H. Akaike, A New Look at the Statistical Model Identification, IEEE Transactions on Automatic Control, vol.19, pp.716-739, 1974.

K. Aki, Space and time spectra of stationary stochastic waves, with special reference to microtremors, Bull Earth Res Inst, vol.35, pp.415-56, 1957.

Y. Akimoto, A. Auger, and N. Hansen, Comparison-based natural gradient optimization in high dimension, Proceedings of the 2014 Conference on Genetic and Evolutionary ComputationGecco '14, pp.373-80, 2014.
URL : https://hal.archives-ouvertes.fr/hal-00997835

J. Akram and D. W. Eaton, A review and appraisal of arrival-time picking methods for downhole microseismic data, Geophysics, vol.81, pp.71-91, 2016.

J. Akram, O. Ovcharenko, and D. Peter, A robust neural network-based approach for microseismic event detection, SEG Technical Program Expanded Abstracts, pp.2929-2962, 2017.

R. Allen, Automatic phase pickers: Their present use and future prospects, Bulletin of the Seismological Society of America, vol.72, pp.225-267, 1982.

G. M. Amdahl, Validity of the single processor approach to achieving large scale computing capabilities, Spring Joint Computer Conference onAfips '67 (Spring), p.483, 1967.

P. J. Angeline, G. M. Saunders, and J. B. Pollack, An evolutionary algorithm that constructs recurrent neural networks, IEEE transactions on Neural Networks, vol.5, pp.54-65, 1994.

P. J. Angeline, Evolutionary optimization versus particle swarm optimization: Philosophy and performance differences, Lecture Notes in Computer Science: Evolutionary Programming VII, vol.1447, pp.601-611, 1998.

A. Auger and N. Hansen, A Restart CMA Evolution Strategy With Increasing Population Size, IEEE Congress on Evolutionary Computation, vol.2, pp.1769-76, 2005.

T. Back, U. Hammel, and H. Schwefel, Evolutionary computation: comments on the history and current state, IEEE Transactions on Evolutionary Computation, vol.1, pp.3-17, 1997.

M. Baer and U. Kradolfer, An automatic phase picker for local and teleseismic events, Bulletin of the Seismological Society of America, vol.77, pp.1437-1482, 1987.

C. Baillard, W. C. Crawford, and V. Ballu, An Automatic Kurtosis-Based P-and S-Phase Picker Designed for Local Seismic Networks, Bulletin of the Seismological Society of America, vol.104, pp.394-409, 2014.

T. Barros, R. Ferrari, and R. Krummenauer, Differential evolution-based optimization procedure for automatic estimation of the common-reflection surface traveltime parameters, Geophysics, vol.80, pp.189-200, 2015.

A. Bavelas, Communication Patterns in Task-Oriented Groups, The Journal of the Acoustical Society of America, vol.22, pp.725-755, 1950.

J. Belhadj, T. Romary, and A. Gesret, New parameterizations for Bayesian seismic tomography, Inverse Problems, vol.34, p.65007, 2018.
URL : https://hal.archives-ouvertes.fr/hal-01884623

H. Beyer, H. Beyer, and H. Schwefel, Evolution strategies -A comprehensive introduction, Natural Computing, vol.1, pp.3-52, 2002.

M. Beyreuther, R. Barsch, and L. Krischer, ObsPy: A Python Toolbox for Seismology. Seismological Research Letters, vol.81, pp.530-533, 2010.

S. D. Billings, Simulated annealing for earthquake location, Geophysical Journal International, vol.118, pp.680-92, 1994.

J. M. Bishop, Stochastic searching networks, First Iee International Conference on, pp.329-360, 1989.

T. Bodin, M. Salmon, and B. Kennett, Probabilistic surface reconstruction from multiple data sets: An example for the Australian Moho, Journal of Geophysical Research: Solid Earth, vol.117, pp.1-13, 2012.

T. Bodin and M. Sambridge, Seismic tomography with the reversible jump algorithm, Geophysical Journal International, vol.178, pp.1411-1447, 2009.

C. Boor and . De, On calculating with B-splines, Journal of Approximation Theory, vol.6, pp.50-62, 1972.

F. Boschetti, M. C. Dentith, and R. D. List, Inversion of seismic refraction data using genetic algorithms, Geophysics, vol.61, pp.1715-1742, 1996.

A. Bottero, A. Gesret, and T. Romary, Stochastic seismic tomography by interacting Markov chains, Geophysical Journal International, vol.207, pp.374-92, 2016.
URL : https://hal.archives-ouvertes.fr/hal-01410415

N. Brantut, A. Schubnel, and Y. Guéguen, Damage and rupture dynamics at the brittle-ductile transition: The case of gypsum, Journal of Geophysical Research, vol.116, p.1404, 2011.

P. W. Buchen and R. Ben-hador, Free-mode surface-wave computations, Geophysical Journal International, vol.124, pp.869-87, 1996.

C. Bunks, F. M. Saleck, and S. Zaleski, Multiscale seismic waveform inversion, Geophysics, vol.60, pp.1457-73, 1995.

J. Calvez, M. E. Craven, and R. C. Klem, Real-Time Microseismic Monitoring of Hydraulic Fracture Treatment: A Tool To Improve Completion and Reservoir Management. SPE Hydraulic Fracturing Technology Conference, p.7, 2007.

J. Capon, R. J. Greenfield, and R. J. Kolker, Multidimensional maximum-likelihood processing of a large aperture seismic array, Proceedings of the IEEE, vol.55, pp.192-211, 1967.

A. Carlisle and G. Dozier, An Off-The-Shelf PSO, Population English Edition, vol.1, pp.1-6, 2001.

P. W. Cary and C. H. Chapman, Automatic 1-D waveform inversion of marine seismic refraction data, Geophysical Journal International, vol.93, pp.527-573, 1988.

C. Chapman, Ray theory and its extensions: WKBJ and Maslov seismogram, Journal of Geophysics, vol.58, pp.27-43, 1985.

G. Chavent, Identification of Functional Parameters in Partial Differential Equations, 1974.

S. Chen, J. Montgomery, and A. Bolufé-röhler, Measuring the curse of dimensionality and its effects on particle swarm optimization and differential evolution, Applied Intelligence, vol.42, pp.514-540, 2015.

C. Cipolla, S. Maxwell, and M. Mack, A Practical Guide to Interpreting Microseismic Measurements, SPE North American Unconventional Gas Conference and, pp.1-28, 2011.

M. Clerc and J. Kennedy, The particle swarm -explosion, stability, and convergence in a multidimensional complex space, IEEE Transactions on Evolutionary Computation, vol.6, pp.58-73, 2002.

M. Clerc, The swarm and the queen: towards a deterministic and adaptive particle swarm optimization, Proceedings of the 1999 Congress on Evolutionary Computation-Cec99 (Cat. No. 99th8406), vol.3, pp.1951-1958, 1999.

E. Conti, V. Madhavan, and F. P. Such, Improving Exploration in Evolution Strategies for Deep Reinforcement Learning via a Population of Novelty-Seeking Agents, 2017.

V. Cervený, Ray tracing algorithms in three-dimensional laterally varying layered structures, Seismic Tomography, pp.99-133, 1987.

V. Cervený, . Seismic-ray, and . Theory, , 2001.

H. Dai and C. Macbeth, The application of back-propagation neural network to automatic picking seismic arrivals from single-component recordings, Journal of Geophysical Research: Solid Earth, vol.102, pp.15105-15118, 1997.

J. L. Daniels, G. A. Waters, L. Calvez, and J. H. , Contacting More of the Barnett Shale Through an Integration of Real-Time Microseismic Monitoring, Petrophysics, and Hydraulic Fracture Design, SPE Annual Technical Conference and Exhibition, 2007.

S. Das and P. N. Suganthan, Differential Evolution: A Survey of the State-of-the-Art, IEEE Transactions on Evolutionary Computation, vol.15, pp.4-31, 2011.

L. Davis, Handbook of genetic algorithms, 1991.

K. De-meersman, J. Kendall, and . Baan-m-van-der, The 1998 Valhall microseismic data set: An integrated study of relocated sources, seismic multiplets, and S-wave splitting, Geophysics, vol.74, pp.183-95, 2009.

K. Deb, Multi-objective optimization using evolutionary algorithms, 2001.

N. Deichmann and D. Giardini, Earthquakes Induced by the Stimulation of an Enhanced Geothermal System below Basel (Switzerland), Seismological Research Letters, vol.80, pp.784-98, 2009.

F. Delbos, J. C. Gilbert, and R. Glowinski, Constrained optimization in seismic reflection tomography: a Gauss-Newton augmented Lagrangian approach, Geophysical Journal International, vol.164, pp.670-84, 2006.

F. Delprat-jannaud and P. Lailly, Ill-posed and well-posed formulations of the reflection travel time tomography problem, Journal of Geophysical Research: Solid Earth, vol.98, pp.6589-605, 1993.

M. Dorigo, V. Maniezzo, and A. Colorni, Ant system: optimization by a colony of cooperating agents, IEEE Transactions on Systems, Man, and Cybernetics, vol.26, pp.29-41, 1996.

N. Drosinos and N. Koziris, Performance comparison of pure MPI vs hybrid MPI-OpenMP parallelization models on SMP clusters, 18th International Parallel and Distributed Processing Symposium, vol.00, pp.15-24, 2004.

S. Duane, A. Kennedy, and B. J. Pendleton, Hybrid Monte Carlo, Physics Letters B, vol.195, pp.216-238, 1987.

R. Eberhart and Y. Shi, Comparing inertia weights and constriction factors in particle swarm optimization, Proceedings of the 2000 Congress on Evolutionary Computation. Cec00 (Cat. No.00TH8512), vol.1, pp.84-92, 2000.

L. Eisner, P. M. Duncan, and W. M. Heigl, Uncertainties in passive seismic monitoring, The Leading Edge, vol.28, pp.648-55, 2009.

Y. L. Ekinci, Ç. Balkaya, and G. Göktürkler, Model parameter estimations from residual gravity anomalies due to simple-shaped sources using Differential Evolution Algorithm, Journal of Applied Geophysics, vol.129, pp.133-180, 2016.

A. Engelbrecht, Particle swarm optimization: Velocity initialization, IEEE, pp.1-8, 2012.

G. I. Evers, B. Ghalia, and M. , Regrouping particle swarm optimization: A new global optimization algorithm with improved performance consistency across benchmarks, 2009 Ieee International Conference on Systems, Man and Cybernetics, pp.3901-3909, 2009.

F. Martínez, J. L. Mukerji, T. , G. Gonzalo, and E. , Reservoir characterization and inversion uncertainty via a family of particle swarm optimizers, Geophysics, vol.77, pp.1-16, 2012.

E. M. Figueiredo and T. B. Ludermir, Investigating the use of alternative topologies on performance of the PSO-ELM, Neurocomputing, vol.127, pp.4-12, 2014.

R. Fletcher and M. Powell, A Rapidly Convergent Descent Method for Minimization, The Computer Journal, vol.6, pp.163-171, 1963.

D. B. Fogel, Applying evolutionary programming to selected traveling salesman problems, Cybernetics and systems, vol.24, pp.27-36, 1993.

D. B. Fogel, An overview of evolutionary programming, Evolutionary Algorithms, pp.89-109, 1999.

C. M. Fonseca and P. J. Fleming, An overview of evolutionary algorithms in multiobjective optimization, Evolutionary computation, vol.3, pp.1-16, 1995.

C. M. Fonseca and P. J. Fleming, Multiobjective optimization and multiple constraint handling with evolutionary algorithms. I. A unified formulation, IEEE Transactions on Systems, Man, and Cybernetics-Part A: Systems and Humans, vol.28, pp.26-37, 1998.

S. Gentili and A. Michelini, Automatic picking of P and S phases using a neural tree, Journal of Seismology, vol.10, pp.39-63, 2006.
URL : https://hal.archives-ouvertes.fr/inria-00367276

G. Pratt, C. Shin, and . Hicks, Gauss-Newton and full Newton methods in frequency-space seismic waveform inversion, Geophysical Journal International, vol.133, pp.341-62, 1998.

A. Gesret, N. Desassis, and M. Noble, Propagation of the velocity model uncertainties to the seismic event location, Geophysical Journal International, vol.200, pp.52-66, 2015.
URL : https://hal.archives-ouvertes.fr/hal-01101233

P. Goldstein and R. J. Archuleta, Array analysis of seismic signals, Geophysical Research Letters, vol.14, pp.13-19, 1987.

Y. Gong and A. Fukunaga, Distributed island-model genetic algorithms using heterogeneous parameter settings, Ieee Congress of Evolutionary Computation (Cec). IEEE, pp.820-827, 2011.

Y. J. Gong, W. N. Chen, and Z. H. Zhan, Distributed evolutionary algorithms and their models: A survey of the state-of-the-art, vol.34, pp.286-300, 2015.

R. Goudie, R. M. Turner, D. Angelis, and D. , MultiBUGS: A parallel implementation of the BUGS modelling framework for faster Bayesian inference, vol.2017, pp.1-19

H. Grandis, M. Menvielle, and M. Roussignol, Bayesian inversion with Markov chains-I. The magnetotelluriconedimensional case, Geophysical Journal International, vol.138, pp.757-68, 1999.

A. V. Grayver and A. V. Kuvshinov, Exploring equivalence domain in nonlinear inverse problems using Covariance Matrix Adaption Evolution Strategy (CMAES) and random sampling, Geophysical Journal International, vol.205, pp.971-87, 2016.

P. J. Green, Reversible Jump Markov Chain Monte Carlo Computation and Bayesian Model Determination, Biometrika, vol.82, p.711, 1995.

Y. Hajizadeh, M. A. Christie, and V. Demyanov, History matching with differential evolution approach; a look at new search strategies, SPE Europec/Eage Annual Conference and Exhibition, 2010.

D. Han and G. Wang, Application of Particle Swarm Optimization to Seismic Location, Third International Conference on Genetic and Evolutionary Computing, pp.641-645, 2009.

N. Hansen, S. D. Müller, and P. Koumoutsakos, Reducing the time complexity of the derandomized evolution strategy with covariance matrix adaptation (CMA-ES), Evolutionary computation, vol.11, pp.1-18, 2003.

N. Hansen and A. Ostermeier, Adapting arbitrary normal mutation distributions in evolution strategies: the covariance matrix adaptation, Proceedings of Ieee International Conference on Evolutionary Computation, pp.312-319, 1996.

N. Hansen, Errata / Addenda for A Method for Handling Uncertainty in Evolutionary Optimization With an Application to Feedback Control of Combustion, IEEE Transactions on Evolutionary Computation, vol.13, pp.180-97, 2010.

N. Hansen, The CMA evolution strategy: A tutorial, vol.102, pp.1-34, 2011.
URL : https://hal.archives-ouvertes.fr/hal-01297037

P. C. Hansen, O. Leary, and D. P. , The Use of the L-Curve in the Regularization of Discrete Ill-Posed Problems, SIAM Journal on Scientific Computing, vol.14, pp.1487-503, 1993.

D. I. Hart, Automated Picking of Seismic First-Arrivals with Neural Networks, pp.13-30, 2003.

N. A. Haskell, The dispersion of surface waves on multilayered media, Bulletin of the seismological Society of America, vol.43, pp.17-34, 1953.

P. S. Hewlett and G. Mendel, Experiments in Plant Hybridisation, Biometrics, vol.22, p.636, 1966.

J. H. Holland, Genetic Algorithms and the Optimal Allocation of Trials, SIAM Journal on Computing, vol.2, pp.88-105, 1973.

R. Hooke and T. A. Jeeves, Direct Search" Solution of Numerical and Statistical Problems, Journal of the ACM, vol.8, pp.212-241, 1961.

J. D. Hunter, Matplotlib: A 2D Graphics Environment, Computing in Science & Engineering, vol.9, pp.90-95, 2007.

L. Improta, A. Zollo, and A. Herrero, Seismic imaging of complex structures by non-linear traveltime inversion of dense wide-angle data: application to a thrust belt, Geophysical Journal International, vol.151, pp.264-78, 2002.
URL : https://hal.archives-ouvertes.fr/hal-00406760

M. Iwan, R. Akmeliawati, and T. Faisal, Performance Comparison of Differential Evolution and Particle Swarm Optimization in Constrained Optimization, Procedia Engineering, vol.41, pp.1323-1331, 2012.

A. G. Jones and R. Hutton, A multi-station magnetotelluric study in southern Scotland -II. Monte-Carlo inversion of the data and its geophysical and tectonic implications, Geophysical Journal International, vol.56, pp.351-68, 1979.

A. G. Jones, B. Olafsdottir, and J. Tiikkainen, Geomagnetic induction studies in Scandinavia. III Magnetotelluric observations, Journal of Geophysics Zeitschrift Geophysik, vol.54, pp.35-50, 1983.

E. Jones, T. Oliphant, P. Peterson, and . Scipy, Open Source Scientific Tools for Python, 2001.

B. Julian and D. Gubbins, Three-dimensional seismic ray tracing, Journal of Geophysics, vol.43, pp.95-114, 1977.

Y. Kassahun and G. Sommer, Efficient reinforcement learning through Evolutionary Acquisition of Neural Topologies, In. ESANN, pp.259-66, 2005.

V. I. Keilis-borok and T. B. Yanovskaya, Inverse seismic problems (structural review), Geophys J, vol.13, pp.223-256, 1967.

J. Kennedy and R. Eberhart, Particle swarm optimization, Proceedings of Icnn'95 -International Conference on Neural Networks, vol.4, pp.1942-1950, 1995.

J. Kennedy, Small worlds and mega-minds: effects of neighborhood topology on particle swarm performance, Proceedings of the 1999 Congress on Evolutionary Computation-Cec99 (Cat. No. 99th8406), vol.3, pp.1931-1939, 1999.

S. Kirkpatrick, C. D. Gelatt, and M. P. Vecchi, Optimization by Simulated Annealing, Science, vol.220, pp.671-80, 1983.

B. Koh, A. D. George, and R. T. Haftka, Parallel asynchronous particle swarm optimization, International Journal for Numerical Methods in Engineering, vol.67, pp.578-95, 2006.

Z. Koren, K. Mosegaard, and E. Landa, Monte Carlo estimation and resolution analysis of seismic background velocities, Journal of Geophysical Research: Solid Earth, vol.96, pp.20289-99, 1991.

J. R. Koza, Automatic Discovery of Reusable Subprograms, 1992.

J. R. Koza, Genetic programming as a means for programming computers by natural selection, Statistics and computing, vol.4, pp.87-112, 1994.

K. N. Krishnanand and D. Ghose, Glowworm swarm based optimization algorithm for multimodal functions with collective robotics applications, Multiagent and Grid Systems, vol.2, pp.209-231, 2006.

L. Küperkoch, T. Meier, and J. Lee, Automated determination of P -phase arrival times at regional and local distances using higher order statistics, Geophysical Journal International, 2010.

S. R. Lagos, J. I. Sabbione, and D. R. Velis, Very fast simulated annealing and particle swarm optimization for microseismic event location, SEG Technical Program Expanded Abstracts, pp.2188-92, 2014.

Y. Lecun, L. Bottou, and G. B. Orr, Efficient BackProp. In, vol.75, pp.9-50, 1998.

J. Lehman, J. Chen, and J. Clune, Safe Mutations for Deep and Recurrent Neural Networks through Output Gradients, 2017.

M. Leonard, Comparison of Manual and Automatic Onset Time Picking, Bulletin of the Seismological Society of America, vol.90, pp.1384-90, 2000.

D. C. Liu and J. Nocedal, On the limited memory BFGS method for large scale optimization, Mathematical Programming, vol.45, pp.503-531, 1989.

A. Lomax, A. Michelini, and A. Curtis, Earthquake location, direct, global-search methods, pp.2-449, 2009.

J. N. Louie and . Faster, better: shear-wave velocity to 100 meters depth from refraction microtremor arrays, Bulletin of the Seismological Society of America, vol.91, pp.347-64, 2001.

Y. Luo and G. T. Schuster, Wave-equation traveltime inversion, Geophysics, vol.56, pp.645-53, 1991.

K. Luu, M. Noble, and A. Gesret, A parallel competitive Particle Swarm Optimization for non-linear first arrival traveltime tomography and uncertainty quantification, Computers & Geosciences, vol.113, pp.81-93, 2018.
URL : https://hal.archives-ouvertes.fr/hal-01885326

K. Luu, M. Noble, and A. Gesret, A competitive particle swarm optimization for nonlinear first arrival traveltime tomography, SEG Technical Program Expanded Abstracts, pp.2740-2744, 2016.
URL : https://hal.archives-ouvertes.fr/hal-01885326

N. Maeda, A Method for Reading and Checking Phase Time in Auto-Processing System of Seismic Wave Data, Zisin (Journal of the Seismological Society of Japan 2nd ser), vol.38, pp.365-79, 1985.

D. Maity, F. Aminzadeh, and M. Karrenbach, Novel hybrid artificial neural network based autopicking workflow for passive seismic data, Geophysical Prospecting, vol.62, pp.834-881, 2014.

A. Malinverno and V. A. Briggs, Expanded uncertainty quantification in inverse problems: Hierarchical Bayes and empirical Bayes, Geophysics, vol.69, pp.1005-10016, 2004.

A. Malinverno and S. Leaney, A Monte Carlo method to quantify uncertainty in the inversion of zero-offset VSP data, SEG Technical Program Expanded Abstracts, pp.2393-2399, 2000.

A. Malinverno and C. Torres-verdín, Bayesian inversion of DC electrical measurements with uncertainties for reservoir monitoring, Inverse Problems, vol.16, pp.1343-56, 2000.

S. Maxwell, T. Urbancic, and N. Steinsberger, Microseismic Imaging of Hydraulic Fracture Complexity in the Barnett Shale, SPE Annual Technical Conference and Exhibition, 2002.

S. C. Maxwell, J. Rutledge, and R. Jones, Petroleum reservoir characterization using downhole microseismic monitoring, Geophysics, vol.75, pp.75-129, 2010.

S. C. Maxwell, Microseismic Location Uncertainty, CSEG Recorder, vol.34, pp.41-47, 2009.

M. D. Mccormack, D. E. Zaucha, and D. W. Dushek, First-break refraction event picking and seismic data trace editing using neural networks, Geophysics, vol.58, pp.67-78, 1993.

W. Mckinney, Data Structures for Statistical Computing in Python, Proceedings of the 9th Python in Science Conference, pp.51-57, 2010.

K. Mckinnon, Convergence of the Nelder-Mead Simplex Method to a Nonstationary Point, SIAM Journal on Optimization, vol.9, pp.148-58, 1998.

M. G. Versuche-Über-pflanzenhybriden, Verhandlungen des naturforschenden Vereines in Brunn, vol.4, pp.3-1866

W. Menke, Geophysical data analysis: Discrete inverse theory, p.293, 2012.

S. Mirjalili, S. M. Mirjalili, L. A. Grey-wolf, and . Optimizer, Advances in Engineering Software, vol.69, pp.46-61, 2014.

L. Mohamed, B. Calderhead, and M. Filippone, Population MCMC methods for history matching and uncertainty quantification, Computational Geosciences, vol.16, pp.423-459, 2012.

L. Mohamed, M. Christie, and V. Demyanov, Comparison of Stochastic Sampling Algorithms for Uncertainty Quantification, SPE Journal, vol.15, pp.31-39, 2010.

L. Mohamed, M. A. Christie, and V. Demyanov, Application of Particle Swarms for History Matching in the Brugge Reservoir, SPE Annual Technical Conference and Exhibition, 2010.

J. B. Molyneux and D. R. Schmitt, First-break timing: Arrival onset times by direct correlation, Geophysics, vol.64, pp.1492-501, 1999.

K. Mosegaard and A. Tarantola, Monte Carlo sampling of solutions to inverse problems, Journal of Geophysical Research: Solid Earth, vol.100, pp.12431-12478, 1995.

M. E. Murat and A. J. Rudman, Automated first arrival picking: a neural network approach, Geophysical Prospecting, vol.40, pp.587-604, 1992.

L. Mussi, Y. S. Nashed, and S. Cagnoni, GPU-based asynchronous particle swarm optimization, Proceedings of the 13th Annual Conference on Genetic and Evolutionary ComputationGecco '11, p.1555, 2011.

S. G. Nash and J. Nocedal, A Numerical Study of the Limited Memory BFGS Method and the TruncatedNewton Method for Large Scale Optimization, SIAM Journal on Optimization, vol.1, pp.358-72, 1991.

S. Nazarian, I. I. Stokoe, and H. Kenneth, Use of spectral analysis of surface waves method for determination of moduli and thicknesses of pavement systems, 1983.

R. M. Neal, Bayesian training of backpropagation networks by the hybrid Monte Carlo method, Tech, vol.1992, pp.1-21

R. M. Neal, Bayesian Learning for Neural Networks, p.341, 1996.

R. M. Neal, Handbook of Markov Chain Monte Carlo

/. Hall and . Crc, , pp.113-62, 2011.

W. Neiswanger, C. Wang, E. A. Xing, and . Exact, Embarrassingly Parallel MCMC, vol.2013, pp.1-16

J. A. Nelder and R. Mead, A Simplex Method for Function Minimization, The Computer Journal, vol.7, pp.308-321, 1965.

T. Nemeth, E. Normark, and F. Qin, Dynamic smoothing in crosswell traveltime tomography, Geophysics, vol.62, pp.168-76, 1997.

A. Nicolas, J. Fortin, and J. Regnet, Brittle and semi-brittle behaviours of a carbonate rock: Influence of water and temperature, Geophysical Journal International, vol.206, pp.438-56, 2016.

M. A. Nielsen, Neural networks and deep learning. Determination press USA, 2015.

M. Noble, A. Gesret, and N. Belayouni, Accurate 3-D finite difference computation of traveltimes in strongly heterogeneous media, Geophysical Journal International, vol.199, pp.1572-85, 2014.
URL : https://hal.archives-ouvertes.fr/hal-01074989

M. Noble, P. Thierry, and C. Taillandier, High-performance 3D first-arrival traveltime tomography, The Leading Edge, vol.29, pp.86-93, 2010.
URL : https://hal.archives-ouvertes.fr/hal-00466368

T. Oliphant, . Guide-to-numpy, and . Usa, , 2006.

N. Padhye, P. Mittal, and K. Deb, Feasibility Preserving Constraint-Handling Strategies for Real Parameter Evolutionary Optimization, 2015.

J. Pallero, J. Fernández-martínez, and S. Bonvalot, Gravity inversion and uncertainty assessment of basement relief via Particle Swarm Optimization, Journal of Applied Geophysics, vol.116, pp.180-91, 2015.
URL : https://hal.archives-ouvertes.fr/hal-01609208

C. B. Park, R. D. Miller, and J. Xia, Multichannel analysis of surface waves, Geophysics, vol.64, pp.800-808, 1999.

F. Pedregosa, G. Varoquaux, and A. Gramfort, Scikit-learn: Machine Learning in Python, Journal of Machine Learning Research, vol.12, pp.2825-2855, 2012.
URL : https://hal.archives-ouvertes.fr/hal-00650905

D. T. Pham, A. Ghanbarzadeh, and E. Koç, The Bees Algorithm-A Novel Tool for Complex Optimisation Problems, Intelligent Production Machines and Systems, pp.454-463, 2006.

P. Agostinetti, N. Giacomuzzi, G. Malinverno, and A. , Local three-dimensional earthquake tomography by trans-dimensional Monte Carlo sampling, Geophysical Journal International, vol.201, pp.1598-617, 2015.

S. Piccand, M. O'neill, and J. Walker, On the scalability of particle swarm optimisation, Ieee Congress on Evolutionary Computation, 2008.

, IEEE, pp.2505-2517, 2008.

R. Plessix, A review of the adjoint-state method for computing the gradient of a functional with geophysical applications, Geophysical Journal International, vol.167, pp.495-503, 2006.

P. Podvin and I. Lecomte, Finite difference computation of traveltimes in very contrasted velocity models: a massively parallel approach and its associated tools, Geophysical Journal International, vol.105, pp.271-84, 1991.

R. Poormirzaee, R. H. Moghadam, and A. Zarean, Inversion seismic refraction data using particle swarm optimization: a case study of Tabriz, Iran. Arabian Journal of Geosciences, vol.8, pp.5981-5990, 2015.

R. Poormirzaee, S-wave velocity profiling from refraction microtremor Rayleigh wave dispersion curves via PSO inversion algorithm, Arabian Journal of Geosciences, vol.9, p.673, 2016.

M. Powell, An efficient method for finding the minimum of a function of several variables without calculating derivatives, The Computer Journal, vol.7, pp.155-62, 1964.

F. Press, Earth models obtained by Monte Carlo Inversion, Journal of Geophysical Research, vol.73, pp.5223-5257, 1968.

F. Press, Earth models consistent with geophysical data, Physics of the Earth and Planetary Interiors, vol.3, pp.3-22, 1970.

K. Price, R. M. Storn, and J. A. Lampinen, Differential evolution: a practical approach to global optimization, 2006.

K. Price, Differential evolution: a fast and simple numerical optimizer, Proceedings of North American Fuzzy Information Processing, pp.524-531, 1996.

R. Rabenseifner, G. Hager, and G. Jost, Hybrid MPI/OpenMP Parallel Programming on Clusters of Multi-Core SMP Nodes, 17th Euromicro International Conference on Parallel, Distributed and Network-Based Processing, pp.427-463, 2009.

A. L. Ramirez, J. J. Nitao, and W. G. Hanley, Stochastic inversion of electrical resistivity changes using a Markov Chain Monte Carlo approach, Journal of Geophysical Research: Solid Earth, vol.110, pp.1-18, 2005.

N. Rawlinson, S. Pozgay, and S. Fishwick, Seismic tomography: A window into deep Earth, Physics of the Earth and Planetary Interiors, vol.178, pp.101-136, 2010.

I. Rechenberg, Evolutionsstrategie: Optimierung technischer Systeme nach Prinzipien der biologischen Evolution, 1973.

T. Romary, Bayesian inversion by parallel interacting Markov chains, Inverse Problems in Science and Engineering, vol.18, pp.111-141, 2010.
URL : https://hal.archives-ouvertes.fr/hal-00505406

E. Ronald and M. Schoenauer, Genetic Lander: An experiment in accurate neuro-genetic control, International Conference on Parallel Problem Solving from Nature, pp.452-61, 1994.
URL : https://hal.archives-ouvertes.fr/hal-01079614

S. Rostami and F. Neri, A fast hypervolume driven selection mechanism for many-objective optimisation problems, Swarm and Evolutionary Computation, vol.34, pp.50-67, 2017.

E. Rothert and S. A. Shapiro, Microseismic monitoring of borehole fluid injections: Data modeling and inversion for hydraulic properties of rocks, Geophysics, vol.68, pp.685-694, 2003.

M. Rumpf and J. Tronicke, Assessing uncertainty in refraction seismic traveltime inversion using a global inversion strategy, Geophysical Prospecting, vol.63, pp.1188-97, 2015.

B. R??ek and M. Kvasni?ka, Differential Evolution Algorithm in the Earthquake Hypocenter Location, Pure and Applied Geophysics, vol.158, pp.667-93, 2001.

T. Ryberg and C. Haberland, Bayesian inversion of refraction seismic traveltime data, Geophysical Journal International, vol.212, pp.1645-56, 2018.

J. I. Sabbione and D. Velis, Automatic first-breaks picking: New strategies and algorithms, Geophysics, vol.75, pp.67-76, 2010.

M. Saka, O. Hasançebi, and Z. Geem, Metaheuristics in structural optimization and discussions on harmony search algorithm, Swarm and Evolutionary Computation, vol.28, pp.88-97, 2016.

M. Sambridge and G. Drijkoningen, Genetic algorithms in seismic waveform inversion, Geophysical Journal International, vol.109, pp.323-365, 1992.

M. Sambridge and K. Gallagher, Earthquake hypocenter location using genetic algorithms, Bulletin of the Seismological Society of America, vol.83, pp.1467-91, 1993.

M. Sambridge, K. M. Mosegaard, and . Carlo, Methods in Geophysical Inverse Problems. Reviews of Geophysics, vol.40, p.1009, 2002.

M. Sambridge, Geophysical inversion with a neighbourhood algorithm-I. Searching a parameter space, Geophysical Journal International, vol.138, pp.479-94, 1999.

M. Sambridge, A Parallel Tempering algorithm for probabilistic sampling and multimodal optimization, Geophysical Journal International, vol.196, pp.357-74, 2014.

C. D. Saragiotis, L. J. Hadjileontiadis, S. M. Panas, and . Pai-s/k, A robust automatic seismic P phase arrival identification scheme, IEEE Transactions on Geoscience and Remote Sensing, vol.40, pp.1395-404, 2002.

S. Sasaki, Characteristics of microseismic events induced during hydraulic fracturing experiments at the Hijiori hot dry rock geothermal energy site, Tectonophysics, vol.289, pp.171-88, 1998.

J. A. Scales and R. Snieder, To Bayes or not to Bayes?, Geophysics, vol.62, pp.1045-1051, 1997.

J. A. Scales and L. Tenorio, Prior information and uncertainty in inverse problems, Geophysics, vol.66, pp.389-97, 2001.

R. Schmidt, Multiple emitter location and signal parameter estimation, IEEE transactions on antennas and propagation, vol.34, pp.276-80, 1986.

J. Schott, M. Roussignol, and M. Menvielle, Bayesian inversion with Markov chains-II. The one-dimensional DC multilayer case, Geophysical Journal International, vol.138, pp.769-83, 1999.

R. Schulze-riegert, J. Axmann, and O. Haase, Optimization Methods for History Matching of Complex Reservoirs, SPE Reservoir Simulation Symposium. Society of Petroleum Engineers, 2001.

J. F. Schutte, J. A. Reinbolt, and B. J. Fregly, Parallel global optimization with the particle swarm algorithm, International Journal for Numerical Methods in Engineering, vol.61, pp.2296-315, 2004.

H. Schwefel, Evolution strategies: A family of non-linear optimization techniques based on imitating some principles of organic evolution, Annals of Operations Research, vol.1, pp.165-172, 1984.

D. Sculley, Web-scale k-means clustering, Proceedings of the 19th international conference on World wide web WWW, p.1177, 2010.

P. Sedlak, Y. Hirose, and M. Enoki, Arrival Time Detection in Thin Multilayer Plates on the Basis of Akaike Information Criterion, Journal of Acoustic Emission, vol.26, pp.182-190, 2008.

M. K. Sen and P. L. Stoffa, Bayesian inference, Gibbs' sampler and uncertainty estimation in geophysical inversion, Geophysical Prospecting, vol.44, pp.313-50, 1996.

N. M. Shapiro and M. Campillo, Emergence of broadband Rayleigh waves from correlations of the ambient seismic noise, Geophysical Research Letters, p.31, 2004.
URL : https://hal.archives-ouvertes.fr/hal-00107919

R. Shaw and S. Srivastava, Particle swarm optimization: A new tool to invert geophysical data, Geophysics, vol.72, pp.75-83, 2007.

A. Shenfield and S. Rostami, Multi-objective evolution of artificial neural networks in multi-class medical diagnosis problems with class imbalance, 2017 Ieee Conference on Computational Intelligence in Bioinformatics and Computational Biology (Cibcb), pp.1-8, 2017.

R. E. Sheriff and L. P. Geldart, Exploration Seismology, 1995.

Y. Shi and R. C. Eberhart, A modified particle swarm optimizer, Ieee International Conference on Evolutionary Computation Proceedings. Ieee World Congress on Computational Intelligence (Cat. No.98TH8360), pp.69-73, 1998.

N. T. Siebel and G. Sommer, Evolutionary reinforcement learning of artificial neural networks, International Journal of Hybrid Intelligent Systems, vol.4, pp.171-83, 2007.

R. Sleeman, T. Eck, and . Van, Robust automatic P-phase picking: an on-line implementation in the analysis of broadband seismogram recordings, Physics of the Earth and Planetary Interiors, vol.113, pp.265-75, 1999.

L. Socco and C. Strobbia, Surface-wave method for near-surface characterization: a tutorial, Near Surface Geophysics, vol.2, pp.165-85, 2004.

L. V. Socco and D. Boiero, Improved Monte Carlo inversion of surface wave data, Geophysical Prospecting, vol.56, pp.357-71, 2008.

X. Song, L. Tang, and X. Lv, Application of particle swarm optimization to interpret Rayleigh wave dispersion curves, Journal of Applied Geophysics, vol.84, pp.1-13, 2012.

K. Sörensen, Metaheuristics-the metaphor exposed, International Transactions in Operational Research, vol.22, pp.3-18, 2015.

K. O. Stanley and R. Miikkulainen, Evolving neural networks through augmenting topologies, Evolutionary computation, vol.10, pp.99-127, 2002.

R. Storn and K. Price, Differential Evolution -A Simple and Efficient Heuristic for global Optimization over Continuous Spaces, Journal of Global Optimization, vol.11, pp.341-59, 1997.

R. Storn, Real-world applications in the communications industry -when do we resort to Differential Evolution?, Ieee Congress on Evolutionary Computation (Cec), pp.765-72, 2017.

F. P. Such, V. Madhavan, and E. Conti, Deep Neuroevolution: Genetic Algorithms Are a Competitive Alternative for Training Deep Neural Networks for Reinforcement Learning, 2017.

C. Taillandier, M. Noble, and H. Chauris, First-arrival traveltime tomography based on the adjoint-state method, Geophysics, 2009.

A. Tarantola and B. Valette, Inverse Problems = Quest for Information, Journal of Geophysics, vol.50, pp.159-70, 1982.

A. Tarantola, Inverse Problem Theory and Methods for Model Parameter Estimation, Society for Industrial; Applied Mathematics, pp.1816-1840, 2005.

W. T. Thomson, Transmission of elastic waves through a stratified solid medium, Journal of applied Physics, vol.21, pp.89-93, 1950.

A. N. Tikhonov, A. V. Goncharsky, and V. V. Stepanov, Numerical methods for the solution of ill-posed problems, 2013.

V. Torczon, On the Convergence of Pattern Search Algorithms, SIAM Journal on Optimization, vol.7, pp.1-25, 1997.

R. Toushmalani, Gravity inversion of a fault by Particle swarm optimization (PSO), SpringerPlus, vol.2, p.315, 2013.

I. C. Trelea, The particle swarm optimization algorithm: Convergence analysis and parameter selection, Information Processing Letters, vol.85, pp.317-342, 2003.
URL : https://hal.archives-ouvertes.fr/hal-01313364

. Trier-j-van and W. W. Symes, Upwind finite-difference calculation of traveltimes, Geophysics, vol.56, pp.812-833, 1991.

J. Tronicke, H. Paasche, and U. Böniger, Crosshole traveltime tomography using particle swarm optimization: A near-surface field example, Geophysics, vol.77, pp.19-32, 2012.

T. J. Ulrych, M. D. Sacchi, and A. Woodbury, A Bayes tour of inversion: A tutorial, Geophysics, vol.66, pp.55-69, 2001.

J. Um and C. Thurber, A fast algorithm for two-point seismic ray tracing, Bulletin of the Seismological Society of America, vol.77, pp.972-86, 1987.

F. Van-den-bergh and A. P. Engelbrecht, A study of particle swarm optimization particle trajectories, Information Sciences, vol.176, pp.937-71, 2006.

, Van Den Bergh F. An analysis of particle swarm optimizers, 2001.

J. Veezhinathan and D. Wagner, A neural network approach to first break picking, Ijcnn International Joint Conference on Neural Networks. IEEE, vol.1, pp.235-275, 1990.

G. Venter and J. Sobieszczanski-sobieski, Parallel Particle Swarm Optimization Algorithm Accelerated by Asynchronous Evaluations, Journal of Aerospace Computing, Information, and Communication, vol.3, pp.123-160, 2006.

R. Versteeg, The Marmousi experience: Velocity model determination on a synthetic complex data set, The Leading Edge, vol.13, pp.927-963, 1994.

J. Vidale, Finite-difference calculation of travel times, Bulletin of the Seismological Society of America, vol.78, pp.2062-76, 1988.

J. Vidale, Finite-difference calculation of traveltimes in three dimensions, Geophysics, vol.55, pp.521-527, 1990.

N. Warpinski, S. Wolhart, and C. Wright, Analysis and Prediction of Microseismicity Induced by Hydraulic Fracturing, SPE Journal, vol.9, pp.24-33, 2004.

N. Warpinski, Microseismic Monitoring: Inside and Out, Journal of Petroleum Technology, vol.61, pp.80-85, 2009.

D. Weyland, A Rigorous Analysis of the Harmony Search Algorithm, International Journal of Applied Metaheuristic Computing, vol.1, pp.50-60, 2010.

D. J. White, Two-Dimensional Seismic Refraction Tomography, Geophysical Journal International, vol.97, pp.223-268, 1989.

D. Whitley, S. Rana, and R. B. Heckendorn, The island model genetic algorithm: On separability, population size and convergence, Journal of Computing and Information Technology, vol.7, pp.33-47, 1999.

D. Whitley, A genetic algorithm tutorial, Statistics and Computing, vol.4, pp.65-85, 1994.

R. A. Wiggins, Monte Carlo inversion of body-wave observations, Journal of Geophysical Research, vol.74, pp.3171-81, 1969.

D. Wilken and W. Rabbel, On the application of Particle Swarm Optimization strategies on Scholtewave inversion, Geophysical Journal International, vol.190, pp.580-94, 2012.

J. Xiong, C. Liu, and Y. Chen, A Non-linear Geophysical Inversion Algorithm for the MT Data Based on Improved Differential Evolution, Engineering Letters, vol.26, 2018.

X. Yang and D. S. , Cuckoo search via Lévy flights, Nature & Biologically Inspired Computing, pp.210-214, 2009.

X. Yang, A new metaheuristic bat-inspired algorithm, Nature Inspired Cooperative Strategies for Optimization, pp.65-74, 2010.

X. Yang, Flower pollination algorithm for global optimization, International Conference on Unconventional Computing and Natural Computation, pp.240-249, 2012.

C. A. Zelt and P. J. Barton, Three-dimensional seismic refraction tomography: A comparison of two methods applied to data from the Faeroe Basin, Journal of Geophysical Research: Solid Earth, vol.103, pp.7187-210, 1998.

H. Zhang, C. Thurber, and C. Rowe, Automatic P-wave arrival detection and picking with multiscale wavelet analysis for single-component recordings, Bulletin of the Seismological Society of America, vol.93, pp.1904-1916, 2003.

J. Zhang and M. N. Toksöz, Nonlinear refraction traveltime tomography, Geophysics, vol.63, pp.1726-1763, 1998.

J. Zhang, C. Wang, and Y. Shi, Three-dimensional crustal structure in central Taiwan from gravity inversion with a parallel genetic algorithm, Geophysics, vol.69, pp.917-941, 2004.

C. Zhou, W. Cai, and Y. Luo, Acoustic wave-equation traveltime and waveform inversion of crosshole seismic data, Geophysics, vol.60, pp.765-73, 1995.

E. Zitzler, Evolutionary Algorithms for Multiobjective Optimization, Methods and Applications. TIK-Schriftenreihe, vol.30, pp.1-122, 1999.

Z. Woo-geem, J. Kim, and G. Loganathan, A New Heuristic Optimization Algorithm: Harmony Search, SIMULATION, vol.76, pp.60-68, 2001.

, Marmousi velocity model. (Top) Velocity model used to generate the traveltime data. (Middle) Low-frequency target velocity model. (Bottom) Ray density map, p.69

, When using random vertically increasing gradient initialization, the optimizers converge faster toward low RMS velocity models. (Right) Example of 100 random vertically increasing gradient velocity models, the color scale indicating their RMS values. For CMA-ES, the model that yields the lowest RMS is chosen as the initial mean vector (red), 4.5 (Left) Average RMS over 20 runs as a function of iteration number

, 2D models (bottom) for different initializations. (Left) Fully random. (Middle) Homogeneous. (Right) Vertically increasing gradient. The mean velocity model (blue) fits the long wavelengths of the target velocity model (black) at all depths for gradient initialization. The results have been obtained using CPSO, 6 1D profiles (top) and, p.71

, Evolution of average RMS (left) and RMS deviation (right) with respect to iteration number for the 3 experiments with the 3 EA

, the mean (blue) and the best (green) velocity models at different locations for the 3 EA. The errors are indicated in gray shade

, the mean (blue) and the best (green) velocity models at different depths for the 3 EA. The errors are indicated in gray shade

, Vertical cross-sections of the difference between the target and mean velocity models

, Horizontal cross-sections of the difference between the target and mean velocity models

, Weighted mean velocity models and associated uncertainties for (top) DE, (middle) CPSO and (bottom) CMA-ES. The main structure and the ray coverage of the target velocity model are superimposed over the results

C. De and C. , on a refraction tomography problem with a population size of 104. (Left) Speed up. (Right) Parallel efficiency

, 1 (Left) Attribute based automated picker seen as a neural network. (Right) Example of multi-attributes onset picker based on a neural network with four input features, one hidden layer and one output

, Bottom) SNR attribute with ?t = 50 samples. The vertical line corresponds to the phase onset given by the global maximum of the SNR attribute. Attribute values are normalized

, Top) Example trace. The shaded area indicates the time window with ?t = 200 samples. (Middle) AIC function. (Bottom) Windowed AIC function with ?t = 200 samples. The vertical line corresponds to the phase onset given by the global minimum of the AIC-W function, vol.87

, Middle) Kurtosis statistics F 1 and removal of negative slopes F 2 . (Bottom) Kurtosis attribute with ?t = 40 samples. The vertical line corresponds to the phase onset given by the global maximum of the Kurtosis attribute. Attribute values are normalized, p.89

, Neural network automated phase onset picking workflow

, The acquisition geometry consists of sixteen piezoelectric transducers, p.90

, Receivers 2, 4, 9, 10 and 11 were not working properly. The vertical lines indicate the manual picks

K. Aic-w and S. , Top) Example trace. (Bottom) Predicted probability map. The manually picked and predicted phase onsets are indicated by the green and blue vertical lines, respectively. The prediction error is shown in blue shade, vol.92

, The vertical lines indicate the predicted picks along with the picking errors in green shade. The seismic traces recorded by receivers 2, 4, 9, 10 and 11 have been rejected by the trained neural network, p.95

, Left) Evolution of the acoustic wave velocity during the experiment. (Right) Acoustic event locations. The color scale indicates the relative origin time, vol.12, p.96

A. , Displacements for P-and S-waves (adapted from levee, p.106

B. , 1 (Left) Modal dispersion curves for a three-layer model (500 m at 500 m/s, 300 m at 1000 m/s, half-space at 500 m/s). The vertical line (green) indicates a slice at

. ;. Hz, Right) Dispersion function at 5 Hz. The positions of the roots (i.e. zeros) correspond to the phase velocities for the different modes. The dispersion function is clipped between -1 and 1

, The velocity models sampled by the different runs of CPSO are represented in the background with the color scale indicating their RMS values. The dashed lines (red) delimit the 68% confidence interval, Left) Picked (red) and inverted dispersion curves. (Right

C. , 1 (Left) 2D Rastrigin PDF sampled by MCMC. Comparison of the sampling capability of (middle) PSO and (right) CPSO on the 2D Rastrigin function, p.119

, Left) 3D acquisition geometry. (Right) P-wave velocity model obtained from CPSO tomography. The 95 percent confidence intervals are represented by the grey lines, C, vol.2

, Elbow" method to determine the optimal number of clusters K. (Right) P-wave centroid models of the two most populated clusters