On the Resolution of Inversion for Orthorhombic Anisotropy

Kazei, Vladimir; Alkhalifah, Tariq

doi:10.3997/2214-4609.201701228

Cited by 5 publications

(2 citation statements)

References 9 publications

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“…In this section, we provide a derivation of the scattering function and generalize it to spectral sensitivities (Kazei & Alkhalifah, ; Kazei, Troyan, et al, ; Podgornova et al, ). By incorporating the spectral sensitivities, we can consider a broad class of anomalies so small that we can neglect the second‐order scattering.…”

Section: Wavenumber Illumination Theorymentioning

confidence: 99%

“…Trade‐offs, also called couplings, between anisotropic parameters occur when different combinations of parameter perturbations lead to almost identical scattering patterns, that is, when different perturbations produce the same elastic wave recordings. The problem of parameter trade‐offs is not new and has been extensively studied in isotropic media (Anikiev et al, ; Köhn et al, ; Tarantola, ; Stenhjem Hagen & Arntsen, ; Virieux & Operto, ; Wu & Aki, ), vertical transversally isotropic (VTI) media (Alkhalifah & Plessix, ; Eaton & Stewart, ; Gholami et al, ; He & Plessix, ), and orthorhombic media (De Hoop et al, ; Oh & Alkhalifah, ; Kazei & Alkhalifah, ; Shaw & Sen, ). Köhn et al () performed a synthetic feasibility investigation on full‐waveform inversion (FWI) for all triclinic elastic parameters, excluding density from the inversion.…”

Section: Introductionmentioning

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: Wavenumber Illumination Theorymentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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

Kazei

Alkhalifah

2019

JGR Solid Earth

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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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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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Multiparameter elastic full-waveform inversion in the presence of azimuthally rotated orthorhombic anisotropy: Application to 9-C land data

Alkhalifah

2017

SEG Technical Program Expanded Abstracts 2017

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On the Resolution of Inversion for Orthorhombic Anisotropy

Cited by 5 publications

References 9 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?

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

Multiparameter elastic full-waveform inversion in the presence of azimuthally rotated orthorhombic anisotropy: Application to 9-C land data

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