Constrained optimization in seismic reflection tomography: a Gauss-Newton augmented Lagrangian approach
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 obser...
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| Vydáno v: | Geophysical journal international Ročník 164; číslo 3; s. 670 - 684 |
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| Hlavní autoři: | , , , |
| Médium: | Journal Article |
| Jazyk: | angličtina |
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Oxford, UK
Blackwell Publishing Ltd
01.03.2006
Blackwell Science Ltd Oxford University Press (OUP) |
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| ISSN: | 0956-540X, 1365-246X |
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| Abstract | 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. |
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| AbstractList | 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. SUMMARY 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. S U M M A R Y 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. |
| Author | Glowinski, R. Delbos, F. Gilbert, J. Ch Sinoquet, D. |
| Author_xml | – sequence: 1 givenname: F. surname: Delbos fullname: Delbos, F. email: Institut Français du Pétrole, 1 & 4 avenue de Bois-Préau, 92852 Rueil-Malmaison, France. delphine.sinoquet@ifp.fr, delphine.sinoquet@ifp.fr organization: Institut Français du Pétrole, 1 & 4 avenue de Bois-Préau, 92852 Rueil-Malmaison, France. E-mail: delphine.sinoquet@ifp.fr – sequence: 2 givenname: J. Ch surname: Gilbert fullname: Gilbert, J. Ch organization: Institut National de la Recherche en Informatique et en Automatique, BP 105, 78153 Le Chesnay Cedex, France – sequence: 3 givenname: R. surname: Glowinski fullname: Glowinski, R. organization: University of Houston, 4800 Calhoun Rd, Houston, TX 77204-3476, USA – sequence: 4 givenname: D. surname: Sinoquet fullname: Sinoquet, D. email: Institut Français du Pétrole, 1 & 4 avenue de Bois-Préau, 92852 Rueil-Malmaison, France. delphine.sinoquet@ifp.fr, delphine.sinoquet@ifp.fr organization: Institut Français du Pétrole, 1 & 4 avenue de Bois-Préau, 92852 Rueil-Malmaison, France. E-mail: delphine.sinoquet@ifp.fr |
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| Keywords | augmented Lagrangian least-squares approach ray tracing SQP algorithm constrained optimization seismic reflection tomography |
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| Snippet | Seismic reflection tomography is a method for determining a subsurface velocity model from the traveltimes of seismic waves reflecting on geological... SUMMARY Seismic reflection tomography is a method for determining a subsurface velocity model from the traveltimes of seismic waves reflecting on geological... S U M M A R Y Seismic reflection tomography is a method for determining a subsurface velocity model from the traveltimes of seismic waves reflecting on... |
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| SubjectTerms | 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 |
| Title | Constrained optimization in seismic reflection tomography: a Gauss-Newton augmented Lagrangian approach |
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