropic media.

scholarly journals An analysis of AVO inversion for postcritical offsets in HTI media

Geophysics ◽  
2013 ◽  
Vol 78 (3) ◽  
pp. N11-N20 ◽  
Author(s):  
Lyubov Skopintseva ◽  
Tariq Alkhalifah
Keyword(s):  
Critical Angle ◽  
Azimuthal Angle ◽  
Spherical Wave ◽  
Transversely Isotropic ◽  
Resolving Power ◽  
Reflection Coefficients ◽  
Avo Analysis ◽  
Avo Inversion ◽  
Hti Media ◽  
Anisotropy Parameters

Azimuthal variations of wavefield characteristics, such as traveltime or reflection amplitude, play an important role in the identification of fractured media. A transversely isotropic medium with a horizontal symmetry axis (HTI medium) is the simplest azimuthally anisotropic model typically used to describe one set of vertical fractures. There exist many techniques in industry to recover anisotropic parameters based on moveout equations and linearized reflection coefficients using such a model. However, most of the methods have limitations in defining properties of the fractures due to linearizations and physical approximations used in their development. Thus, azimuthal analysis of traveltimes based on normal moveout ellipses recovers a maximum of three medium parameters instead of the required five. Linearizations made in plane-wave reflection coefficients (PWRCs) limit the amplitude-versus-offset (AVO) analysis to small incident angles and weak-contrast interfaces. Inversion based on azimuthal AVO for small offsets encounters nonuniqueness in the resolving power of the anisotropy parameters. Extending the AVO analysis and inversion to and beyond the critical reflection angle increases the amount of information recovered from the medium. However, well-accepted PWRCs are not valid in the vicinity of the critical angle and beyond it, due to frequency and spherical wave effects. Recently derived spherical and effective reflection coefficient (ERC) methods overcome this problem. We extended the ERCs approach to HTI media to analyze the potential of near- and postcritical reflections in azimuthal AVO analysis. From the sensitivity analysis, we found that ERCs are sensitive to different sets of parameters prior to and beyond the critical angle, which is useful in enhancing our resolution of the anisotropy parameters. Additionally, the resolution of the parameters depends on a sufficient azimuthal coverage in the acquisition setup. The most stable AVO results for the azimuthal acquisition setup with minimum number of lines (three) are achieved when the azimuthal angle between lines is greater than 45°.

Anisotropic Born scattering for the qP scalar wavefield using a low-rank symbol approximation

Geophysics ◽  
2021 ◽  
pp. 1-74
Author(s):  
Iury Araújo ◽  
Murillo Nascimento ◽  
Jesse Costa ◽  
Alan Souza ◽  
Jörg Schleicher
Keyword(s):  
Anisotropic Medium ◽  
Mathematical Formulation ◽  
Hamiltonian Formulation ◽  
Anisotropic Media ◽  
Low Rank ◽  
Direct Access ◽  
S Wave ◽  
Evolution Operators ◽  
Individual Parameter ◽  
Reflection Data

We present a procedure to derive low-rank evolution operators in the mixed space-wavenumber domain for modeling the qP Born-scattered wavefield at perturbations of an anisotropic medium under the pseudo-acoustic approximation. To approximate the full wavefield, this scattered field is then added to the reference wavefield obtained with the corresponding low-rank evolution operator in the background medium. Being built upon a Hamiltonian formulation using the dispersion relation for qP waves, this procedure avoids pseudo-S-wave artifacts and provides a unified approach for linearizing anisotropic pseudo-acoustic evolution operators. Therefore it is immediately applicable to any arbitrary class of anisotropy. As an additional asset, the scattering operators explicitly contain the sensitivity kernels of the Born-scattered wavefield with respect to the anisotropic medium parameters. This enables direct access to important information like its offset dependence or directional characteristics as a function of the individual parameter perturbations. For our numerical tests, we specify the operators for a mildly anisotropic tilted transversly isotropic (TTI) medium. We validate our implementation in a simple model with weak contrasts and simulate reflection data in the BP TTI model to show that the procedure works in a more realistic scenario. The Born-scattering results indicate that our procedure is applicable to strongly heterogeneous anisotropic media. Moreover, we use the analytical capabilities of the kernels by means of sensitivity tests to demonstrate that using two different medium parameterizations leads to different results. The mathematical formulation of the method is such that it allows for an immediate application to least-squares migration in pseudo-acoustic anisotropic media.

Effective elastic properties of rocks with transversely isotropic background permeated by a set of vertical fracture cluster

Geophysics ◽  
2021 ◽  
pp. 1-78
Author(s):  
Da Shuai ◽  
Alexey Stovas ◽  
Jianxin Wei ◽  
Bangrang Di ◽  
Yang Zhao
Keyword(s):  
Standard Deviation ◽  
Elastic Wave ◽  
Significant Influence ◽  
Transversely Isotropic ◽  
Azimuth Angle ◽  
Effective Medium ◽  
P Wave ◽  
Wave Velocities ◽  
Anisotropy Parameters ◽  
Vertical Fractures

The linear slip theory is gradually being used to characterize seismic anisotropy. If the transversely isotropic medium embeds vertical fractures (VFTI medium), the effective medium becomes orthorhombic. The vertical fractures, in reality, may exist in any azimuth angle which leads the effective medium to be monoclinic. We apply the linear slip theory to create a monoclinic medium by only introducing three more physical meaning parameters: the fracture preferred azimuth angle, the fracture azimuth angle, and the angular standard deviation. First, we summarize the effective compliance of a rock as the sum of the background matrix compliance and the fracture excess compliance. Then, we apply the Bond transformation to rotate the fractures to be azimuth dependent, introduce a Gaussian function to describe the fractures' azimuth distribution assuming that the fractures are statistically distributed around the preferred azimuth angle, and average each fracture excess compliance over azimuth. The numerical examples investigate the influence of the fracture azimuth distribution domain and angular standard deviation on the effective stiffness coefficients, elastic wave velocities, and anisotropy parameters. Our results show that the fracture cluster parameters have a significant influence on the elastic wave velocities. The fracture azimuth distribution domain and angular standard deviation have a bigger influence on the orthorhombic anisotropy parameters in the ( x2, x3) plane than that in the ( x1, x3) plane. The fracture azimuth distribution domain and angular standard deviation have little influence on the monoclinic anisotropy parameters responsible for the P-wave NMO ellipse and have a significant influence on the monoclinic anisotropy parameters responsible for the S1- and S2-wave NMO ellipse. The effective monoclinic can be degenerated into the VFTI medium.

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