The noise conjugate gradient method reduces the saddle point problem in full waveform inversion

2018 ◽  
Author(s):  
Zhang Jiannan ◽  
Sun leiming ◽  
Dan Zhiwei ◽  
Li Sanfu ◽  
Zeng Weihui
Keyword(s):  
Saddle Point ◽  
Conjugate Gradient Method ◽  
Conjugate Gradient ◽  
Gradient Method ◽  
Waveform Inversion ◽  
Saddle Point Problem ◽  
Point Problem ◽  
Full Waveform Inversion ◽  
Full Waveform

scholarly journals The conjugate gradient method

2018 ◽  
Vol 37 (4) ◽  
pp. 296-298 ◽  
Author(s):  
Karl Schleicher
Keyword(s):  
Least Squares ◽  
Conjugate Gradient Method ◽  
Conjugate Gradient ◽  
Gradient Method ◽  
Waveform Inversion ◽  
Linear Inversion ◽  
Large Computer ◽  
Traveltime Tomography ◽  
Full Waveform ◽  
Least Squares Migration

The conjugate gradient method can be used to solve many large linear geophysical problems — for example, least-squares parabolic and hyperbolic Radon transform, traveltime tomography, least-squares migration, and full-waveform inversion (FWI) (e.g., Witte et al., 2018 ). This tutorial revisits the “Linear inversion tutorial” ( Hall, 2016 ) that estimated reflectivity by deconvolving a known wavelet from a seismic trace using least squares. This tutorial solves the same problem using the conjugate gradient method. This problem is easy to understand, and the concepts apply to other applications. The conjugate gradient method is often used to solve large problems because the least-squares algorithm is much more expensive — that is, even a large computer may not be able to find a useful solution in a reasonable amount of time.

Full waveform inversion by deconvolution gradient method

2012 ◽  
Author(s):  
Fuchun Gao ◽  
Paul Williamson ◽  
Henri Houllevigue
Keyword(s):  
Gradient Method ◽  
Waveform Inversion ◽  
Full Waveform Inversion ◽  
Full Waveform

Conjugate Gradient Method for Rank Deficient Saddle Point Problems

2004 ◽  
Vol 35 (2-4) ◽  
pp. 139-154 ◽  
Author(s):  
X. Wu ◽  
B.P.B. Silva ◽  
J.Y. Yuan
Keyword(s):  
Saddle Point ◽  
Conjugate Gradient Method ◽  
Conjugate Gradient ◽  
Gradient Method ◽  
Saddle Point Problems

Accelerating Hessian-free Gauss-Newton full-waveform inversion via l-BFGS preconditioned conjugate-gradient algorithm

Geophysics ◽  
2017 ◽  
Vol 82 (2) ◽  
pp. R49-R64 ◽  
Author(s):  
Wenyong Pan ◽  
Kristopher A. Innanen ◽  
Wenyuan Liao
Keyword(s):  
Conjugate Gradient ◽  
Random Noise ◽  
Waveform Inversion ◽  
Initial Guess ◽  
Gradient Algorithm ◽  
Preconditioned Conjugate Gradient ◽  
Model Parameters ◽  
Full Waveform Inversion ◽  
Numerical Examples ◽  
Full Waveform

Full-waveform inversion (FWI) has emerged as a powerful strategy for estimating subsurface model parameters by iteratively minimizing the difference between synthetic data and observed data. The Hessian-free (HF) optimization method represents an attractive alternative to Newton-type and gradient-based optimization methods. At each iteration, the HF approach obtains the search direction by approximately solving the Newton linear system using a matrix-free conjugate-gradient (CG) algorithm. The main drawback with HF optimization is that the CG algorithm requires many iterations. In our research, we develop and compare different preconditioning schemes for the CG algorithm to accelerate the HF Gauss-Newton (GN) method. Traditionally, preconditioners are designed as diagonal Hessian approximations. We additionally use a new pseudo diagonal GN Hessian as a preconditioner, making use of the reciprocal property of Green’s function. Furthermore, we have developed an [Formula: see text]-BFGS inverse Hessian preconditioning strategy with the diagonal Hessian approximations as an initial guess. Several numerical examples are carried out. We determine that the quasi-Newton [Formula: see text]-BFGS preconditioning scheme with the pseudo diagonal GN Hessian as the initial guess is most effective in speeding up the HF GN FWI. We examine the sensitivity of this preconditioning strategy to random noise with numerical examples. Finally, in the case of multiparameter acoustic FWI, we find that the [Formula: see text]-BFGS preconditioned HF GN method can reconstruct velocity and density models better and more efficiently compared with the nonpreconditioned method.

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