scholarly journals Regularized full-waveform inversion with automated salt flooding

Geophysics ◽  
2019 ◽  
Vol 84 (4) ◽  
pp. R569-R582 ◽  
Author(s):  
Mahesh Kalita ◽  
Vladimir Kazei ◽  
Yunseok Choi ◽  
Tariq Alkhalifah
Keyword(s):  
Optimization Problem ◽  
Waveform Inversion ◽  
Dominant Frequency ◽  
Model Parameters ◽  
Constant Density ◽  
Data Sets ◽  
Full Waveform Inversion ◽  
Data Set ◽  
Low Frequencies ◽  
Full Waveform

Full-waveform inversion (FWI) attempts to resolve an ill-posed nonlinear optimization problem to retrieve the unknown subsurface model parameters from seismic data. In general, FWI fails to obtain an adequate representation of models with large high-velocity structures over a wide region, such as salt bodies and the sediments beneath them, in the absence of low frequencies in the recorded seismic signal, due to nonlinearity and nonuniqueness. We alleviate the ill posedness of FWI associated with data sets affected by salt bodies using model regularization. We have split the optimization problem into two parts: First, we minimize the data misfit and the total variation in the model, seeking to achieve an inverted model with sharp interfaces; and second, we minimize sharp velocity drops with depth in the model. Unlike conventional industrial salt flooding, our technique requires minimal human intervention and no information about the top of the salt. Those features are demonstrated on data sets of the BP 2004 and Sigsbee2A models, synthesized from a Ricker wavelet of dominant frequency 5.5 Hz and minimum frequency 3 Hz. We initiate the inversion process with a simple model in which the velocity increases linearly with depth. The model is well-retrieved when the same constant density acoustic code is used to simulate the observed data, which is still one of the most common FWI tests. Moreover, our technique allows us to reconstruct a reasonable depiction of the salt structure from the data synthesized independently with the BP 2004 model with variable density. In the Sigsbee2A model, we manage to even capture some of the fine layering beneath the salt. In addition, we evaluate the versatility of our method on a field data set from the Gulf of Mexico.

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.

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 Evolutionary full-waveform inversion

2020 ◽  
Vol 224 (1) ◽  
pp. 306-311
Author(s):  
Dirk Philip van Herwaarden ◽  
Michael Afanasiev ◽  
Solvi Thrastarson ◽  
Andreas Fichtner
Keyword(s):  
Seismic Data ◽  
Waveform Inversion ◽  
Data Sets ◽  
Full Waveform Inversion ◽  
Data Set ◽  
New Approach ◽  
Full Waveform ◽  
Upper Mantle Structure ◽  
Data Coverage ◽  
D Model

SUMMARY We present a new approach to full-waveform inversion (FWI) that enables the assimilation of data sets that expand over time without the need to reinvert all data. This evolutionary inversion rests on a reinterpretation of stochastic Limited-memory Broyden–Fletcher–Goldfarb–Shanno (L-BFGS), which randomly exploits redundancies to achieve convergence without ever considering the data set as a whole. Specifically for seismological applications, we consider a dynamic mini-batch stochastic L-BFGS, where the size of mini-batches adapts to the number of sources needed to approximate the complete gradient. As an illustration we present an evolutionary FWI for upper-mantle structure beneath Africa. Starting from a 1-D model and data recorded until 1995, we sequentially add contemporary data into an ongoing inversion, showing how (i) new events can be added without compromising convergence, (ii) a consistent measure of misfit can be maintained and (iii) the model evolves over times as a function of data coverage. Though applied retrospectively in this example, our method constitutes a possible approach to the continuous assimilation of seismic data volumes that often tend to grow exponentially.

Breakthrough acquisition and technologies for subsalt imaging

Geophysics ◽  
2011 ◽  
Vol 76 (5) ◽  
pp. WB41-WB51 ◽  
Author(s):  
Denes Vigh ◽  
Jerry Kapoor ◽  
Nick Moldoveanu ◽  
Hongyan Li
Keyword(s):  
Velocity Field ◽  
Inversion Layer ◽  
Waveform Inversion ◽  
Full Waveform Inversion ◽  
Reverse Time ◽  
Reverse Time Migration ◽  
Data Set ◽  
Low Frequencies ◽  
Full Waveform ◽  
Time Migration

The recently introduced method of wide-azimuth data acquisition offers better illumination, noise attenuation, and lower frequencies to more accurately determine a velocity field for imaging. For the field data experiment to demonstrate the technologies, we used a Gulf of Mexico (GOM) wide-azimuth data set that allows us to take advantage of possible low frequencies, relatively large crossline offsets, and increased illumination. The input data was processed through true 3D azimuthal surface-related multiple elimination (SRME) with zero-phasing and debubble. Eliminating the surface-related multiples aids the velocity determination and helps uncover the subsalt sediments at the final imaging stage. After the initial velocity derivation, which was constrained to wells and geology, full-waveform inversion (FWI) was used to further update the velocity field to achieve an enhanced image. The methodology used follows the top-down approach where suprasalt sediment model is developed followed by the top of salt, salt flanks, base of salt, and finished with a limited subsalt update. To approximate the observed data by using an acoustic inversion procedure, the propagator includes effects of attenuation, anisotropy, acquisition source, and receiver depth. The geological environment is salt related, which implies that the observed data is highly elastic, even though it is input to an acoustic full waveform inversion. To use the proper constraints for the inversion, layer-stripping method is used to develop the high-resolution velocity field. The inversion stages were carefully quality controlled through gather displays to ensure the kinematics were honored. We then demonstrated the benefit of the FWI velocity field by comparing the images derived with the traditional ray-based tomographic velocity field versus the velocity field derived by FWI performing reverse time migration to produce these images. Finally, the images were compared at key well locations to evaluate the robustness of the workflow.

scholarly journals Waveform inversion based on wavefield decomposition

Geophysics ◽  
2016 ◽  
Vol 81 (6) ◽  
pp. R457-R470 ◽  
Author(s):  
Fang Wang ◽  
Daniela Donno ◽  
Hervé Chauris ◽  
Henri Calandra ◽  
François Audebert
Keyword(s):  
Waveform Inversion ◽  
Low Frequency ◽  
Velocity Model ◽  
Model Parameters ◽  
Data Set ◽  
Low Frequencies ◽  
Full Waveform ◽  
Highly Nonlinear ◽  
Gradient Based ◽  
Wavefield Decomposition

Full-waveform inversion (FWI) is a technique for determining the optimal model parameters by minimizing the seismic data misfit between observed and modeled data. The objective function may be highly nonlinear if the model is complex and low-frequency data are missing. If a data set mainly contains reflections, this problem particularly prevents the gradient-based methods from recovering the long wavelengths of the velocity model. Several authors observed that nonlinearity could be reduced by progressively introducing higher wavenumbers to the model. We have developed a new inversion workflow to solve this problem by breaking down the FWI gradient formula into four terms after wavefield decomposition and then selecting proper terms to invert for the short- and long-wavelength components of the velocity model alternately. Numerical tests applied on a 2D synthetic model indicate that this method is efficient at recovering the long wavelengths of the velocity model using mainly offset-limited reflection events. The source does not need to contain low frequencies. The initial velocity model may have large errors that would otherwise prevent convergence for conventional FWI.

scholarly journals Acoustic full-waveform inversion in an elastic world

Geophysics ◽  
2018 ◽  
Vol 83 (3) ◽  
pp. R257-R271 ◽  
Author(s):  
Òscar Calderón Agudo ◽  
Nuno Vieira da Silva ◽  
Michael Warner ◽  
Joanna Morgan
Keyword(s):  
Wave Velocity ◽  
Waveform Inversion ◽  
Velocity Model ◽  
P Wave ◽  
Data Sets ◽  
Full Waveform Inversion ◽  
Data Set ◽  
Velocity Models ◽  
Full Waveform ◽  
Elastic Data

Full-waveform inversion (FWI) is a technique used to obtain high-quality velocity models of the subsurface. Despite the elastic nature of the earth, the anisotropic acoustic wave equation is typically used to model wave propagation in FWI. In part, this simplification is essential for being efficient when inverting large 3D data sets, but it has the adverse effect of reducing the accuracy and resolution of the recovered P-wave velocity models, as well as a loss in potential to constrain other physical properties, such as the S-wave velocity given that amplitude information in the observed data set is not fully used. Here, we first apply conventional acoustic FWI to acoustic and elastic data generated using the same velocity model to investigate the effect of neglecting the elastic component in field data and we find that it leads to a loss in resolution and accuracy in the recovered velocity model. Then, we develop a method to mitigate elastic effects in acoustic FWI using matching filters that transform elastic data into acoustic data and find that it is applicable to marine and land data sets. Tests show that our approach is successful: The imprint of elastic effects on the recovered P-wave models is mitigated, leading to better-resolved models than those obtained after conventional acoustic FWI. Our method requires a guess of [Formula: see text] and is marginally more computationally demanding than acoustic FWI, but much less so than elastic FWI.

scholarly journals Full-waveform inversion in acoustic orthorhombic media and application to a North Sea data set

Geophysics ◽  
2018 ◽  
Vol 83 (5) ◽  
pp. C179-C193 ◽  
Author(s):  
Nabil Masmoudi ◽  
Tariq Alkhalifah
Keyword(s):  
North Sea ◽  
Waveform Inversion ◽  
Computational Cost ◽  
Model Parameters ◽  
Full Waveform Inversion ◽  
Data Set ◽  
Model Inversion ◽  
Multistage Model ◽  
Full Waveform ◽  
Trade Offs

Full-waveform inversion (FWI) in anisotropic media is challenging, mainly because of the large computational cost, especially in 3D, and the potential trade-offs between the model parameters needed to describe such media. By analyzing the trade-offs and understanding the resolution limits of the inversion, we can constrain FWI to focus on the main parameters the data are sensitive to and push the inversion toward more reliable models of the subsurface. Orthorhombic anisotropy is one of the most practical approximations of the earth subsurface that takes into account the natural horizontal layering and the vertical fracture network. We investigate the feasibility of a multiparameter FWI for an acoustic orthorhombic model described by six parameters. We rely on a suitable parameterization based on the horizontal velocity and five dimensionless anisotropy parameters. This particular parameterization allows a multistage model inversion strategy in which the isotropic, then, the vertical transverse isotropic, and finally the orthorhombic model can be successively updated. We applied our acoustic orthorhombic inversion on the SEG-EAGE overthrust synthetic model. The observed data used in the inversion are obtained from an elastic variable density version of the model. The quality of the inverted model suggests that we may recover only four parameters, with different resolution scales depending on the scattering potential of these parameters. Therefore, these results give useful insights on the expected resolution of the inverted parameters and the potential constraints that could be applied to an orthorhombic model inversion. We determine the efficiency of the inversion approach on real data from the North Sea. The inverted model is in agreement with the geologic structures and well-log information.

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.

scholarly journals Normalized nonzero-lag crosscorrelation elastic full-waveform inversion

Geophysics ◽  
2019 ◽  
Vol 84 (1) ◽  
pp. R1-R10 ◽  
Author(s):  
Zhendong Zhang ◽  
Tariq Alkhalifah ◽  
Zedong Wu ◽  
Yike Liu ◽  
Bin He ◽  
...  
Keyword(s):  
Field Data ◽  
Extreme Values ◽  
Time Lag ◽  
Waveform Inversion ◽  
Optimal Time ◽  
Full Waveform Inversion ◽  
Data Set ◽  
Velocity Models ◽  
Full Waveform ◽  
The Earth

Full-waveform inversion (FWI) is an attractive technique due to its ability to build high-resolution velocity models. Conventional amplitude-matching FWI approaches remain challenging because the simplified computational physics used does not fully represent all wave phenomena in the earth. Because the earth is attenuating, a sample-by-sample fitting of the amplitude may not be feasible in practice. We have developed a normalized nonzero-lag crosscorrelataion-based elastic FWI algorithm to maximize the similarity of the calculated and observed data. We use the first-order elastic-wave equation to simulate the propagation of seismic waves in the earth. Our proposed objective function emphasizes the matching of the phases of the events in the calculated and observed data, and thus, it is more immune to inaccuracies in the initial model and the difference between the true and modeled physics. The normalization term can compensate the energy loss in the far offsets because of geometric spreading and avoid a bias in estimation toward extreme values in the observed data. We develop a polynomial-type weighting function and evaluate an approach to determine the optimal time lag. We use a synthetic elastic Marmousi model and the BigSky field data set to verify the effectiveness of the proposed method. To suppress the short-wavelength artifacts in the estimated S-wave velocity and noise in the field data, we apply a Laplacian regularization and a total variation constraint on the synthetic and field data examples, respectively.

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