Elastic full-waveform inversion for VTI media: Methodology and sensitivity analysis

Kamath, Nishant; Tsvankin, Ilya

doi:10.1190/geo2014-0586.1

Cited by 87 publications

(53 citation statements)

References 33 publications

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“…We define R P s , R SV s , and R SH s as source radiation patterns of incident P-, SV-and SH-waves from the seismic source f s . The six terms R P−P m;Q , R P−SV m;Q , R P−SH m;Q , R SV−SV m;Q , R SV−SH m;Q , and R SH−SH m;Q indicate parameter radiation patterns in different parameterizations (Q) recently considered (Gholami et al, 2013a;Operto et al, 2013;Alkhalifah and Plessix, 2014;Kamath and Tsvankin, 2016;Oh and Alkhalifah, 2016). In this study, we ignore R The schematic diagrams illustrating the mechanism of the total radiation response R Total and the definition of the angles that are used throughout the paper: for incident (a) P-wave and (b) S-wave.…”

Section: Sh−shmentioning

confidence: 99%

Elastic orthorhombic anisotropic parameter inversion: An analysis of parameterization

Alkhalifah

2016

GEOPHYSICS

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CitationOh ABSTRACTThe resolution of a multiparameter full-waveform inversion (FWI) is highly influenced by the parameterization used in the inversion algorithm, as well as the data quality and the sensitivity of the data to the elastic parameters because the scattering patterns of the partial derivative wavefields (PDWs) vary with parameterization. For this reason, it is important to identify an optimal parameterization for elastic orthorhombic FWI by analyzing the radiation patterns of the PDWs for many reasonable model parameterizations. We have promoted a parameterization that allows for the separation of the anisotropic properties in the radiation patterns. The central parameter of this parameterization is the horizontal P-wave velocity, with an isotropic scattering potential, influencing the data at all scales and directions. This parameterization decouples the influence of the scattering potential given by the P-wave velocity perturbation from the polar changes described by two dimensionless parameter perturbations and from the azimuthal variation given by three additional dimensionless parameters perturbations. In addition, the scattering potentials of the P-wave velocity perturbation are also decoupled from the elastic influences given by one S-wave velocity and two additional dimensionless parameter perturbations. The vertical S-wave velocity is chosen with the best resolution obtained from S-wave reflections and converted waves, and little influence on P-waves in conventional surface seismic acquisition. The influence of the density on observed data can be absorbed by one anisotropic parameter that has a similar radiation pattern. The additional seven dimensionless parameters describe the polar and azimuth variations in the P-and S-waves that we may acquire, with some of the parameters having distinct influences on the recorded data on the earth's surface. These characteristics of the new parameterization offer the potential for a multistage inversion from high symmetry anisotropy to lower symmetry ones.

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Section: Sh−shmentioning

confidence: 99%

Elastic orthorhombic anisotropic parameter inversion: An analysis of parameterization

Alkhalifah

2016

GEOPHYSICS

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“…Raknes & Arntsen 2014;Ovcharenko et al 2018). Since elastic anisotropic waveform inversions have higher computational costs to their isotropic counterparts, they only recently became the focus of attention (Köhn et al 2015;Podgornova et al 2015;Owusu et al 2016;Bergslid et al 2015;Oh & Alkhalifah 2016;Kamath & Tsvankin 2016). Feasibility and resolution studies for 3-D inversions are still computationally expensive, therefore they are often performed either in 2-D (Podgornova et al 2015) or with very few simultaneous (encoded) shots (Köhn et al 2015).…”

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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“…For efficient estimation of the elastic element, the gradient of the elastic element of the misfit function E is theoretically obtained based on the wave equation 4) . (5) where is the elastic element, is the wave field propagated from the source, and is the wave field from the receiver.…”

Section: Methods (1) Governing Equationmentioning

confidence: 99%

“…The model parameter is updated by the following. (4) For the kth iteration, the model parameters, step length, and gradient are defined as , and , respectively. The model was updated using the conjugate gradient method.…”

Section: Methods (1) Governing Equationmentioning

confidence: 99%

Estimation of shear wave anisotropy of transversely isotropic medium by full waveform inversion

Fuse

Mikada

Takekawa

2017

Recent Advances in Exploration Geophysics

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It is necessary to obtain an accurate underground velocity structure to grasp the image of subsurface in seismic survey. Among various estimation methodologies, borehole logging is one of the best ways accurately to estimate the rock elastic properties of the ground around the wellbore. In the conventional study, the combination of Alford rotation with slowness time coherence (STC) has been applied to estimate both the formation velocity and the azimuth angles under the existence of azimuthal anisotropy in the formation. However, it has been revealed the approach with Alford rotation could fail or gives improper estimates when the axis of symmetry of the anisotropic later does not lie in the plane orthogonal to the well axis.In this study, we conduct numerical simulation for transversely isotropic medium (TI) which has 5 independent stiffness elements in 3-dimensional logging model. In recent years, full waveform inversion (FWI) has been focused which could estimate physical properties by using all information of waveforms. We investigate the feasibility of FWI to detect the orientation and dip of TI. We introduce the Euler angles into TI to estimate the stiffness parameters by FWI instead of estimating the stiffness parameters as orthorhombic medium under a hypothesis that the stable solution can be obtained by introducing the Euler angles. This approach can reduce unknowns in FWI, i.e. computational efficiency and stability of inversion could be improved. The result clearly indicates that the FWI for anisotropic medium is effective in order to detect the shear wave anisotropy and stable solution could be obtained according to misfit function even when the anisotropic layer has the dip and orientation.

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Elastic full-waveform inversion for VTI media: Methodology and sensitivity analysis

Cited by 87 publications

References 33 publications

Elastic orthorhombic anisotropic parameter inversion: An analysis of parameterization

Elastic orthorhombic anisotropic parameter inversion: An analysis of parameterization

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

Estimation of shear wave anisotropy of transversely isotropic medium by full waveform inversion

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