Orthorhombic media: Modeling elastic wave behavior in a vertically fractured earth

Schoenberg, Michael; Helbig, Klaus

doi:10.1190/1.1444297

Cited by 361 publications

(219 citation statements)

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“…The elastic properties of most hydrocarbon reservoirs can be wellapproximated using orthorhombic anisotropy (Schoenberg & Helbig 1997;Tsvankin 1997;Ivanov & Stovas 2016) on the scale of common exploration seismic wavelengths. Systems of orthogonal fractures or vertical layering within a reservoir can be described by macroscale orthorhombic media; see Fig.…”

Section: Introductionmentioning

confidence: 99%

Waveform inversion for orthorhombic anisotropy with P waves: feasibility and resolution

Kazei

Alkhalifah

2018

Geophysical Journal International

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Summary Various parameterizations have been suggested to simplify inversions of first arrivals, or P −waves, in orthorhombic anisotropic media, but the number and type of retrievable parameters have not been decisively determined. We show that only six parameters can be retrieved from the dynamic linearized inversion of P −waves. These parameters are different from the six parameters needed to describe the kinematics of P −waves. Reflection-based radiation patterns from the P − P scattered waves are remapped into the spectral domain to allow for our resolution analysis based on the effective angle of illumination concept. Singular value decomposition of the spectral sensitivities from various azimuths, offset coverage scenarios, and data bandwidths allows us to quantify the resolution of different parameterizations, taking into account the signal-to-noise ratio in a given experiment. According to our singular value analysis, when the primary goal of inversion is determining the velocity of the P −waves, gradually adding anisotropy of lower orders (isotropic, vertically transversally isotropic, orthorhombic) in hierarchical parameterization is the best choice. Hierarchical parametrization reduces the tradeoff between the parameters and makes gradual introduction of lower anisotropy orders straightforward. When all the anisotropic parameters affecting P −wave propagation need to be retrieved simultaneously, the classic parameterization of orthorhombic medium with elastic stiffness matrix coefficients and density is a better choice for inversion. We provide estimates of the number and set of parameters that can be retrieved from surface seismic data in different acquisition scenarios. To set up an inversion process, the singular values determine the number of parameters that can be inverted and the resolution matrices from the parameterizations can be used to ascertain the set of parameters that can be resolved.

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Section: Introductionmentioning

confidence: 99%

Waveform inversion for orthorhombic anisotropy with P waves: feasibility and resolution

Kazei

Alkhalifah

2018

Geophysical Journal International

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“…Based on the dispersion relation of an orthorhombic medium, Schoenberg and Helbig (1997) pointed out that the difference between the orthorhombic equations in a plane symmetry and TI equations in a plane containing the rotational symmetry axis appears only with the inclusion of the cross-plane uncoupled-wave (SH) equation. This is because in general the two shear modes do not have the same velocity even when they propagate in the principal axial directions.…”

Section: Interpretation Of the Measurements Using An Equivalent Ti Modelmentioning

confidence: 99%

Sonic logging in deviated boreholes of an anisotropic formation: Laboratory study

Zhu¹,

Chi²,

Toksöz³

2006

SEG Technical Program Expanded Abstracts 2006

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Deepwater field development requires drilling of deviated or horizontal wells. Most formations encountered can be highly anisotropic and P-and S-wave velocities vary with propagation directions. Sonic logs acquired in these wells need to be corrected before they can be applied in formation evaluation and seismic applications. In this study, we make use of a laboratory model made of an approximate transversely isotropic Phenolite to study acoustic logging in deviated wells. We drill holes at various deviations relative to the symmetry axis in the Phenolite block. Then we perform monopole and dipole sonic measurements in these holes and extract the qP, qSV, SH, and Stoneley wave velocities using the slowness-time domain semblance method. The velocities measured using monopole and dipole loggings vary with borehole deviations. We also measure the qP, qSV, and SH wave velocities using body waves at the same angles as the well deviations. We then compute the theoretical qP, qSV, SH, and Stoneley wave velocities based on an equivalent transverse isotropic model of the Phenolite. We find the qP, qSV , and SH wave velocities obtained using the body wave measurement and acoustic logging method agree with the theoretical predictions. The Stoneley wave velocities predicted by the theory also agree reasonably well with the logging measurements.

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“…Now, we find that an orthorhombic medium is a good enough model to describe many geologic settings especially those that exhibit azimuthal variation behavior (Tsvankin et al, 2010). Such medium describes one or two orthogonal sets of parallel vertical fractures embedded in a transversely isotropic (TI) or a purely isotropic host rock (Wild and Crampin, 1991;Schoenberg and Helbig, 1997;Bakulin et al, 2000). If the sedimentation and fractures are dipping (but orthogonal), this leads to tilted orthorhombic media.…”

Section: Introductionmentioning

confidence: 99%

Traveltime approximations and parameter estimation for orthorhombic media

Masmoudi

Alkhalifah

2016

GEOPHYSICS

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Building anisotropy models is necessary for seismic modeling and imaging. However, anisotropy estimation is challenging due to the trade-off between inhomogeneity and anisotropy. Luckily, we can estimate the anisotropy parameters if we relate them analytically to traveltimes. Using perturbation theory, we have developed traveltime approximations for orthorhombic media as explicit functions of the anellipticity parameters η 1 , η 2 , and Δχ in inhomogeneous background media. The parameter Δχ is related to Tsvankin-Thomsen notation and ensures easier computation of traveltimes in the background model. Specifically, our expansion assumes an inhomogeneous ellipsoidal anisotropic background model, which can be obtained from well information and stacking velocity analysis. We have used the Shanks transform to enhance the accuracy of the formulas. A homogeneous medium simplification of the traveltime expansion provided a nonhyperbolic moveout description of the traveltime that was more accurate than other derived approximations. Moreover, the formulation provides a computationally efficient tool to solve the eikonal equation of an orthorhombic medium, without any constraints on the background model complexity. Although, the expansion is based on the factorized representation of the perturbation parameters, smooth variations of these parameters (represented as effective values) provides reasonable results. Thus, this formulation provides a mechanism to estimate the three effective parameters η 1 , η 2 , and Δχ. We have derived Dix-type formulas for orthorhombic medium to convert the effective parameters to their interval values.

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Orthorhombic media: Modeling elastic wave behavior in a vertically fractured earth

Cited by 361 publications

References 20 publications

Waveform inversion for orthorhombic anisotropy with P waves: feasibility and resolution

Waveform inversion for orthorhombic anisotropy with P waves: feasibility and resolution

Sonic logging in deviated boreholes of an anisotropic formation: Laboratory study

Traveltime approximations and parameter estimation for orthorhombic media

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