Source-independent extended waveform inversion based on space-time source extension: Frequency-domain implementation

Geophysics ◽  
2018 ◽  
Vol 83 (5) ◽  
pp. R449-R461 ◽  
Author(s):  
Guanghui Huang ◽  
Rami Nammour ◽  
William W. Symes
Keyword(s):  
Source Function ◽  
Random Noise ◽  
A Priori ◽  
Waveform Inversion ◽  
Low Frequency ◽  
Inversion Method ◽  
Target Velocity ◽  
Extended Source ◽  
Full Waveform ◽  
Time Variables

Source signature estimation from seismic data is a crucial ingredient for successful application of seismic migration and full-waveform inversion (FWI). If the starting velocity deviates from the target velocity, FWI method with on-the-fly source estimation may fail due to the cycle-skipping problem. We have developed a source-based extended waveform inversion method, by introducing additional parameters in the source function, to solve the FWI problem without the source signature as a priori. Specifically, we allow the point source function to be dependent on spatial and time variables. In this way, we can easily construct an extended source function to fit the recorded data by solving a source matching subproblem; hence, it is less prone to cycle skipping. A novel source focusing annihilator, defined as the distance function from the real source position, is used for penalizing the defocused energy in the extended source function. A close data fit avoiding the cycle-skipping problem effectively makes the new method less likely to suffer from local minima, which does not require extreme low-frequency signals in the data. Numerical experiments confirm that our method can mitigate cycle skipping in FWI and is robust against random noise.

Comparison of source-independent methods of elastic waveform inversion

Geophysics ◽  
2006 ◽  
Vol 71 (6) ◽  
pp. R91-R100 ◽  
Author(s):  
Kun Xu ◽  
Stewart A. Greenhalgh ◽  
MiaoYue Wang
Keyword(s):  
Elastic Wave ◽  
Frequency Domain ◽  
Numerical Experiments ◽  
Random Noise ◽  
Waveform Inversion ◽  
Seismic Inversion ◽  
Inversion Method ◽  
Practical Procedure ◽  
Wave Inversion ◽  
Full Waveform

In this paper, we investigate several source-independent methods of nonlinear full-waveform inversion of multicomponent elastic-wave data. This includes iterative estimation of source signature (IES), standard trace normalization (STN), and average trace normalization (ATN) inversion methods. All are based on the finite-element method in the frequency domain. One synthetic elastic crosshole model is used to compare the recovered images with all these methods as well as the known source signature (KSS) inversion method. The numerical experiments show that the IES method is superior to both STN and ATN methods in two-component, elastic-wave inversion in the frequency domain when the source signature is unknown. The STN and ATN methods have limitations associated with near-zero amplitudes (or polarity reversals) in traces from one of the components, which destroy the energy balance in the normalized traces and cause a loss of frequency information. But the ATN method is somewhat superior to the STN method in suppressing random noise and improving stability, as the developed formulas and the numerical experiments show. We suggest the IES method as a practical procedure for multicomponent seismic inversion.

Impedance inversion by using the low-frequency full-waveform inversion result as an a priori model

Geophysics ◽  
2019 ◽  
Vol 84 (2) ◽  
pp. R149-R164 ◽  
Author(s):  
Sanyi Yuan ◽  
Shangxu Wang ◽  
Yaneng Luo ◽  
Wanwan Wei ◽  
Guanchao Wang
Keyword(s):  
A Priori ◽  
Complex Structure ◽  
Waveform Inversion ◽  
Low Frequency ◽  
Real Data ◽  
Well Logs ◽  
Low Frequencies ◽  
Impedance Model ◽  
Full Waveform ◽  
Impedance Inversion

Prestack acoustic full-waveform inversion (FWI) can provide long-wavelength components of the P-wave velocity by using low frequencies and long-offset direct/diving/refracted waves, which could be simulated via a large space grid, and it is weakly sensitive to density. Poststack impedance inversion can usually quickly yield high-resolution impedance, and it is sensitive to density. Therefore, we have combined these two methods to develop an FWI-driven impedance inversion. Our method first uses FWI to obtain the long-wavelength velocity with a guaranteed overlap between the high frequencies of the velocity and the low frequencies of the poststack data. Then, the fitting rock-physics relationship between the density and the velocity is adopted to translate the FWI velocity into the low-frequency impedance. Finally, the resulting low-frequency impedance is used to construct an a priori constraint for poststack impedance inversion. The method has the ability to solve the overlap between the FWI-based converted prior impedance model and poststack data, and it can thereby yield a broadband absolute impedance result. We adopt a Marmousi II model example and a real data case to test the performances of the FWI-driven impedance inversion and indicate its advantages compared with the conventional well-driven impedance inversion that uses well logs and interpreted horizons to build the prior impedance model. The synthetic data example demonstrates that well-driven impedance inversion produces a result with a relatively large deviation to the true impedance model at complex structure zones. However, FWI-driven impedance inversion favorably recovers all interesting sediment layers at complex structure zones. The real data example illustrates that well-driven impedance inversion yields a result with a distinct footprint of the prior model created from well logs and horizons. On the other hand, we find that FWI-driven impedance inversion yields a geologically reasonable solution, which not only conforms to the time-space variation trend of the well logs, but it also reveals a basin structural-depositional evolution.

scholarly journals Elastic envelope inversion using multicomponent seismic data without low frequency

2014 ◽  
Vol 1 (2) ◽  
pp. 1757-1802
Author(s):  
C. Huang ◽  
L. Dong ◽  
Y. Liu ◽  
B. Chi
Keyword(s):  
Seismic Data ◽  
Waveform Inversion ◽  
Synthetic Data ◽  
Low Frequency ◽  
Velocity Model ◽  
Inversion Method ◽  
Full Waveform Inversion ◽  
S Wave ◽  
Full Waveform ◽  
Multicomponent Data

Abstract. Low frequency is a key issue to reduce the nonlinearity of elastic full waveform inversion. Hence, the lack of low frequency in recorded seismic data is one of the most challenging problems in elastic full waveform inversion. Theoretical derivations and numerical analysis are presented in this paper to show that envelope operator can retrieve strong low frequency modulation signal demodulated in multicomponent data, no matter what the frequency bands of the data is. With the benefit of such low frequency information, we use elastic envelope of multicomponent data to construct the objective function and present an elastic envelope inversion method to recover the long-wavelength components of the subsurface model, especially for the S-wave velocity model. Numerical tests using synthetic data for the Marmousi-II model prove the effectiveness of the proposed elastic envelope inversion method, especially when low frequency is missing in multicomponent data and when initial model is far from the true model. The elastic envelope can reduce the nonlinearity of inversion and can provide an excellent starting model.

scholarly journals Eigenvector models for solving the seismic inverse problem for the Helmholtz equation

2020 ◽  
Vol 221 (1) ◽  
pp. 394-414 ◽  
Author(s):  
Florian Faucher ◽  
Otmar Scherzer ◽  
Hélène Barucq
Keyword(s):  
Inverse Problem ◽  
Wave Speed ◽  
Waveform Inversion ◽  
Low Frequency ◽  
Inversion Method ◽  
Reconstruction Procedure ◽  
Salt Domes ◽  
Full Waveform ◽  
Acoustic Media ◽  
Speed Parameter

SUMMARY We study the seismic inverse problem for the recovery of subsurface properties in acoustic media. In order to reduce the ill-posedness of the problem, the heterogeneous wave speed parameter is represented using a limited number of coefficients associated with a basis of eigenvectors of a diffusion equation, following the regularization by discretization approach. We compare several choices for the diffusion coefficient in the partial differential equations, which are extracted from the field of image processing. We first investigate their efficiency for image decomposition (accuracy of the representation with respect to the number of variables). Next, we implement the method in the quantitative reconstruction procedure for seismic imaging, following the full waveform inversion method, where the difficulty resides in that the basis is defined from an initial model where none of the actual structures is known. In particular, we demonstrate that the method may be relevant for the reconstruction of media with salt-domes. We use the method in 2-D and 3-D experiments, and show that the eigenvector representation compensates for the lack of low-frequency information, it eventually serves us to extract guidelines for the implementation of the method.

scholarly journals Reciprocity-gap misfit functional for Distributed Acoustic Sensing, combining data from passive and active sources

Geophysics ◽  
2020 ◽  
pp. 1-59 ◽  
Author(s):  
Florian Faucher ◽  
Maarten V. de Hoop ◽  
Otmar Scherzer
Keyword(s):  
Quantitative Imaging ◽  
A Priori ◽  
Waveform Inversion ◽  
Low Frequency ◽  
Inversion Method ◽  
Acoustic Sensing ◽  
Use Of Data ◽  
Combining Data ◽  
Distributed Acoustic Sensing ◽  
Priori Information

Quantitative imaging of sub-surface Earth’s properties in elastic media is performed from Distributed Acoustic Sensing data. A new misfit functional based upon the reciprocity-gap is designed, taking cross-correlations of displacement and strain, and these products further associate an observation with a simulation. In comparison with other misfit functionals, this one has the advantage to only require little a-priori information on the exciting sources. In particular, the misfit criterion enables the use of data from regional earthquakes (teleseismic events can be included as well), followed by exploration data to perform a multi-resolution reconstruction. The data from regional earthquakes contain the low-frequency content which is missing in the exploration ones, allowing for the recovery of the long spatial wavelength, even with very few sources. These data are used to build prior models for the subsequent reconstruction from the higher-frequency exploration data. This gives the elastic Full Reciprocity-gap Waveform Inversion method, and we demonstrate its performance with a pilot experiment for elastic isotropic reconstruction.

scholarly journals Probing depth and lateral variations of upper-mantle seismic anisotropy from full-waveform inversion of teleseismic body-waves

2020 ◽  
Vol 222 (1) ◽  
pp. 352-387 ◽  
Author(s):  
Stephen Beller ◽  
Sébastien Chevrot
Keyword(s):  
Seismic Anisotropy ◽  
A Priori ◽  
Waveform Inversion ◽  
Elasticity Tensor ◽  
Body Waves ◽  
Symmetry Class ◽  
Inversion Method ◽  
Full Waveform Inversion ◽  
Anisotropic Models ◽  
Full Waveform

SUMMARY While seismic anisotropy can potentially provide crucial insights into mantle dynamics, 3-D imaging of seismic anisotropy is still a challenging problem. Here, we present an extension of our regional full-waveform inversion method to image seismic anisotropy in the lithosphere and asthenosphere from teleseismic P and S waveforms. The models are parametrized in terms of density and the 21 elastic coefficients of the fourth-order elasticity tensor. The inversion method makes no a priori assumptions on the symmetry class or on the orientation of the symmetry axes. Instead, the elasticity tensors in the final models are decomposed with the projection method. This method allows us to determine the orientation of the symmetry axes and to extract the contributions of each symmetry class. From simple synthetic experiments, we demonstrate that our full-waveform inversion method is able to image complex 3-D anisotropic structures. In particular, the method is able to almost perfectly recover the general orientation of the symmetry axis or complex layered anisotropic models, which are both extremely challenging problems. We attribute this success to the joint exploitation of both P and S teleseismic waves, which constrain different parts of the elasticity tensor. Another key ingredient is the pre-conditioning of the gradient with an approximate inverse Hessian computed with scattering integrals. The inverse Hessian is crucial for mitigating the artefacts resulting from the uneven (mostly vertical) illumination of teleseismic acquisitions.

Volume source-based extended waveform inversion

Geophysics ◽  
2018 ◽  
Vol 83 (5) ◽  
pp. R369-R387 ◽  
Author(s):  
Guanghui Huang ◽  
Rami Nammour ◽  
William W. Symes
Keyword(s):  
Penalty Function ◽  
Source Parameters ◽  
Waveform Inversion ◽  
Low Frequency ◽  
Model Space ◽  
Velocity Model ◽  
Inversion Method ◽  
Inversion Algorithm ◽  
Full Waveform ◽  
Data Frequency

Full-waveform inversion (FWI) faces the persistent challenge of cycle skipping, which can result in stagnation of the iterative methods at uninformative models with poor data fit. Extended reformulations of FWI avoid cycle skipping through adding auxiliary parameters to the model so that a good data fit can be maintained throughout the inversion process. The volume-based matched source waveform inversion algorithm introduces source parameters by relaxing the location constraint of source energy: It is permitted to spread in space, while being strictly localized at time [Formula: see text]. The extent of source energy spread is penalized by weighting the source energy with distance from the survey source location. For transmission data geometry (crosswell, diving wave, etc.) and transparent (nonreflecting) acoustic models, this penalty function is stable with respect to the data-frequency content, unlike the standard FWI objective. We conjecture that the penalty function is actually convex over much larger region in model space than is the FWI objective. Several synthetic examples support this conjecture and suggest that the theoretical limitation to pure transmission is not necessary: The inversion method can converge to a solution of the inverse problem in the absence of low-frequency data from an inaccurate initial velocity model even when reflections and refractions are present in the data along with transmitted energy.

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

Symmetry ◽  
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.

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