The resolving power of seismic amplitude data: An anisotropic inversion/migration approach

Hoop, Maarten V. de; Spencer, Carl; Burridge, Robert

doi:10.1190/1.1444595

Cited by 53 publications

(69 citation statements)

References 43 publications

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“…Identifiable combinations of parameters can be divided into two groups -the first three Resolution of P −wave orthorhombic inversion 21 singular vectors show slightly higher sensitivity than the other three, which is in agreement with de Hoop et al (1999). The most interesting fact is that, despite previously published works (de Hoop et al 1999;Oh & Alkhalifah 2016), in the case of perfect illumination, the gap in this standard parameterization is within one order of magnitude and all six parameters can principally be determined, granted good quality data. Finally, we set the threshold for the resolution matrix to 0.1 of the highest singular value (this corresponds to the eigen values of the Hessian above 0.01) and create the resolution matrix for this case.…”

Section: Ij ρ Parameterizationsupporting

confidence: 65%

“…In the standard parameterization, we see two levels of singular values very clearly (de Hoop et al 1999), yet the levels are within one order of magnitude. All six independently determinable parameters have approximately the same impact on the data and, thus, all of them can be determined in well-illuminated areas (Fig.…”

Section: Hierarchical Parameterizationmentioning

confidence: 99%

“…Eaton & Stewart (1994) were the first to discover the importance of the scattering function in anisotropic media and established a resolution analysis for vertically incident qP-waves in vertically transversally isotropic (VTI) media. De Hoop et al (1999) derived a similar analysis for orthorhombic parameter perturbations that focused on reflections in an isotropic background. Reflection-based radiation patterns were used to analyze the ability of anisotropic elastic FWI to estimate VTI parameters using only P-waves in various parameterizations (Gholami et al 2013b;Alkhalifah & Plessix 2014).…”

Section: Introductionmentioning

confidence: 99%

“…With the assumption of an isotropic background, the resolution can be investigated visually using the reflection-based radiation patterns (Alkhalifah & Plessix 2014;Oh & Alkhalifah 2016) and quantitatively using the singular value decomposition (SVD) analysis of those patterns (Eaton & Stewart 1994;de Hoop et al 1999;Podgornova et al 2015). Eaton & Stewart (1994) were the first to discover the importance of the scattering function in anisotropic media and established a resolution analysis for vertically incident qP-waves in vertically transversally isotropic (VTI) media.…”

Section: Introductionmentioning

confidence: 99%

See 3 more Smart Citations

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: Ij ρ Parameterizationsupporting

confidence: 65%

Section: Hierarchical Parameterizationmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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

Kazei

Alkhalifah

2018

Geophysical Journal International

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“…For the case of a point scatterer δρ(K) = const, δĉ i jkl (K) = const, equation 2 provides the radiation pattern or scattering function of these scatterers (Eaton and Stewart, 1994;de Hoop et al, 1999;Shaw and Sen, 2004). Under the plane-wave and Born applicability assumptions, equation 2 generalizes the point scatterer radiation patterns to arbitrary perturbations.…”

Section: Theorymentioning

confidence: 99%

On the Resolution of Inversion for Orthorhombic Anisotropy

Kazei

Alkhalifah²

2017

Proceedings

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SummaryWe investigate the resolution of elastic anisotropic inversion for orthorhombic media with P-waves by remapping classic radiation patterns into the wavenumber domain. We show analytically that dynamic linearized inversion (linearized reverse-time migration and full-waveform inversion) for orthorhombic anisotropy based on longitudinal waves is fundamentally sensitive to emph{six} parameters only and density, in which the perturbing effects can be represented by particular anisotropy configuration. Singular value decomposition of spectral sensitivities allows us to provide estimates of the number of parameters one could invert in specific acquisition settings, and with certain parametrization. In most acquisition scenarios, a hierarchical parameterization based on the $P$, and $S$-wave velocities, along with dimensionless parameters that describe the anisotropy as velocity ratio in the radial and azimuthal directions, minimizes the tradeoff and increases the sensitivity of the data to velocity compared to the standard (stiffness, density) parametrization. These features yield more robust velocity estimation, by focusing the inversion on a subset of invertible parameters.

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Full Wavefield Inversion of Anisotropic Elastic Parameters in the Time Domain

Zhang¹,

Wang²,

Li³

et al. 2003

Chinese J of Geophysics

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By the finite element equation of anisotropic elastic waves, an expression to directly calculate the Jacobian matrix is derived, which is the same as the finite element forward modeling equation in form. Therefore, all of the elements of Jacobian matrix can be obtained through finite element forward modeling. Also, in order to improve the efficiency and accuracy of the inversion system, problems such as the efficiency and accuracy of the forward modeling system, absorbing boundary conditions and so on, are studied. Finally, anisotropic model inversion is carried out with the finite element inversion system. Inversion results of a stratified model and a laterally heterogeneous model accord with real models very well even though the initial models have great deviations.

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The resolving power of seismic amplitude data: An anisotropic inversion/migration approach

Cited by 53 publications

References 43 publications

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

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

On the Resolution of Inversion for Orthorhombic Anisotropy

Full Wavefield Inversion of Anisotropic Elastic Parameters in the Time Domain

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