Constrained optimization in seismic reflection tomography: a Gauss-Newton augmented Lagrangian approach

• Published in: Geophysical journal international Vol. 164; no. 3; pp. 670 - 684
• Main Authors: Delbos, F., Gilbert, J. Ch, Glowinski, R., Sinoquet, D.
• Format: Journal Article
• Language: English
• Published: Oxford, UK Blackwell Publishing Ltd 01.03.2006; Blackwell Science Ltd; Oxford University Press (OUP)
• Subjects: Algorithms; augmented Lagrangian; constrained optimization; Earth Sciences; Geology; least-squares approach; Mathematical models; Optimization; ray tracing; Reflection; Sciences of the Universe; Seismic engineering; Seismic phenomena; seismic reflection tomography; SQP algorithm; Tomography; augmented Lagrangian; least-squares approach; ray tracing; SQP algorithm; constrained optimization; seismic reflection tomography
• ISSN: 0956-540X; 1365-246X
• DOI: 10.1111/j.1365-246X.2005.02729.x

Seismic reflection tomography is a method for determining a subsurface velocity model from the traveltimes of seismic waves reflecting on geological interfaces. From an optimization viewpoint, the problem consists in minimizing a non-linear least-squares function measuring the mismatch between observed traveltimes and those calculated by ray tracing in this model. The introduction of a priori information on the model is crucial to reduce the under-determination. The contribution of this paper is to introduce a technique able to take into account geological a priori information in the reflection tomography problem expressed as inequality constraints in the optimization problem. This technique is based on a Gauss-Newton (GN) sequential quadratic programming approach. At each GN step, a solution to a convex quadratic optimization problem subject to linear constraints is computed thanks to an augmented Lagrangian algorithm. Our choice for this optimization method is motivated and its original aspects are described. First applications on real data sets are presented to illustrate the potential of the approach in practical use of reflection tomography.