Time-domain finite-difference modeling for attenuative anisotropic media

Bai, Tong; Tsvankin, Ilya

doi:10.1190/geo2015-0424.1

Cited by 73 publications

(30 citation statements)

References 34 publications

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“…The relaxation function for arbitrarily anisotropic attenuative media can be found in Bai and Tsvankin (). For a single relaxation mechanism, that function has the form (no index summation is assumed):

{normalΨ}_{i j k l} false(t false) = C_{i j k l}^{R} (1 + τ_{i j k l} e^{- t / τ^{σ}}) H false(t false),

where

C_{i j k l}^{R} = {normalΨ}_{i j k l} false(t \to \infty false)

is called the ‘relaxed stiffness,’

τ^{σ}

denotes the stress relaxation time determined by the reference frequency (frequency at which velocity and attenuation parameters are defined), the parameters

τ_{i j k l}

control the difference between the stress and strain relaxation time (and, therefore, they determine the magnitude of attenuation in anisotropic media), and

H (t)

is the Heaviside function.…”

Section: Methodsmentioning

confidence: 99%

“…The P‐ and SV‐wave attenuation in VTI media is conveniently described by the Thomsen‐style parameters

A_{P 0}

A_{S 0}

ε_{Q}

and

δ_{Q}

(Zhu and Tsvankin ; Bai and Tsvankin ).

A_{P 0}

and

A_{S 0}

are the vertical (symmetry‐axis) P‐ and S‐wave attenuation coefficients, the parameter

ε_{Q}

depends on the fractional difference between the P‐wave attenuation coefficients in the horizontal and vertical directions and

δ_{Q}

controls the curvature of the P‐wave attenuation coefficient at the symmetry axis.…”

Section: Methodsmentioning

confidence: 99%

“…The time‐domain viscoelastic stress (

σ_{i j}

)–strain(

ε_{k l}

) relationship can be written as

σ_{i j} = C_{i j k l}^{U} ε_{k l} + Δ C_{i j k l} r_{k l},

where

r_{k l}

are the memory variables, which satisfy the following partial differential equations (Bai and Tsvankin ):

\frac{\partial r_{k l}}{\partial t} = - \frac{1}{τ^{σ}} (r_{k l} + ε_{k l}) .

…”

Section: Methodsmentioning

confidence: 99%

“…In the framework of the generalized standard linear solid model, Bai and Tsvankin () develop a time‐domain finite‐difference modelling algorithm for anisotropic attenuative media, which produces nearly frequency‐independent elements

Q_{i j}

of the quality‐factor matrix. Employing that simulator, Bai et al .…”

Section: Introductionmentioning

confidence: 99%

“…In the framework of the generalized standard linear solid model, Bai and Tsvankin (2016) develop a time-domain finitedifference modelling algorithm for anisotropic attenuative media, which produces nearly frequency-independent elements Q i j of the quality-factor matrix. Employing that simulator, Bai et al (2017) design a time-domain WI methodology for estimation of the attenuation parameters of VTI (transversely isotropic with a vertical symmetry axis) media.…”

Section: Introductionmentioning

confidence: 99%

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Source‐independent waveform inversion for attenuation estimation in anisotropic media

Bai

Tsvankin

2019

Geophysical Prospecting

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In previous publications, we presented a waveform‐inversion algorithm for attenuation analysis in heterogeneous anisotropic media. However, waveform inversion requires an accurate estimate of the source wavelet, which is often difficult to obtain from field data. To address this problem, here we adopt a source‐independent waveform‐inversion algorithm that obviates the need for joint estimation of the source signal and attenuation coefficients. The key operations in that algorithm are the convolutions (1) of the observed wavefield with a reference trace from the modelled data and (2) of the modelled wavefield with a reference trace from the observed data. The influence of the source signature on attenuation estimation is mitigated by defining the objective function as the ℓ2‐norm of the difference between the two convolved data sets. The inversion gradients for the medium parameters are similar to those for conventional waveform‐inversion techniques, with the exception of the adjoint sources computed by convolution and cross‐correlation operations. To make the source‐independent inversion methodology more stable in the presence of velocity errors, we combine it with the local‐similarity technique. The proposed algorithm is validated using transmission tests for a homogeneous transversely isotropic model with a vertical symmetry axis that contains a Gaussian anomaly in the shear‐wave vertical attenuation coefficient. Then the method is applied to the inversion of reflection data for a modified transversely isotropic model from Hess. It should be noted that due to the increased nonlinearity of the inverse problem, the source‐independent algorithm requires a more accurate initial model to obtain inversion results comparable to those produced by conventional waveform inversion with the actual wavelet.

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{normalΨ}_{i j k l} false(t false) = C_{i j k l}^{R} (1 + τ_{i j k l} e^{- t / τ^{σ}}) H false(t false),

where

C_{i j k l}^{R} = {normalΨ}_{i j k l} false(t \to \infty false)

is called the ‘relaxed stiffness,’

τ^{σ}

denotes the stress relaxation time determined by the reference frequency (frequency at which velocity and attenuation parameters are defined), the parameters

τ_{i j k l}

control the difference between the stress and strain relaxation time (and, therefore, they determine the magnitude of attenuation in anisotropic media), and