Constrained full-waveform inversion by model reparameterization

Geophysics ◽  
2012 ◽  
Vol 77 (2) ◽  
pp. R117-R127 ◽  
Author(s):  
Antoine Guitton ◽  
Gboyega Ayeni ◽  
Esteban Díaz
Keyword(s):  
Waveform Inversion ◽  
Model Space ◽  
Real Data ◽  
Velocity Model ◽  
Full Waveform Inversion ◽  
Coherent Noise ◽  
Low Frequencies ◽  
Full Waveform ◽  
Geological Information ◽  
Ill Posed

The waveform inversion problem is inherently ill-posed. Traditionally, regularization schemes are used to address this issue. For waveform inversion, where the model is expected to have many details reflecting the physical properties of the Earth, regularization and data fitting can work in opposite directions: the former smoothing and the latter adding details to the model. We propose constraining estimated velocity fields by reparameterizing the model. This technique, also called model-space preconditioning, is based on directional Laplacian filters: It preserves most of the details of the velocity model while smoothing the solution along known geological dips. Preconditioning also yields faster convergence at early iterations. The Laplacian filters have the property to smooth or kill local planar events according to a local dip field. By construction, these filters can be inverted and used in a preconditioned waveform inversion strategy to yield geologically meaningful models. We illustrate with 2D synthetic and field data examples how preconditioning with nonstationary directional Laplacian filters outperforms traditional waveform inversion when sparse data are inverted and when sharp velocity contrasts are present. Adding geological information with preconditioning could benefit full-waveform inversion of real data whenever irregular geometry, coherent noise and lack of low frequencies are present.

Which parameterization is suitable for acoustic vertical transverse isotropic full waveform inversion? Part 2: Synthetic and real data case studies from Valhall

Geophysics ◽  
2013 ◽  
Vol 78 (2) ◽  
pp. R107-R124 ◽  
Author(s):  
Yaser Gholami ◽  
Romain Brossier ◽  
Stéphane Operto ◽  
Vincent Prieux ◽  
Alessandra Ribodetti ◽  
...  
Keyword(s):  
Waveform Inversion ◽  
Real Data ◽  
Velocity Model ◽  
Oil Field ◽  
Full Waveform Inversion ◽  
Trade Off ◽  
Wave Speeds ◽  
Wide Aperture ◽  
Full Waveform ◽  
Transverse Isotropic

It is necessary to account for anisotropy in full waveform inversion (FWI) of wide-azimuth and wide-aperture seismic data in most geologic environments, for correct depth positioning of reflectors, and for reliable estimations of wave speeds as a function of the direction of propagation. In this framework, choosing a suitable anisotropic subsurface parameterization is a central issue in monoparameter and multiparameter FWI. This is because this parameterization defines the influence of each physical parameter class on the data as a function of the scattering angle, and hence the resolution of the parameter reconstruction, and on the potential trade-off between different parameter classes. We apply monoparameter and multiparameter frequency-domain acoustic vertical transverse isotropic FWI to synthetic and real wide-aperture data, representative of the Valhall oil field. We first show that reliable monoparameter FWI can be performed to build a high-resolution velocity model (for the vertical, the horizontal, or normal move-out velocity), provided that the background models of two Thomsen parameters describe the long wavelengths of the subsurface sufficiently accurately. Alternatively, we show the feasibility of the joint reconstruction of two wave speeds (e.g., the vertical and horizontal wave speeds) with limited trade-off effects, while Thomsen parameter [Formula: see text] is kept fixed during the inversion. The influence of the wave speeds on the data for a limited range of scattering angles when combined each other can, however, significantly hamper the resolution with which the two wave speeds are imaged. These conclusions inferred from the application to the real data are fully consistent with those inferred from the theoretical parameterization analysis of acoustic vertical transverse isotropic FWI performed in the companion report.

Image-guided sparse-model full waveform inversion

Geophysics ◽  
2012 ◽  
Vol 77 (4) ◽  
pp. R189-R198 ◽  
Author(s):  
Yong Ma ◽  
Dave Hale ◽  
Bin Gong ◽  
Zhaobo (Joe) Meng
Keyword(s):  
Waveform Inversion ◽  
Model Space ◽  
Model Parameters ◽  
Full Waveform Inversion ◽  
Widespread Application ◽  
Low Frequencies ◽  
Sparse Model ◽  
Image Guided ◽  
Full Waveform ◽  
Recorded Data

Multiple problems, including high computational cost, spurious local minima, and solutions with no geologic sense, have prevented widespread application of full waveform inversion (FWI), especially FWI of seismic reflections. These problems are fundamentally related to a large number of model parameters and to the absence of low frequencies in recorded seismograms. Instead of inverting for all the parameters in a dense model, image-guided full waveform inversion inverts for a sparse model space that contains far fewer parameters. We represent a model with a sparse set of values, and from these values, we use image-guided interpolation (IGI) and its adjoint operator to compute finely and uniformly sampled models that can fit recorded data in FWI. Because of this sparse representation, image-guided FWI updates more blocky models, and this blockiness in the model space mitigates the absence of low frequencies in recorded data. Moreover, IGI honors imaged structures, so image-guided FWI built in this way yields models that are geologically sensible.

scholarly journals Full-waveform inversion with extrapolated low-frequency data

Geophysics ◽  
2016 ◽  
Vol 81 (6) ◽  
pp. R339-R348 ◽  
Author(s):  
Yunyue Elita Li ◽  
Laurent Demanet
Keyword(s):  
Waveform Inversion ◽  
Low Frequency ◽  
Velocity Model ◽  
Propagation Model ◽  
Full Waveform Inversion ◽  
Frequency Data ◽  
Local Minima ◽  
Bandwidth Extension ◽  
Low Frequencies ◽  
Full Waveform

The availability of low-frequency data is an important factor in the success of full-waveform inversion (FWI) in the acoustic regime. The low frequencies help determine the kinematically relevant, low-wavenumber components of the velocity model, which are in turn needed to avoid convergence of FWI to spurious local minima. However, acquiring data less than 2 or 3 Hz from the field is a challenging and expensive task. We have explored the possibility of synthesizing the low frequencies computationally from high-frequency data and used the resulting prediction of the missing data to seed the frequency sweep of FWI. As a signal-processing problem, bandwidth extension is a very nonlinear and delicate operation. In all but the simplest of scenarios, it can only be expected to lead to plausible recovery of the low frequencies, rather than their accurate reconstruction. Even so, it still requires a high-level interpretation of band-limited seismic records into individual events, each of which can be extrapolated to a lower (or higher) frequency band from the nondispersive nature of the wave-propagation model. We have used the phase-tracking method for the event separation task. The fidelity of the resulting extrapolation method is typically higher in phase than in amplitude. To demonstrate the reliability of bandwidth extension in the context of FWI, we first used the low frequencies in the extrapolated band as data substitute, to create the low-wavenumber background velocity model, and then we switched to recorded data in the available band for the rest of the iterations. The resulting method, extrapolated FWI, demonstrated surprising robustness to the inaccuracies in the extrapolated low-frequency data. With two synthetic examples calibrated so that regular FWI needs to be initialized at 1 Hz to avoid local minima, we have determined that FWI based on an extrapolated [1, 5] Hz band, itself generated from data available in the [5, 15] Hz band, can produce reasonable estimations of the low-wavenumber velocity models.

scholarly journals Full-waveform inversion and joint migration inversion with an automatic directional total variation constraint

Geophysics ◽  
2019 ◽  
Vol 84 (2) ◽  
pp. R175-R183 ◽  
Author(s):  
Shan Qu ◽  
Eric Verschuur ◽  
Yangkang Chen
Keyword(s):  
Total Variation ◽  
Waveform Inversion ◽  
Velocity Model ◽  
Full Waveform Inversion ◽  
L1 Norm ◽  
Reflection Data ◽  
Full Waveform ◽  
Ill Posed ◽  
Laplacian Smoothing ◽  
The Impact

As full-waveform inversion (FWI) is a nonunique and typically ill-posed inversion problem, it needs proper regularization to avoid cycle skipping. To reduce the nonlinearity of FWI, we have developed joint migration inversion (JMI) as an alternative, explaining the reflection data with decoupled velocity and reflectivity parameters. However, the velocity update may also suffer from being trapped in local minima. To optimally include geologic information, we have developed FWI/JMI with directional total variation (TV) as an L1-norm regularization on the velocity. We design the directional TV operator based on the local dip field, instead of ignoring the local structural direction of the subsurface and only using horizontal and vertical gradients in the traditional TV. The local dip field is estimated using plane-wave destruction based on a raw reflectivity model, which is usually calculated from the initial velocity model. With two complex synthetic examples, based on the Marmousi model, we determine that our method is much more effective compared with FWI/JMI without regularization and FWI/JMI with the conventional TV regularization. In the JMI-based example, we also determine that L1 directional TV works better than L2 directional Laplacian smoothing. In addition, by comparing these two examples, it can be seen that the impact of regularization is larger for FWI than for JMI because in JMI the velocity model only explains the propagation effects and, thereby, makes it less sensitive to the details in the velocity model.

An overview of full-waveform inversion in exploration geophysics

Geophysics ◽  
2009 ◽  
Vol 74 (6) ◽  
pp. WCC1-WCC26 ◽  
Author(s):  
J. Virieux ◽  
S. Operto
Keyword(s):  
High Performance ◽  
Waveform Inversion ◽  
Real Data ◽  
Quantitative Information ◽  
Full Waveform Inversion ◽  
Low Frequencies ◽  
Fitting Procedure ◽  
Full Waveform ◽  
Resolution Imaging ◽  
Starting Model

Full-waveform inversion (FWI) is a challenging data-fitting procedure based on full-wavefield modeling to extract quantitative information from seismograms. High-resolution imaging at half the propagated wavelength is expected. Recent advances in high-performance computing and multifold/multicomponent wide-aperture and wide-azimuth acquisitions make 3D acoustic FWI feasible today. Key ingredients of FWI are an efficient forward-modeling engine and a local differential approach, in which the gradient and the Hessian operators are efficiently estimated. Local optimization does not, however, prevent convergence of the misfit function toward local minima because of the limited accuracy of the starting model, the lack of low frequencies, the presence of noise, and the approximate modeling of thewave-physics complexity. Different hierarchical multiscale strategies are designed to mitigate the nonlinearity and ill-posedness of FWI by incorporating progressively shorter wavelengths in the parameter space. Synthetic and real-data case studies address reconstructing various parameters, from [Formula: see text] and [Formula: see text] velocities to density, anisotropy, and attenuation. This review attempts to illuminate the state of the art of FWI. Crucial jumps, however, remain necessary to make it as popular as migration techniques. The challenges can be categorized as (1) building accurate starting models with automatic procedures and/or recording low frequencies, (2) defining new minimization criteria to mitigate the sensitivity of FWI to amplitude errors and increasing the robustness of FWI when multiple parameter classes are estimated, and (3) improving computational efficiency by data-compression techniques to make 3D elastic FWI feasible.

scholarly journals Resolving high frequency anomalies of gas cloud using full waveform inversion

2016 ◽  
Vol 59 (1) ◽  
Author(s):  
Srichand Prajapati ◽  
Deva Ghosh
Keyword(s):  
High Resolution ◽  
Physical Properties ◽  
Cloud Model ◽  
Waveform Inversion ◽  
Velocity Model ◽  
Full Waveform Inversion ◽  
Low Frequencies ◽  
High Frequencies ◽  
Full Waveform ◽  
Gas Cloud

<p>High resolution models with structurally improved results significant to the physical properties of rocks in geologically complex areas require advance modeling methodologies. Low frequencies are required to understand the geological properties of the rocks while high frequencies is needed to address the structural challenges. Recent industry success in inversion have shown the accurate and robust results for the low frequencies. In this work, we provide a strategy to resolve geologically complex area such as gas cloud (at high frequencies) using full waveform inversion (FWI) based on 2D wave equation. Our contribution here, is the improvement in FWI imaging by: (i) solving the wave field equation to recover high resolution inversion results which is consistence to physical properties and shows structural enhancements; (ii) estimating the distribution of local minima which is largely affected by initial velocity model. To validate our approach, we demonstrate algorithms on synthetic gas cloud model.</p>

Wave-equation reflection traveltime inversion with dynamic warping and full-waveform inversion

Geophysics ◽  
2013 ◽  
Vol 78 (6) ◽  
pp. R223-R233 ◽  
Author(s):  
Yong Ma ◽  
Dave Hale
Keyword(s):  
Wave Equation ◽  
Waveform Inversion ◽  
Velocity Model ◽  
Full Waveform Inversion ◽  
Local Minima ◽  
Low Frequencies ◽  
Traveltime Inversion ◽  
Velocity Models ◽  
Full Waveform ◽  
Dynamic Warping

In reflection seismology, full-waveform inversion (FWI) can generate high-wavenumber subsurface velocity models but often suffers from an objective function with local minima caused mainly by the absence of low frequencies in seismograms. These local minima cause cycle skipping when the low-wavenumber component in the initial velocity model for FWI is far from the true model. To avoid cycle skipping, we discovered a new wave-equation reflection traveltime inversion (WERTI) to update the low-wavenumber component of the velocity model, while using FWI to only update high-wavenumber details of the model. We implemented the low- and high-wavenumber inversions in an alternating way. In WERTI, we used dynamic image warping (DIW) to estimate the time shifts between recorded data and synthetic data. When compared with correlation-based techniques often used in traveltime estimation, DIW can avoid cycle skipping and estimate the time shifts accurately, even when shifts vary rapidly. Hence, by minimizing traveltime shifts estimated by dynamic warping, WERTI reduces errors in reflection traveltime inversion. Then, conventional FWI uses the low-wavenumber component estimated by WERTI as a new initial model and thereby refines the model with high-wavenumber details. The alternating combination of WERTI and FWI mitigates the velocity-depth ambiguity and can recover subsurface velocities using only high-frequency reflection data.

scholarly journals Full-Waveform Inversion for Imaging Faulted Structures: A Case Study from the Japan Trench Forearc Slope

2021 ◽  
Author(s):  
Ehsan Jamali Hondori ◽  
Chen Guo ◽  
Hitoshi Mikada ◽  
Jin-Oh Park
Keyword(s):  
Seismic Data ◽  
Initial Velocity ◽  
Waveform Inversion ◽  
Velocity Model ◽  
Control Measures ◽  
Japan Trench ◽  
Full Waveform Inversion ◽  
Full Waveform ◽  
Time Migration ◽  
Shallow Sediments

AbstractFull-waveform inversion (FWI) of limited-offset marine seismic data is a challenging task due to the lack of refracted energy and diving waves from the shallow sediments, which are fundamentally required to update the long-wavelength background velocity model in a tomographic fashion. When these events are absent, a reliable initial velocity model is necessary to ensure that the observed and simulated waveforms kinematically fit within an error of less than half a wavelength to protect the FWI iterative local optimization scheme from cycle skipping. We use a migration-based velocity analysis (MVA) method, including a combination of the layer-stripping approach and iterations of Kirchhoff prestack depth migration (KPSDM), to build an accurate initial velocity model for the FWI application on 2D seismic data with a maximum offset of 5.8 km. The data are acquired in the Japan Trench subduction zone, and we focus on the area where the shallow sediments overlying a highly reflective basement on top of the Cretaceous erosional unconformity are severely faulted and deformed. Despite the limited offsets available in the seismic data, our carefully designed workflow for data preconditioning, initial model building, and waveform inversion provides a velocity model that could improve the depth images down to almost 3.5 km. We present several quality control measures to assess the reliability of the resulting FWI model, including ray path illuminations, sensitivity kernels, reverse time migration (RTM) images, and KPSDM common image gathers. A direct comparison between the FWI and MVA velocity profiles reveals a sharp boundary at the Cretaceous basement interface, a feature that could not be observed in the MVA velocity model. The normal faults caused by the basal erosion of the upper plate in the study area reach the seafloor with evident subsidence of the shallow strata, implying that the faults are active.

A new parameter set for anisotropic multiparameter full-waveform inversion and application to a North Sea data set

Geophysics ◽  
2016 ◽  
Vol 81 (4) ◽  
pp. U25-U38 ◽  
Author(s):  
Nuno V. da Silva ◽  
Andrew Ratcliffe ◽  
Vetle Vinje ◽  
Graham Conroy
Keyword(s):  
North Sea ◽  
Waveform Inversion ◽  
Real Data ◽  
Model Parameters ◽  
Full Waveform Inversion ◽  
Radiation Patterns ◽  
Data Set ◽  
Full Waveform ◽  
Seismic Image ◽  
Central North Sea

Parameterization lies at the center of anisotropic full-waveform inversion (FWI) with multiparameter updates. This is because FWI aims to update the long and short wavelengths of the perturbations. Thus, it is important that the parameterization accommodates this. Recently, there has been an intensive effort to determine the optimal parameterization, centering the fundamental discussion mainly on the analysis of radiation patterns for each one of these parameterizations, and aiming to determine which is best suited for multiparameter inversion. We have developed a new parameterization in the scope of FWI, based on the concept of kinematically equivalent media, as originally proposed in other areas of seismic data analysis. Our analysis is also based on radiation patterns, as well as the relation between the perturbation of this set of parameters and perturbation in traveltime. The radiation pattern reveals that this parameterization combines some of the characteristics of parameterizations with one velocity and two Thomsen’s parameters and parameterizations using two velocities and one Thomsen’s parameter. The study of perturbation of traveltime with perturbation of model parameters shows that the new parameterization is less ambiguous when relating these quantities in comparison with other more commonly used parameterizations. We have concluded that our new parameterization is well-suited for inverting diving waves, which are of paramount importance to carry out practical FWI successfully. We have demonstrated that the new parameterization produces good inversion results with synthetic and real data examples. In the latter case of the real data example from the Central North Sea, the inverted models show good agreement with the geologic structures, leading to an improvement of the seismic image and flatness of the common image gathers.

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