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 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 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.

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.

Assisting salt model building with reflection full-waveform inversion

2019 ◽  
Vol 7 (2) ◽  
pp. SB43-SB52 ◽  
Author(s):  
Adriano Gomes ◽  
Joe Peterson ◽  
Serife Bitlis ◽  
Chengliang Fan ◽  
Robert Buehring
Keyword(s):  
Model Building ◽  
Waveform Inversion ◽  
Low Frequency ◽  
Velocity Model ◽  
Full Waveform Inversion ◽  
Reflection Data ◽  
Full Waveform ◽  
Velocity Model Building ◽  
Wave Limit ◽  
Rabbit Ears

Inverting for salt geometry using full-waveform inversion (FWI) is a challenging task, mostly due to the lack of extremely low-frequency signal in the seismic data, the limited penetration depth of diving waves using typical acquisition offsets, and the difficulty in correctly modeling the amplitude (and kinematics) of reflection events associated with the salt boundary. However, recent advances in reflection FWI (RFWI) have allowed it to use deep reflection data, beyond the diving-wave limit, by extracting the tomographic term of the FWI reflection update, the so-called rabbit ears. Though lacking the resolution to fully resolve salt geometry, we can use RFWI updates as a guide for refinements in the salt interpretation, adding a partially data-driven element to salt velocity model building. In addition, we can use RFWI to update sediment velocities in complex regions surrounding salt, where ray-based approaches typically struggle. In reality, separating the effects of sediment velocity errors from salt geometry errors is not straightforward in many locations. Therefore, iterations of RFWI plus salt scenario tests may be necessary. Although it is still not the fully automatic method that has been envisioned for FWI, this combined approach can bring significant improvement to the subsalt image, as we examine on field data examples from the Gulf of Mexico.

scholarly journals Optimal coding of blended seismic sources for 2D full waveform inversion in time

2018 ◽  
Vol 8 (2) ◽  
Author(s):  
Katherine Flórez ◽  
Sergio Alberto Abreo Carrillo ◽  
Ana Beatriz Ramírez Silva
Keyword(s):  
Waveform Inversion ◽  
Velocity Model ◽  
Computational Time ◽  
Inversion Method ◽  
Single Shot ◽  
Full Waveform Inversion ◽  
Velocity Models ◽  
Full Waveform ◽  
Seismic Image ◽  
Blended Data

Full Waveform Inversion (FWI) schemes are gradually becoming more common in the oil and gas industry, as a new tool for studying complex geological zones, based on their reliability for estimating velocity models. FWI is a non-linear inversion method that iteratively estimates subsurface characteristics such as seismic velocity, starting from an initial velocity model and the preconditioned data acquired. Blended sources have been used in marine seismic acquisitions to reduce acquisition costs, reducing the number of times that the vessel needs to cross the exploration delineation trajectory. When blended or simultaneous without previous de-blending or separation, stage data are used in the reconstruction of the velocity model with the FWI method, and the computational time is reduced. However, blended data implies overlapping single shot-gathers, producing interference that affects the result of seismic approaches, such as FWI or seismic image migration. In this document, an encoding strategy is developed, which reduces the overlap areas within the blended data to improve the final velocity model with the FWI method.

scholarly journals Full-waveform inversion with extrapolated low-frequency data

Geophysics ◽  
2016 ◽  
Vol 81 (6) ◽  
pp. R339-R348 ◽  
Author(s):  
Yunyue Elita Li ◽  
Laurent Demanet
Keyword(s):  
Waveform Inversion ◽  
Low Frequency ◽  
Velocity Model ◽  
Propagation Model ◽  
Full Waveform Inversion ◽  
Frequency Data ◽  
Local Minima ◽  
Bandwidth Extension ◽  
Low Frequencies ◽  
Full Waveform

The availability of low-frequency data is an important factor in the success of full-waveform inversion (FWI) in the acoustic regime. The low frequencies help determine the kinematically relevant, low-wavenumber components of the velocity model, which are in turn needed to avoid convergence of FWI to spurious local minima. However, acquiring data less than 2 or 3 Hz from the field is a challenging and expensive task. We have explored the possibility of synthesizing the low frequencies computationally from high-frequency data and used the resulting prediction of the missing data to seed the frequency sweep of FWI. As a signal-processing problem, bandwidth extension is a very nonlinear and delicate operation. In all but the simplest of scenarios, it can only be expected to lead to plausible recovery of the low frequencies, rather than their accurate reconstruction. Even so, it still requires a high-level interpretation of band-limited seismic records into individual events, each of which can be extrapolated to a lower (or higher) frequency band from the nondispersive nature of the wave-propagation model. We have used the phase-tracking method for the event separation task. The fidelity of the resulting extrapolation method is typically higher in phase than in amplitude. To demonstrate the reliability of bandwidth extension in the context of FWI, we first used the low frequencies in the extrapolated band as data substitute, to create the low-wavenumber background velocity model, and then we switched to recorded data in the available band for the rest of the iterations. The resulting method, extrapolated FWI, demonstrated surprising robustness to the inaccuracies in the extrapolated low-frequency data. With two synthetic examples calibrated so that regular FWI needs to be initialized at 1 Hz to avoid local minima, we have determined that FWI based on an extrapolated [1, 5] Hz band, itself generated from data available in the [5, 15] Hz band, can produce reasonable estimations of the low-wavenumber velocity models.

Constrained full-waveform inversion by model reparameterization

Geophysics ◽  
2012 ◽  
Vol 77 (2) ◽  
pp. R117-R127 ◽  
Author(s):  
Antoine Guitton ◽  
Gboyega Ayeni ◽  
Esteban Díaz
Keyword(s):  
Waveform Inversion ◽  
Model Space ◽  
Real Data ◽  
Velocity Model ◽  
Full Waveform Inversion ◽  
Coherent Noise ◽  
Low Frequencies ◽  
Full Waveform ◽  
Geological Information ◽  
Ill Posed

The waveform inversion problem is inherently ill-posed. Traditionally, regularization schemes are used to address this issue. For waveform inversion, where the model is expected to have many details reflecting the physical properties of the Earth, regularization and data fitting can work in opposite directions: the former smoothing and the latter adding details to the model. We propose constraining estimated velocity fields by reparameterizing the model. This technique, also called model-space preconditioning, is based on directional Laplacian filters: It preserves most of the details of the velocity model while smoothing the solution along known geological dips. Preconditioning also yields faster convergence at early iterations. The Laplacian filters have the property to smooth or kill local planar events according to a local dip field. By construction, these filters can be inverted and used in a preconditioned waveform inversion strategy to yield geologically meaningful models. We illustrate with 2D synthetic and field data examples how preconditioning with nonstationary directional Laplacian filters outperforms traditional waveform inversion when sparse data are inverted and when sharp velocity contrasts are present. Adding geological information with preconditioning could benefit full-waveform inversion of real data whenever irregular geometry, coherent noise and lack of low frequencies are present.

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 Full-intensity waveform inversion

Geophysics ◽  
2018 ◽  
Vol 83 (6) ◽  
pp. R649-R658 ◽  
Author(s):  
Yike Liu ◽  
Bin He ◽  
Huiyi Lu ◽  
Zhendong Zhang ◽  
Xiao-Bi Xie ◽  
...  
Keyword(s):  
Objective Function ◽  
Waveform Inversion ◽  
Low Frequency ◽  
Velocity Model ◽  
Low Frequencies ◽  
Full Waveform ◽  
Seismic Waveform ◽  
Using Data ◽  
Full Intensity ◽  
Starting Model

Many full-waveform inversion schemes are based on the iterative perturbation theory to fit the observed waveforms. When the observed waveforms lack low frequencies, those schemes may encounter convergence problems due to cycle skipping when the initial velocity model is far from the true model. To mitigate this difficulty, we have developed a new objective function that fits the seismic-waveform intensity, so the dependence of the starting model can be reduced. The waveform intensity is proportional to the square of its amplitude. Forming the intensity using the waveform is a nonlinear operation, which separates the original waveform spectrum into an ultra-low-frequency part and a higher frequency part, even for data that originally do not have low-frequency contents. Therefore, conducting multiscale inversions starting from ultra-low-frequency intensity data can largely avoid the cycle-skipping problem. We formulate the intensity objective function, the minimization process, and the gradient. Using numerical examples, we determine that the proposed method was very promising and could invert for the model using data lacking low-frequency information.

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