Seismic full-waveform inversion using minimization of virtual scattering sources

Geophysics ◽  
2020 ◽  
Vol 85 (3) ◽  
pp. R299-R311
Author(s):  
Donguk Lee ◽  
Sukjoon Pyun
Keyword(s):  
Newton Method ◽  
Scattering Problem ◽  
Waveform Inversion ◽  
Synthetic Data ◽  
Inverse Scattering Problem ◽  
Simulated Data ◽  
Model Space ◽  
Full Waveform Inversion ◽  
Velocity Inversion ◽  
Full Waveform

Full-waveform inversion (FWI) is a powerful tool for imaging underground structures with high resolution; however, this approach commonly suffers from the cycle-skipping issue. Recently, various FWI methods have been suggested to address this problem. Such methods are mainly classified into either data-space manipulation or model-space extension. We developed an alternative FWI method that belongs to the latter class. First, we define the virtual scattering source based on perturbation theory. The virtual scattering source is estimated by minimizing the differences between observed and simulated data with a regularization term penalizing the weighted virtual scattering source. The inverse problem for obtaining the virtual scattering source can be solved by the linear conjugate gradient method. The inverted virtual scattering source is used to update the wavefields; thus, it helps FWI to better approximate the nonlinearity of the inverse scattering problem. As the second step, the virtual scattering source is minimized to invert the velocity model. By assuming that the variation of the reconstructed wavefield is negligible, we can apply an approximated full Newton method to the velocity inversion with reasonable cost comparable to the Gauss-Newton method. From the numerical examples using synthetic data, we confirm that the proposed method performs better and more robust than the simple gradient-based FWI method. In addition, we show that our objective function has fewer local minima, which helps to mitigate the cycle-skipping problem.

scholarly journals Constrained Full Waveform Inversion for Borehole Multicomponent Seismic Data

Geosciences ◽  
2019 ◽  
Vol 9 (1) ◽  
pp. 45
Author(s):  
Marwan Charara ◽  
Christophe Barnes
Keyword(s):  
Inverse Problem ◽  
Spatial Correlation ◽  
Seismic Data ◽  
Waveform Inversion ◽  
Synthetic Data ◽  
Model Space ◽  
Elastic Model ◽  
Full Waveform Inversion ◽  
Spatial Correlations ◽  
Full Waveform

Full-waveform inversion for borehole seismic data is an ill-posed problem and constraining the problem is crucial. Constraints can be imposed on the data and model space through covariance matrices. Usually, they are set to a diagonal matrix. For the data space, signal polarization information can be used to evaluate the data uncertainties. The inversion forces the synthetic data to fit the polarization of observed data. A synthetic inversion for a 2D-2C data estimating a 1D elastic model shows a clear improvement, especially at the level of the receivers. For the model space, horizontal and vertical spatial correlations using a Laplace distribution can be used to fill the model space covariance matrix. This approach reduces the degree of freedom of the inverse problem, which can be quantitatively evaluated. Strong horizontal spatial correlation distances favor a tabular geological model whenever it does not contradict the data. The relaxation of the spatial correlation distances from large to small during the iterative inversion process allows the recovery of geological objects of the same size, which regularizes the inverse problem. Synthetic constrained and unconstrained inversions for 2D-2C crosswell data show the clear improvement of the inversion results when constraints are used.

scholarly journals Adding Prior Information in FWI through Relative Entropy

Entropy ◽  
2021 ◽  
Vol 23 (5) ◽  
pp. 599
Author(s):  
Danilo Cruz ◽  
João de Araújo ◽  
Carlos da Costa ◽  
Carlos da Silva
Keyword(s):  
Inverse Problem ◽  
Relative Entropy ◽  
Global Minimum ◽  
Prior Information ◽  
Waveform Inversion ◽  
Petroleum Industry ◽  
Synthetic Data ◽  
Full Waveform Inversion ◽  
Full Waveform

Full waveform inversion is an advantageous technique for obtaining high-resolution subsurface information. In the petroleum industry, mainly in reservoir characterisation, it is common to use information from wells as previous information to decrease the ambiguity of the obtained results. For this, we propose adding a relative entropy term to the formalism of the full waveform inversion. In this context, entropy will be just a nomenclature for regularisation and will have the role of helping the converge to the global minimum. The application of entropy in inverse problems usually involves formulating the problem, so that it is possible to use statistical concepts. To avoid this step, we propose a deterministic application to the full waveform inversion. We will discuss some aspects of relative entropy and show three different ways of using them to add prior information through entropy in the inverse problem. We use a dynamic weighting scheme to add prior information through entropy. The idea is that the prior information can help to find the path of the global minimum at the beginning of the inversion process. In all cases, the prior information can be incorporated very quickly into the full waveform inversion and lead the inversion to the desired solution. When we include the logarithmic weighting that constitutes entropy to the inverse problem, we will suppress the low-intensity ripples and sharpen the point events. Thus, the addition of entropy relative to full waveform inversion can provide a result with better resolution. In regions where salt is present in the BP 2004 model, we obtained a significant improvement by adding prior information through the relative entropy for synthetic data. We will show that the prior information added through entropy in full-waveform inversion formalism will prove to be a way to avoid local minimums.

Application of the variable projection scheme for frequency-domain full-waveform inversion

Geophysics ◽  
2013 ◽  
Vol 78 (6) ◽  
pp. R249-R257 ◽  
Author(s):  
Maokun Li ◽  
James Rickett ◽  
Aria Abubakar
Keyword(s):  
Frequency Domain ◽  
Waveform Inversion ◽  
Simulated Data ◽  
Calibration Procedure ◽  
Full Waveform Inversion ◽  
Inversion Algorithm ◽  
Unknown Parameters ◽  
Variable Projection ◽  
Full Waveform ◽  
Data Calibration

We found a data calibration scheme for frequency-domain full-waveform inversion (FWI). The scheme is based on the variable projection technique. With this scheme, the FWI algorithm can incorporate the data calibration procedure into the inversion process without introducing additional unknown parameters. The calibration variable for each frequency is computed using a minimum norm solution between the measured and simulated data. This process is directly included in the data misfit cost function. Therefore, the inversion algorithm becomes source independent. Moreover, because all the data points are considered in the calibration process, this scheme increases the robustness of the algorithm. Numerical tests determined that the FWI algorithm can reconstruct velocity distributions accurately without the source waveform information.

Tackling cycle skipping in full-waveform inversion with intermediate data

Geophysics ◽  
2019 ◽  
Vol 84 (3) ◽  
pp. R411-R427 ◽  
Author(s):  
Gang Yao ◽  
Nuno V. da Silva ◽  
Michael Warner ◽  
Di Wu ◽  
Chenhao Yang
Keyword(s):  
Objective Function ◽  
Waveform Inversion ◽  
Synthetic Data ◽  
Velocity Model ◽  
Full Waveform Inversion ◽  
Data Set ◽  
Intermediate Data ◽  
Full Waveform ◽  
L2 Norm ◽  
Recorded Data

Full-waveform inversion (FWI) is a promising technique for recovering the earth models for exploration geophysics and global seismology. FWI is generally formulated as the minimization of an objective function, defined as the L2-norm of the data residuals. The nonconvex nature of this objective function is one of the main obstacles for the successful application of FWI. A key manifestation of this nonconvexity is cycle skipping, which happens if the predicted data are more than half a cycle away from the recorded data. We have developed the concept of intermediate data for tackling cycle skipping. This intermediate data set is created to sit between predicted and recorded data, and it is less than half a cycle away from the predicted data. Inverting the intermediate data rather than the cycle-skipped recorded data can then circumvent cycle skipping. We applied this concept to invert cycle-skipped first arrivals. First, we picked up the first breaks of the predicted data and the recorded data. Second, we linearly scaled down the time difference between the two first breaks of each shot into a series of time shifts, the maximum of which was less than half a cycle, for each trace in this shot. Third, we moved the predicted data with the corresponding time shifts to create the intermediate data. Finally, we inverted the intermediate data rather than the recorded data. Because the intermediate data are not cycle-skipped and contain the traveltime information of the recorded data, FWI with intermediate data updates the background velocity model in the correct direction. Thus, it produces a background velocity model accurate enough for carrying out conventional FWI to rebuild the intermediate- and short-wavelength components of the velocity model. Our numerical examples using synthetic data validate the intermediate-data concept for tackling cycle skipping and demonstrate its effectiveness for the application to first arrivals.

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.

New tools for 2D full-waveform inversion: applications on Brazilian Pre-Salt velocity model from Santos Basin

2020 ◽  
Author(s):  
Henrique Santos ◽  
Claus Eikmeier ◽  
Ernani Volpe
Keyword(s):  
Oil And Gas ◽  
Model Building ◽  
Waveform Inversion ◽  
Numerical Algorithms ◽  
Velocity Model ◽  
Southeastern Brazil ◽  
Full Waveform Inversion ◽  
Case Scenario ◽  
Velocity Inversion ◽  
Full Waveform

<p>In this work, we present full-waveform inversion (FWI) results of a typical Brazilian Pre-Salt model (Santos Basin) using new open-source tools. The large accumulations of oil with excellent quality and high commercial value discovered in the pre-salt carbonates of southeastern Brazil, especially in the Santos Basin, have made this province one of the most prospective in the world. Velocity model building in areas of highly complex geology (like the Santos Basin) remains a challenging step in seismic processing. FWI proved to be an efficient tool for the determination of high-resolution details in multiparameter models of complex subsurface structures, and it has been applied in different geophysical problem scales. However, since FWI is a computationally and mathematically challenging problem, many issues remain open, such as more efficient ways to deal with multiparameter inversion problems such crosstalk and different orders of magnitude in the seismic signal for different classes of parameters. Inversions for more than one class of parameters are of particular importance in the estimation of the physical properties of rocks (poroacoustic or poroelastic applications), for example, to monitoring oil and gas reservoirs and for monitoring the injection of carbon dioxide into geological structures. Also, programming complex numerical algorithms for each application is time-consuming and often evades the expertise of researchers from the geoscientific community. In this sense, a high-level computational tool for simulations and inversions would greatly improve the working time for researchers. Existing finite difference based FWI tools such as Devito, and finite elements based partial differential equations (PDE) solvers tools such as FEniCS and Firedrake are being explored and used for these purposes. In this work, we initially present an FWI acoustic isotropic inversion test (velocity inversion only), performed with the Devito software while a particular code is being developed in FEniCS and Firedrake computer programs. Devito is also a new and under development software and therefore must be tested under different conditions. Our first numerical results indicate the potential of using freely available computational programs in a real case scenario.</p>

Simultaneous estimation of velocity and density in acoustic multiparameter full-waveform inversion using an improved scattering-integral approach

Geophysics ◽  
2016 ◽  
Vol 81 (6) ◽  
pp. R399-R415 ◽  
Author(s):  
Jizhong Yang ◽  
Yuzhu Liu ◽  
Liangguo Dong
Keyword(s):  
Newton Method ◽  
Waveform Inversion ◽  
Integral Approach ◽  
Normal Equation ◽  
Simultaneous Estimation ◽  
Model Parameters ◽  
Full Waveform Inversion ◽  
Trade Off ◽  
Full Waveform ◽  
Diffraction Patterns

Density is known to be difficult to reconstruct in multiparameter full-waveform inversion (FWI). This difficulty results from the similarity of the diffraction patterns of velocity and density at small scattering angles. In addition, the sensitivities of seismic data with respect to velocity and density have different orders of magnitude which make the inversion ill-conditioned. The inverse Hessian has been shown to mitigate the coupling effects and rescale the magnitudes of different parameters, such that reliable updates for all parameters are available. We have investigated the possibility of simultaneous estimations of velocity and density in acoustic media using the truncated Gauss-Newton method. The model updates are calculated using a matrix-free conjugate gradient solution of the Gauss-Newton normal equation. The gradients of the misfit function with respect to the model parameters and the Hessian-vector products are computed using an improved scattering-integral approach. To give some insights into the trade-off effects between velocity and density, and the imaging resolution in FWI, the sensitivity kernels of both parameters are numerically calculated in homogeneous background models, and their spatial distributions and characteristics are analyzed. The synthetic experiments on a canonical inclusion model and the 2004 BP model confirm that, in cases in which the Gauss-Newton approximate Hessian, especially its off-diagonal blocks, is accurately taken into account, the truncated Gauss-Newton method can effectively mitigate the trade-off effects between velocity and density and provide accelerated convergence rate. Hence, well-resolved velocity and density models are expected.

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