• Nelson Ricardo Coelho Flores Zuniga Departamento de Geofísica, Instituto de Astronomia, Geofísica e Ciências Atmosféricas, Universidade de São Paulo, Brazil



Optimization Algorithms, Nonhyperbolic, Travel-Time, Seismic Inversion, Multiparametric

Abstract [English]

Even with previous works having studied about the accuracy and objective function of several nonhyperbolic multiparametric travel-time approximations for velocity analysis, they lack tests concerning different optimization algorithms and how they influence the accuracy and processing time. Once many approximations were tested and found the multimodal one which presented the best accuracy results, it is possible to perform a velocity analysis with different global search optimization algorithms. The minimization of the curve calculated with the converted wave moveout equation to the observed curve can be done for each optimization algorithm selected in this work. The travel-time curves tested here are the PP and PS reflection events coming from the interface of the top of an offshore ultra-deep reservoir. After the inversion routine have been performed, it is possible to define the processing time and the accuracy of each optimization algorithm for this kind of problem.


Download data is not yet available.


Aarts EHL, van Laarhoven PJM. Statistical cooling: A general approach to combinatorial optimization problems. Phillips Journal Research, 40, 1985, 193-226.

Alkhalifah T, Tsvankin I. Velocity analysis for transversely isotropic Media. Geophysics, 60, 1995,1550-1566. DOI:

Barros PA, Kirby MR, Mavris DN. Impact of sampling techniques selection on the creation of response surface models. SAE Transaction-Journal of Aerospace, 113, 2004, 1682-1693. DOI:

Barton RR. Metamodeling: A state of the art review. Proceedings of the 1994 Winter Simulation Conference, Expanded Abstract, 1994, 237-244.

Bélisle CJ, Romeijn HE, Smith RL. Hit-and-run algorithm for generating multivariate distributions. Mathematics of Operations Research, 18, 1993, 255-266. DOI:

Blias E. Long-offset NMO approximations for a layered VTI model: Model study. 79th Annual International Meeting, Society of Exploration Geophysics, Expanded Abstract, Houston, 2009, 3745-3749. DOI:

Dix CH. Seismic velocities from surface measurements. Geophysics, 20, 1955, 68-86. DOI:

Golikov P, Stovas A. Accuracy comparison of nonhyperbolic moveout approximations for qP-waves in VTI media. Journal of Geophysics and Engineering, 9, 2012, 428-432. DOI:

Hansen N. The CMA evolution strategy: A computing review. Towards a New Evolutionary Computation, 2006, 75-102. DOI:

Holmström K, Quttineh NH, Edvall MM. An adaptive radial basis algorithm (ARBF) for expensive black-box mixed-integer constrained global optimization. Optimization and Engineering, 9, 2008, 311-339. DOI:

Horst R, Pardalos PM, Thoai NV. Introduction to global optimization. 2nd ed. Dordrecht: Kluwer Academic Publusher, 2000, 354. DOI:

Huyer W, Neumaier A. Global optmization by multilevel coordinate search. Journal of Global Optimization, 14, 1999, 331-355. DOI:

Huyer W, Neumaier A. SNOBFIT – Stable Noisy optimization by branch and fit. ACM Transactions on Mathematical Software, 35, 2008, 1-25. DOI:

Jones DR. A taxonomy of the global optimization methods based on response surface. Journal of Global Optimization, 21, 2001, 345-383. DOI:

Jones DR, Schonlau M, Welch J. Efficient global optimization of expensive black-box functions. Journal of Global Optimization, 13, 1998, 455-492. DOI:

Kirkpatrick S, Gelatt CD, Vecchi P. Optimization by simulated annealing. Science, 220, 1983, 671-680. DOI:

Li XY, Yuan J. Converted-waves moveout and parameter estimation for transverse isotropy. 61st EAGE Conference, Expanded Abstract, 1999, 4-35.

Li XY, Yuan J. Converted wave imaging in inhomogeneous, anisotropic media: Part I. Parameter estimation. 63rd EAGE Conference, Amsterdam, The Netherlands., Expanded Abstract, 2001, 109. DOI:

Li XY, Converted-wave moveout analysis revisited: The search for a standard approach. 73rd Annual International Meeting, Society of Exploration Geophysics, Expanded Abstract, 2003, 805-808. DOI:

Malovichko AA. A new representation of the traveltime curve of reflected waves in horizontally layered media. Applied Geophysics (in Russian), 91, 1978, 47-53.

Margrave GF. New seismic modelling facilities in Matlab. CREWES Research Report, 12, 2000.

Margrave GF. Numerical methods explorations seismology with algorithms in Matlab. CREWES Research Report, 2003.

Matheron G. Principles of geostatistics. Economic Geology, 58, 1967, 1246-1266. DOI:

Metropolis N, Rosenbluth AW, Rosenbluth MN, Teller AH, Teller E. Equation of state calculations by fast computing machine. The Journal of Chemical Physics, 21, 1953, 1087-1092. DOI:

Muir F, Dellinger J. A practical anisotropic system, in SEP-44. Stanford Exploration Project, 1985, 55-58.

Neumaier A, Shcherbina R, Huyer W, Vinkó T. A comparison of complete global optimization solvers. Mathematical Programming, 103, 2005, 335-356. DOI:

Pintér JD. Global optimization in action: Continuous and Lipschitz optimization. Algorithms, Implementations and Applications, Kluwer Academic Publisher, 1995, 422.

Pintér JD, Holmström K, Göran AO, Edvall MM.. User’s Guide for TOMLAB/LGO. TOMLAB Optimization, 2006.

Rios LM, Sahinidis NV. Derivative-free optimization: A review of algorithms and comparison of softwares implementations. Journal of Global Optimization, 56, 2013, 1247-1293. DOI:

Romeo F, Sangiovani-Vincentelli A. A theoretical framework for simulated annealing. Algorithmica, 6, 1991, 302-345. DOI:

Schonlau M. Compute Experiments and Global Optimization. PhD Thesis, University of Waterloo, 1997, 131.

Telraky T, Sotirov R. Multi-start approach to global conic optimization. ISE Archives of Working Papers, 2010.

Thomsen L. Weak elastic anisotropy. Geophysics, 51, 1986, 1954-1966. DOI:

Thorbecke JW, Draganov D. Finite-difference modeling experiment for seismic interferometry. Geophysics, 76, 2012, H1-H18. DOI:

Ursin B, Stovas A. Traveltime approximations for a layered transversely isotropic medium. Geophysics, 71, 2006, 23-33. DOI:

Vaz AIF, Vicente LN. A particle swarm pattern search method for bound constrained global optimization. Journal of Global Optimization, 39, 2007, 197-219. DOI:

Yuan J, Li XY. Comverted wave anisotropic parameter estimation from conversion point. 64th EAGE conference, Expanded Abstract, 2002, 253.

Zuniga NRCF. Análise comparativa de aproximações não-hiperbólicas dos tempos de trânsito de dados sísmicos multicomponente utilizando tecnologia OBN. Master’s Thesis, Universidade de São Paulo, Brazil, 2017, 86. DOI:

Zuniga NRCF, Bokhonok O, Diogo LA. Comparison of nonhyperbolic travel-time approximations for multicomponent seismic data. 14th SBGf Congress, Expanded Abstract, Rio de Janeiro, Brazil, 2015, 1176-1181. DOI:

Zuniga NRCF, Molina EC, Prado RL. Inversion of multicomponent seismic data for VTI medium using the globalized Nelder-Mead optimization algorithm. 3th EAGE/SBGf Workshop, Expanded Abstract. Rio de Janeiro, Brazil, 2016a. DOI:

Zuniga NRCF, Molina EC, Prado RL. Inversion of multicomponent seismic data of the Santos Basin. Far East Hydrocarbons, Expanded Abstract, 2016b. DOI:

Zuniga NRCF, Molina EC, Prado RL. Comparison of travel-time approximations for unconventional reservoirs from Santos Basin, Brazil. Brazilian Journal of Geophysics, 35, 2017, 271-286. DOI:

Zuniga NRCF, Ribeiro FB, Priimenko VI. Relation between the model and the topography of the objective function in a velocity analysis using a nonhyperbolic multicomponent travel-time approximation. Brazilian Journal of Geophysics, 36(4), 2018, 1-10. DOI:




How to Cite