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

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.

Download Full-text

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

Geophysics ◽

10.1190/geo2019-0834.1 ◽

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.

Download Full-text

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

Interpretation ◽

10.1190/int-2015-0214.1 ◽

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.

Download Full-text

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

Geophysics ◽

10.1190/geo2019-0529.1 ◽

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.

Download Full-text

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

Geophysics ◽

10.1190/geo2017-0738.1 ◽

2018 ◽

Vol 83 (5) ◽

pp. C179-C193 ◽

Cited By ~ 11

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.

Download Full-text

Application of an Improved Ultrasound Full-Waveform Inversion in Bone Quantitative Measurement

Symmetry ◽

10.3390/sym13020260 ◽

2021 ◽

Vol 13 (2) ◽

pp. 260

Author(s):

Meng Suo ◽

Dong Zhang ◽

Yan Yang

Keyword(s):

Nonlinear Equations ◽

Waveform Inversion ◽

Optimal Solution ◽

Inversion Method ◽

Full Waveform Inversion ◽

Inversion Algorithm ◽

Elastic Wave Equation ◽

Full Waveform ◽

Ultrasonic Propagation ◽

Joint Velocity

Inspired by the large number of applications for symmetric nonlinear equations, an improved full waveform inversion algorithm is proposed in this paper in order to quantitatively measure the bone density and realize the early diagnosis of osteoporosis. The isotropic elastic wave equation is used to simulate ultrasonic propagation between bone and soft tissue, and the Gauss–Newton algorithm based on symmetric nonlinear equations is applied to solve the optimal solution in the inversion. In addition, the authors use several strategies including the frequency-grid multiscale method, the envelope inversion and the new joint velocity–density inversion to improve the result of conventional full-waveform inversion method. The effects of various inversion settings are also tested to find a balanced way of keeping good accuracy and high computational efficiency. Numerical inversion experiments showed that the improved full waveform inversion (FWI) method proposed in this paper shows superior inversion results as it can detect small velocity–density changes in bones, and the relative error of the numerical model is within 10%. This method can also avoid interference from small amounts of noise and satisfy the high precision requirements for quantitative ultrasound measurements of bone.

Download Full-text

A new parameter set for anisotropic multiparameter full-waveform inversion and application to a North Sea data set

Geophysics ◽

10.1190/geo2015-0349.1 ◽

2016 ◽

Vol 81 (4) ◽

pp. U25-U38 ◽

Cited By ~ 32

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.

Download Full-text

Normalized nonzero-lag crosscorrelation elastic full-waveform inversion

Geophysics ◽

10.1190/geo2018-0082.1 ◽

2019 ◽

Vol 84 (1) ◽

pp. R1-R10 ◽

Cited By ~ 11

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.

Download Full-text