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.

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.

Extending the useful angle range for elastic inversion through the amplitude-versus-angle full-waveform inversion method

Geophysics ◽  
2018 ◽  
Vol 83 (3) ◽  
pp. R213-R226 ◽  
Author(s):  
Sérgio A. M. Oliveira ◽  
Igor L. S. Braga ◽  
Murillo B. Lacerda ◽  
Geovane F. Ouverney ◽  
Anderson W. P. de Franco
Keyword(s):  
Incidence Angle ◽  
Waveform Inversion ◽  
Computational Cost ◽  
Reliable Estimate ◽  
Inversion Method ◽  
Full Waveform Inversion ◽  
Angle Of Incidence ◽  
Data Set ◽  
Full Waveform ◽  
Amplitude Versus

We have developed the amplitude versus angle full-waveform inversion (AVA-FWI) method. This method considers the complete seismic response of the layered medium, and so it is capable of correctly handling seismic amplitudes from prestack data with a wide angle range. This capability is very important because a reliable estimate of the elastic parameters and the density requires an incidence angle that goes beyond 30°. Our method inputs seismic traces from prestack time-migrated gathers ordered by angle of incidence and works under the local 1D assumption. AVA-FWI is a nonlinear inversion based on forward modeling by the reflectivity method, which substantially increases its computational cost with respect to conventional AVA inversion. To address this problem, we developed an efficient routine for angle gather modeling and a new method for differential seismogram generation that greatly reduces the amount of computation involved in this task. The AVA-FWI method was applied to synthetic data and to a geophysical reservoir characterization case study using the North Viking Graben open data set.

Central-difference time-lapse 4D seismic full waveform inversion

Geophysics ◽  
2020 ◽  
pp. 1-42
Author(s):  
Wei Zhou ◽  
David Lumley
Keyword(s):  
High Resolution ◽  
Seismic Velocity ◽  
Waveform Inversion ◽  
Computational Cost ◽  
Time Lapse ◽  
Full Waveform Inversion ◽  
Central Difference ◽  
Data Set ◽  
Velocity Inversion ◽  
Full Waveform

Repeated seismic surveys contain valuable information regarding time-lapse (4D) changes in the subsurface. Full waveform inversion (FWI) of seismic data can provide high-resolution estimates of 4D change. We propose a new time-domain 2D acoustic time-lapse FWI method based on the central-difference scheme with higher-order mathematical accuracy and reasonable computational cost. The method is rigorously tested on the SEAM 4D time-lapse model and OBN data set. High-resolution 4D velocity estimates are obtained, which show strong ~25% velocity increases in a 75 m-thick gas layer, as well as weaker (5%) changes due to geomechanical effects, the latter of which are poorly recovered by the conventional parallel 4D FWI method. We also perform the bootstrap 4D FWI method and the result is contaminated by strong artifacts in the underburden, whereas the proposed central-difference method has fewer underburden artifacts allowing more reliable interpretations. In this realistic case study, acoustic FWI erroneously overfits the elastic scattered waves, and cannot fit the strong elastic 4D coda waves at all. The results show that the proposed central-difference 4D FWI method within the acoustic approximation may be a practical solution for time-lapse seismic velocity inversion.

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.

An application of full-waveform inversion to land data using the pseudo-Hessian matrix

2016 ◽  
Vol 4 (4) ◽  
pp. T627-T635
Author(s):  
Yikang Zheng ◽  
Wei Zhang ◽  
Yibo Wang ◽  
Qingfeng Xue ◽  
Xu Chang
Keyword(s):  
Hessian Matrix ◽  
Waveform Inversion ◽  
Computational Cost ◽  
Velocity Model ◽  
Surface Velocity ◽  
Full Waveform Inversion ◽  
Data Set ◽  
Near Surface ◽  
Full Waveform ◽  
The Time Domain

Full-waveform inversion (FWI) is used to estimate the near-surface velocity field by minimizing the difference between synthetic and observed data iteratively. We apply this method to a data set collected on land. A multiscale strategy is used to overcome the local minima problem and the cycle-skipping phenomenon. Another obstacle in this application is the slow convergence rate. The inverse Hessian can enhance the poorly blurred gradient in FWI, but obtaining the full Hessian matrix needs intensive computation cost; thus, we have developed an efficient method aimed at the pseudo-Hessian in the time domain. The gradient in our FWI workflow is preconditioned with the obtained pseudo-Hessian and a synthetic example verifies its effectiveness in reducing computational cost. We then apply the workflow on the land data set, and the inverted velocity model is better resolved compared with traveltime tomography. The image and angle gathers we get from the inversion result indicate more detailed information of subsurface structures, which will contribute to the subsequent seismic interpretation.

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.

Full-waveform inversion for signal enhancement of weak amplitude phases using beamforming and adjoint methods

2020 ◽  
Author(s):  
Maria Koroni ◽  
Andreas Fichtner
Keyword(s):  
Epicentral Distance ◽  
Average Distance ◽  
Waveform Inversion ◽  
Computational Cost ◽  
Signal Enhancement ◽  
Time Shift ◽  
Model Parameters ◽  
Full Waveform Inversion ◽  
Full Waveform ◽  
Phase Alignment

&lt;p&gt;In this study, we develop a new adjoint- and full-waveform inversion approach for low-amplitude seismic phases that are typically below noise in individual recordings. The methodology aims at enhancing weak signals from body wave phases, which can be used in full-waveform inversion for inferring structural and boundary parameters in the earth. The new approach is based on the formulation of misfit functionals and corresponding adjoint sources for stacks of suitably time-shifted recordings.&amp;#160;&lt;/p&gt;&lt;p&gt;To tackle this problem, we compute synthetic waveforms using spectral-elements for models with and without topographic variations along mantle discontinuities. We focus on global underside reflections which are reportedly almost always undetectable in real seismograms due to their low amplitudes and are considerably affected by topography. We enforce phase alignment on a chosen reference seismogram recorded at an average distance among the selected stations. A time shift towards the reference is applied to all seismograms according to their epicentral distance calculated by 1-D ray tracing. A set of time shifts is calculated by cross-correlation in time windows around predicted traveltimes of the desired phase. Using this set of time shifts, we sum the waveforms creating the main stack for each model.&lt;/p&gt;&lt;p&gt;We use the two linear stacks as &lt;em&gt;observed&lt;/em&gt; and &lt;em&gt;synthetic&lt;/em&gt; (with and without topography, respectively) and develop a least-squares misfit measurement which gives rise to an adjoint source determined by the time shift between stacks. The expectation is that computing the traveltime Fr&amp;#233;chet kernel with respect to volumetric and boundary model parameters will show the exact sensitivity of the enhanced signal and save time from computing each station kernel separately. Upon achieving signal enhancement of the desired phases, we can ensure that these can be used for better informing updates of the initial model given the higher quality measurement of the observable.&lt;/p&gt;&lt;p&gt;This method once fully developed will allow us to leverage information of many recordings by reducing incoherent signal and enhancing weak seismic phases. The computation of sensitivity kernels in our study has a twofold importance. Firstly, it helps us realise whether the stacking technique indeed enhances the desired signal and whether it is ideal for precursor waves. Secondly, the exact sensitivity kernels show us the way of incorporating finite-frequency effects of weak but informative phases and introducing non-linear inversion for improving imaging while reducing some computational cost.&amp;#160;&lt;/p&gt;&lt;p&gt;&amp;#160;&lt;/p&gt;

scholarly journals Hybrid frequency-domain full-waveform inversion using ray+Born sensitivity kernels

Geophysics ◽  
2020 ◽  
Vol 85 (4) ◽  
pp. R339-R347
Author(s):  
Ramzi Djebbi ◽  
Tariq Alkhalifah
Keyword(s):  
Frequency Domain ◽  
Ray Tracing ◽  
Waveform Inversion ◽  
Hybrid Approach ◽  
Computational Cost ◽  
Equation Modeling ◽  
Inversion Method ◽  
Model Parameters ◽  
Full Waveform Inversion ◽  
Full Waveform

Full-waveform inversion (FWI) using the scattering integral (SI) approach is an explicit formulation of the inversion optimization problem. The inversion procedure is straightforward, and the dependence of the data residuals on the model parameters is clear. However, the biggest limitation associated with this approach is the huge computational cost in conventional exploration seismology applications. Modeling from each of the source and receiver locations is required to compute the update at every iteration, and that is prohibitively expensive, especially for 3D problems. To deal with this issue, we have developed a hybrid implementation of frequency-domain FWI, in which forward modeling is combined with ray tracing to compute the update. We use the sensitivity kernels computed from dynamic ray tracing to build the gradient. The data residual is still computed using finite-difference wavefield modeling. With ray theory, the Green’s function can be approximated using a coarser grid compared to wave-equation modeling. Therefore, the memory requirements, as well as the computational cost, are reduced significantly. Considering that in transmission FWI long-to-intermediate wavelengths are updated during the early iterations, we obtain accurate inverted models. The inversion scheme captured the anomaly embedded in the homogeneous background medium. For more complex models, the hybrid inversion method helps in improving the initial model with little cost compared with conventional SI inversion approaches. The accuracy of the inversion results shows the effectiveness of the hybrid approach for 3D realistic problems.

A Bayesian approach to estimate uncertainty for full-waveform inversion using a priori information from depth migration

Geophysics ◽  
2016 ◽  
Vol 81 (5) ◽  
pp. R307-R323 ◽  
Author(s):  
Hejun Zhu ◽  
Siwei Li ◽  
Sergey Fomel ◽  
Georg Stadler ◽  
Omar Ghattas
Keyword(s):  
Waveform Inversion ◽  
Computational Cost ◽  
Covariance Operator ◽  
Maximum A Posteriori ◽  
Model Parameters ◽  
Full Waveform Inversion ◽  
Posterior Distributions ◽  
A Posteriori ◽  
Model Uncertainties ◽  
Full Waveform

Full-waveform inversion (FWI) enables us to obtain high-resolution subsurface images; however, estimating model uncertainties associated with this technique is still a challenging problem. We have used a Bayesian inference framework to estimate model uncertainties associated with FWI. The uncertainties were assessed based on an a posteriori covariance operator, evaluated at the maximum a posteriori model. For the prior distribution, we have used a spatially nonstationary covariance operator based on a plane-wave construction with local dips measured from migrated images. Preconditioned frequency-domain FWI was used to estimate the maximum a posteriori model. Efficient manipulation of the posterior covariance was based on a low-rank approximation of the data misfit Hessian preconditioned by the prior covariance operator. The strong decay of the singular values indicated that data were mostly informative about a low-dimensional subspace of model parameters. To reduce computational cost of the randomized singular value decomposition, we have used a Hessian approximation based on point-spread functions. The 2D numerical examples with synthetic data confirmed that the method can effectively estimate uncertainties for FWI. Visual comparisons of random samples drawn from the prior and posterior distributions have allowed us to evaluate model uncertainties. Furthermore, we found out how statistical quantities, such as means and pointwise standard deviation fields, can be efficiently extracted from the prior and posterior distributions. These fields helped us to objectively assess subsurface images provided by FWI.

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.

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