Full-waveform inversion with an exponentially encoded optimal-transport norm

2017 ◽  
Author(s):  
Lingyun Qiu ◽  
Jaime Ramos-Martínez ◽  
Alejandro Valenciano ◽  
Yunan Yang ◽  
Björn Engquist
Keyword(s):  
Optimal Transport ◽  
Waveform Inversion ◽  
Full Waveform Inversion ◽  
Full Waveform

A Graph-Space Optimal Transport Approach for Full Waveform Inversion

2018 ◽  
Author(s):  
L. Metivier ◽  
A. Allain ◽  
R. Brossier ◽  
Q. Merigot ◽  
E. Oudet ◽  
...  
Keyword(s):  
Optimal Transport ◽  
Waveform Inversion ◽  
Full Waveform Inversion ◽  
Full Waveform ◽  
Transport Approach

scholarly journals Increasing the robustness and applicability of full-waveform inversion: An optimal transport distance strategy

2016 ◽  
Vol 35 (12) ◽  
pp. 1060-1067 ◽  
Author(s):  
L. Métivier ◽  
R. Brossier ◽  
Q. Mérigot ◽  
E. Oudet ◽  
J. Virieux
Keyword(s):  
Optimal Transport ◽  
Waveform Inversion ◽  
Full Waveform Inversion ◽  
Transport Distance ◽  
Full Waveform

A graph-space approach to optimal transport for full-waveform inversion

2018 ◽  
Author(s):  
L. Métivier ◽  
A. Allain ◽  
R. Brossier ◽  
Q. Mérigot ◽  
E. Oudet ◽  
...  
Keyword(s):  
Optimal Transport ◽  
Waveform Inversion ◽  
Full Waveform Inversion ◽  
Full Waveform ◽  
Space Approach

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.

Optimal Transport Full Waveform Inversion - Applications

2020 ◽  
Author(s):  
D. Carotti ◽  
O. Hermant ◽  
S. Masclet ◽  
M. Reinier ◽  
J. Messud ◽  
...  
Keyword(s):  
Optimal Transport ◽  
Waveform Inversion ◽  
Full Waveform Inversion ◽  
Full Waveform

scholarly journals Application of optimal transport and the quadratic Wasserstein metric to full-waveform inversion

Geophysics ◽  
2018 ◽  
Vol 83 (1) ◽  
pp. R43-R62 ◽  
Author(s):  
Yunan Yang ◽  
Björn Engquist ◽  
Junzhe Sun ◽  
Brittany F. Hamfeldt
Keyword(s):  
Least Squares ◽  
Optimal Transport ◽  
Waveform Inversion ◽  
Transportation Cost ◽  
Velocity Model ◽  
Seismic Inversion ◽  
Full Waveform Inversion ◽  
Wasserstein Metric ◽  
Full Waveform ◽  
Adjoint State

Conventional full-waveform inversion (FWI) using the least-squares norm as a misfit function is known to suffer from cycle-skipping issues that increase the risk of computing a local rather than the global minimum of the misfit. The quadratic Wasserstein metric has proven to have many ideal properties with regard to convexity and insensitivity to noise. When the observed and predicted seismic data are considered to be two density functions, the quadratic Wasserstein metric corresponds to the optimal cost of rearranging one density into the other, in which the transportation cost is quadratic in distance. Unlike the least-squares norm, the quadratic Wasserstein metric measures not only amplitude differences but also global phase shifts, which helps to avoid cycle-skipping issues. We have developed a new way of using the quadratic Wasserstein metric trace by trace in FWI and compare it with the global quadratic Wasserstein metric via the solution of the Monge-Ampère equation. We incorporate the quadratic Wasserstein metric technique into the framework of the adjoint-state method and apply it to several 2D examples. With the corresponding adjoint source, the velocity model can be updated using a quasi-Newton method. Numerical results indicate the effectiveness of the quadratic Wasserstein metric in alleviating cycle-skipping issues and sensitivity to noise. The mathematical theory and numerical examples demonstrate that the quadratic Wasserstein metric is a good candidate for a misfit function in seismic inversion.

Optimal transport for mitigating cycle skipping in full-waveform inversion: A graph-space transform approach

Geophysics ◽  
2018 ◽  
Vol 83 (5) ◽  
pp. R515-R540 ◽  
Author(s):  
Ludovic Métivier ◽  
Aude Allain ◽  
Romain Brossier ◽  
Quentin Mérigot ◽  
Edouard Oudet ◽  
...  
Keyword(s):  
Seismic Data ◽  
Optimal Transport ◽  
Waveform Inversion ◽  
P Wave ◽  
Imaging Method ◽  
Convexity Property ◽  
Full Waveform Inversion ◽  
Low Frequencies ◽  
Transport Distance ◽  
Full Waveform

Optimal transport distance has been recently promoted as a tool to measure the discrepancy between observed and seismic data within the full-waveform-inversion strategy. This high-resolution seismic imaging method, based on a data-fitting procedure, suffers from the nonconvexity of the standard least-squares discrepancy measure, an issue commonly referred to as cycle skipping. The convexity of the optimal transport distance with respect to time shifts makes it a good candidate to provide a more convex misfit function. However, the optimal transport distance is defined only for the comparison of positive functions, while seismic data are oscillatory. A review of the different attempts proposed in the literature to overcome this difficulty is proposed. Their limitations are illustrated: Basically, the proposed strategies are either not applicable to real data, or they lose the convexity property of optimal transport. On this basis, we introduce a novel strategy based on the interpretation of the seismic data in the graph space. Each individual trace is considered, after discretization, as a set of Dirac points in a 2D space, where the amplitude becomes a geometric attribute of the data. This ensures the positivity of the data, while preserving the geometry of the signal. The differentiability of the misfit function is obtained by approximating the Dirac distributions through 2D Gaussian functions. The interest of this approach is illustrated numerically by computing misfit-function maps in schematic examples before moving to more realistic synthetic full-waveform exercises, including the Marmousi model. The better convexity of the graph-based optimal transport distance is shown. On the Marmousi model, starting from a 1D linearly increasing initial model, with data without low frequencies (no energy less than 3 Hz), a meaningful estimation of the P-wave velocity model is recovered, outperforming previously proposed optimal-transport-based misfit functions.

Acoustic Land Full Waveform Inversion on a Broadband Land Dataset: the Impact of Optimal Transport

2019 ◽  
Author(s):  
A. Sedova ◽  
J. Messud ◽  
H. Prigent ◽  
S. Masclet ◽  
G. Royle ◽  
...  
Keyword(s):  
Optimal Transport ◽  
Waveform Inversion ◽  
Full Waveform Inversion ◽  
Full Waveform ◽  
The Impact

scholarly journals Measuring the misfit between seismograms using an optimal transport distance: application to full waveform inversion

2016 ◽  
Vol 205 (1) ◽  
pp. 345-377 ◽  
Author(s):  
L. Métivier ◽  
R. Brossier ◽  
Q. Mérigot ◽  
E. Oudet ◽  
J. Virieux
Keyword(s):  
Optimal Transport ◽  
Waveform Inversion ◽  
Full Waveform Inversion ◽  
Transport Distance ◽  
Full Waveform
Sign in / Sign up

Export Citation Format

Share Document