Estimating a starting model for full-waveform inversion using a global optimization method

Geophysics ◽  
2016 ◽  
Vol 81 (4) ◽  
pp. R211-R223 ◽  
Author(s):  
Debanjan Datta ◽  
Mrinal K. Sen
Keyword(s):  
Global Optimization ◽  
Local Minimum ◽  
Waveform Inversion ◽  
Synthetic Data ◽  
Velocity Model ◽  
Optimization Method ◽  
Full Waveform Inversion ◽  
Global Optimization Method ◽  
Full Waveform ◽  
Starting Model

Full-waveform inversion (FWI) has become a popular method to estimate elastic earth properties from seismograms. It is formulated as a data-fitting least-squares minimization problem that iteratively updates an initial velocity model with the scaled gradient of the misfit until a satisfactory match between the real and synthetic data is obtained. However, such a local optimization approach can converge to a local minimum if the starting model used is not close enough to an optimal model. We have developed a two-step process in which we first estimate a starting model using a global optimization method. Unlike local optimization methods, a global optimization method starts with a random starting model and is not generally susceptible to be trapped in a local minimum. The starting model for FWI that we aim to estimate is sparsely parameterized and contains a set of interfaces and velocities that are used to represent the entire velocity model. We have obtained the depth of the interfaces and the velocities by minimizing the data misfit in the least-squares sense using a global optimization method called very fast simulated annealing (VFSA). Once the sparse velocity model was obtained from VFSA, we used that as a starting model in a conventional gradient-based FWI to obtain the final model. We have applied the proposed method to one synthetic data set and two field data sets from offshore India. The proposed method was able to estimate a velocity model that was not cycle skipped for realistic frequency bands. We have demonstrated that with the proper choice of model parameterization and optimization parameters, the global and gradient optimization algorithms converge in a finite number of iterations. We have determined that the resulting algorithm is computationally feasible in two dimensions and accurate for practical implementation of FWI.

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.

Source-domain full waveform inversions

Geophysics ◽  
2020 ◽  
pp. 1-50
Author(s):  
Yulang Wu ◽  
George A. McMechan
Keyword(s):  
Differential Operators ◽  
Waveform Inversion ◽  
Synthetic Data ◽  
Velocity Model ◽  
Low Noise ◽  
Full Waveform Inversion ◽  
Virtual Source ◽  
Reflected Waves ◽  
Source Domain ◽  
Full Waveform

Conventional full waveform inversion (FWI) updates a velocity model by minimizing the data residuals between predicted and observed data, at the receiver positions. We propose a new full waveform inversion to update the velocity model by minimizing virtual source artifacts, at the receiver positions, in the source domain (SFWI). Virtual source artifacts are created by replacing the propagating source wavefield by the forward-time observed data at the receiver positions, as a data-residual constraint. Therefore, no matter whether the velocity model is correct or not, the data residuals, at the receiver positions, are always forced to be zero. If the velocity model is correct, this data-residual constraint has no effect on the wavefield, since the predicted data is the same as the observed data. However, if the estimated velocity model is incorrect, the mismatch between the replaced forward-time observed data and the incorrect predicted upgoing waves (e.g., reflected waves) at the receiver positions, will produce downgoing artifact waves. Thus, the data-residual constraint behaves as a virtual source to create artifact wavefields. By minimizing the virtual source artifacts (equivalent to producing the artifact wavefield), the velocity model can be iteratively updated toward the true velocity model. Similar to conventional FWI, SFWI can be implemented in either the frequency or the time domain, which is unlike previous source-domain solutions, which have to be implemented only in the frequency domain, to solve the normal equations. SFWI does more over-fitting of noisy observed data than conventional FWI does, because noise is amplified by the differential operators when calculating the virtual source artifacts. Tests on synthetic data show that the SFWI inverts for the velocity model more accurately than conventional FWI for noise-free or low-noise data.

scholarly journals Full waveform inversion in time and frequency domain of velocity modeling in seismic imaging: FWISIMAT a Matlab code

2018 ◽  
Vol 22 (4) ◽  
pp. 291-300
Author(s):  
Sagar Singh ◽  
Ali Ismet Kanli ◽  
Sagarika Mukhopadhyay
Keyword(s):  
Frequency Domain ◽  
Seismic Imaging ◽  
Waveform Inversion ◽  
Velocity Model ◽  
Full Waveform Inversion ◽  
Initial Model ◽  
Final Model ◽  
Full Waveform ◽  
True Model ◽  
Starting Model

This paper investigates the capability of acoustic Full Waveform Inversion (FWI) in building Marmousi velocity model, in time and frequency domain. FWI is an iterative minimization of misfit between observed and calculated data which is generally solved in three segments: forward modeling, which numerically solves the wave equation with an initial model, gradient computation of the objective function, and updating the model parameters, with a valid optimization method. FWI codes developed in MATLAB herein FWISIMAT (Full Waveform Inversion in Seismic Imaging using MATLAB) are successfully implemented using the Marmousi velocity model as the true model. An initial model is obtained by smoothing the true model to initiate FWI procedure. Smoothing ensures an adequate starting model for FWI, as the FWI procedure is known to be sensitive on the starting model. The final model is compared with the true model to review the number of recovered velocities. FWI codes developed in MATLAB herein FWISIMAT (Full Waveform Inversion in Seismic Imaging using MATLAB) are successfully implemented usingMarmousi velocity model astrue model. An initial model is derived from smoothing the true model to initiate FWI procedure. Smoothing ensures an adequate starting model for FWI, as the FWI procedure is known to be sensitive onstarting model. The final model is compared with the true model to review theamount of recovered velocities. 

scholarly journals Skeletonized wave-equation inversion in vertical symmetry axis media without too much math

2017 ◽  
Vol 5 (3) ◽  
pp. SO21-SO30 ◽  
Author(s):  
Shihang Feng ◽  
Gerard T. Schuster
Keyword(s):  
Wave Equation ◽  
Symmetry Axis ◽  
Waveform Inversion ◽  
Synthetic Data ◽  
Full Waveform Inversion ◽  
Data Set ◽  
Traveltime Inversion ◽  
Anisotropic Models ◽  
Full Waveform ◽  
Starting Model

We have developed a tutorial for skeletonized inversion of pseudo-acoustic anisotropic vertical symmetry axis (VTI) data. We first invert for the anisotropic models using wave-equation traveltime inversion. Here, the skeletonized data are the traveltimes of transmitted and/or reflected arrivals that lead to simpler misfit functions and more robust convergence compared with full-waveform inversion. This provides a good starting model for waveform inversion. The effectiveness of this procedure is illustrated with synthetic data examples and a marine data set recorded in the Gulf of Mexico.

scholarly journals From tomography to full-waveform inversion with a single objective function

Geophysics ◽  
2014 ◽  
Vol 79 (2) ◽  
pp. R55-R61 ◽  
Author(s):  
Tariq Alkhalifah ◽  
Yunseok Choi
Keyword(s):  
Objective Function ◽  
Initial Velocity ◽  
Waveform Inversion ◽  
Synthetic Data ◽  
Velocity Model ◽  
Full Waveform Inversion ◽  
Half Cycle ◽  
Velocity Models ◽  
Full Waveform ◽  
Single Objective

In full-waveform inversion (FWI), a gradient-based update of the velocity model requires an initial velocity that produces synthetic data that are within a half-cycle, everywhere, from the field data. Such initial velocity models are usually extracted from migration velocity analysis or traveltime tomography, among other means, and are not guaranteed to adhere to the FWI requirements for an initial velocity model. As such, we evaluated an objective function based on the misfit in the instantaneous traveltime between the observed and modeled data. This phase-based attribute of the wavefield, along with its phase unwrapping characteristics, provided a frequency-dependent traveltime function that was easy to use and quantify, especially compared to conventional phase representation. With a strong Laplace damping of the modeled, potentially low-frequency, data along the time axis, this attribute admitted a first-arrival traveltime that could be compared with picked ones from the observed data, such as in wave equation tomography (WET). As we relax the damping on the synthetic and observed data, the objective function measures the misfit in the phase, however unwrapped. It, thus, provided a single objective function for a natural transition from WET to FWI. A Marmousi example demonstrated the effectiveness of the approach.

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 Adaptive waveform inversion: Theory

Geophysics ◽  
2016 ◽  
Vol 81 (6) ◽  
pp. R429-R445 ◽  
Author(s):  
Michael Warner ◽  
Lluís Guasch
Keyword(s):  
Waveform Inversion ◽  
Computational Cost ◽  
Synthetic Data ◽  
Velocity Model ◽  
Seismic Inversion ◽  
New Method ◽  
Low Frequencies ◽  
Full Waveform ◽  
True Model ◽  
Starting Model

Conventional full-waveform seismic inversion attempts to find a model of the subsurface that is able to predict observed seismic waveforms exactly; it proceeds by minimizing the difference between the observed and predicted data directly, iterating in a series of linearized steps from an assumed starting model. If this starting model is too far removed from the true model, then this approach leads to a spurious model in which the predicted data are cycle skipped with respect to the observed data. Adaptive waveform inversion (AWI) provides a new form of full-waveform inversion (FWI) that appears to be immune to the problems otherwise generated by cycle skipping. In this method, least-squares convolutional filters are designed that transform the predicted data into the observed data. The inversion problem is formulated such that the subsurface model is iteratively updated to force these Wiener filters toward zero-lag delta functions. As that is achieved, the predicted data evolve toward the observed data and the assumed model evolves toward the true model. This new method is able to invert synthetic data successfully, beginning from starting models and under conditions for which conventional FWI fails entirely. AWI has a similar computational cost to conventional FWI per iteration, and it appears to converge at a similar rate. The principal advantages of this new method are that it allows waveform inversion to begin from less-accurate starting models, does not require the presence of low frequencies in the field data, and appears to provide a better balance between the influence of refracted and reflected arrivals upon the final-velocity model. The AWI is also able to invert successfully when the assumed source wavelet is severely in error.

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