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.

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.

Whole Earth Full-Waveform Inversion With Wavefield Adapted Meshes

2020 ◽  
Author(s):  
Solvi Thrastarson ◽  
Dirk-Philip van Herwaarden ◽  
Lion Krischer ◽  
Christian Boehm ◽  
Martin van Driel ◽  
...  
Keyword(s):  
Stochastic Optimization ◽  
High Performance ◽  
Waveform Inversion ◽  
Computational Cost ◽  
Real Data ◽  
Global Scale ◽  
Full Waveform Inversion ◽  
Optimization Scheme ◽  
Continental Scale ◽  
Full Waveform

<p>With the steadily increasing availability and density of seismic data, full-waveform inversion (FWI) can reveal the Earth's subsurface with unprecedented resolution. FWI, however, carries a significant computational burden. Even with the ever-increasing power of high-performance computing resources, these massive compute requirements inhibit substantial progress, and require algorithmic and technological innovations for global and continental scale inversions.<br>In this contribution, we present an approach to FWI where we achieve significant computational savings through wavefield adapted meshing [1] combined with a stochastic optimization scheme [2]. This twofold strategy allows us (a) to solve the wave equation at lower costs, and (b) to reduce the number of required simulations. In laterally smooth media, we can construct meshes which are adapted to the expected complexity of the wavefield. By optimally designing a unique mesh for each source, we can reduce the computational cost of the forward and adjoint simulations by an order of magnitude. The stochastic optimization scheme is based on a dynamic mini-batch L-BFGS approach, which adaptively subsamples the event catalogue and requires significantly fewer wavefield simulations to converge to a model than conventional FWI. An additional benefit of the dynamic mini-batches is that they seamlessly allow for the inclusion of more sources in an inversion without a considerable additional computational cost.<br>We demonstrate a prototype FWI for this approach towards a global scale inversion with real data.<br><br>[1] Thrastarson, S., van Driel, M., Krischer, L., Afanasiev, M., Boehm, C., van Herwaarden, DP., Fichtner, A., 2019. Accelerating numerical wave propagation by wavefield adapted meshes, Part II: Full-waveform inversion. <em>Submitted to Geophysical Journal International</em><br>[2] van Herwaarden, DP., Boehm, C., Afanasiev, M., Krischer, L., van Driel, M., Thrastarson, S., Trampert, J., Fichtner, A. 2019. Accelerated full-waveform inversion using dynamic mini-batches. <em>Submitted to Geophysical Journal International</em></p>

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.

FULL-WAVEFORM INVERSION WITH SOURCE AND RECEIVER COUPLING EFFECTS CORRECTION

Geophysics ◽  
2021 ◽  
pp. 1-37
Author(s):  
Xinhai Hu ◽  
Wei Guoqi ◽  
Jianyong Song ◽  
Zhifang Yang ◽  
Minghui Lu ◽  
...  
Keyword(s):  
Waveform Inversion ◽  
Nonlinear Least Squares ◽  
Real Data ◽  
Model Parameters ◽  
Full Waveform Inversion ◽  
Linear Inversion ◽  
Near Surface ◽  
Model Parameter ◽  
Full Waveform ◽  
Coupling Factors

Coupling factors of sources and receivers vary dramatically due to the strong heterogeneity of near surface, which are as important as the model parameters for the inversion success. We propose a full waveform inversion (FWI) scheme that corrects for variable coupling factors while updating the model parameter. A linear inversion is embedded into the scheme to estimate the source and receiver factors and compute the amplitude weights according to the acquisition geometry. After the weights are introduced in the objective function, the inversion falls into the category of separable nonlinear least-squares problems. Hence, we could use the variable projection technique widely used in source estimation problem to invert the model parameter without the knowledge of source and receiver factors. The efficacy of the inversion scheme is demonstrated with two synthetic examples and one real data test.

Targeted stacking of weak seismic phases for improving mantle discontinuity imaging using full-waveform inversion

2021 ◽  
Author(s):  
Maria Koroni ◽  
Andreas Fichtner
Keyword(s):  
Seismic Waves ◽  
Waveform Inversion ◽  
Real Data ◽  
Full Waveform Inversion ◽  
Finite Frequency ◽  
Adjoint Methods ◽  
Frequency Sensitivity ◽  
Full Waveform ◽  
Discontinuity Structure ◽  
Mantle Discontinuity

<p>This study is a continuation of our efforts to connect adjoint methods and full-waveform inversion to common beamforming techniques, widely used and developed for signal enhancement. Our approach is focusing on seismic waves traveling in the Earth's mantle, which are phases commonly used to image internal boundaries, being however quite difficult to observe in real data. The main goal is to accentuate precursor waves arriving in well-known times before some major phase. These waves generate from interactions with global discontinuities in the mantle, thus being the most sensitive seismic phases and therefore most suitable for better understanding of discontinuity seismic structure. </p><p>Our work is based on spectral-element wave propagation which allows us to compute exact synthetic waveforms and adjoint methods for the calculation of sensitivity kernels. These tools are the core of full-waveform inversion and by our efforts we aim to incorporate more parts of the waveform in such inversion schemes. We have shown that targeted stacking of good quality waveforms arriving from various directions highlights the weak precursor waves. It additionally makes their traveltime finite frequency sensitivity prominent. This shows that we can benefit from using these techniques and exploit rather difficult parts of the seismogram.  It was also shown that wave interference is not easily avoided, but coherent phases arriving before the main phase also stack well and show on the sensitivity kernels. This does not hamper the evaluation of waveforms, as in a misfit measurement process one can exploit more phases on the body wave parts of seismograms.</p><p>In this study, we go a step forward and present recent developments of the approach relating to the effects of noise and a real data experiment. Realistic noise is added to synthetic waveforms in order to assess the methodology in a more pragmatic scenario. The addition of noise shows that stacking of coherent seismic phases is still possible and the sensitivity kernels of their traveltimes are not largely distorted, the precursor waves contribute sufficiently to their traveltime finite-frequency sensitivity kernels.<br>Using a well-located seismic array, we apply the method to real data and try to examine the possibilities of using non-ideal waveforms to perform imaging of the mantle discontinuity structure on the specific areas. In order to make the most out of the dense array configuration, we try subgroups of receivers for the targeted stacking and by moving along the array we aim at creating a cluster of stacks. The main idea is to use the subgroups as single receivers and create an evaluation of seismic discontinuity structure using information from each stack belonging to a subgroup. <br>Ideally, we aim at improving the tomographic images of discontinuities of selected regions by exploiting weaker seismic waves, which are nonetheless very informative.</p>

Full-waveform inversion of salt models using shape optimization and simulated annealing

Geophysics ◽  
2019 ◽  
Vol 84 (5) ◽  
pp. R793-R804 ◽  
Author(s):  
Debanjan Datta ◽  
Mrinal K. Sen ◽  
Faqi Liu ◽  
Scott Morton
Keyword(s):  
Simulated Annealing ◽  
Least Squares ◽  
Level Set ◽  
Waveform Inversion ◽  
Optimization Techniques ◽  
Model Parameters ◽  
Full Waveform Inversion ◽  
Velocity Models ◽  
Full Waveform ◽  
Starting Model

A good starting model is imperative in full-waveform inversion (FWI) because it solves a least-squares inversion problem using a local gradient-based optimization method. A suboptimal starting model can result in cycle skipping leading to poor convergence and incorrect estimation of subsurface properties. This problem is especially crucial for salt models because the strong velocity contrasts create substantial time shifts in the modeled seismogram. Incorrect estimation of salt bodies leads to velocity inaccuracies in the sediments because the least-squares gradient aims to reduce traveltime differences without considering the sharp velocity jump between sediments and salt. We have developed a technique to estimate velocity models containing salt bodies using a combination of global and local optimization techniques. To stabilize the global optimization algorithm and keep it computationally tractable, we reduce the number of model parameters by using sparse parameterization formulations. The sparse formulation represents sediments using a set of interfaces and velocities across them, whereas a set of ellipses represents the salt body. We use very fast simulated annealing (VFSA) to minimize the misfit between the observed and synthetic data and estimate an optimal model in the sparsely parameterized space. The VFSA inverted model is then used as a starting model in FWI in which the sediments and salt body are updated in the least-squares sense. We partition model updates into sediment and salt updates in which the sediments are updated like conventional FWI, whereas the shape of the salt is updated by taking the zero crossing of an evolving level set surface. Our algorithm is tested on two 2D synthetic salt models, namely, the Sigsbee 2A model and a modified SEG Advanced Modeling Program (SEAM) Phase I model while fixing the top of the salt. We determine the efficiency of the VFSA inversion and imaging improvements from the level set FWI approach and evaluate a few sources of uncertainty in the estimation of salt shapes.

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