A limited-memory quasi-Newton inversion for 1D magnetotellurics

Geophysics ◽  
2006 ◽  
Vol 71 (5) ◽  
pp. G191-G196 ◽  
Author(s):  
Anna Avdeeva ◽  
Dmitry Avdeev
Keyword(s):  
Inverse Problem ◽  
Large Scale ◽  
Convergence Rates ◽  
Earth Model ◽  
Problem Solution ◽  
Data Set ◽  
Electromagnetic Problems ◽  
Limited Memory ◽  
Conductivity Structure ◽  
Quasi Newton

We apply a limited-memory quasi-Newton (QN) method to the 1D magnetotelluric (MT) inverse problem. Using this method we invert a realistic synthetic MT impedance data set calculated for a layered earth model. The calculation of gradients based on the adjoint method speeds up the inverse problem solution many times. In addition, regularization stabilizes the QN inversion result and a few correction pairs are sufficient to produce reasonable results. Comparison with the L-BFGS-B algorithm shows similar convergence rates. This study is a first step towards the solution of large-scale electromagnetic problems, with a full treatment of the 3D conductivity structure of the earth.

scholarly journals The Adjoint Method for the Inverse Problem of Option Pricing

2014 ◽  
Vol 2014 ◽  
pp. 1-7 ◽  
Author(s):  
Shou-Lei Wang ◽  
Yu-Fei Yang ◽  
Yu-Hua Zeng
Keyword(s):  
Inverse Problem ◽  
Option Pricing ◽  
Implied Volatility ◽  
Adjoint Method ◽  
Numerical Examples ◽  
Limited Memory ◽  
Minimization Procedure ◽  
Volatility Function ◽  
The Cost ◽  
Quasi Newton

The estimation of implied volatility is a typical PDE inverse problem. In this paper, we propose theTV-L1model for identifying the implied volatility. The optimal volatility function is found by minimizing the cost functional measuring the discrepancy. The gradient is computed via the adjoint method which provides us with an exact value of the gradient needed for the minimization procedure. We use the limited memory quasi-Newton algorithm (L-BFGS) to find the optimal and numerical examples shows the effectiveness of the presented method.

Improving teleseismic event locations using a three-dimensional Earth model

1996 ◽  
Vol 86 (3) ◽  
pp. 788-796 ◽  
Author(s):  
Gideon P. Smith ◽  
Göran Ekström
Keyword(s):  
Large Scale ◽  
Three Dimensional ◽  
The United States ◽  
Earth Model ◽  
Published Data ◽  
S Wave ◽  
Origin Time ◽  
Data Set ◽  
Station Corrections ◽  
Earth Models

Abstract A comparison is made between seismic event locations derived from standard spherically symmetric Earth models (JB, PREM, IASP91) and a recent Earth model (S&P12/WM13) that incorporates large-scale lateral heterogeneity of P- and S-wave velocities in the mantle. Events with known hypocentral coordinates are located in the different Earth models using standard methods. Two sets of events are considered: a data set of 26 explosions, including primarily nuclear weapons test explosions and peaceful nuclear explosions in the United States and former USSR; and a published data set of 82 well-located earthquakes with a more even global distribution. IASP91 and PREM are shown to offer similar errors in event location and origin time estimates with respect to the JB model. The three-dimensional (3D) model S&P12/WM13 offers improvement in event locations over all three one-dimensional (1D) models with, or without, station corrections. For the explosion events, the average mislocation distance is reduced by approximately 40%; for the earthquakes, the improvements are smaller. Corrections for crustal thickness beneath source and receiver are found to be of similar magnitude to the mantle corrections, but use of station corrections together with the three-dimensional mantle model provide the best locations.

scholarly journals A Newton-Like Trust Region Method for Large-Scale Unconstrained Nonconvex Minimization

2013 ◽  
Vol 2013 ◽  
pp. 1-6 ◽  
Author(s):  
Yang Weiwei ◽  
Yang Yueting ◽  
Zhang Chenhui ◽  
Cao Mingyuan
Keyword(s):  
Large Scale ◽  
Trust Region Method ◽  
Trust Region ◽  
Test Problems ◽  
Nonconvex Minimization ◽  
Trust Region Subproblem ◽  
Newton Equation ◽  
Limited Memory ◽  
Quasi Newton ◽  
Approximate Hessian

We present a new Newton-like method for large-scale unconstrained nonconvex minimization. And a new straightforward limited memory quasi-Newton updating based on the modified quasi-Newton equation is deduced to construct the trust region subproblem, in which the information of both the function value and gradient is used to construct approximate Hessian. The global convergence of the algorithm is proved. Numerical results indicate that the proposed method is competitive and efficient on some classical large-scale nonconvex test problems.

scholarly journals On solving large-scale limited-memory quasi-Newton equations

2017 ◽  
Vol 515 ◽  
pp. 196-225 ◽  
Author(s):  
Jennifer B. Erway ◽  
Roummel F. Marcia
Keyword(s):  
Large Scale ◽  
Limited Memory ◽  
Quasi Newton

Two-dimensional anisotropic magnetotelluric inversion using a limited-memory quasi-Newton method

Geophysics ◽  
2021 ◽  
pp. 1-71
Author(s):  
Guo Yu ◽  
Colin G. Farquharson ◽  
Qibin Xiao ◽  
Man Li
Keyword(s):  
Inverse Problem ◽  
Objective Function ◽  
Hessian Matrix ◽  
Two Dimensional ◽  
Inversion Algorithm ◽  
Anisotropic Models ◽  
Limited Memory ◽  
Iterative Minimization ◽  
Special Cases ◽  
Quasi Newton

We have developed a two-dimensional (2D) anisotropic magnetotelluric (MT) inversion algorithm that uses a limited-memory quasi-Newton (QN) method for bounds-constrained optimization. This algorithm solves the inverse problem, which is non-linear, by iterative minimization of linearized approximations of the classical Tikhonov regularized objective function. The QN approximation for the Hessian matrix is only implemented for the data-misfit term of the objective function; the part of the Hessian matrix for the regularization is explicitly computed. This adjustment results in a better approximation for the data-misfit term in particular. The inversion algorithm considers arbitrary anisotropy, and is extended for special cases including azimuthal and vertical anisotropy. The algorithm is shown to be stable and converges rapidly for several simple anisotropic models. These synthetic tests also confirm that the anisotropic inversion produces a correct anomaly with different but equivalent anisotropic parameters. We also consider a complex 2D anisotropic model; the successful results for this model further confirm that the inversion algorithm presented here, which uses the novel modified limited-memory QN approach, is capable of solving the 2D anisotropic magnetotelluric inverse problem. Finally, we present a practical application on MT data collected in northern Tibet to demonstrate the effectiveness and stability of our algorithm.

Sign in / Sign up

Export Citation Format

Share Document