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°.

Small-angle AVO response of PS-waves in tilted transversely isotropic media

Geophysics ◽  
2006 ◽  
Vol 71 (5) ◽  
pp. C69-C79 ◽  
Author(s):  
Jyoti Behura ◽  
Ilya Tsvankin
Keyword(s):  
Small Angle ◽  
Symmetry Axis ◽  
Transversely Isotropic ◽  
Normal Incidence ◽  
Analytic Solutions ◽  
Reflection Coefficients ◽  
Axis Orientation ◽  
Avo Inversion ◽  
Anisotropy Parameters ◽  
Ti Media

Field records for small source-receiver offsets often contain intensive converted PS-waves that may be caused by the influence of anisotropy on either side of the reflector. Here, we study the small-angle reflection coefficients of the split converted [Formula: see text]- and [Formula: see text]-waves ([Formula: see text] and [Formula: see text]) for a horizontal interface separating two transversely isotropic (TI) media with arbitrary orientations of the symmetry axis. The normal-incidence reflection coefficients [Formula: see text] and [Formula: see text] vanish when both half-spaces have a horizontal symmetry plane, which happens if the symmetry axis is vertical or horizontal (i.e., if the medium is VTI or HTI). For a tilted symmetry axis in either medium, however, the magnitude of the reflection coefficients can reach substantial values that exceed 0.1, even if the anisotropy strength is moderate. To study the influence exerted by the orientation of the symmetry axis and the anisotropy parameters, we develop concise weak-contrast, weak-anisotropyapproximations for the PS-wave reflection coefficients and com-pare them with exact numerical results. In particular, the analytic solutions show that the contributions made by the Thomsen parameters [Formula: see text] and [Formula: see text] and the symmetry-axis tilt [Formula: see text] to the coefficients [Formula: see text] and [Formula: see text] can be expressed through the first derivative of the P-wave phase velocity at normal incidence. If the symmetry-axis orientation and anisotropy parameters do not change across the interface, the normal-incidence reflection coefficients are insignificant, regardless of the strength of the velocity and density contrast. The AVO (amplitude variation with offset) gradients of the PS-waves are influenced primarily by the anisotropy of the incidence medium that causes shear-wave splitting and determines the partitioning of energy between the [Formula: see text] and [Formula: see text] modes. Because of their substantial amplitude, small-angle PS reflections in TI media contain valuable information for anisotropic AVO inversion of multicomponent data. Our analytic solutions provide a foundation for linear AVO-inversion algorithms and can be used to guide nonlinear inversion that is based on the exact reflection coefficients.

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.

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.

The effect of interface curvature on AVO inversion of near-critical and postcritical PP-reflections

Geophysics ◽  
2012 ◽  
Vol 77 (5) ◽  
pp. N1-N16 ◽  
Author(s):  
Lyubov Skopintseva ◽  
Arkady Aizenberg ◽  
Milana Ayzenberg ◽  
Martin Landrø ◽  
Tatyana Nefedkina
Keyword(s):  
Plane Wave ◽  
Critical Angle ◽  
Wave Reflection ◽  
Incidence Angle ◽  
Reflection Coefficients ◽  
Energy Propagation ◽  
Seismic Parameters ◽  
Avo Inversion ◽  
Long Offset ◽  
Interface Curvature

Widely exploited in the industry, amplitude-variation-with-offset (AVO) inversion techniques are based on weak-contrast approximations of the plane-wave reflection coefficients. These approximations are valid for plane waves reflected at almost flat interfaces with weak contrasts in seismic parameters and for reflection angles below the critical angle. Regardless of the underlying assumptions, linearized coefficients provide a simple and physically adequate tool to accurately invert AVO data for seismic parameters at precritical angles. However, the accuracy of linearized coefficients drastically decreases with increasing incidence angle. Limitations occur around and beyond the critical ray, where the effect of wavefront curvature becomes prominent and thus can no more be neglected. The effective reflection coefficients generalize the plane-wave reflection coefficients for waves generated by point sources and reflected at curved interfaces. They account for the wavefront curvature and are adequate at any incidence angle. Our previous studies have shown that including the reflections around and beyond the critical angle in the AVO inversion significantly improves the accuracy of estimated parameters. However, the interface curvature also must have its contribution to the long-offset AVO inversion. We find that the interface curvature affects the energy propagation along the ray tube and the energy diffusion across the ray tube. The energy propagation along the tube is characterized by the geometrical spreading, which is strongly affected by interface curvature. The transverse diffusion is captured by the effective reflection coefficients which are less influenced by interface curvature. The long-offset AVO inversion is thus sensitive to interface curvature through a combination of several wave propagation factors.

Exact elastic impedance matrices for transversely isotropic medium

Geophysics ◽  
2016 ◽  
Vol 81 (2) ◽  
pp. C1-C15 ◽  
Author(s):  
Feng Zhang ◽  
Xiang-Yang Li
Keyword(s):  
Shale Gas ◽  
Isotropic Medium ◽  
Seismic Reflection ◽  
Transversely Isotropic ◽  
Seismic Inversion ◽  
P Wave ◽  
Reflection Coefficients ◽  
Angle Of Incidence ◽  
Transversely Isotropic Medium ◽  
Anisotropy Parameters

Conventional elastic impedances are derived as scalars by means of the integration of reflectivity. In this sense, they are attributes of the seismic reflection but not the intrinsic physical property of the subsurface media. The derivation of these expressions shares the same assumptions as the reflectivity approximations, such as weak impedance contrast, small angle of incidence, or weak anisotropic media, and thus it limits the accuracy and interpretation capability. The exact P/SV impedance matrices relating the stress and strain represent the mechanical property of the subsurface media and yield reflection coefficients at an arbitrary angle of incidence. We have extended the impedance matrices to a transversely isotropic medium. The resulting elastic impedances (stress/velocity ratios) can be used to characterize those unconventional reservoir formations with strong seismic anisotropy, such as shale-gas and coal-bed methane. Our numerical analyses determined their variations with the phase angle and anisotropy parameters. The exact expressions of the P- and S-wave elastic impedances are used to model the seismic reflection coefficients, and thus they can be inverted simultaneously if all of the types of reflection waves are available. We then derive approximations of quasi-P-wave elastic impedances for seismic inversion of anisotropy parameters and further interpretation. Our applications on real logs and seismic data for a turbidite fan reservoir and a shale-gas reservoir determined the robust interpretation capability of derived elastic impedances in lithology characterizations.

Seismic critical-angle anisotropy analysis in the τ -p domain

Geophysics ◽  
2009 ◽  
Vol 74 (4) ◽  
pp. A53-A57 ◽  
Author(s):  
Samik Sil ◽  
Mrinal K. Sen
Keyword(s):  
Critical Angle ◽  
Seismic Anisotropy ◽  
Anisotropy Parameter ◽  
Transversely Isotropic ◽  
Seismic Line ◽  
Full Wave ◽  
Current Implementation ◽  
Approximation Errors ◽  
Anisotropy Parameters ◽  
Axis Of Symmetry

Seismic critical-angle reflectometry is a relatively new field for estimating seismic anisotropy parameters. The theory relates changes in the critical angle with azimuth of the seismic line to the principal axis and anisotropy parameters. Current implementation of the critical-angle reflectometry process has certain shortcomings in that the critical angle is determined from critical offset and the process is vulnerable to different approximation errors. Seismic critical-angle analysis in the plane-wave [Formula: see text] domain can handle these issues and has the potential to become an independent tool for estimating anisotropy parameters. The theory of seismic critical-angle reflectometry is modified to make it suitable for [Formula: see text] domain analysis. Then using full-wave synthetic seismograms at three different azimuths for a transversely isotropic medium with a horizontal axis of symmetry (HTI), the effectiveness of anisotropy parameter estimation is demonstrated.

scholarly journals Body‐wave radiation patterns and AVO in transversely isotropic media

Geophysics ◽  
1995 ◽  
Vol 60 (5) ◽  
pp. 1409-1425 ◽  
Author(s):  
Ilya Tsvankin
Keyword(s):  
Reflection Coefficient ◽  
Radiation Pattern ◽  
Transversely Isotropic ◽  
P Wave ◽  
Wave Radiation ◽  
Reflection Coefficients ◽  
Radiation Patterns ◽  
Avo Analysis ◽  
Transversely Isotropic Media ◽  
Isotropic Media

The angular dependence of reflection coefficients may be significantly distorted in the presence of elastic anisotropy. However, the influence of anisotropy on amplitude variation with offset (AVO) analysis is not limited to reflection coefficients. AVO signatures (e.g., AVO gradient) in anisotropic media are also distorted by the redistribution of energy along the wavefront of the wave traveling down to the reflector and back up to the surface. Significant anisotropy above the target horizon may be rather typical of sand‐shale sequences commonly encountered in AVO analysis. Here, I examine the influence of P‐ and S‐wave radiation patterns on AVO in the most common anisotropic model—transversely isotropic media. A concise analytic solution, obtained in the weak‐anisotropy approximation, provides a convenient way to estimate the impact of the distortions of the radiation patterns on AVO results. It is shown that the shape of the P‐wave radiation pattern in the range of angles most important to AVO analysis (0–40°) is primarily dependent on the difference between Thomsen parameters ε and δ. For media with ε − δ > 0 (the most common case), the P‐wave amplitude may drop substantially over the first 25–40° from vertical. There is no simple correlation between the strength of velocity anisotropy and angular amplitude variations. For instance, for models with a fixed positive ε − δ the amplitude distortions are less pronounced for larger values of ε and δ. The distortions of the SV‐wave radiation pattern are usually much more significant than those for the P‐wave. The anisotropic directivity factor for the incident wave may be of equal or greater importance for AVO than the influence of anisotropy on the reflection coefficient. Therefore, interpretation of AVO anomalies in the presence of anisotropy requires an integrated approach that takes into account not only the reflection coefficient but also the wave propagation above the reflector.

scholarly journals Estimation of the anisotropy parameters of transversely isotropic shales with a tilted symmetry axis

2012 ◽  
Vol 190 (2) ◽  
pp. 1197-1203 ◽  
Author(s):  
Dariush Nadri ◽  
Joël Sarout ◽  
Andrej Bóna ◽  
David Dewhurst
Keyword(s):  
Symmetry Axis ◽  
Transversely Isotropic ◽  
Anisotropy Parameters

scholarly journals A new traveltime approximation for TI media

Geophysics ◽  
2012 ◽  
Vol 77 (4) ◽  
pp. C37-C42 ◽  
Author(s):  
Alexey Stovas ◽  
Tariq Alkhalifah
Keyword(s):  
Power Series ◽  
Eikonal Equation ◽  
Transversely Isotropic ◽  
Transversely Isotropic Medium ◽  
Efficient Tool ◽  
Trade Off ◽  
Background Medium ◽  
The Common ◽  
Anisotropy Parameters ◽  
Ti Media

In a transversely isotropic (TI) medium, the trade-off between inhomogeneity and anisotropy can dramatically reduce our capability to estimate anisotropy parameters. By expanding the TI eikonal equation in power series in terms of the aneliptic parameter [Formula: see text], we derive an efficient tool to estimate (scan) for [Formula: see text] in a generally inhomogeneous, elliptically anisotropic background medium. For a homogeneous-tilted transversely isotropic medium, we obtain an analytic nonhyperbolic moveout equation that is accurate for large offsets. In the common case where we do not have well information and it is necessary to resolve the vertical velocity, the background medium can be assumed isotropic, and the traveltime equations becomes simpler. In all cases, the accuracy of this new TI traveltime equation exceeds previously published formulations and demonstrates how [Formula: see text] is better resolved at small offsets when the tilt is large.

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