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.

scholarly journals A parameterization study for elastic VTI full-waveform inversion of hydrophone components: Synthetic and North Sea field data examples

Geophysics ◽  
2017 ◽  
Vol 82 (6) ◽  
pp. R299-R308 ◽  
Author(s):  
Antoine Guitton ◽  
Tariq Alkhalifah
Keyword(s):  
North Sea ◽  
Waveform Inversion ◽  
Transversely Isotropic ◽  
Horizontal Velocity ◽  
Full Waveform Inversion ◽  
Ocean Bottom ◽  
S Wave ◽  
Data Set ◽  
Full Waveform ◽  
Streamer Data

Choosing the right parameterization to describe a transversely isotropic medium with a vertical symmetry axis (VTI) allows us to match the scattering potential of these parameters to the available data in a way that avoids a potential tradeoff and focuses on the parameters to which the data are sensitive. For 2D elastic full-waveform inversion in VTI media of pressure components and for data with a reasonable range of offsets (as with those found in conventional streamer data acquisition systems), assuming that we have a kinematically accurate normal moveout velocity ([Formula: see text]) and anellipticity parameter [Formula: see text] (or horizontal velocity [Formula: see text]) obtained from tomographic methods, a parameterization in terms of horizontal velocity [Formula: see text], [Formula: see text], and [Formula: see text] is preferred to the more conventional parameterization in terms of [Formula: see text], [Formula: see text], and [Formula: see text]. In the [Formula: see text], [Formula: see text], and [Formula: see text] parameterization and for reasonable scattering angles (<[Formula: see text]), [Formula: see text] acts as a “garbage collector” and absorbs most of the amplitude discrepancies between the modeled and observed data, more so when density [Formula: see text] and S-wave velocity [Formula: see text] are not inverted for (a standard practice with streamer data). On the contrary, in the [Formula: see text], [Formula: see text], and [Formula: see text] parameterization, [Formula: see text] is mostly sensitive to large scattering angles, leaving [Formula: see text] exposed to strong leakages from [Formula: see text] mainly. These assertions will be demonstrated on the synthetic Marmousi II as well as a North Sea ocean bottom cable data set, in which inverting for the horizontal velocity rather than the vertical velocity yields more accurate models and migrated images.

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.

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.

Full-waveform inversion with alternating source and model update for shallow seismic

2020 ◽  
Author(s):  
Dmitry Borisov ◽  
Julian Ivanov ◽  
Shelby L. Peterie ◽  
Richard D. Miller
Keyword(s):  
Waveform Inversion ◽  
Full Waveform Inversion ◽  
Full Waveform ◽  
Shallow Seismic ◽  
Model Update

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.

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