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.

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 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.

Elastic vertically transversely isotropic full-waveform inversion using cross-gradient constraints — An application toward high-level radioactive waste repository monitoring

Geophysics ◽  
2020 ◽  
Vol 85 (4) ◽  
pp. R313-R323
Author(s):  
Edgar Manukyan ◽  
Hansruedi Maurer
Keyword(s):  
Radioactive Waste ◽  
Waveform Inversion ◽  
Transversely Isotropic ◽  
Full Waveform Inversion ◽  
Trade Off ◽  
Radioactive Waste Repository ◽  
High Level Radioactive Waste ◽  
Full Waveform ◽  
Waste Repository ◽  
High Level

Anisotropic seismic full-waveform inversion (FWI) is a challenging task. In the case of 2D vertically transversely isotropic (VTI) media, there are five independent model parameters. This relatively large number of different parameter types imposes significant trade-off issues and makes the inversion parameterization a challenging task. The problem is less severe in a crosshole configuration, in which a wider angular coverage of the region of interest is available. There exist many suggestions for suitable inversion parameterizations. We have determined that, for a crosshole configuration, a relatively simple velocity-based parameterization provides a good FWI reconstruction of the subsurface. Furthermore, considerable improvements of the tomographic images can be achieved by supplying structural similarity constraints using cross gradients to the inversion problem. With two synthetic data sets, we determine that a structurally constrained VTI FWI workflow produces sharper subsurface images without adversely affecting the parameter trade-off issue. With a second synthetic experiment, we find that structurally constrained VTI FWI is robust to major differences in anomaly locations for different parameter types. We successfully applied the methodology to a crosshole data set acquired to image a downscaled version of a high-level radioactive waste repository. The resulting tomograms allowed a narrow highly fractured zone to be imaged.

scholarly journals A priori estimates of attraction basins for velocity model reconstruction by time-harmonic full-waveform inversion and data-space reflectivity formulation

Geophysics ◽  
2020 ◽  
Vol 85 (3) ◽  
pp. R223-R241 ◽  
Author(s):  
Florian Faucher ◽  
Guy Chavent ◽  
Hélène Barucq ◽  
Henri Calandra
Keyword(s):  
Optimization Problems ◽  
A Priori ◽  
Waveform Inversion ◽  
Velocity Model ◽  
Successful Implementation ◽  
Full Waveform Inversion ◽  
Complex Frequency ◽  
Data Space ◽  
Full Waveform ◽  
Attraction Basins

The determination of background velocity by full-waveform inversion (FWI) is known to be hampered by the local minima of the data misfit caused by the phase shifts associated with background perturbations. Attraction basins for the underlying optimization problems can be computed around any nominal velocity model, and they guarantee that the misfit functional has only one (global) minimum. The attraction basins are further associated with tolerable error levels representing the maximal allowed distance between the (observed) data and the simulations (i.e., the acceptable noise level). The estimates are defined a priori, and they only require the computation of (possibly many) the first- and second-order directional derivatives of the (model to synthetic) forward map. The geometry of the search direction and the frequency influence the size of the attraction basins, and the complex frequency can be used to enlarge the basins. The size of the attraction basins for the perturbation of background velocities in classic FWI (global model parameterization) and the data-space reflectivity reformulation (migration-based traveltime [MBTT]) are compared: The MBTT reformulation substantially increases the size of the attraction basins (by a factor of 4–15). Practically, this reformulation compensates for the lack of low-frequency data. Our analysis provides guidelines for a successful implementation of the MBTT reformulation.

A recipe for practical full-waveform inversion in anisotropic media: An analytical parameter resolution study

Geophysics ◽  
2014 ◽  
Vol 79 (3) ◽  
pp. R91-R101 ◽  
Author(s):  
Tariq Alkhalifah ◽  
René-Édouard Plessix
Keyword(s):  
Waveform Inversion ◽  
Transversely Isotropic ◽  
Anisotropic Media ◽  
Horizontal Velocity ◽  
Isotropic Case ◽  
Full Waveform Inversion ◽  
Symmetry Direction ◽  
Velocity Anisotropy ◽  
Full Waveform ◽  
Model Update

In multiparameter full-waveform inversion (FWI) and specifically one describing the anisotropic behavior of the medium, it is essential that we have an understanding of the parameter resolution possibilities and limits. Because the imaging kernel is at the heart of the inversion engine (the model update), we drew our development and choice of parameters from what we have experienced in imaging seismic data in anisotropic media. In representing the most common (first-order influence and gravity induced) acoustic anisotropy, specifically, a transversely isotropic medium with a vertical symmetry direction (VTI), with the [Formula: see text]-wave normal moveout velocity, anisotropy parameters [Formula: see text], and [Formula: see text], we obtained a perturbation radiation pattern that has limited trade-off between the parameters. Because [Formula: see text] is weakly resolvable from the kinematics of [Formula: see text]-wave propagation, we can use it to play the role that density plays in improving the data fit for an imperfect physical model that ignores the elastic nature of the earth. An FWI scheme that starts from diving waves would benefit from representing the acoustic VTI model with the [Formula: see text]-wave horizontal velocity, [Formula: see text], and [Formula: see text]. In this representation, the diving waves will help us first resolve the horizontal velocity and then reflections, if the nonlinearity is properly handled, could help us resolve [Formula: see text], and [Formula: see text] could help improve the amplitude fit (instead of the density). The model update wavenumber for acoustic anisotropic FWI is very similar to that for the isotropic case, which is mainly dependent on the scattering angle and frequency.

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