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>

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.

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>

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.

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.

scholarly journals Accelerating numerical wave propagation by wavefield adapted meshes. Part II: full-waveform inversion

2020 ◽  
Vol 221 (3) ◽  
pp. 1591-1604 ◽  
Author(s):  
Solvi Thrastarson ◽  
Martin van Driel ◽  
Lion Krischer ◽  
Christian Boehm ◽  
Michael Afanasiev ◽  
...  
Keyword(s):  
Wave Propagation ◽  
Wave Equation ◽  
Waveform Inversion ◽  
Computational Cost ◽  
Spectral Element ◽  
Full Waveform Inversion ◽  
Full Waveform ◽  
Order Of Magnitude ◽  
Numerical Wave ◽  
Expected Complexity

SUMMARY We present a novel full-waveform inversion (FWI) approach which can reduce the computational cost by up to an order of magnitude compared to conventional approaches, provided that variations in medium properties are sufficiently smooth. Our method is based on the usage of wavefield adapted meshes which accelerate the forward and adjoint wavefield simulations. By adapting the mesh to the expected complexity and smoothness of the wavefield, the number of elements needed to discretize the wave equation can be greatly reduced. This leads to spectral-element meshes which are optimally tailored to source locations and medium complexity. We demonstrate a workflow which opens up the possibility to use these meshes in FWI and show the computational advantages of the approach. We provide examples in 2-D and 3-D to illustrate the concept, describe how the new workflow deviates from the standard FWI workflow, and explain the additional steps in detail.

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