Resolution of VTI anisotropy with elastic full-waveform inversion: theory and basic numerical examples

Podgornova, Olga; Leaney, Scott; Liang, Lin

doi:10.1093/gji/ggy116

Cited by 18 publications

(9 citation statements)

References 20 publications

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“…Kazei, Troyan, et al () provided a quantitative wavenumber illumination analysis of the spectrum covered by head waves and diving waves. Podgornova et al (, ) analyzed the resolvability of elastic parameter spectra in elastic VTI media. Kazei and Alkhalifah () presented spectral coverage and resolution for orthorhombic parameters.…”

Section: Scattering Radiation Patterns Of Elastic Parametersmentioning

confidence: 99%

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Scattering Radiation Pattern Atlas: What Anisotropic Elastic Properties Can Body Waves Resolve?

Kazei

Alkhalifah

2019

JGR Solid Earth

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Full‐waveform inversion (FWI) optimizes the subsurface properties of geophysical Earth models in such a way that the modeled data, based on these subsurface properties, match the observed data. The anisotropic properties, whether monoclinic, orthorhombic, triclinic, or vertical transversally isotropic (VTI), of the subsurface, be it a fractured reservoir or the core‐mantle boundary, are necessary to describe the observed wave phenomena. There are no principal limitations on the complexity of the anisotropy that can be inverted using FWI. However, the question remains—what kind of anisotropic descriptions of the elastic properties of the Earth can or cannot be inverted reliably from seismic waveforms? We reveal the resolution that can be achieved through reconstructions of each elastic parameter by building vertical resolution patterns from the scattering radiation patterns of body waves. A visual analysis of these patterns indicates “trade‐offs,” that is, perturbations of parameters that have the same reflection‐based scattering patterns as other perturbations. Each trade‐off leads to an apparent ambiguity in the inversion, which must be addressed by additional assumptions, constraints, or regularizations. For orthorhombic media, we find the exact trade‐offs that exist between parameters. Our parameterization isolates the VTI parameters, and therefore, we also obtain trade‐offs for every scattering mode for VTI media. We discover that only monoclinic parameters are recoverable from the first‐order scattering of monotypic waves. We summarize the trade‐offs in tables for easy reference. This paper is intended to be useful for researchers setting up anisotropic FWI problems, and interpreting or controlling the quality of such inversions.

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Section: Scattering Radiation Patterns Of Elastic Parametersmentioning

confidence: 99%

“…Its rank is equal to the maximum number of resolvable parameters. Matrix

double-struckS

can also be linked to the Hessian of standard FWI (Kazei & Alkhalifah, ; Podgornova et al, ).…”

Section: Spectral Sensitivity Matrices and Numerical Analysis Of Tradmentioning

confidence: 99%

Scattering Radiation Pattern Atlas: What Anisotropic Elastic Properties Can Body Waves Resolve?

Kazei

Alkhalifah

2019

JGR Solid Earth

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“…Unlike monotypic waves, where non-zero vertical wavenumbers are illuminated by reflections and only zero purely vertical wavenumbers are recoverable from pure transmissions. The wavenumber coverage of converted waves is produced by both converted transmissions and converted reflections (Podgornova et al, 2018;Alkhalifah, 2018a, 2019). Combining (1) and (3), we derive an expression for the amplitude of scattered P-SV and P-SH waves: Figure 2: (a) Spectral sensitivities to vertical wavenumbers for P − P scattering in C i j , ρ parameterization.…”

Section: Converted Wavesmentioning

confidence: 99%

“…Kinematic features of P-, S- (Stovas, 2015(Stovas, , 2017 and converted waves in general orthorhombic media are rather complicated, which leads us towards full-waveform inversion in orthorhombic media (de Hoop et al, 1999;Köhn et al, 2015;Oh and Alkhalifah, 2016). Recently, wavenumber illumination analysis (Devaney, 1984;Mora, 1989;Kazei et al, 2013) was adopted to reveal the number of anisotropic parameters resolvable from different types of data (Podgornova et al, 2015;Kazei and Alkhalifah, 2018b;Podgornova et al, 2018;Kazei and Alkhalifah, 2019). Here, we extend the scattering radiation pattern analysis in the wavenumber domain and compare several parameterizations in it.…”

Section: Introductionmentioning

confidence: 99%

Wavenumber illumination analysis validation: Which elastic anisotropic parameters can we resolve?

Kazei

Kabanov

Alkhalifah

2019

SEG Technical Program Expanded Abstracts 2019

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Vertical fractures are often embedded into a finely layered medium, which leads to an effective medium with orthorhombic anisotropy. Ten independent parameters are necessary to completely characterize such a medium, including density and excluding rotations. Through wavenumber illumination analysis, it has been shown that only six of these parameters can be reliably inverted from P − P scattered energy. Here, we demonstrate that with the addition of converted waves, nine parameters can principally be recovered. We also demonstrate that the one-dimensional null space is along a linear combination of the shear-wave dimensionless parameters, γ 1 and γ 2 , or a linear combination of the elastic coefficients C 12 and C 66 parameters. This null space can be captured by the Thomsen γ parameter if it is introduced into the parameterization. Finally and most importantly, there is still a lot of skepticism around the applicability of multiparameter model wavenumber illumination analysis, so we validate the radiation patterns using finite-difference modeling code. We find that theoretical scattering patterns are in good agreement with numerically modeled wavefields scattered from thin layers. The latter is a step towards applications of similar analysis, initially in the framework of time-lapse monitoring of the reservoirs, where the perturbations of parameters are generally small.

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“…The first questions that arise when setting up a multiparameter full-waveform inversion are how many and which parameters can be inverted. Here, we extend the scattering radiation pattern analysis in the wavenumber domain (Devaney, 1984;Mora, 1989;Kazei et al, 2013;Podgornova et al, 2018;Alkhalifah, 2018, 2019) to the inversion of S waves.…”

Section: Introductionmentioning

confidence: 99%

On the Resolution of S Waves for Orthorhombic Parameters From the Wavenumber Illumination Prospective

Kazei¹,

Alkhalifah²

2019

81st EAGE Conference and Exhibition 2019

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Orthorhombic anisotropy is typical of naturally fractured reservoirs. This type of anisotropy is caused by a single system of vertical fractures embedded in a horizontally layered medium. Arbitrary orthorhombic elastic anisotropy can be characterized by ten independent parameters, one of which is density. In the best of circumstances, only six of these parameters can be reliably inverted from the P-wave scattered energy. Thus, we access the resolution of S-wave inversion from the wavenumber illumination perspective and show that S waves can resolve the remaining orthorhombic parameters. TopicsSeismic Anisotropy in Fractured Reservoirs, Seismic Imaging -Theory, Full Waveform Seismic Inversion Main objectiveInvestigate spatial resolution for the orthorhombic inversion of S waves. New aspectsThe null-space of the orthorhombic inversion of S waves is derived analytically. The concept of the effective illumination angle is applied to understand the number of recoverable parameters.

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Resolution of VTI anisotropy with elastic full-waveform inversion: theory and basic numerical examples

Cited by 18 publications

References 20 publications

Scattering Radiation Pattern Atlas: What Anisotropic Elastic Properties Can Body Waves Resolve?

Scattering Radiation Pattern Atlas: What Anisotropic Elastic Properties Can Body Waves Resolve?

Wavenumber illumination analysis validation: Which elastic anisotropic parameters can we resolve?

On the Resolution of S Waves for Orthorhombic Parameters From the Wavenumber Illumination Prospective

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