Applications of hybrid genetic algorithms in seismic tomography

Almost all earth sciences inverse problems are nonlinear and involve a large number of unknown parameters, making the application of analytical inversion methods quite restrictive. In practice, most analytical methods are local in nature and rely on a linearized form of the problem equations, adopti...

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Published in:	Journal of applied geophysics Vol. 75; no. 3; pp. 479 - 489
Main Authors:	Soupios, Pantelis, Akca, Irfan, Mpogiatzis, Petros, Basokur, Ahmet T., Papazachos, Constantinos
Format:	Journal Article
Language:	English
Published:	Oxford Elsevier B.V 01.11.2011 Elsevier
Subjects:	Applied geophysics Derivatives Earth sciences Earth, ocean, space Exact sciences and technology Genetic algorithms Geophysics Internal geophysics Least-squares methods Mathematical analysis Mathematical models Nonlinearity Seismic engineering Seismic phenomena Seismic tomography Least-squares methods Geophysics Seismic tomography Genetic algorithms algorithms projects global Earth solution optimization tomography wavelength models inverse problem efficiency geologic sections sampling testing foundations geophysics least-squares velocity subsurface anomalies instability geometry travel time
ISSN:	0926-9851, 1879-1859
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Abstract	Almost all earth sciences inverse problems are nonlinear and involve a large number of unknown parameters, making the application of analytical inversion methods quite restrictive. In practice, most analytical methods are local in nature and rely on a linearized form of the problem equations, adopting an iterative procedure which typically employs partial derivatives in order to optimize the starting (initial) model by minimizing a misfit (penalty) function. Unfortunately, especially for highly non-linear cases, the final model strongly depends on the initial model, hence it is prone to solution-entrapment in local minima of the misfit function, while the derivative calculation is often computationally inefficient and creates instabilities when numerical approximations are used. An alternative is to employ global techniques which do not rely on partial derivatives, are independent of the misfit form and are computationally robust. Such methods employ pseudo-randomly generated models (sampling an appropriately selected section of the model space) which are assessed in terms of their data-fit. A typical example is the class of methods known as genetic algorithms (GA), which achieves the aforementioned approximation through model representation and manipulations, and has attracted the attention of the earth sciences community during the last decade, with several applications already presented for several geophysical problems. In this paper, we examine the efficiency of the combination of the typical regularized least-squares and genetic methods for a typical seismic tomography problem. The proposed approach combines a local (LOM) and a global (GOM) optimization method, in an attempt to overcome the limitations of each individual approach, such as local minima and slow convergence, respectively. The potential of both optimization methods is tested and compared, both independently and jointly, using the several test models and synthetic refraction travel-time date sets that employ the same experimental geometry, wavelength and geometrical characteristics of the model anomalies. Moreover, real data from a crosswell tomographic project for the subsurface mapping of an ancient wall foundation are used for testing the efficiency of the proposed algorithm. The results show that the combined use of both methods can exploit the benefits of each approach, leading to improved final models and producing realistic velocity models, without significantly increasing the required computation time. ► We combined the least-squares and genetic methods in seismic tomography problems. ► The proposed approach combines a local and a global optimization method. ► The hybrid algorithm can exploit the benefits of each approach improving the models.
AbstractList	Almost all earth sciences inverse problems are nonlinear and involve a large number of unknown parameters, making the application of analytical inversion methods quite restrictive. In practice, most analytical methods are local in nature and rely on a linearized form of the problem equations, adopting an iterative procedure which typically employs partial derivatives in order to optimize the starting (initial) model by minimizing a misfit (penalty) function. Unfortunately, especially for highly non-linear cases, the final model strongly depends on the initial model, hence it is prone to solution-entrapment in local minima of the misfit function, while the derivative calculation is often computationally inefficient and creates instabilities when numerical approximations are used. An alternative is to employ global techniques which do not rely on partial derivatives, are independent of the misfit form and are computationally robust. Such methods employ pseudo-randomly generated models (sampling an appropriately selected section of the model space) which are assessed in terms of their data-fit. A typical example is the class of methods known as genetic algorithms (GA), which achieves the aforementioned approximation through model representation and manipulations, and has attracted the attention of the earth sciences community during the last decade, with several applications already presented for several geophysical problems. In this paper, we examine the efficiency of the combination of the typical regularized least-squares and genetic methods for a typical seismic tomography problem. The proposed approach combines a local (LOM) and a global (GOM) optimization method, in an attempt to overcome the limitations of each individual approach, such as local minima and slow convergence, respectively. The potential of both optimization methods is tested and compared, both independently and jointly, using the several test models and synthetic refraction travel-time date sets that employ the same experimental geometry, wavelength and geometrical characteristics of the model anomalies. Moreover, real data from a crosswell tomographic project for the subsurface mapping of an ancient wall foundation are used for testing the efficiency of the proposed algorithm. The results show that the combined use of both methods can exploit the benefits of each approach, leading to improved final models and producing realistic velocity models, without significantly increasing the required computation time. Almost all earth sciences inverse problems are nonlinear and involve a large number of unknown parameters, making the application of analytical inversion methods quite restrictive. In practice, most analytical methods are local in nature and rely on a linearized form of the problem equations, adopting an iterative procedure which typically employs partial derivatives in order to optimize the starting (initial) model by minimizing a misfit (penalty) function. Unfortunately, especially for highly non-linear cases, the final model strongly depends on the initial model, hence it is prone to solution-entrapment in local minima of the misfit function, while the derivative calculation is often computationally inefficient and creates instabilities when numerical approximations are used. An alternative is to employ global techniques which do not rely on partial derivatives, are independent of the misfit form and are computationally robust. Such methods employ pseudo-randomly generated models (sampling an appropriately selected section of the model space) which are assessed in terms of their data-fit. A typical example is the class of methods known as genetic algorithms (GA), which achieves the aforementioned approximation through model representation and manipulations, and has attracted the attention of the earth sciences community during the last decade, with several applications already presented for several geophysical problems. In this paper, we examine the efficiency of the combination of the typical regularized least-squares and genetic methods for a typical seismic tomography problem. The proposed approach combines a local (LOM) and a global (GOM) optimization method, in an attempt to overcome the limitations of each individual approach, such as local minima and slow convergence, respectively. The potential of both optimization methods is tested and compared, both independently and jointly, using the several test models and synthetic refraction travel-time date sets that employ the same experimental geometry, wavelength and geometrical characteristics of the model anomalies. Moreover, real data from a crosswell tomographic project for the subsurface mapping of an ancient wall foundation are used for testing the efficiency of the proposed algorithm. The results show that the combined use of both methods can exploit the benefits of each approach, leading to improved final models and producing realistic velocity models, without significantly increasing the required computation time. ► We combined the least-squares and genetic methods in seismic tomography problems. ► The proposed approach combines a local and a global optimization method. ► The hybrid algorithm can exploit the benefits of each approach improving the models.
Author	Papazachos, Constantinos Mpogiatzis, Petros Soupios, Pantelis Basokur, Ahmet T. Akca, Irfan
Author_xml	– sequence: 1 givenname: Pantelis surname: Soupios fullname: Soupios, Pantelis email: soupios@chania.teicrete.gr organization: Laboratory of Geophysics and Seismology, Department of Natural Resources and Environment, Technological Educational Institute of Crete, 3 Romanou Chalepa, 73133, Chania, Crete, Greece – sequence: 2 givenname: Irfan surname: Akca fullname: Akca, Irfan email: Irfan.Akca@eng.ankara.edu.tr organization: Ankara University, Faculty of Engineering, Department of Geophysical Engineering, Tandogan Kampusu, 06100 Ankara, Turkey – sequence: 3 givenname: Petros surname: Mpogiatzis fullname: Mpogiatzis, Petros email: petrosbogiatzis@fas.harvard.edu organization: Harvard University, Seismology Group, Hoffman Laboratory, 20 Oxford Street, Cambridge, MA 02138, USA – sequence: 4 givenname: Ahmet T. surname: Basokur fullname: Basokur, Ahmet T. email: Ahmet.T.Basokur@eng.ankara.edu.tr organization: Ankara University, Faculty of Engineering, Department of Geophysical Engineering, Tandogan Kampusu, 06100 Ankara, Turkey – sequence: 5 givenname: Constantinos surname: Papazachos fullname: Papazachos, Constantinos email: kpapaza@geo.auth.gr organization: Geophysical Laboratory, Department of Geology, Aristotle University of Thessaloniki, Greece
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Snippet	Almost all earth sciences inverse problems are nonlinear and involve a large number of unknown parameters, making the application of analytical inversion...
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SubjectTerms	Applied geophysics Derivatives Earth sciences Earth, ocean, space Exact sciences and technology Genetic algorithms Geophysics Internal geophysics Least-squares methods Mathematical analysis Mathematical models Nonlinearity Seismic engineering Seismic phenomena Seismic tomography
Title	Applications of hybrid genetic algorithms in seismic tomography
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