Reliability of the slowness and slowness-polarization methods for anisotropy estimation in VTI media from 3C walkaway VSP data

Geophysics ◽  
2013 ◽  
Vol 78 (5) ◽  
pp. WC93-WC102 ◽  
Author(s):  
Mehdi Asgharzadeh ◽  
Andrej Bóna ◽  
Roman Pevzner ◽  
Milovan Urosevic ◽  
Boris Gurevich
Keyword(s):  
Polarization Vector ◽  
Estimation Errors ◽  
Local Anisotropy ◽  
Weak Anisotropy ◽  
Polarization Measurements ◽  
Slowness Vector ◽  
Wide Range ◽  
Walkaway Vsp ◽  
Anisotropy Parameters ◽  
Vti Media

We studied the validity of qP-wave slowness and slowness-polarization methods for estimating local anisotropy parameters in transversely isotropic (TI) media by quantifying the estimation errors in a numerical exercise. We generated numerical slownesses and polarizations over two aperture ranges corresponding to a short offset walkaway vertical seismic profiling (VSP) and a long offset walkaway VSP for a range of TI models with vertical axis of symmetry (VTI). Synthetic data are equisampled over the phase angle range and contaminated with Gaussian noise. We inverted the data and compared the anisotropy parameters of the optimal model with the true model. We found that the selection of a proper methodology for VTI parameter estimation based on walkaway VSP measurements was mostly dependent on our ability to accurately estimate either horizontal components of qP-wave slowness vector or the polarization vector. With data contaminated with noise, methods that include the horizontal component of the slowness vector had greater accuracy than the methods that replace this information with polarization measurements. The estimations are particularly accurate when a wide range of propagation angle was available. For short offsets, only parameter [Formula: see text] could be reliably estimated. In the absence of long offsets, depending on the accuracy of polarization measurements, the method based on the weak anisotropy approximation for qP-wave velocity in VTI media or the method based on slowness and polarization vectors could be used to estimate [Formula: see text] and [Formula: see text]. If the horizontal components of the slowness vector were not available (a heterogeneous overburden), we used methods that were based on local measurements of the polarization vector. We found that, with accurate measurements of the polarization vector, the method based on exact relationship between vertical slowness and polarization dip could be used to estimate VTI parameters even for the cases in which the wide offset range was not available.

Long-offset moveout for VTI using Padé approximation

Geophysics ◽  
2016 ◽  
Vol 81 (5) ◽  
pp. C219-C227 ◽  
Author(s):  
Hanjie Song ◽  
Yingjie Gao ◽  
Jinhai Zhang ◽  
Zhenxing Yao
Keyword(s):  
Padé Approximation ◽  
Pade Approximation ◽  
Practical Applications ◽  
Long Offset ◽  
Wide Range ◽  
Isotropic Media ◽  
Transversally Isotropic ◽  
Error Accumulation ◽  
Anisotropy Parameters ◽  
Vti Media

The approximation of normal moveout is essential for estimating the anisotropy parameters of the transversally isotropic media with vertical symmetry axis (VTI). We have approximated the long-offset moveout using the Padé approximation based on the higher order Taylor series coefficients for VTI media. For a given anellipticity parameter, we have the best accuracy when the numerator is one order higher than the denominator (i.e., [[Formula: see text]]); thus, we suggest using [4/3] and [7/6] orders for practical applications. A [7/6] Padé approximation can handle a much larger offset and stronger anellipticity parameter. We have further compared the relative traveltime errors between the Padé approximation and several approximations. Our method shows great superiority to most existing methods over a wide range of offset (normalized offset up to 2 or offset-to-depth ratio up to 4) and anellipticity parameter (0–0.5). The Padé approximation provides us with an attractive high-accuracy scheme with an error that is negligible within its convergence domain. This is important for reducing the error accumulation especially for deeper substructures.

Weak anisotropy-attenuation parameters

Geophysics ◽  
2009 ◽  
Vol 74 (5) ◽  
pp. WB203-WB213 ◽  
Author(s):  
Václav Vavryčuk
Keyword(s):  
Quality Factor ◽  
Propagation Velocity ◽  
Elastic Anisotropy ◽  
Polarization Vector ◽  
Linear Functions ◽  
Weak Anisotropy ◽  
Simple Modification ◽  
Velocity Anisotropy ◽  
Slowness Vector ◽  
Lower Accuracy

Velocity anisotropy and attenuation in weakly anisotropic and weakly attenuating structures can be treated uniformly using weak anisotropy-attenuation (WAA) parameters. The WAA parameters are constructed in a way analogous to weak anisotropy (WA) parameters designed for weak elastic anisotropy. The WAA parameters generalize WA parameters by incorporating attenuation effects. They can be represented alternatively by one set of complex values or by two sets of real values. Assuming high-frequency waves and using the first-order perturbation theory, all basic wave quantities such as the slowness vector, the polarization vector, propagation velocity, attenuation, and the quality factor are linear functions of WAA parameters. Numerical modeling shows that perturbation equations have different accuracy for different wave quantities. The propagation velocity usually is calculated with high accuracy. However, the attenuation and quality factor can be reproduced with appreciably lower accuracy. This happens mostly when the strength of velocity anisotropy is higher than 10% and attenuation is moderate or weak [Formula: see text]. In this case, the errors of the attenuation or [Formula: see text]-factor can attain values comparable to the strength of anisotropy or even higher. A simple modification of the equations by including some higher-order perturbations improves accuracy by three to four times.

scholarly journals Local Determination of Weak Anisotropy Parameters from Walkaway VSP qP-Wave Data in the Java Sea Region

2004 ◽  
Vol 48 (1) ◽  
pp. 215-231 ◽  
Author(s):  
E. Gomes ◽  
X. Zheng ◽  
I. Pšenčík ◽  
S. Horne ◽  
S. Leaney
Keyword(s):  
Weak Anisotropy ◽  
Wave Data ◽  
Walkaway Vsp ◽  
Local Determination ◽  
Java Sea ◽  
Anisotropy Parameters

scholarly journals Estimation of in situ anisotropy parameters from two perpendicular walkaway VSP lines in South Pars field

2019 ◽  
Vol 16 (5) ◽  
pp. 926-938 ◽  
Author(s):  
Mohammad Mahdi Abedi ◽  
Mahtab Rashidi Fard ◽  
Mohammad Ali Riahi
Keyword(s):  
Wave Propagation ◽  
P Wave ◽  
Reasonable Assumption ◽  
Polarization Angle ◽  
Orthorhombic Symmetry ◽  
Weak Anisotropy ◽  
Estimated Parameters ◽  
Walkaway Vsp ◽  
Anisotropy Parameters

Abstract Vertical phase slowness and polarization angle are the in situ parameters of P-wave propagation that can be derived from walkaway vertical seismic profiling (VSP) data. To use these data for estimating anisotropy parameters, we obtain an explicit equation of vertical slowness as a function of polarization angle for P-wave propagation in transversely isotropic with vertical symmetry axis (VTI) media. We use this equation to estimate anisotropy parameters of a target layer in the South Pars field, Iran. This field is one of the world's largest gas fields. We show that the orthorhombic symmetry is a reasonable assumption for this layer, providing some geological and petrophysical information. Two walkaway VSP lines along the symmetry axes of the presumed orthorhombic layer are used to estimate its parameters. Seven is the maximum number of parameters that can be estimated using P-wave data in this acquisition pattern. Of those estimated parameters are six of the Tsvankin style parameters for orthorhombic media, plus an approximate combination of two others that define vertical S-wave splitting. We show that a previous method, which is based on weak anisotropy approximation, leads to considerable errors, even in models where the magnitude of anisotropy parameters do not exceed 0.1. We design a numerical experiment to study the reliability of the estimated parameters by the exact approach and show the importance of acquisition pattern in this regard. To show applicability, these parameters are used to estimate the in situ fracture properties of the studied layer.

scholarly journals P-Wave-Only Inversion of Challenging Walkaway VSP Data for Detailed Estimation of Local Anisotropy and Reservoir Parameters: A Case Study of Seismic Processing in Northern Poland

Energies ◽  
2021 ◽  
Vol 14 (8) ◽  
pp. 2061
Author(s):  
Mateusz Zaręba ◽  
Tomasz Danek ◽  
Michał Stefaniuk
Keyword(s):  
Seismic Signal ◽  
Field Conditions ◽  
P Wave ◽  
Quality Data ◽  
Local Anisotropy ◽  
Processing Scheme ◽  
Vsp Data ◽  
Walkaway Vsp ◽  
Anisotropy Parameters ◽  
Detailed Interpretation

In this paper, we present a detailed analysis of walkaway vertical seismic profiling (VSP) data, which can be used to obtain Thomsen parameters using P-wave-only inversion. Data acquisition took place in difficult field conditions, which influenced the quality of the data. Therefore, this paper also shows a seismic data processing scheme that allows the estimation of correct polarization angles despite poor input data quality. Moreover, we showed that it is possible to obtain reliable and detailed values of Thomsen’s anisotropy parameters for data that are challenging due to extremely difficult field conditions during acquisition and the presence of an overburden of salt and anhydrite (Zechstein formation). This complex is known for its strong seismic signal-attenuating properties. We designed a special processing workflow with a signal-matching procedure that allows reliable estimation of polarization angles for low-quality data. Additionally, we showed that P-wave-only inversion for the estimation of local anisotropy parameters can be used as valuable additional input for detailed interpretation of geological media, even if anisotropy is relatively low.

Normal moveout from dipping reflectors in anisotropic media

Geophysics ◽  
1995 ◽  
Vol 60 (1) ◽  
pp. 268-284 ◽  
Author(s):  
Ilya Tsvankin
Keyword(s):  
Symmetry Axis ◽  
Transverse Isotropy ◽  
Transversely Isotropic ◽  
Anisotropic Media ◽  
Weak Anisotropy ◽  
Anisotropic Models ◽  
Transversely Isotropic Media ◽  
Wide Range ◽  
Isotropic Media ◽  
The Difference

Description of reflection moveout from dipping interfaces is important in developing seismic processing methods for anisotropic media, as well as in the inversion of reflection data. Here, I present a concise analytic expression for normal‐moveout (NMO) velocities valid for a wide range of homogeneous anisotropic models including transverse isotropy with a tilted in‐plane symmetry axis and symmetry planes in orthorhombic media. In transversely isotropic media, NMO velocity for quasi‐P‐waves may deviate substantially from the isotropic cosine‐of‐dip dependence used in conventional constant‐velocity dip‐moveout (DMO) algorithms. However, numerical studies of NMO velocities have revealed no apparent correlation between the conventional measures of anisotropy and errors in the cosine‐of‐dip DMO correction (“DMO errors”). The analytic treatment developed here shows that for transverse isotropy with a vertical symmetry axis, the magnitude of DMO errors is dependent primarily on the difference between Thomsen parameters ε and δ. For the most common case, ε − δ > 0, the cosine‐of‐dip–corrected moveout velocity remains significantly larger than the moveout velocity for a horizontal reflector. DMO errors at a dip of 45 degrees may exceed 20–25 percent, even for weak anisotropy. By comparing analytically derived NMO velocities with moveout velocities calculated on finite spreads, I analyze anisotropy‐induced deviations from hyperbolic moveout for dipping reflectors. For transversely isotropic media with a vertical velocity gradient and typical (positive) values of the difference ε − δ, inhomogeneity tends to reduce (sometimes significantly) the influence of anisotropy on the dip dependence of moveout velocity.

Determination of Weak Anisotropy Parameters Using Traveltimes and Polarisations

2003 ◽  
Author(s):  
S.M. Soukina ◽  
D. Gajewski ◽  
B.M. Kashtan
Keyword(s):  
Weak Anisotropy ◽  
Anisotropy Parameters

Anisotropic full-waveform inversion of crosshole seismic data: A vertical symmetry axis field data application

Geophysics ◽  
2019 ◽  
Vol 84 (1) ◽  
pp. B15-B32 ◽  
Author(s):  
Shaun Hadden ◽  
R. Gerhard Pratt ◽  
Brendan Smithyman
Keyword(s):  
Symmetry Axis ◽  
Waveform Inversion ◽  
Full Waveform Inversion ◽  
S Waves ◽  
Traveltime Tomography ◽  
Full Waveform ◽  
Anisotropy Parameters ◽  
Vti Media ◽  
Ti Media ◽  
Acoustic Approximation

Anisotropic waveform tomography (AWT) uses anisotropic traveltime tomography followed by anisotropic full-waveform inversion (FWI). Such an approach is required for FWI in cases in which the geology is likely to exhibit anisotropy. An important anisotropy class is that of transverse isotropy (TI), and the special case of TI media with a vertical symmetry axis (VTI) media is often used to represent elasticity in undeformed sedimentary layering. We have developed an approach for AWT that uses an acoustic approximation to simulate waves in VTI media, and we apply this approach to crosshole data. In our approach, the best-fitting models of seismic velocity and Thomsen VTI anisotropy parameters are initially obtained using anisotropic traveltime tomography, and they are then used as the starting models for VTI FWI within the acoustic approximation. One common problem with the acoustic approach to TI media is the generation of late-arriving (spurious) S-waves as a by-product of the equation system. We used a Laplace-Fourier approach that effectively damps the spurious S-waves to suppress artifacts that might otherwise corrupt the final inversion results. The results of applying AWT to synthetic data illustrate the trade-offs in resolution between the two parameter classes of velocity and anisotropy, and they also verify anisotropic traveltime tomography as a valid method for generating starting models for FWI. The synthetic study further indicates the importance of smoothing the anisotropy parameters before proceeding to FWI inversions of the velocity parameter. The AWT technique is applied to real crosshole field gathers from a sedimentary environment in Western Canada, and the results are compared with the results from a simpler (elliptical) anisotropy model. The transversely isotropic approach yields an FWI image of the vertical velocity that (1) exhibits a superior resolution and (2) better predicts the field data than does the elliptical approach.

scholarly journals Standardization of Offshore Surface Wind Speeds

2016 ◽  
Vol 55 (5) ◽  
pp. 1107-1121 ◽  
Author(s):  
Y. C. He ◽  
P. W. Chan ◽  
Q. S. Li
Keyword(s):  
Shallow Water ◽  
Surface Wind ◽  
Reference Conditions ◽  
Deep Ocean ◽  
Topographic Effects ◽  
Strong Wind ◽  
Estimation Errors ◽  
Wind Speeds ◽  
Wide Range ◽  
Wind Measurements

AbstractWind measurement offers an essential data source for a wide range of practices in the fields of meteorology and wind engineering. However, records of surface winds are usually influenced by terrain/topographic effects, and direct usage of raw data may bring in nonignorable errors for follow-up applications. A data-driven standardization scheme was recently proposed by the authors to convert the surface wind measurements over rugged terrain into their potential values corresponding to reference conditions, that is, for neutral winds at a height of 10 m above open flat terrain (z0 = 0.03 m). As a complementary part of the preceding work, this study focuses on the standardization of surface wind speeds with marine exposures. The effect of wind strength on the roughness of the sea surface is further taken into account, with emphasis on the difference between deep-ocean and shallow-water cases. As an application example, wind measurements at a buoy site near the coastal line (water depth is 14 m) are adjusted to their potential values, which are then compared with those at a nearby station. The good agreement between the two sets of results demonstrates the accuracy and effectiveness of the standardization method. It is also found that the behavior of roughness length scale over shallow water may differ noticeably from that over deep ocean, especially under strong wind conditions, and an inappropriate usage of marine roughness predictors may result in significant estimation errors.

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