Abstract
Probabilistic earthquake location with non-linear, global search methods allows the use of 3D models and produces comprehensive uncertainty and resolution information represented by a probability density function over the unknown hypocentral parameters. We describe a probabilistic earthquake location methodology and introduce an efficient Metropolis-Gibbs, non-linear, global sampling algorithm to obtain such locations. Using synthetic travel times generated in a 3D model, we examine the locations and uncertainties given by an exhaustive grid-search and the Metropolis-Gibbs sampler using 3D and layered velocity models, and by a iterative, linear method in the layered model. We also investigate the relation of average station residuals to known static delays in the travel times, and the quality of the recovery of known focal mechanisms. With the 3D model and exact data, the location probability density functions obtained with the Metropolis-Gibbs method are nearly identical to those of the slower but exhaustive grid-search. The location PDFs can be large and irregular outside of a station network even for the case of exact data. With location in the 3D model and static shifts added to the data, there are systematic biases in the event locations. Locations using the layered model show that both linear and global methods give systematic biases in the event locations and that the error volumes do not include the “true” location — absolute event locations and errors are not recovered. The iterative, linear location method can fail for locations near sharp contrasts in velocity and outside of a network. Metropolis-Gibbs is a practical method to obtain complete, probabilistic locations for large numbers of events and for location in 3D models. It is only about 10 times slower than linearized methods but is stable for cases where linearized methods fail. The exhaustive grid-search method is about 1000 times slower than linearized methods but is useful for location of smaller number of events and to obtain accurate images of location probability density functions that may be highly-irregular.
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References
Aki, K., and P.G. Richards (1980) Quantitative seismology, W.H. Freeman, San Francisco.
Billings, S.D. (1994) Simulated annealing for earthquake location, Geophys. J. Int., 118, 680692.
Calvert, A., F. Gomez, D. Seber, M. Barazangi, N. Jabour, A. Ibenbrahim, A. and Demnati (1997) An integrated geophysical investigation of recent seismicity in the Al-Hoceima region of North Morocco, Bull. Seism. Soc. Am. 87, 637–651.
Dreger, D., R. Uhrhammer, M. Pasyanos, J. Frank, and B. Romanowicz (1998) Regional and far-regional earthquake locations and source parameters using sparse broadband networks: A test on the Ridgecrest sequence, Bull. Seism. Soc. Am. 88, 1353–1362.
Geiger, L. (1912) Probability method for the determination of earthquake epicenters from the arrival time only (translated from German), Bull. St. Louis Univ. 8 (1), 56–71.
Goldberg, D.E. (1989) Genetic Algorithms in Search, Optimization and Machine Learning, Addison-Wesley, Reading, MA.
Goldberg, D.E., and J. Richardson (1987) Genetic algorithms with sharing for multimodal function optimization, in J.J. Grefenstette (Ed.), Genetic Algorithms and their Applications, Proceedings of the Second International Conference on Genetic Algorithms and their applications, Lawrence Erlbaum Associates, Hillsdale, NJ, 41–49.
Gresta, S., L. Peruzza, D. Slejko and G. Distefano (1998) Inferences on the main volcano-tectonic structures at Mt. Etna (Sicily) from a probabilistic seismological approach, J. Seis. 2, 105–116.
Hammersley, J.M., and D.C. Handscomb (1967) Monte Carlo Methods, Methuen, London.
Holland, J.H. (1992) Adaptation in natural and artificial systems, Bradford Books/MIT Press, Cambridge, MA, 211 pp.
Jones, R.H., and R.C. Stewart (1997) A method for determining significant structures in a cloud of earthquakes, J. Geophys. Res. 102, 8245–8254.
Keilis-Book, V.I., and T.B. Yanovskaya (1967) Inverse problems in seismology (structural review), Geophys. J. R. Astr. Soc. 13, 223–234.
Kennett, B.L.N. (1992) Locating oceanic earthquakes — the influence of regional models and location criteria, Geophys. J. Int. 108, 848–854.
Kirkpatrick, S., C.D. Gelatt, and M.P. Vecchi (1983) Optimization by simulated annealing, Science 220, 671–680.
Lahr, J.C. (1989) HYPOELLIPSENersion 2.0: A computer program for determining local earthquake hypocentral parameters, magnitude and first motion pattern, U.S. Geol. Surv. Open-File Rep. 89–116, 92 p.
Lepage, G.P. (1978) A new algorithm for adaptive multidimensional integration, J. Comp. Phys. 27, 192–203.
Le Meur, H. (1994) Tomographie tridimensionelle a partor des temps des premieres arrivées des ondes P et S, application a la région de Patras (Grece), These de Doctorate, Université Paris VII, France.
Le Meur, H., J. Virieux, and P. Podvin (1997) Seismic tomogrphy of the Gulf of Corinth: a comparison of methods, Ann. Geofis. 40, 1–24.
Lomax, A., and R. Snieder (1995) Identifying sets of acceptable solutions to non-linear, geophysical inverse problems which have complicated misfit functions, Nonlinear Processes in Geophys. 2, 222–227.
Mohammadioun G., and P. Dervin (1995) A full scale laboratory for seismic studies in Southeastern France: The Middle Durance Fault, in Proc. 5th International Conference on Seismic Zonation, Ouest Editions, 2, 1635–1642
Metropolis, N., A.W. Rosenbluth, M.N. Rosenbluth, A.H. Teller, and E. Teller (1953) Equation of state calculations by fast computing machines, J. Chem. Phys. 1, 1087–1092.
Mosegaard, K., and A. Tarantola (1995) Monte Carlo sampling of solutions to inverse problems, J. Geophys. Res. 100, 12431–12447.
Moser, T.J., T. van Eck, and G. Nolet (1992) Hypocenter determination in strongly heterogeneous earth models using the shortest path method, J. Geophys. Res. 97, 6563–6572.
Nelson, G.D., and J.E. Vidale (1990) Earthquake locations by 3-D finite-difference travel times, Bull. Seism. Soc. Am. 80, 395–410.
Nolte, B., and L.N. Frazer (1994) Vertical seismic profile inversion with genetic algorithms, Geophys. J Int. 117, 162–178.
Pavlis, G.L. (1986) Appraising earthquake hypocenter location errors: a complete practical approach for single event locations, Bull. Seism. Soc. Am. 76, 1699–1717.
Podvin, P. and I. Lecomte (1991) Finite difference computations of traveltimes in very contrasted velocity models: a massively parallel approach and its associated tools, Geophys. J. Int. 105, 271–284.
Press, F. (1968) Earth models obtained by Monte Carlo inversions, J. Geophys. Res. 73, 5223–5234.
Press, W.H., S.A. Teukolosky, W.T. Vetterling, and B.P. Flannery (1993) Numerical recipies in C: the art of scientific computing, Cambridge Univ. Press, Cambridge, 994 pp.
Reasenberg, P. and D. Oppenheimer (1985) FPFIT, FPPLOT and FPPAGE: FORTRAN computer programs for calculating and plotting earthquake fault-plane solutions, U.S. Geol. Surv. Open-File Rep. 85–739, 109 p.
Rothman, D.H. (1985) Nonlinear inversion, statistical mechanics, and residual statics estimation, Geophysics 50, 2784–2796.
Sambridge, M. and G. Drijkoningen (1992) Genetic algorithms in seismic waveform inversion, Geophys. J Int. 109, 323–342.
Sambridge, M. and K. Gallagher (1993) Earthquake hypocenter location using genetic algorithms, Bull. Seism. Soc. Am. 83 1467–1491.
Sambridge, M.S., and B.L.N. Kennett (1986) A novel method of hypocenter location, Geophys. J R. Astron. Soc. 87, 313–331.
Scales, J. A., M. L. Smith, and T.L. Fischer (1992) Global optimization methods for multimodal inverse problems, J Comp. Phys. 103, 258–268.
Schwartz, S.Y., and G.D. Nelson (1991) Loma Prieta aftershock relocation with S-P traveltimes: effects of 3D structure and true error estimates, Bull. Seism. Soc. Am. 81, 1705–1725.
Shearer, P.M. (1997) Improving local earthquake locations using the Ll norm and waveform cross correlation: Application to the Whittier Narrows, California, aftershock sequence., J. Geophys. Res. 102, 8269–8283.
Sen, M.K., and P.L. Stoffa (1995) Global optimization methods in geophysical inversion, Elsevier, Amsterdam, 281 p.
Stoffa, P.L., and M.K. Sen (1991) Nonlinear multiparameter optimization using genetic algorithms: Inversion of plane-wave seismograms, Geophysics 56, 1794–1810.
Tarantola, A. (1987) Inverse problem theory: Methods for data fitting and model parameter estimation, Elsevier, Amsterdam, 613 p.
Tarantola, A. and B. Valette (1982) Inverse problems = quest for information, J Geophys., 50, 159–170.
Vidale, J.E. (1988) Finite-difference calculation of travel times, Bull. Seism. Soc. Am., 78, 2062–2078.
Vilardo, G., G. De Natale, G. Milano, and U. Coppa (1996) The seismicity of Mt. Vesuvius, Tectonophys., 261, 127–138.
Volant P., C. Berge, P. Dervin, M. Cushing., G. Mohammadiou and F. Mathieu (2000) The Southeastern Durance fault permanent network: preliminary results, J. Seism.,in press.
Wiggins, R. A. (1969) Monte Carlo inversion of body wave observations, J Geophys. Res. 74, 3171–3181.
Wittlinger, G., G. Herquel, and T. Nakache (1993) Earthquake location in strongly heterogeneous media, Geophys. J Int. 115, 759–777.
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Lomax, A., Virieux, J., Volant, P., Berge-Thierry, C. (2000). Probabilistic Earthquake Location in 3D and Layered Models. In: Thurber, C.H., Rabinowitz, N. (eds) Advances in Seismic Event Location. Modern Approaches in Geophysics, vol 18. Springer, Dordrecht. https://doi.org/10.1007/978-94-015-9536-0_5
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DOI: https://doi.org/10.1007/978-94-015-9536-0_5
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