2D frequency-domain elastic full-waveform inversion using the block-diagonal pseudo-Hessian approximation

Geophysics ◽  
2016 ◽  
Vol 81 (5) ◽  
pp. R247-R259 ◽  
Author(s):  
Yuwei Wang ◽  
Liangguo Dong ◽  
Yuzhu Liu ◽  
Jizhong Yang
Keyword(s):  
Frequency Domain ◽  
Wave Velocity ◽  
Hessian Matrix ◽  
Waveform Inversion ◽  
Full Waveform Inversion ◽  
S Wave ◽  
Trade Off ◽  
Full Waveform ◽  
Trade Offs ◽  
Block Diagonal

Elastic full-waveform inversion (EFWI) of multicomponent seismic data is a powerful tool for estimating the subsurface elastic parameters with high accuracy. However, the trade-offs between multiple parameters increase the nonlinearity of EFWI. Although the conventional diagonal-approximate Hessian matrix describes the illumination and limited bandwidth effects, it ignores the trade-off effects and decreases the convergence rate of EFWI. We have developed a block-diagonal pseudo-Hessian operator for 2D frequency-domain EFWI to take into account the approximate trade-offs among the P-wave (compressional-wave) velocity, S-wave (shear-wave) velocity, and density without extra computational costs on forward simulations. The Hessian matrix tends toward a block-diagonal matrix as the frequency grows to infinity; thus, the proposed block-diagonal pseudo-Hessian matrix is more accurate at higher frequencies. The inverse of the block-diagonal pseudo-Hessian matrix is used as a preconditioner for the nonlinear conjugate-gradient method to simultaneously reconstruct P- and S-wave velocities and density. This approach effectively mitigates the crosstalk artifacts by correcting the gradients from the trade-off effects and produces more rapid inversion convergence, which becomes more significant at higher frequencies. Synthetic experiments on an inclusion model and the elastic Marmousi2 model demonstrate its feasibility and validity in EFWI.

scholarly journals Interparameter trade-off quantification for isotropic-elastic full-waveform inversion with various model parameterizations

Geophysics ◽  
2019 ◽  
Vol 84 (2) ◽  
pp. R185-R206 ◽  
Author(s):  
Wenyong Pan ◽  
Kristopher A. Innanen ◽  
Yu Geng ◽  
Junxiao Li
Keyword(s):  
Wave Velocity ◽  
Waveform Inversion ◽  
P Wave ◽  
Physical Parameters ◽  
Full Waveform Inversion ◽  
S Wave ◽  
Trade Off ◽  
Full Waveform ◽  
Trade Offs ◽  
P Wave Velocity

Simultaneous determination of multiple physical parameters using full-waveform inversion (FWI) suffers from interparameter trade-off difficulties. Analyzing the interparameter trade-offs in different model parameterizations of isotropic-elastic FWI, and thus determining the appropriate model parameterization, are critical for efficient inversion and obtaining reliable inverted models. Five different model parameterizations are considered and compared including velocity-density, modulus-density, impedance-density, and two velocity-impedance parameterizations. The scattering radiation patterns are first used for interparameter trade-off analysis. Furthermore, a new framework is developed to evaluate the interparameter trade-off based upon multiparameter Hessian-vector products: Multiparameter point spread functions (MPSFs) and interparameter contamination sensitivity kernels (ICSKs), which provide quantitative, second-order measurements of the interparameter contaminations. In the numerical experiments, the interparameter trade-offs in various model parameterizations are evaluated using the MPSFs and ICSKs. Inversion experiments are carried out with simple Gaussian-anomaly models and a complex Marmousi model. Overall, the parameterization of the P-wave velocity, S-wave velocity, and density, and the parameterization of the P-wave velocity, S-wave velocity, and S-wave impedance perform best for reconstructing all of the physical parameters. Isotropic-elastic FWI of the Hussar low-frequency data set with various model parameterizations verifies our conclusions.

Seismic imaging of complex onshore structures by 2D elastic frequency-domain full-waveform inversion

Geophysics ◽  
2009 ◽  
Vol 74 (6) ◽  
pp. WCC105-WCC118 ◽  
Author(s):  
Romain Brossier ◽  
Stéphane Operto ◽  
Jean Virieux
Keyword(s):  
Free Surface ◽  
Surface Waves ◽  
Frequency Domain ◽  
Wave Velocity ◽  
Waveform Inversion ◽  
Surface Effects ◽  
Full Waveform Inversion ◽  
S Wave ◽  
Velocity Models ◽  
Full Waveform

Quantitative imaging of the elastic properties of the subsurface at depth is essential for civil engineering applications and oil- and gas-reservoir characterization. A realistic synthetic example provides for an assessment of the potential and limits of 2D elastic full-waveform inversion (FWI) of wide-aperture seismic data for recovering high-resolution P- and S-wave velocity models of complex onshore structures. FWI of land data is challenging because of the increased nonlinearity introduced by free-surface effects such as the propagation of surface waves in the heterogeneous near-surface. Moreover, the short wavelengths of the shear wavefield require an accurate S-wave velocity starting model if low frequencies are unavailable in the data. We evaluated different multiscale strategies with the aim of mitigating the nonlinearities. Massively parallel full-waveform inversion was implemented in the frequency domain. The numerical optimization relies on a limited-memory quasi-Newton algorithm thatoutperforms the more classic preconditioned conjugate-gradient algorithm. The forward problem is based upon a discontinuous Galerkin (DG) method on triangular mesh, which allows accurate modeling of free-surface effects. Sequential inversions of increasing frequencies define the most natural level of hierarchy in multiscale imaging. In the case of land data involving surface waves, the regularization introduced by hierarchical frequency inversions is not enough for adequate convergence of the inversion. A second level of hierarchy implemented with complex-valued frequencies is necessary and provides convergence of the inversion toward acceptable P- and S-wave velocity models. Among the possible strategies for sampling frequencies in the inversion, successive inversions of slightly overlapping frequency groups is the most reliable when compared to the more standard sequential inversion of single frequencies. This suggests that simultaneous inversion of multiple frequencies is critical when considering complex wave phenomena.

Parameterization analysis and field validation of VTI-elastic full-waveform inversion in a walk-away vertical seismic profile configuration

Geophysics ◽  
2020 ◽  
Vol 85 (3) ◽  
pp. B87-B107 ◽  
Author(s):  
Wenyong Pan ◽  
Kristopher A. Innanen ◽  
Yanfei Wang
Keyword(s):  
Wave Velocity ◽  
Waveform Inversion ◽  
Seismic Profile ◽  
P Wave ◽  
Full Waveform Inversion ◽  
Walk Away ◽  
S Wave ◽  
Full Waveform ◽  
Trade Offs ◽  
Vsp Data

Elastic full-waveform inversion (FWI) in transversely isotropic media with a vertical symmetry axis (VTI) is applied to field walk-away vertical seismic profile (W-VSP) data acquired in Western Canada. The performance of VTI-elastic FWI is significantly influenced by the model parameterization choice. Synthetic analysis based on specific field survey configuration is carried out to evaluate three different VTI-elastic model parameterizations. Interparameter trade-offs are quantified using the recently introduced interparameter contamination sensitivity kernel approach. Synthetic results suggest that neglecting anisotropy leads to inaccurate velocity estimations. For the conventional vertical velocity-Thomsen’s parameter parameterization (i.e., vertical P-wave velocity, vertical S-wave velocity, Thomsen’s parameters [Formula: see text] and [Formula: see text]), a sequential inversion strategy is designed to reduce strong natural interparameter trade-offs. The model parameterizations of elastic-constant ([Formula: see text], [Formula: see text], [Formula: see text], and [Formula: see text]) and velocity-based (vertical, horizontal, and normal move-out P-wave velocities and vertical S-wave velocity) models appear to suffer from fewer interparameter trade-offs, providing more reliable velocity and anisotropy models. Results derived from application of VTI-elastic FWI to the field W-VSP data set tend to support the synthetic conclusions. Multiparameter point spread functions are calculated to quantify the local interparameter trade-offs of the inverted models. The output inversion results are interpreted to provide valuable references regarding the target hydrocarbon reservoir.

Full-waveform inversion of multicomponent data for horizontally layered VTI media

Geophysics ◽  
2013 ◽  
Vol 78 (5) ◽  
pp. WC113-WC121 ◽  
Author(s):  
Nishant Kamath ◽  
Ilya Tsvankin
Keyword(s):  
Joint Inversion ◽  
Hessian Matrix ◽  
Waveform Inversion ◽  
Transversely Isotropic ◽  
Media Analysis ◽  
Full Waveform Inversion ◽  
S Wave ◽  
Full Waveform ◽  
The Time Domain ◽  
Vti Media

Although full-waveform inversion (FWI) has shown significant promise in reconstructing heterogeneous velocity fields, most existing methodologies are limited to acoustic models. We extend FWI to multicomponent (PP and PS) data from anisotropic media, with the current implementation limited to a stack of horizontal, homogeneous VTI (transversely isotropic with a vertical symmetry axis) layers. The algorithm is designed to estimate the interval vertical P- and S-wave velocities ([Formula: see text] and [Formula: see text]) and Thomsen parameters [Formula: see text] and [Formula: see text] from long-spread PP and PSV reflections. The forward-modeling operator is based on the anisotropic reflectivity technique, and the inversion is performed in the time domain using the gradient (Gauss-Newton) method. We employ nonhyperbolic semblance analysis and Dix-type equations to build the initial model. To identify the medium parameters constrained by the data, we perform eigenvalue/eigenvector decomposition of the approximate Hessian matrix for a VTI layer embedded between isotropic media. Analysis of the eigenvectors shows that the parameters [Formula: see text], [Formula: see text], [Formula: see text], and [Formula: see text] (density is assumed to be known) can be resolved not only by joint inversion of PP and PS data, but also with PP reflections alone. Although the inversion becomes more stable with increasing spreadlength-to-depth ([Formula: see text]) ratio, the parameters of the three-layer model are constrained even by PP data acquired on conventional spreads ([Formula: see text]). For multilayered VTI media, the sensitivity of the objective function to the interval parameters decreases with depth. Still, it is possible to resolve [Formula: see text], [Formula: see text], [Formula: see text], and [Formula: see text] for the deeper layers using PP-waves, if the ratio [Formula: see text] for the bottom of the layer reaches two. Mode-converted waves provide useful additional constraints for FWI, which become essential for smaller spreads. The insights gained here by examining horizontally layered models should help guide the inversion for heterogeneous TI media.

Frequency-domain full waveform inversion with plane-wave data

Geophysics ◽  
2013 ◽  
Vol 78 (1) ◽  
pp. R13-R23 ◽  
Author(s):  
Yi Tao ◽  
Mrinal K. Sen
Keyword(s):  
Plane Wave ◽  
Frequency Domain ◽  
Model Updating ◽  
Linear Time ◽  
Hessian Matrix ◽  
Waveform Inversion ◽  
Full Waveform Inversion ◽  
Full Waveform ◽  
Adjoint State ◽  
The Cost

We derived an efficient frequency-domain full waveform inversion (FWI) method using plane-wave encoded shot records. The forward modeling involved application of position dependent linear time shifts at all source locations. This was followed by propagation of wavefields into the medium from all shotpoints simultaneously. The gradient of the cost function needed in the FWI was calculated first by transforming the densely sampled seismic data into the frequency-ray parameter domain and then backpropagating the residual wavefield using an adjoint-state approach. We used a Gauss-Newton framework for model updating. The approximate Hessian matrix was formed with a plane-wave encoding strategy, which required a summation over source and receiver ray parameters of the Green’s functions. Plane-wave encoding considerably reduces the computational burden and crosstalk artifacts are effectively suppressed by stacking over different ray parameters. It also has the advantage of directional illumination of the selected targets. Numerical examples show the accuracy and efficiency of our method.

scholarly journals Application of a complete workflow for 2D elastic full-waveform inversion to recorded shallow-seismic Rayleigh waves

Geophysics ◽  
2017 ◽  
Vol 82 (2) ◽  
pp. R109-R117 ◽  
Author(s):  
Lisa Groos ◽  
Martin Schäfer ◽  
Thomas Forbriger ◽  
Thomas Bohlen
Keyword(s):  
Wave Velocity ◽  
Rayleigh Waves ◽  
Waveform Inversion ◽  
Velocity Model ◽  
Full Waveform Inversion ◽  
S Wave ◽  
Full Waveform ◽  
Shallow Seismic ◽  
Lateral Variations ◽  
Seismic Rayleigh Waves

The S-wave velocity of the shallow subsurface can be inferred from shallow-seismic Rayleigh waves. Traditionally, the dispersion curves of the Rayleigh waves are inverted to obtain the (local) S-wave velocity as a function of depth. Two-dimensional elastic full-waveform inversion (FWI) has the potential to also infer lateral variations. We have developed a novel workflow for the application of 2D elastic FWI to recorded surface waves. During the preprocessing, we apply a line-source simulation (spreading correction) and perform an a priori estimation of the attenuation of waves. The iterative multiscale 2D elastic FWI workflow consists of the preconditioning of the gradients in the vicinity of the sources and a source-wavelet correction. The misfit is defined by the least-squares norm of normalized wavefields. We apply our workflow to a field data set that has been acquired on a predominantly depth-dependent velocity structure, and we compare the reconstructed S-wave velocity model with the result obtained by a 1D inversion based on wavefield spectra (Fourier-Bessel expansion coefficients). The 2D S-wave velocity model obtained by FWI shows an overall depth dependency that agrees well with the 1D inversion result. Both models can explain the main characteristics of the recorded seismograms. The small lateral variations in S-wave velocity introduced by FWI additionally explain the lateral changes of the recorded Rayleigh waves. The comparison thus verifies the applicability of our 2D FWI workflow and confirms the potential of FWI to reconstruct shallow small-scale lateral changes of S-wave velocity.

Cavity detection by SH-wave Full Waveform Inversion — A reflection-focused approach

Geophysics ◽  
2021 ◽  
pp. 1-65
Author(s):  
Rebekka Mecking ◽  
Daniel Köhn ◽  
Matthias Meinecke ◽  
Wolfgang Rabbel
Keyword(s):  
Wave Velocity ◽  
Automatic Gain Control ◽  
Waveform Inversion ◽  
Geophysical Methods ◽  
Gain Control ◽  
Full Waveform Inversion ◽  
S Wave ◽  
Low Velocity ◽  
Full Waveform ◽  
Tunnel System

The detection of cavities with geophysical methods is a challenging task for which a general approach has not yet been found. We show that viscoelastic SH full waveform inversion (FWI), focusing primarily on reflection events, is able to accurately locate the position of cavities, areas of decompacted sediments and, more generally, seismic low-velocity anomalies down to 30 m depth. The key for a successful FWI application is the enhancement of the reflected wavefield relative to the surface wavefield. For this purpose, we applied automatic gain control normalization in the objective function. By focusing the inversion on the reflected wavefield, we demonstrate that one can differentiate between air-filled cavities with zero shear-wave velocity and low-velocity zones. Additionally, we test the FWI approach on a field dataset, with a known collapsed tunnel system inside a 32 m high, monumental, antique grave mound. The results show that the location and extent, as well as density and S-wave velocity of the collapsed tunnel system, can be determined with sufficient accuracy by applying a 2D FWI approach to intersecting profiles, despite the 3D nature of the problem.

Elastic full-waveform inversion for VTI media: A synthetic parameterization study

Geophysics ◽  
2017 ◽  
Vol 82 (5) ◽  
pp. C163-C174 ◽  
Author(s):  
Nishant Kamath ◽  
Ilya Tsvankin ◽  
Esteban Díaz
Keyword(s):  
Hessian Matrix ◽  
Waveform Inversion ◽  
Transversely Isotropic ◽  
Multiscale Approach ◽  
Constant Density ◽  
Full Waveform Inversion ◽  
The North ◽  
Reflection Data ◽  
Full Waveform ◽  
Trade Offs

One of the main challenges for full-waveform inversion (FWI) is taking into account both anisotropy and elasticity. Here, we perform elastic FWI for a synthetic 2D VTI (transversely isotropic with a vertical symmetry axis) model based on the geologic section at Valhall field in the North Sea. Multicomponent surface data are generated by a finite-difference code. We apply FWI in the time domain using a multiscale approach with three frequency bands. An approximate inverse Hessian matrix, computed using the L-BFGS-B algorithm, is employed to scale the gradients of the objective function and improve the convergence. In the absence of significant diving-wave energy in the deeper part of the section, the model is updated primarily with reflection data. An oblique displacement source, which excites sufficiently intensive shear waves in the conventional offset range, helps provide more accurate updates in the Shear-wave vertical velocity, especially in the shallow layers. We test three model parameterizations, which exhibit different radiation patterns and, therefore, create different parameter trade-offs. Whereas most examples are for a constant-density model, we also generate a density field using Gardner’s relationship and invert for the density along with the velocity parameters. The parameterizations that combine velocities and anisotropy coefficients generally yield superior results to the one that includes only velocities, provided that a reasonably accurate initial model is available.

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