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.

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.

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.

Efficient 3D elastic full-waveform inversion using wavefield reconstruction methods

Geophysics ◽  
2016 ◽  
Vol 81 (2) ◽  
pp. R45-R55 ◽  
Author(s):  
Espen Birger Raknes ◽  
Wiktor Weibull
Keyword(s):  
Particle Velocity ◽  
Large Scale ◽  
Waveform Inversion ◽  
Transversely Isotropic ◽  
Reconstruction Method ◽  
Full Waveform Inversion ◽  
Reverse Time ◽  
Full Waveform ◽  
Time Migration ◽  
Reconstruction Methods

In reverse time migration (RTM) or full-waveform inversion (FWI), forward and reverse time propagating wavefields are crosscorrelated in time to form either the image condition in RTM or the misfit gradient in FWI. The crosscorrelation condition requires both fields to be available at the same time instants. For large-scale 3D problems, it is not possible, in practice, to store snapshots of the wavefields during forward modeling due to extreme storage requirements. We have developed an approximate wavefield reconstruction method that uses particle velocity field recordings on the boundaries to reconstruct the forward wavefields during the computation of the reverse time wavefields. The method is computationally effective and requires less storage than similar methods. We have compared the reconstruction method to a boundary reconstruction method that uses particle velocity and stress fields at the boundaries and to the optimal checkpointing method. We have tested the methods on a 2D vertical transversely isotropic model and a large-scale 3D elastic FWI problem. Our results revealed that there are small differences in the results for the three methods.

Full-waveform inversion with borehole constraints for elastic VTI media

Geophysics ◽  
2020 ◽  
Vol 85 (6) ◽  
pp. R553-R563
Author(s):  
Sagar Singh ◽  
Ilya Tsvankin ◽  
Ehsan Zabihi Naeini
Keyword(s):  
Objective Function ◽  
Reservoir Characterization ◽  
Waveform Inversion ◽  
Low Frequency ◽  
Rock Physics ◽  
Anisotropic Media ◽  
Full Waveform Inversion ◽  
Full Waveform ◽  
Trade Offs ◽  
Vti Media

The nonlinearity of full-waveform inversion (FWI) and parameter trade-offs can prevent convergence toward the actual model, especially for elastic anisotropic media. The problems with parameter updating become particularly severe if ultra-low-frequency seismic data are unavailable, and the initial model is not sufficiently accurate. We introduce a robust way to constrain the inversion workflow using borehole information obtained from well logs. These constraints are included in the form of rock-physics relationships for different geologic facies (e.g., shale, sand, salt, and limestone). We develop a multiscale FWI algorithm for transversely isotropic media with a vertical symmetry axis (VTI media) that incorporates facies information through a regularization term in the objective function. That term is updated during the inversion by using the models obtained at the previous inversion stage. To account for lateral heterogeneity between sparse borehole locations, we use an image-guided smoothing algorithm. Numerical testing for structurally complex anisotropic media demonstrates that the facies-based constraints may ensure the convergence of the objective function towards the global minimum in the absence of ultra-low-frequency data and for simple (even 1D) initial models. We test the algorithm on clean data and on surface records contaminated by Gaussian noise. The algorithm also produces a high-resolution facies model, which should be instrumental in reservoir characterization.

Assisting salt model building with reflection full-waveform inversion

2019 ◽  
Vol 7 (2) ◽  
pp. SB43-SB52 ◽  
Author(s):  
Adriano Gomes ◽  
Joe Peterson ◽  
Serife Bitlis ◽  
Chengliang Fan ◽  
Robert Buehring
Keyword(s):  
Model Building ◽  
Waveform Inversion ◽  
Low Frequency ◽  
Velocity Model ◽  
Full Waveform Inversion ◽  
Reflection Data ◽  
Full Waveform ◽  
Velocity Model Building ◽  
Wave Limit ◽  
Rabbit Ears

Inverting for salt geometry using full-waveform inversion (FWI) is a challenging task, mostly due to the lack of extremely low-frequency signal in the seismic data, the limited penetration depth of diving waves using typical acquisition offsets, and the difficulty in correctly modeling the amplitude (and kinematics) of reflection events associated with the salt boundary. However, recent advances in reflection FWI (RFWI) have allowed it to use deep reflection data, beyond the diving-wave limit, by extracting the tomographic term of the FWI reflection update, the so-called rabbit ears. Though lacking the resolution to fully resolve salt geometry, we can use RFWI updates as a guide for refinements in the salt interpretation, adding a partially data-driven element to salt velocity model building. In addition, we can use RFWI to update sediment velocities in complex regions surrounding salt, where ray-based approaches typically struggle. In reality, separating the effects of sediment velocity errors from salt geometry errors is not straightforward in many locations. Therefore, iterations of RFWI plus salt scenario tests may be necessary. Although it is still not the fully automatic method that has been envisioned for FWI, this combined approach can bring significant improvement to the subsalt image, as we examine on field data examples from the Gulf of Mexico.

Anisotropic full-waveform inversion with tilt-angle recovery

Geophysics ◽  
2017 ◽  
Vol 82 (3) ◽  
pp. R135-R151 ◽  
Author(s):  
Herurisa Rusmanugroho ◽  
Ryan Modrak ◽  
Jeroen Tromp
Keyword(s):  
Tilt Angle ◽  
Transverse Isotropy ◽  
A Priori ◽  
Waveform Inversion ◽  
Transversely Isotropic ◽  
Seismic Wave Propagation ◽  
Full Waveform Inversion ◽  
Full Waveform ◽  
Anisotropic Strength ◽  
Global Seismology

By allowing spatial variations in the direction of the anisotropic fast axis, tilted transverse isotropy (TTI) helps to image complex or steeply dipping structures. Without a priori geologic constraints, however, recovery of all the anisotropic parameters can be nontrivial and nonunique. We adopt two methods for TTI inversion with tilt-angle recovery: one based on the familiar Voigt parameters, and another based on the so-called Chen and Tromp parameters known from regional and global seismology. These parameterizations arise naturally in seismic wave propagation and facilitate straightforward recovery of the tilt angle and anisotropic strength. In numerical experiments with vertical transversely isotropic starting models and TTI target models, we find that the Voigt as well as the Chen and Tromp parameters allow quick and robust recovery of steeply dipping anticlinal structures.

scholarly journals A GPU implementation of the second order adjoint state theory to quantify the uncertainty on FWI results

2018 ◽  
Vol 8 (2) ◽  
Author(s):  
Sergio Alberto Abreo ◽  
Ana Beatríz Ramírez- Silva ◽  
Oscar Mauricio Reyes- Torres
Keyword(s):  
Wave Equation ◽  
Probability Distribution ◽  
Hessian Matrix ◽  
Waveform Inversion ◽  
Computational Cost ◽  
State Theory ◽  
Second Order ◽  
Full Waveform Inversion ◽  
Full Waveform ◽  
Adjoint State

The second order scattering information provided by the Hessian matrix and its inverse plays an important role in both, parametric inversion and uncertainty quantification. On the one hand, for parameter inversion, the Hessian guides the descent direction such that the cost function minimum is reached with less iterations. On the other hand, it provides a posteriori information of the probability distribution of the parameters obtained after full waveform inversion, as a function of the a priori probability distribution information. Nevertheless, the computational cost of the Hessian matrix represents the main obstacle in the state-of-the-art for practical use of this matrix from synthetic or real data. The second order adjoint state theory provides a strategy to compute the exact Hessian matrix, reducing its computational cost, because every column of the matrix can be obtained by performing two forward and two backward propagations. In this paper, we first describe an approach to compute the exact Hessian matrix for the acoustic wave equation with constant density. We then provide an analysis of the use of the Hessian matrix for uncertainty quantification of the full waveform inversion of the velocity model for a synthetic example, using the 2D acoustic and isotropic wave equation operator in time.

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