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 nonlinear 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 constraints in the optimization problem. This technique is based on a Gauss-Newton sequential quadratic programming approach. At each Gauss-Newton 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. The efficiency of the method is demonstrated on a 2D OBC real data set and on a 3D real data set: the introduction of constraints coming both from well logs and from geological knowledge allows us to reduce the under-determination of both inverse problems.
Article
View Constrained optimization in seismic reflection tomography: an SQP augmented Lagrangian approach