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High-order optimization methods for large-scale 3D CSEM data inversion

Amaya, Manuel
Doctoral thesis
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http://hdl.handle.net/11250/2365341
Date
2015
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  • Institutt for matematiske fag [1435]
Abstract
Marine controlled-source electromagnetic (CSEM) method is a non-invasive offshore

technique used, in association with magnetotelluric and seismic data, for the

study of the oceanographic lithosphere and hydrocarbon reservoir exploration. CSEM

data are often used in optimization processes that produce an electrical resistivity

imaging of the subsurface. CSEM research shows interest for developing high-order

optimization methods, able to achieve faster convergences without investing too much

manual effort building initial inversion models. As a result, 3D CSEM industry has

started a transition from quasi-Newton to Gauss-Newton methods.

The large numerical complexity is a limiting factor when applying the Gauss-

Newton method for the 3D inversion of CSEM data. These problems can involve

O(106) inversion parameters and O(105) forward simulations, resulting in a Jacobian

matrix of O(100 TB) and a Gauss-Newton Hessian matrix of O(1 TB). There

are some papers that propose methods to reduce the memory complexity and others

that present schemes to reduce the time complexity. However there is not a proposal

to significantly reduce the total numerical complexity of the 3D Gauss-Newton optimization

method without affecting the parameterization of the problem.

The first main contribution of this thesis is a method for obtaining a low-rank

approximation of the Gauss-Newton Hessian matrix that dramatically reduces the numerical

complexity of the 3D CSEM Gauss-Newton optimization without altering the

parameterization of the resistivity models. For large-scale surveys, it can reduce the

number of forward simulations between 10-100 times, and it also reduces the memory

complexity, from O(TB) to O(GB). It is based on simulating groups of distant phaseencoded

sources, instead of single-source simulations. The resultant small number

of simulations motivated the development of a matrix free recursive direct solver to

obtain the model updates at each iteration with a reduced memory usage. A study of

the associated cross-talk noise and inversion results validates this proposal.

The second main contribution of this thesis is the introduction, apparently for the

first time in 3D CSEM, of the Newton and the Halley class methods. This opens the

state-of-the-art frontiers to higher-order methods where the computation of a Green

function per model parameter is required. Initially, the numerical complexity of these

methods makes their use unapproachable. In this research it is concluded that it is possible

to apply these methods with the same memory complexity as in a Gauss-Newton

method, and with a contained time complexity. It is proposed the use of a finitedifference

frequency-domain direct solver for on-the-fly computations of the Green

functions, a reduced memory construction of the systems matrices and the modification

of a trust-region solver to handle the indefiniteness of these matrices. Synthetic

3D CSEM survey inversion results demonstrate the feasibility of this method.
Has parts
Paper 1: Amaya Benitez, Manuel; Boman, Linus; Morten, Jan Petter. A Low-rank Approximation to the Hessian for 3D CSEM Gauss-Newton Inversion. EAGE Conferences & Exhibitions - The final published version is available at http://dx.doi.org/10.3997/2214-4609.20141099

Paper 2: Amaya Benitez, Manuel; Morten, Jan Petter; Boman, Linus. Efficient computation of approximate low-rank Hessian for 3D CSEM inversion. SEG annual meeting; 2014 - The final published version is available at http://dx.doi.org/10.1190/segam2014-0493.1

Paper 3: Manuel Amaya, Jan Petter Morten, and Linus Boman., A low-rank approximation for large-scale 3D CSEM Gauss-Newton inversion

Paper 4: M. Amaya, K. R. Hansen and J.P. Morten., 3D CSEM data inversion using Newton and Halley class methods - This is an author-created, un-copyedited version of an article accepted for publication/published in [insert name of journal]. IOP Publishing Ltd is not responsible for any errors or omissions in this version of the manuscript or any version derived from it
Publisher
NTNU
Series
Doctoral thesis at NTNU;2015:273

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