Anisotropic geometrical-spreading correction for wide-azimuth P-wave reflections

Geophysics ◽  
2006 ◽  
Vol 71 (5) ◽  
pp. D161-D170 ◽  
Author(s):  
Xiaoxia Xu ◽  
Ilya Tsvankin
Keyword(s):  
Transversely Isotropic ◽  
Azimuthal Anisotropy ◽  
P Wave ◽  
Fractured Reservoir ◽  
Geometrical Spreading ◽  
Spreading Factor ◽  
Velocity Anisotropy ◽  
Reflection Data ◽  
Fitting Procedure ◽  
Avo Attributes

Compensation for geometrical spreading along a raypath is one of the key steps in AVO (amplitude-variation-with-offset) analysis, in particular, for wide-azimuth surveys. Here, we propose an efficient methodology to correct long-spread, wide-azimuth reflection data for geometrical spreading in stratified azimuthally anisotropic media. The P-wave geometrical-spreading factor is expressed through the reflection traveltime described by a nonhyperbolic moveout equation that has the same form as in VTI (transversely isotropic with a vertical symmetry axis) media. The adapted VTI equation is parameterized by the normal-moveout (NMO) ellipse and the azimuthally varying anellipticity parameter [Formula: see text]. To estimate the moveout parameters, we apply a 3D nonhyperbolic semblance algorithm of Vasconcelos and Tsvankin that operates simultaneously with traces at all offsets andazimuths. The estimated moveout parameters are used as the input in our geometrical-spreading computation. Numerical tests for models composed of orthorhombic layers with strong, depth-varying velocity anisotropy confirm the high accuracy of our travetime-fitting procedure and, therefore, of the geometrical-spreading correction. Because our algorithm is based entirely on the kinematics of reflection arrivals, it can be incorporated readily into the processing flow of azimuthal AVO analysis. In combination with the nonhyperbolic moveout inversion, we apply our method to wide-azimuth P-wave data collected at the Weyburn field in Canada. The geometrical-spreading factor for the reflection from the top of the fractured reservoir is clearly influenced by azimuthal anisotropy in the overburden, which should cause distortions in the azimuthal AVO attributes. This case study confirms that the azimuthal variation of the geometrical-spreading factor often is comparable to or exceeds that of the reflection coefficient.

Geometrical spreading of P-waves in horizontally layered, azimuthally anisotropic media

Geophysics ◽  
2005 ◽  
Vol 70 (5) ◽  
pp. D43-D53 ◽  
Author(s):  
Xiaoxia Xu ◽  
Ilya Tsvankin ◽  
Andrés Pech
Keyword(s):  
Transversely Isotropic ◽  
Anisotropic Media ◽  
Azimuthal Velocity ◽  
Azimuthal Anisotropy ◽  
P Wave ◽  
Geometrical Spreading ◽  
Weak Anisotropy ◽  
P Waves ◽  
Anisotropic Models ◽  
Wide Range

For processing and inverting reflection data, it is convenient to represent geometrical spreading through the reflection traveltime measured at the earth's surface. Such expressions are particularly important for azimuthally anisotropic models in which variations of geometrical spreading with both offset and azimuth can significantly distort the results of wide-azimuth amplitude-variation-with-offset (AVO) analysis. Here, we present an equation for relative geometrical spreading in laterally homogeneous, arbitrarily anisotropic media as a simple function of the spatial derivatives of reflection traveltimes. By employing the Tsvankin-Thomsen nonhyperbolic moveout equation, the spreading is represented through the moveout coefficients, which can be estimated from surface seismic data. This formulation is then applied to P-wave reflections in an orthorhombic layer to evaluate the distortions of the geometrical spreading caused by both polar and azimuthal anisotropy. The relative geometrical spreading of P-waves in homogeneous orthorhombic media is controlled by five parameters that are also responsible for time processing. The weak-anisotropy approximation, verified by numerical tests, shows that azimuthal velocity variations contribute significantly to geometrical spreading, and the existing equations for transversely isotropic media with a vertical symmetry axis (VTI) cannot be applied even in the vertical symmetry planes. The shape of the azimuthally varying spreading factor is close to an ellipse for offsets smaller than the reflector depth but becomes more complicated for larger offset-to-depth ratios. The overall magnitude of the azimuthal variation of the geometrical spreading for the moderately anisotropic model used in the tests exceeds 25% for a wide range of offsets. While the methodology developed here is helpful in modeling and analyzing anisotropic geometrical spreading, its main practical application is in correcting the wide-azimuth AVO signature for the influence of the anisotropic overburden.

Estimation of interval anisotropy parameters using velocity-independent layer stripping

Geophysics ◽  
2009 ◽  
Vol 74 (5) ◽  
pp. WB117-WB127 ◽  
Author(s):  
Xiaoxiang Wang ◽  
Ilya Tsvankin
Keyword(s):  
Symmetry Plane ◽  
Synthetic Data ◽  
Single Layer ◽  
Transversely Isotropic ◽  
P Wave ◽  
Correlated Noise ◽  
Fractured Reservoir ◽  
Processing Parameter ◽  
Reflection Data ◽  
Error Amplification

Moveout analysis of long-spread P-wave data is widely used to estimate the key time-processing parameter [Formula: see text] in layered transversely isotropic media with a vertical symmetry axis (VTI). Inversion for interval [Formula: see text] values, however, suffers from instability caused by the trade-off between the effective moveout parameters and by subsequent error amplification during Dix-type layer stripping. We propose an alternative approach to nonhyperbolic moveout inversion based on the velocity-independent layer-stripping (VILS) method of Dewangan and Tsvankin. Also, we develop the 3D version of VILS and apply it to interval parameter estimation in orthorhombic media using wide-azimuth, long-spread data. If the overburden is laterally homogeneous and has a horizontal symmetry plane, VILS produces the exact interval traveltime-offset function in the target layer without knowledgeof the velocity field. Hence, Dix-type differentiation of moveout parameters used in existing techniques is replaced by the much more stable layer stripping of reflection traveltimes. The interval traveltimes are then inverted for the moveout parameters using the single-layer nonhyperbolic moveout equation. The superior accuracy and stability of the algorithm are illustrated on ray-traced synthetic data for typical VTI and orthorhombic models. Even small correlated noise in reflection traveltimes causes substantial distortions in the interval [Formula: see text] values computed by conventional Dix-type differentiation. In contrast, the output of VILS is insensitive to mild correlated traveltime errors. The algorithm is also tested on wide-azimuth P-wave reflection data recorded above a fractured reservoir at Rulison field in Colorado. The interval moveout parameters estimated by VILS in the shale layer above the reservoir are more plausible and less influenced by noise than those obtained by the Dix-type method.

P-wave and S-wave azimuthal anisotropy at a naturally fractured gas reservoir, Bluebell‐Altamont Field, Utah

Geophysics ◽  
1999 ◽  
Vol 64 (4) ◽  
pp. 1312-1328 ◽  
Author(s):  
Heloise B. Lynn ◽  
Wallace E. Beckham ◽  
K. Michele Simon ◽  
C. Richard Bates ◽  
M. Layman ◽  
...  
Keyword(s):  
Azimuthal Anisotropy ◽  
P Wave ◽  
Fracture Density ◽  
Wave Reflections ◽  
S Wave ◽  
Gas Reservoir ◽  
Green River ◽  
Wave Data ◽  
Reflection Data ◽  
Naturally Fractured

Reflection P- and S-wave data were used in an investigation to determine the relative merits and strengths of these two data sets to characterize a naturally fractured gas reservoir in the Tertiary Upper Green River formation. The objective is to evaluate the viability of P-wave seismic to detect the presence of gas‐filled fractures, estimate fracture density and orientation, and compare the results with estimates obtained from the S-wave data. The P-wave response to vertical fractures must be evaluated at different source‐receiver azimuths (travelpaths) relative to fracture strike. Two perpendicular lines of multicomponent reflection data were acquired approximately parallel and normal to the dominant strike of Upper Green River fractures as obtained from outcrop, core analysis, and borehole image logs. The P-wave amplitude response is extracted from prestack amplitude variation with offset (AVO) analysis, which is compared to isotropic‐model AVO responses of gas sand versus brine sand in the Upper Green River. A nine‐component vertical seismic profile (VSP) was also obtained for calibration of S-wave reflections with P-wave reflections, and support of reflection S-wave results. The direction of the fast (S1) shear‐wave component from the reflection data and the VSP coincides with the northwest orientation of Upper Green River fractures, and the direction of maximum horizontal in‐situ stress as determined from borehole ellipticity logs. Significant differences were observed in the P-wave AVO gradient measured parallel and perpendicular to the orientation of Upper Green River fractures. Positive AVO gradients were associated with gas‐producing fractured intervals for propagation normal to fractures. AVO gradients measured normal to fractures at known waterwet zones were near zero or negative. A proportional relationship was observed between the azimuthal variation of the P-wave AVO gradient as measured at the tops of fractured intervals, and the fractional difference between the vertical traveltimes of split S-waves (the “S-wave anisotropy”) of the intervals.

Analysis of multiazimuthal VSP data for anisotropy and AVO

Geophysics ◽  
1999 ◽  
Vol 64 (4) ◽  
pp. 1172-1180 ◽  
Author(s):  
W. Scott Leaney ◽  
Colin M. Sayers ◽  
Douglas E. Miller
Keyword(s):  
Fractured Reservoirs ◽  
Vertical Axis ◽  
Horizontal Stress ◽  
Azimuthal Anisotropy ◽  
Carbonate Reservoir ◽  
P Wave ◽  
Fractured Reservoir ◽  
Data Set ◽  
Vsp Data ◽  
The Impact

Multioffset vertical seismic profile (VSP) experiments, commonly referred to as walkaways, enable anisotropy to be measured reliably in the field. The results can be fed into modeling programs to study the impact of anisotropy on velocity analysis, migration, and amplitude versus offset (AVO). Properly designed multioffset VSPs can also provide the target AVO response measured under optimum conditions, since the wavelet is recorded just above the reflectors of interest with minimal reflection point dispersal. In this paper, the multioffset VSP technique is extended to include multioffset azimuths, and a multiazimuthal multiple VSP data set acquired over a carbonate reservoir is analyzed for P-wave anisotropy and AVO. Direct arrival times down to the overlying shale and reflection times and amplitudes from the carbonate are analyzed. Data analysis involves a three‐term fit to account for nonhyperbolic moveout, dip, and azimuthal anisotropy. Results indicate that the overlying shale is transversely isotropic with a vertical axis of symmetry (VTI), while the carbonate shows 4–5% azimuthal anisotropy in traveltimes. The fast direction is consistent with the maximum horizontal stress orientation determined from break‐out logs and is also consistent with the strike of major faults. AVO analysis of the reflection from the top of the carbonate layer shows a critical angle reduction in the fast direction and maximum gradient in the slow direction. This agrees with modeling and indicates a greater amplitude sensitivity in the slow direction—the direction perpendicular to fracture strike. In principle, 3-D surveys should have wide azimuthal coverage to characterize fractured reservoirs. If this is not possible, it is important to have azimuthal line coverage in the minimum horizontal stress direction to optimize the use of AVO for fractured reservoir characterization. This direction can be obtained from multiazimuthal walkaways using the azimuthal P-wave analysis techniques presented.

Analytic study of the geometrical spreading of P-waves in a layered transversely isotropic medium with a vertical symmetry axis

Geophysics ◽  
2000 ◽  
Vol 65 (4) ◽  
pp. 1305-1315 ◽  
Author(s):  
Hongbo Zhou ◽  
George A. McMechan
Keyword(s):  
Isotropic Medium ◽  
Symmetry Axis ◽  
Transverse Isotropy ◽  
Analytical Formula ◽  
Transversely Isotropic ◽  
P Wave ◽  
Geometrical Spreading ◽  
Transversely Isotropic Medium ◽  
Weak Anisotropy ◽  
Special Cases

An analytical formula for geometrical spreading is derived for a horizontally layered transversely isotropic medium with a vertical symmetry axis (VTI). With this expression, geometrical spreading can be determined using only the anisotropy parameters in the first layer, the traveltime derivatives, and the source‐receiver offset. Explicit, numerically feasible expressions for geometrical spreading are obtained for special cases of transverse isotropy (weak anisotropy and elliptic anisotropy). Geometrical spreading can be calculated for transversly isotropic (TI) media by using picked traveltimes of primary nonhyperbolic P-wave reflections without having to know the actual parameters in the deeper subsurface; no ray tracing is needed. Synthetic examples verify the algorithm and show that it is numerically feasible for calculation of geometrical spreading. For media with a few (4–5) layers, relative errors in the computed geometrical spreading remain less than 0.5% for offset/depth ratios less than 1.0. Errors that change with offset are attributed to inaccuracy in the expression used for nonhyberbolic moveout. Geometrical spreading is most sensitive to errors in NMO velocity, followed by errors in zero‐offset reflection time, followed by errors in anisotropy of the surface layer. New relations between group and phase velocities and between group and phase angles are shown in appendices.

scholarly journals Physical and numerical modeling of tuning and diffraction in azimuthally anisotropic media

Geophysics ◽  
2000 ◽  
Vol 65 (5) ◽  
pp. 1613-1621 ◽  
Author(s):  
Richard L. Gibson ◽  
Stephen Theophanis ◽  
M. Nafi Toksöz
Keyword(s):  
Numerical Modeling ◽  
Fractured Reservoirs ◽  
Homogeneous Model ◽  
Azimuthal Anisotropy ◽  
P Wave ◽  
Orthorhombic Symmetry ◽  
Fractured Reservoir ◽  
Sh Wave ◽  
Wave Data ◽  
Ray Methods

Fractured reservoirs are an important target for exploration and production geophysics, and the azimuthal anisotropy often associated with these reservoirs can strongly influence seismic wave propagation. We created a physical model of a fractured reservoir to simulate some of these propagation effects. The reservoir is represented by a phenolite disk that is thin with respect to the elastic wavelengths in the experiment, creating model dimensions that are representative of realistic reservoirs. Phenolite is strongly anisotropic with orthorhombic symmetry, which suggests that azimuthal amplitude versus offset (AVO) effects should be obvious in data. We acquired both SH- and P-wave data in common‐offset gathers with a near offset and a far offset and found that although the SH-wave data show clear azimuthal variations in AVO, the P-wave signals show no apparent changes with azimuth. We then applied numerical modeling to analyze the data. Because ray methods cannot model diffractions from the disk edge, we first used a ray‐Born technique to simulate variations in waveforms associated with such scattering. The synthetic seismograms reproduced variations in the SH-wave waveforms accurately, though the amplitude contrast between acquisition azimuths was overestimated. Assuming a laterally homogeneous model, we then applied ray methods to simulate tuning effects in SH- and P-wave data and confirmed that in spite of the large contrasts in elastic properties, the tuning of the P-wave reflections from the thin disk changed so there was negligible contrast in AVO with azimuth. Models of field scale reservoirs showed that the same effects could be expected for field applications.

Seismic traveltime analysis for azimuthally anisotropic media: Theory and experiment

Geophysics ◽  
1997 ◽  
Vol 62 (5) ◽  
pp. 1570-1582 ◽  
Author(s):  
Colin M. Sayers ◽  
Daniel A. Ebrom
Keyword(s):  
Model Simulation ◽  
Symmetry Plane ◽  
Transversely Isotropic ◽  
Bedding Plane ◽  
Seismic Profile ◽  
Azimuthal Anisotropy ◽  
P Wave ◽  
Principal Axes ◽  
Physical Model Simulation ◽  
Single Set

Natural fractures in reservoirs, and in the caprock overlying the reservoir, play an important role in determining fluid flow during production. The density and orientation of sets of fractures is therefore of great interest. Rocks possessing an anisotropic fabric and a preferred orientation of fractures display both polar and azimuthal anisotropy. Sedimentary rocks containing several sets of vertical fractures may be approximated as having monoclinic symmetry with symmetry plane parallel to the layers if, in the absence of fractures, the rock is transversely isotropic with symmetry axis perpendicular to the bedding plane. A nonhyperbolic traveltime equation, which can be used in the presence of azimuthally anisotropic layered media, can be obtained from an expansion of the inverse‐squared ray velocity in spherical harmonics. For a single set of aligned fractures, application of this equation to traveltime data acquired at a sufficient number of azimuths allows the strike of the fractures to be estimated. Analysis of the traveltimes measured in a physical model simulation of a reverse vertical seismic profile in an azimuthally anisotropic medium shows the medium to be orthorhombic with principal axes in agreement with those given by an independent shear‐wave experiment. In contrast to previous work, no knowledge of the orientation of the symmetry planes is required. The method is therefore applicable to P‐wave data collected at multiple azimuths using multiple offset vertical seismic profiling (VSP) techniques.

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.

Lithospheric structure of the Trans-Hudson Orogen from seismic refraction - wide-angle reflection studies

2005 ◽  
Vol 42 (4) ◽  
pp. 435-456 ◽  
Author(s):  
Balázs Németh ◽  
Ron M Clowes ◽  
Zoltan Hajnal
Keyword(s):  
Seismic Refraction ◽  
Suture Zone ◽  
P Wave ◽  
Limited Area ◽  
Lithospheric Structure ◽  
Complex Deformation ◽  
Velocity Anisotropy ◽  
Metamorphic History ◽  
The North ◽  
Reflection Data

The Trans-Hudson Orogen (THO) is the world's largest Paleoproterozoic orogenic belt. Data from three refraction profiles are used to investigate its lithospheric structure in Saskatchewan and Manitoba. R1 crosses the orogen from the Hearne craton on the west to the Superior craton on the east; R2 and R3 are along the orogen. P-wave velocity structural models are generated using a ray-based technique. On line R1, higher crustal velocities in its eastern part coincide with rocks of the Flin Flon – Namew gneiss complex. Depth to Moho is in the 40–45 km range and equates to that from the reflection data, including a small crustal root below the Sask minicontinent. Along lines R2 and R3, depth to Moho varies from about 40 km up to 55 km at the north end of R2 and south end of R3. In general, variations in crustal velocity and depth to Moho do not correlate with the location and extent of geological domains; they appear to reflect the complex deformation and metamorphic history of the crustal rocks. Mantle velocities are high, ~8.2 km/s. However a limited area shows prominent velocity anisotropy, with values of 8.6 km/s along R2 and R3 and 8.1 km/s along R1. We speculate that the observed anisotropy represents an ~100-km-wide mantle suture zone resulting from the collision of Archean plates. The suture zone accommodated limited extensional deformation, associated with a counterclockwise rotation of the Superior plate, to generate the anisotropy. In this model, the lithospheric mantle of the THO internal domains and Sask craton are detached.

3-D moveout inversion in azimuthally anisotropic media with lateral velocity variation: Theory and a case study

Geophysics ◽  
1999 ◽  
Vol 64 (4) ◽  
pp. 1202-1218 ◽  
Author(s):  
Vladimir Grechka ◽  
Ilya Tsvankin
Keyword(s):  
Correction Term ◽  
Anisotropic Media ◽  
Azimuthal Anisotropy ◽  
P Wave ◽  
Velocity Variation ◽  
Variation Theory ◽  
Fractured Reservoir ◽  
Lateral Velocity ◽  
Data Set ◽  
Zero Offset

Reflection moveout recorded over an azimuthally anisotropic medium (e.g., caused by vertical or dipping fractures) varies with the azimuth of the source‐receiver line. Normal‐moveout (NMO) velocity, responsible for the reflection traveltimes on conventional‐length spreads, forms an elliptical curve in the horizontal plane. While this result remains valid in the presence of arbitrary anisotropy and heterogeneity, the inversion of the NMO ellipse for the medium parameters has been discussed so far only for horizontally homogeneous models above a horizontal or dipping reflector. Here, we develop an analytic moveout correction for weak lateral velocity variation in horizontally layered azimuthally anisotropic media. The correction term is proportional to the curvature of the zero‐offset traveltime surface at the common midpoint and, therefore, can be estimated from surface seismic data. After the influence of lateral velocity variation on the effective NMO ellipses has been stripped, the generalized Dix equation can be used to compute the interval ellipses and evaluate the magnitude of azimuthal anisotropy (measured by P-wave NMO velocity) within the layer of interest. This methodology was applied to a 3-D “wide‐azimuth” data set acquired over a fractured reservoir in the Powder River Basin, Wyoming. The processing sequence included 3-D semblance analysis (based on the elliptical NMO equation) for a grid of common‐midpoint “supergathers,” spatial smoothing of the effective NMO ellipses and zero‐offset traveltimes, correction for lateral velocity variation, and generalized Dix differentiation. Our estimates of depth‐varying fracture trends in the survey area, based on the interval P-wave NMO ellipses, are in good agreement with the results of outcrop and borehole measurements and the rotational analysis of four‐ component S-wave data.

Sign in / Sign up

Export Citation Format

Share Document