scholarly journals Polynomial amplitude versus azimuth inversion in horizontally transverse isotropic media, as tested on fractured coal seams in the Surat Basin

2017 ◽  
Vol 57 (2) ◽  
pp. 776 ◽  
Author(s):  
Joseph Kremor ◽  
Randall Taylor ◽  
Khalid Amrouch
Keyword(s):  
Fourier Method ◽  
Compressional Wave ◽  
Seismic Inversion ◽  
Seismic Survey ◽  
Weak Anisotropy ◽  
Anisotropic Component ◽  
Hti Media ◽  
Transverse Isotropic ◽  
Anisotropy Parameters ◽  
Amplitude Versus

A new technique of amplitude versus azimuth (AVAZ) seismic inversion in horizontally transverse isotropic (HTI) media is presented. AVAZ is an effective method of characterising anisotropic variation within individual reflectors as well as characterising fractures. The compressional wave reflectivity equation in HTI media has been reformulated into a parabolic form that allows for fast and efficient inversion. The isotropic component of the azimuthal reflectivity has been separated precisely from the anisotropic component and the anisotropic component has been decoupled exactly into its constituent elliptic and anelliptic components. The exact isotropic, elliptic and anelliptic amplitude versus offset (AVO) gradient equations in HTI media are presented herein and the amount of error associated with previous approximations is also defined under the assumption of weak anisotropy. A method of calculating Thomsen’s weak anisotropy parameters using these AVO gradient terms is then outlined. Compared with the elliptic method, there is reduced error incorporated in the new AVAZ method and the error relationships of this method are compared with the Fourier method. Data from an open file 3D wide azimuth seismic survey in the Surat Basin were inverted to demonstrate the effectiveness of the techniques which are presented herein. Seismic amplitudes from six azimuthal stacks were extracted over two horizons and inverted around a well where full-wave sonic and density logs were acquired. For both horizons, the error between the inverted anisotropy parameters from seismic and the inverted anisotropy parameters from wire line logs were found to be less than 5% for both horizons.

Anisotropy parameter inversion from sonic and density logs in horizontally transverse isotropic media

2017 ◽  
Vol 57 (2) ◽  
pp. 772
Author(s):  
Joseph Kremor ◽  
Khalid Amrouch
Keyword(s):  
Wave Velocity ◽  
Symmetry Plane ◽  
Anisotropy Parameter ◽  
Compressional Wave ◽  
Fracture Plane ◽  
Compressional Wave Velocity ◽  
Transverse Waves ◽  
Hti Media ◽  
Transverse Isotropic ◽  
Anisotropy Parameters

A methodology of calculating anisotropy parameters in horizontally transverse isotropic (HTI) media using a Backus average-like algorithm is presented herein. Anisotropy parameters in HTI media are calculated by mapping the stiffness parameters that exist in HTI media and vertically transverse isotropic (VTI) media by tilting the Christoffel equations. Fast and slow transverse waves, compressional wave and density logs are used as inputs into the averaging algorithm and, from these, anisotropy parameters are calculated over a predefined averaging window. From the results, the horizontal compressional wave velocity in the direction of the symmetry plane of isotropy can be determined, as can the compressional wave velocity that is perpendicular to the symmetry plane. When the anisotropy is caused by a single set of vertical fractures, these correspond to the directions perpendicular to and parallel to the fracture plane respectively. In cases where the thickness of the bed of interest is thin, a workflow is presented to choose an averaging length that will allow for the calculation of anisotropy parameters and velocities in thin beds. This technique was applied to a coal seam gas well situated in the Surat Basin and anisotropy parameters were calculated over two horizons.

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.

Geometrical spreading in a layered transversely isotropic medium with vertical symmetry axis

Geophysics ◽  
2003 ◽  
Vol 68 (6) ◽  
pp. 2082-2091 ◽  
Author(s):  
Bjørn Ursin ◽  
Ketil Hokstad
Keyword(s):  
Ray Tracing ◽  
Seismic Data ◽  
Symmetry Axis ◽  
Transversely Isotropic ◽  
Analytical Approximation ◽  
Geometrical Spreading ◽  
S Wave ◽  
Weak Anisotropy ◽  
P Waves ◽  
Amplitude Versus

Compensation for geometrical spreading is important in prestack Kirchhoff migration and in amplitude versus offset/amplitude versus angle (AVO/AVA) analysis of seismic data. We present equations for the relative geometrical spreading of reflected and transmitted P‐ and S‐wave in horizontally layered transversely isotropic media with vertical symmetry axis (VTI). We show that relatively simple expressions are obtained when the geometrical spreading is expressed in terms of group velocities. In weakly anisotropic media, we obtain simple expressions also in terms of phase velocities. Also, we derive analytical equations for geometrical spreading based on the nonhyperbolic traveltime formula of Tsvankin and Thomsen, such that the geometrical spreading can be expressed in terms of the parameters used in time processing of seismic data. Comparison with numerical ray tracing demonstrates that the weak anisotropy approximation to geometrical spreading is accurate for P‐waves. It is less accurate for SV‐waves, but has qualitatively the correct form. For P waves, the nonhyperbolic equation for geometrical spreading compares favorably with ray‐tracing results for offset‐depth ratios less than five. For SV‐waves, the analytical approximation is accurate only at small offsets, and breaks down at offset‐depth ratios less than unity. The numerical results are in agreement with the range of validity for the nonhyperbolic traveltime equations.

scholarly journals Seismic AVOA Inversion for Weak Anisotropy Parameters and Fracture Density in a Monoclinic Medium

2020 ◽  
Vol 10 (15) ◽  
pp. 5136 ◽  
Author(s):  
Zijian Ge ◽  
Shulin Pan ◽  
Jingye Li
Keyword(s):  
Fractured Rock ◽  
Synthetic Data ◽  
Transversely Isotropic ◽  
P Wave ◽  
Inversion Method ◽  
Fracture Density ◽  
Weak Anisotropy ◽  
Amplitude Versus Offset ◽  
Porosity And Permeability ◽  
Transverse Isotropic

In shale gas development, fracture density is an important lithologic parameter to properly characterize reservoir reconstruction, establish a fracturing scheme, and calculate porosity and permeability. The traditional methods usually assume that the fracture reservoir is one set of aligned vertical fractures, embedded in an isotropic background, and estimate some alternative parameters associated with fracture density. Thus, the low accuracy caused by this simplified model, and the intrinsic errors caused by the indirect substitution, affect the estimation of fracture density. In this paper, the fractured rock of monoclinic symmetry assumes two non-orthogonal vertical fracture sets, embedded in a transversely isotropic background. Firstly, assuming that the fracture radius, width, and orientation are known, a new form of P-wave reflection coefficient, in terms of weak anisotropy (WA) parameters and fracture density, was obtained by substituting the stiffness coefficients of vertical transverse isotropic (VTI) background, normal, and tangential fracture compliances. Then, a linear amplitude versus offset and azimuth (AVOA) inversion method, of WA parameters and fracture density, was constructed by using Bayesian theory. Tests on synthetic data showed that WA parameters, and fracture density, are stably estimated in the case of seismic data containing a moderate noise, which can provide a reliable tool in fracture prediction.

Quartic moveout coefficient: 3D description and application to tilted TI media

Geophysics ◽  
2003 ◽  
Vol 68 (5) ◽  
pp. 1600-1610 ◽  
Author(s):  
Andres Pech ◽  
Ilya Tsvankin ◽  
Vladimir Grechka
Keyword(s):  
Heterogeneous Media ◽  
Symmetry Axis ◽  
High Sensitivity ◽  
Transversely Isotropic ◽  
Seismic Inversion ◽  
P Wave ◽  
Individual Values ◽  
Weak Anisotropy ◽  
Essential Information ◽  
Ti Media

Nonhyperbolic (long‐spread) moveout provides essential information for a number of seismic inversion/processing applications, particularly for parameter estimation in anisotropic media. Here, we present an analytic expression for the quartic moveout coefficient A4 that controls the magnitude of nonhyperbolic moveout of pure (nonconverted) modes. Our result takes into account reflection‐point dispersal on irregular interfaces and is valid for arbitrarily anisotropic, heterogeneous media. All quantities needed to compute A4 can be evaluated during the tracing of the zero‐offset ray, so long‐spread moveout can be modeled without time‐consuming multioffset, multiazimuth ray tracing. The general equation for the quartic coefficient is then used to study azimuthally varying nonhyperbolic moveout of P‐waves in a dipping transversely isotropic (TI) layer with an arbitrary tilt ν of the symmetry axis. Assuming that the symmetry axis is confined to the dip plane, we employed the weak‐anisotropy approximation to analyze the dependence of A4 on the anisotropic parameters. The linearized expression for A4 is proportional to the anellipticity coefficient η ≈ ε − δ and does not depend on the individual values of the Thomsen parameters. Typically, the magnitude of nonhyperbolic moveout in tilted TI media above a dipping reflector is highest near the reflector strike, whereas deviations from hyperbolic moveout on the dip line are substantial only for mild dips. The azimuthal variation of the quartic coefficient is governed by the tilt ν and reflector dip φ and has a much more complicated character than the NMO–velocity ellipse. For example, if the symmetry axis is vertical (VTI media, ν = 0) and the dip φ < 30°, A4 goes to zero on two lines with different azimuths where it changes sign. If the symmetry axis is orthogonal to the reflector (this model is typical for thrust‐and‐fold belts), the strike‐line quartic coefficient is defined by the well‐known expression for a horizontal VTI layer (i.e., it is independent of dip), while the dip‐line A4 is proportional to cos4 φ and rapidly decreases with dip. The high sensitivity of the quartic moveout coefficient to the parameter η and the tilt of the symmetry axis can be exploited in the inversion of wide‐azimuth, long‐spread P‐wave data for the parameters of TI media.

An analysis of the crust–mantle boundary in Hudson Bay from gravity and seismic observations

1968 ◽  
Vol 5 (5) ◽  
pp. 1297-1303 ◽  
Author(s):  
J. R. Weber ◽  
A. K. Goodacre
Keyword(s):  
Gravity Anomaly ◽  
Gravity Anomalies ◽  
Gravitational Effect ◽  
Compressional Wave ◽  
Seismic Survey ◽  
Hudson Bay ◽  
Mantle Boundary ◽  
Crustal Velocity ◽  
Velocity Variations ◽  
Crustal Density

A study of the results of the gravity and seismic surveys in Hudson Bay in 1965 has shown that the gravitational effect of a two-layer model based on the seismically determined depths has no correlation with the observed gravity anomalies. On the profile from Churchill to Povungnituk the gravity and seismic observations can be reconciled by postulating lateral variations of the acoustic compressional wave velocity within the crust. A crustal model has been calculated—using the same time-terms and the same mean crustal velocity—whose gravitational effect fits the observed gravity. The velocity varies from 6.15 to 6.56 km/s and the postulated depths are almost entirely within the confidence limits of the original model.In order to test the hypothesis, the postulated velocity variations have been compared with the lower refractor velocities of the shallow seismic survey, based on the assumption that the crustal velocities ought to be systematically higher than the crystalline surface velocities and that there may be a correlation between variations in crustal and surface velocities. The test is inconclusive because bottom refractor velocities are higher than crustal velocities in two areas where volcanic flows and high-velocity sediments may be present.The case of linearly related velocity (V) and density (ρ) variations has been analyzed and it is shown that the gravitational effect of the crust–mantle boundary undulations may be completely masked or even overbalanced by density changes in the crust if [Formula: see text]. The crust can be characterized by having dominant velocity variations (in which case the gravity anomaly reflects the undulations of the crust–mantle boundary) or dominant density variations (in which case the gravity anomaly inversely reflects the crust–mantle boundary undulations) depending on the relationship between average crustal density and average crustal velocity.

First-order ray tracing for qP waves in inhomogeneous, weakly anisotropic media

Geophysics ◽  
2005 ◽  
Vol 70 (6) ◽  
pp. D65-D75 ◽  
Author(s):  
Ivan Pšenčík ◽  
Véronique Farra
Keyword(s):  
Ray Tracing ◽  
Anisotropic Media ◽  
Order Accuracy ◽  
Weak Anisotropy ◽  
Higher Symmetry ◽  
First Order ◽  
Isotropic Media ◽  
Anisotropy Parameters ◽  
Order Quantities ◽  
Relative Errors

We propose approximate ray-tracing equations for qP-waves propagating in smooth, inhomogeneous, weakly anisotropic media. For their derivation, we use perturbation theory, in which deviations of anisotropy from isotropy are considered to be the first-order quantities. The proposed ray-tracing equations and corresponding traveltimes are of the first order. Accuracy of the traveltimes can be increased by calculating a secondorder correction along first-order rays. The first-order ray-tracing equations for qP-waves propagating in a general weakly anisotropic medium depend on only 15 weak-anisotropy parameters (generalization of Thomsen’s parameters). The equations are thus considerably simpler than the exact ray-tracing equations. For higher-symmetry anisotropic media the equations differ only slightly from equations for isotropic media. They can thus substitute for the traditional isotropic ray tracers used in seismic processing. For vanishing anisotropy, the first-order ray-tracing equations reduce to standard, exact ray-tracing equations for isotropic media. Numerical tests for configuration and models used in seismic prospecting indicate negligible dependence of accuracy of calculated traveltimes on inhomogeneity of the medium. For anisotropy of about 8%, considered in the examples presented, the relative errors of the traveltimes, including the second-order correction, are well under 0.05%; for anisotropy of about 20%, they do not exceed 0.3%.

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.

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