文件列表:

tomo (0, 2018-10-01)
tomo\.__afs169E (0, 2006-11-28)
tomo\.travel_times.m.swp (12288, 2006-11-29)
tomo\bgls_interface.dat (20989, 2018-11-18)
tomo\bgls_ttimes.dat (30048, 2018-11-18)
tomo\make_data.m (4744, 2006-11-29)
tomo\travel_times.m (1563, 2006-11-29)
tomo\ttime.m (3505, 2006-11-29)
tomo\新建文本文档.txt (98, 2018-06-16)

The Seismic Reflection Tomography problem ^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^ This file contains the Matlab programs that have been used to realize the unconstrained optimization example described in section 7 (A Case Study: Seismic Reflection Tomography) of the book Numerical Optimization - Theoretical and Practical Aspects (Second Edition) by J. Frédéric Bonnans, J. Charles Gilbert, Claude Lemaréchal, and Claudia A. Sagastizábal Springer, series Universitext, 2006, XIV, 494 p., 52 illus., Softcover ISBN-10: 3-540-35445-X ISBN-13: 978-3-540-35445-1 See http://www-rocq.inria.fr/~gilbert/bgls for more information on this so-called BGLS book. The problem can be used (and has been used) as a computational exercise in unconstrained numerical optimization for students learning this discipline. In the following, we describe the problem and explain how to use the Matlab files of the problem directory. Firther information is contained in the book. REQUIREMENTS: The programs use the "Optimization" and "Spline" toolboxes of Matlab. 1) Introduction ^^^^^^^^^^^^^^^ Seismic reflection tomography is a method for determining a subsurface velocity model from the traveltimes of seismic waves reflecting on geological interfaces. In this simplified example, we are just interested in recovering the position of a reflection interface, discarding the recovering of the wave velocity, which is supposed to be the constant one. 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. 2) Building the data ^^^^^^^^^^^^^^^^^^^^ In Matlab, by typing make_data the data related to the step-pyramid interface are built and stored in the files bgls_interface.dat: description of the bgls_ttimes.dat: travel times of the rays reflecting on the step-pyramid interface from sources to receivers. The program uses the following Matlab functions: travel_times: computes all the travel times ttime: computes a single travel time for a given source and receiver. During the computation of the travel times, the ray tracing show the rays on the plot. This operation can take a while ... References ^^^^^^^^^^ F. Delbos, J.Ch. Gilbert, R. Glowinski, and D. Sinoquet. Constrained optimization in seismic reflection tomography: a Gauss-Newton augmented Lagrangian approach. Geophysical Journal International, 1***:670-684, 2006. F. Delprat-Jannaud and P. Lailly. What information on the Earth model do reflection travel times hold? Journal of Geophysical Research, 97:1***27-1***44, 1992. F. Delprat-Jannaud and P. Lailly. Ill-posed and well-posed formulations of the reflection travel time tomography problem. Journal of Geophysical Research, ***:6589-6605, 1993. R. Glowinski and Q.-H. Tran. Constrained optimization in reflexion tomography: the augmented Lagrangian method. East-West J. Numer. Math., 1(3):213-234, 1993.

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