Controlled-order multiple waveform inversion

Geophysics ◽  
2020 ◽  
Vol 85 (3) ◽  
pp. R243-R250 ◽  
Author(s):  
Yike Liu ◽  
Bin He ◽  
Yingcai Zheng
Keyword(s):  
Wave Propagation ◽  
Objective Function ◽  
Waveform Inversion ◽  
Full Waveform Inversion ◽  
Initial Model ◽  
Numerical Examples ◽  
Full Waveform ◽  
Wide Range ◽  
True Model ◽  
The Difference

Traditional full-waveform inversion (FWI) seeks to find the best model by minimizing an objective function defined as the difference between the model-predicted and observed data in amplitude and phase. In principle, FWI should fit all wave types including direct waves, diving waves, primaries, and multiples. However, when an initial model is far from the true model, FWI will encounter difficulties in matching multiples. Physically, multiples may contain more subsurface information compared to primary and diving waves. Multiples cover a wide range of reflection angles during wave propagation and offer the advantage of imaging the shadow zones that cannot be reached or are poorly illuminated by primary reflections. We have developed a new method of waveform inversion using multiples. We first separate the multiples into different orders. The objective function we seek to minimize consists of the data difference between the modeled data using a lower order multiple as the source and the higher order multiple as data. This method is called controlled-order multiple waveform inversion (CMWI). Our numerical examples determined that the CMWI is a promising method to improve velocity updates.

scholarly journals Land seismic multiparameter full waveform inversion in elastic VTI media by simultaneously interpreting body waves and surface waves with an optimal transport based objective function

2019 ◽  
Vol 219 (3) ◽  
pp. 1970-1988 ◽  
Author(s):  
Weiguang He ◽  
Romain Brossier ◽  
Ludovic Métivier ◽  
René-Édouard Plessix
Keyword(s):  
Objective Function ◽  
Surface Waves ◽  
Least Squares ◽  
Optimal Transport ◽  
Waveform Inversion ◽  
Body Waves ◽  
Model Parameters ◽  
Full Waveform Inversion ◽  
Initial Model ◽  
Full Waveform

SUMMARY Land seismic multiparameter full waveform inversion in anisotropic media is challenging because of high medium contrasts and surface waves. With a data-residual least-squares objective function, the surface wave energy usually masks the body waves and the gradient of the objective function exhibits high values in the very shallow depths preventing from recovering the deeper part of the earth model parameters. The optimal transport objective function, coupled with a Gaussian time-windowing strategy, allows to overcome this issue by more focusing on phase shifts and by balancing the contributions of the different events in the adjoint-source and the gradients. We first illustrate the advantages of the optimal transport function with respect to the least-squares one, with two realistic examples. We then discuss a vertical transverse isotropic (VTI) example starting from a quasi 1-D isotropic initial model. Despite some cycle-skipping issues in the initial model, the inversion based on the windowed optimal transport approach converges. Both the near-surface complexities and the variations at depth are recovered.

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. 

Objective-Function Behavior in Acoustic Full-Waveform Inversion

2013 ◽  
Vol 56 (5) ◽  
pp. 685-703
Author(s):  
DONG Liang-Guo ◽  
CHI Ben-Xin ◽  
TAO Ji-Xia ◽  
LIU Yu-Zhu
Keyword(s):  
Objective Function ◽  
Waveform Inversion ◽  
Full Waveform Inversion ◽  
Full Waveform

scholarly journals Accelerating Numerical Wave Propagation by Wavefield Adapted Meshes, Part II: Full-Waveform Inversion

2019 ◽  
Author(s):  
Solvi Thrastarson ◽  
Martin van Driel ◽  
Lion Krischer ◽  
Dirk-Philip van Herwaarden ◽  
Christian Boehm ◽  
...  
Keyword(s):  
Wave Propagation ◽  
Waveform Inversion ◽  
Full Waveform Inversion ◽  
Full Waveform ◽  
Numerical Wave

3D elastic full-waveform inversion of surface waves in the presence of irregular topography using an envelope-based misfit function

Geophysics ◽  
2018 ◽  
Vol 83 (1) ◽  
pp. R1-R11 ◽  
Author(s):  
Dmitry Borisov ◽  
Ryan Modrak ◽  
Fuchun Gao ◽  
Jeroen Tromp
Keyword(s):  
Surface Wave ◽  
Objective Function ◽  
Surface Waves ◽  
Large Scale ◽  
Body Wave ◽  
Waveform Inversion ◽  
Full Waveform Inversion ◽  
S Wave ◽  
Near Surface ◽  
Full Waveform

Full-waveform inversion (FWI) is a powerful method for estimating the earth’s material properties. We demonstrate that surface-wave-driven FWI is well-suited to recovering near-surface structures and effective at providing S-wave speed starting models for use in conventional body-wave FWI. Using a synthetic example based on the SEG Advanced Modeling phase II foothills model, we started with an envelope-based objective function to invert for shallow large-scale heterogeneities. Then we used a waveform-difference objective function to obtain a higher-resolution model. To accurately model surface waves in the presence of complex tomography, we used a spectral-element wave-propagation solver. Envelope misfit functions are found to be effective at minimizing cycle-skipping issues in surface-wave inversions, and surface waves themselves are found to be useful for constraining complex near-surface features.

Full-waveform inversion with borehole constraints for elastic VTI media

Geophysics ◽  
2020 ◽  
Vol 85 (6) ◽  
pp. R553-R563
Author(s):  
Sagar Singh ◽  
Ilya Tsvankin ◽  
Ehsan Zabihi Naeini
Keyword(s):  
Objective Function ◽  
Reservoir Characterization ◽  
Waveform Inversion ◽  
Low Frequency ◽  
Rock Physics ◽  
Anisotropic Media ◽  
Full Waveform Inversion ◽  
Full Waveform ◽  
Trade Offs ◽  
Vti Media

The nonlinearity of full-waveform inversion (FWI) and parameter trade-offs can prevent convergence toward the actual model, especially for elastic anisotropic media. The problems with parameter updating become particularly severe if ultra-low-frequency seismic data are unavailable, and the initial model is not sufficiently accurate. We introduce a robust way to constrain the inversion workflow using borehole information obtained from well logs. These constraints are included in the form of rock-physics relationships for different geologic facies (e.g., shale, sand, salt, and limestone). We develop a multiscale FWI algorithm for transversely isotropic media with a vertical symmetry axis (VTI media) that incorporates facies information through a regularization term in the objective function. That term is updated during the inversion by using the models obtained at the previous inversion stage. To account for lateral heterogeneity between sparse borehole locations, we use an image-guided smoothing algorithm. Numerical testing for structurally complex anisotropic media demonstrates that the facies-based constraints may ensure the convergence of the objective function towards the global minimum in the absence of ultra-low-frequency data and for simple (even 1D) initial models. We test the algorithm on clean data and on surface records contaminated by Gaussian noise. The algorithm also produces a high-resolution facies model, which should be instrumental in reservoir characterization.

scholarly journals Full-waveform inversion, Part 3: Optimization

2018 ◽  
Vol 37 (2) ◽  
pp. 142-145 ◽  
Author(s):  
Philipp Witte ◽  
Mathias Louboutin ◽  
Keegan Lensink ◽  
Michael Lange ◽  
Navjot Kukreja ◽  
...  
Keyword(s):  
Objective Function ◽  
Wave Equations ◽  
Waveform Inversion ◽  
Full Waveform Inversion ◽  
Acoustic Wave Equation ◽  
Automated Generation ◽  
Domain Specific ◽  
Full Waveform ◽  
Adjoint State ◽  
Adjoint State Method

This tutorial is the third part of a full-waveform inversion (FWI) tutorial series with a step-by-step walkthrough of setting up forward and adjoint wave equations and building a basic FWI inversion framework. For discretizing and solving wave equations, we use Devito ( http://www.opesci.org/devito-public ), a Python-based domain-specific language for automated generation of finite-difference code ( Lange et al., 2016 ). The first two parts of this tutorial ( Louboutin et al., 2017 , 2018 ) demonstrated how to solve the acoustic wave equation for modeling seismic shot records and how to compute the gradient of the FWI objective function using the adjoint-state method. With these two key ingredients, we will now build an inversion framework that can be used to minimize the FWI least-squares objective function.

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