Abstract
Earthquake location is a well-defined inverse problem to which the mathematical fundamentals of existing methodologies were established nearly a century ago. However, in quantitative seismology, achieving accurate, bias-free earthquake locations still remains to be the one of most important and challenging tasks. In this article, we give an overview on various earthquake location methods, that vary from linearized to nonlinear, from grid search to probabilistic algorithms. We review single and multiple-event location techniques, along with computational complexities of each algorithm. An example from a real-world earthquake location problem is given to highlight the importance of data availability in achieving bias-free earthquake locations. We discuss earthquake location accuracy, and uncertainty estimation that originate from measurement and modelling errors. We end with a list that summarizes publicly available earthquake location software packages. We conclude with an outlook for future directions towards data driven machine learning techniques in earthquake location research.
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References
Asim, K.M., Martínez-Álvarez, F., Idris, A., Iqbal, T.: Earthquake prediction model using support vector regressor and hybrid neural networks. PLoS ONE 13(7), e0199004 (2018). https://doi.org/10.1371/journal.pone.0199004
Bergman, E.A., Benz, H.M., Karasözen, E., Yeck, W.: Global catalog of calibrated earthquake locations. https://www.sciencebase.gov/catalog/item/59fb91fde4b0531197b16ac7 (2020)
Billings, S.D., Kennett, B.L.N., Sambridge, M.S.: Hypocentre location: genetic algorithms incorporating problem-specific information. Geophys. J. Int. 118(3), 693–706 (1994). https://doi.org/10.1111/j.1365-246X.1994.tb03994.x
Bondár, I., McLaughlin, K.: Seismic location bias and uncertainty in the presence of correlated and non-Gaussian travel-time errors. Bull. Seismol. Soc. Am. 99(1), 172 (2009). https://doi.org/10.1785/0120080922
Bondár, I., Myers, S.C., Engdahl, E.R.: Earthquake location. In: Beer, M., Kougioumtzoglou, I.A., Patelli, E., Au, I.S.K. (eds.) Encyclopedia of Earthquake Engineering. Springer, Berlin (2014). https://doi.org/10.1007/978-3-642-36197-5_184-1
Boyd, T.M., Snoke, J.A.: Error estimates in some commonly used earthquake location programs. Seismol. Res. Lett. 55(2), 3–6 (1984). https://doi.org/10.1785/gssrl.55.2.3
Buland, R.: The mechanics of locating earthquakes. Bull. Seismol. Soc. Am. 66(1), 173–187 (1976)
Buland, R., Chapman, C.H.: The computation of seismic travel times. Bull. Seismol. Soc. Am. 73(5), 1271 (1983)
Copley, A., Karasözen, E., Oveisi, B., Elliott, J.R., Samsonov, S., Nissen, E.: Seismogenic faulting of the sedimentary sequence and laterally variable material properties in the Zagros Mountains (Iran) revealed by the August 2014 Murmuri (E. Dehloran) earthquake sequence. Geophys. J. Int. 203, 1436–1459 (2015). https://doi.org/10.1093/gji/ggv365
Croux, C., Rousseeuw, P.J.: Time-efficient algorithms for two highly robust estimators of scale. In: Dodge, Y., Whittaker, J. (eds.) Computational Statistics, pp. 411–428. Physica-Verlag HD, Heidelberg (1992)
DeVries, P.M.R., Viégas, F., Wattenberg, M., Meade, B.J.: Deep learning of aftershock patterns following large earthquakes. Nature 560(7720), 632–634 (2018). https://doi.org/10.1038/s41586-018-0438-y
Dewey, J.W.: Seismic studies with the method of joint hypocenter determination. Ph.D. thesis, University of California (1971)
Dewey, J.W.: Seismicity and tectonics of Western Venezuala. Bull. Seismol. Soc. Am. 62, 1711–1751 (1972)
Douglas, A.: Joint epicentre determination. Nature 215, 47–48 (1967)
Engdahl, E., Bergman, E.: Identification and validation of reference events within the area being regionally monitored by IMS stations in Asia and North Africa. Tech. rep., Colorado Univ. at Boulder (2000)
Engdahl, E.R., van der Hilst, R., Buland, R.: Global teleseismic earthquake relocation with improved travel times and procedures for depth determination. Bull. Seismol. Soc. Am. 88(3), 722 (1998)
Evernden, J.F.: Precision of epicenters obtained by small numbers of world-wide stations. Bull. Seismol. Soc. Am. 59(3), 1365 (1969)
Felix, W., Schaff, D.P.: Large-scale relocation of two decades of Northern California seismicity using cross-correlation and double-difference methods. J. Geophys. Res. Solid Earth (2008). https://doi.org/10.1029/2007JB005479
Flinn, E.A.: Confidence regions and error determinations for seismic event location. Rev. Geophys. 3(1), 157–185 (1965). https://doi.org/10.1029/RG003i001p00157
Fröhlich, C.: An efficient method for joint hypocenter determination for large groups of earthquakes. Comput. Geosci. 5(3), 387–389 (1979). https://doi.org/10.1016/0098-3004(79)90034-7
Geiger, L.: Probability method for the determination of earthquake epicenters from the arrival time only. Bull. St. Louis. Univ 8, 60–71 (1912)
Gelman, A., Carlin, J.B., Stern, H.S., Dunson, D.B., Vehtari, A., Rubin, D.B.: Bayesian Data Analysis, Texts in Statistical Science Series, 3rd edn. CRC Press, Boca Raton (2014)
Got, J.L., Fréchet, J., Klein, F.W.: Deep fault plane geometry inferred from multiplet relative relocation beneath the south flank of Kilauea. J. Geophys. Res. Solid Earth 99(B8), 15375–15386 (1994). https://doi.org/10.1029/94JB00577
Havskov, J., Ottemöller, L.: Location. In: Havskov, J. (ed.) Routine Data Processing in Earthquake Seismology: With Sample Data, Exercises and Software, pp. 101–149. Springer, Dordrecht (2010). https://doi.org/10.1007/978-90-481-8697-6_5
Havskov, J., Bormann, P., Schweitzer, J.: Seismic source location. In: Borman, P. (ed.) New Manual of Seismological Observatory Practice 2 (NMSOP-2), pp. 1–36. Deutsches GeoForschungsZentrum, Potsdam (2012)
Husen, S., Hardebeck, J.L.: Earthquake location accuracy (2010). https://doi.org/10.5078/corssa-55815573. http://www.corssa.org
Jordan, T.H., Sverdrup, K.A.: Teleseismic location techniques and their application to earthquake clusters in the South-Central Pacific. Bull. Seismol. Soc. Am. 71(4), 1105 (1981)
Karasözen, E., Nissen, E., Büyükakpınar, P., Cambaz, M., Kahraman, M., Kalkan-Ertan, E., Abgarmi, B., Bergman, E., Ghods, A., Özacar, A.: The 2017 July 20 \(M_w\) 6.6 Bodrum–Kos earthquake illuminates active faulting in the Gulf of Gökova, SW Turkey. Geophys. J. Int. 214(1), 185–199 (2018)
Kennett, B.L.N., Engdahl, E.R.: Traveltimes for global earthquake location and phase identification. Geophys. J. Int. 105(2), 429–465 (1991). https://doi.org/10.1111/j.1365-246X.1991.tb06724.x
Kennett, B.L., Engdahl, E.R., Buland, R.: Constraints on seismic velocities in the Earth from traveltimes. Geophys. J. Int. 122(1), 108–124 (1995). https://doi.org/10.1111/j.1365-246X.1995.tb03540.x
Kirkpatrick, S., Gelatt, C.D., Vecchi, M.P.: Optimization by simulated annealing. Science 220(4598), 671–680 (1983). https://doi.org/10.1126/science.220.4598.671
Kissling, E.: Geotomography with local earthquake data. Rev. Geophys. 26, 659–698 (1988). https://doi.org/10.1029/RG026i004p00659
Klein, F.: User’s guide to HYPOINVERSE–2000, a Fortran program to solve for earthquake locations and magnitudes (2002)
Kong, Q., Trugman, D.T., Ross, Z.E., Bianco, M.J., Meade, B.J., Gerstoft, P.: Machine learning in seismology: turning data into insights. Seismol. Res. Lett. 90(1), 3–14 (2018). https://doi.org/10.1785/0220180259
Lahr, J.: HYPOELLIPSE, a computer program for determining local earthquake hypocentral parameters, magnitude and first motion pattern (1999). Revised i 2012
Lee, W., Lahr, J.: HYPO71, a computer program for determining hypocenter, magnitude and first motion pattern of local earthquakes (1972)
Lepage, G.P.: A new algorithm for adaptive multidimensional integration. J. Comput. Phys. 27(2), 192–203 (1978). https://doi.org/10.1016/0021-9991(78)90004-9
Lienert, B., Berg, E., Frazer, N.: “hypocenter”: an earthquake location method using centred, scaled and adaptively damped least squares. Bull. Seismol. Soc. Am. 76, 771–783 (1986)
Lin, G., Shearer, P.: Tests of relative earthquake location techniques using synthetic data. J. Geophys. Res. Solid Earth (2005). https://doi.org/10.1029/2004JB003380
Lin, G., Shearer, P.: The COMPLOC earthquake location package. Seismol. Res. Lett. 77(4), 440–444 (2006). https://doi.org/10.1785/gssrl.77.4.440
Lomax, A., Curtis, A.: Fast, probabilistic earthquake location in 3D models using oct-tree importance sampling (2001). www.alomax.net/nlloc/octtree
Lomax, A., Virieux, J., Volant, P., Berge-Thierry, C.: Probabilistic earthquake location in 3D and layered models. In: Thurber, C.H., Rabinowitz, N. (eds.) Advances in Seismic Event Location, pp. 101–134. Springer, Netherlands (2000). https://doi.org/10.1007/978-94-015-9536-0_5
Lomax, A., Michelini, A., Curtis, A.: Earthquake location, direct, global-search methods. In: Meyers, R.A. (ed.) Extreme Environmental Events: Complexity in Forecasting and Early Warning, pp. 230–254. Springer, New York (2011). https://doi.org/10.1007/978-1-4419-7695-6_16
Malcolm, S.: Geophysical inversion with a neighborhood algorithm-I: searching a parameter space. Geophys. J. Int. 138(2), 479–494 (1999). https://doi.org/10.1046/j.1365-246X.1999.00876.x
Menke, W.: Geophysical Data Analysis: Discrete Inverse Theory, 3rd edn. Elsevier/Academic Press, Amsterdam (2012). 10.1016/B978-0-12-397160-9.00001-1
Milne, J.: Earthquakes and Other Earth Movements. Appelton, New York (1986)
Mosegaard, K., Tarantola, A.: Monte Carlo sampling of solutions to inverse problems. J. Geophys. Res. Solid Earth 100(B7), 12431–12447 (1995). https://doi.org/10.1029/94JB03097
Myers, S.C., Johannesson, G., Hanley, W.: A Bayesian hierarchical method for multiple-event seismic location. Geophys. J. Int. 171(3), 1049–1063 (2007). https://doi.org/10.1111/j.1365-246X.2007.03555.x
Myers, S.C., Johannesson, G., Hanley, W.: Incorporation of probabilistic seismic phase labels into a Bayesian multiple-event seismic locator. Geophys. J. Int. (2009). https://doi.org/10.1111/j.1365-246X.2008.04070.x
Myers, S.C., Johannesson, G., Simmons, N.A.: Global-scale p wave tomography optimized for prediction of teleseismic and regional travel times for Middle East events: 1: data set development. J. Geophys. Res. Solid Earth (2011). https://doi.org/10.1029/2010JB007967.B04304
Neal, R.M.: Slice sampling. Ann. Stat. 31(3), 705–767 (2003). https://doi.org/10.1214/aos/1056562461
Nealy, J.L., Benz, H.M., Hayes, G.P., Bergman, E.A., Barnhart, W.D.: The 2008 Wells, Nevada, earthquake sequence: source constraints using calibrated multiple-event relocation and InSAR. Bull. Seismol. Soc. Am. 107(3), 1107–1117 (2017)
Pavlis, G.L., Vernon, F., Harvey, D., Quinlan, D.: The generalized earthquake-location GENLOC package: an earthquake-location library. Comput. Geosci. 30(9), 1079–1091 (2004). https://doi.org/10.1016/j.cageo.2004.06.010
Pujol, J.: Comments on the joint determination of hypocenters and station corrections. Bull. Seismol. Soc. Am. 78(3), 1179 (1988)
Pujol, J.: Joint event location—the JHD technique and applications to data from local seismic networks. In: Thurber, C.H., Rabinowitz, N. (eds.) Advances in Seismic Event Location, pp. 163–204. Springer, Dordrecht (2000). https://doi.org/10.1007/978-94-015-9536-0_7
Reid, H.: The Mechanics of the Earthquake, Vol. II of The California Earthquake of April 18, 1906 (1910)
Richards-Dinger, K.B., Shearer, P.M.: Earthquake locations in southern California obtained using source-specific station terms. J. Geophys. Res. Solid Earth 105(B5), 10939–10960 (2000). https://doi.org/10.1029/2000JB900014
Ritzwoller, M.H., Shapiro, N.M., Levshin, A.L., Bergman, E.A., Engdahl, E.R.: Ability of a global three-dimensional model to locate regional events. J. Geophys. Res. Solid Earth (2003). https://doi.org/10.1029/2002JB002167.2353
Robert, C.P., Casella, G.: Monte Carlo statistical methods. Springer Texts in Statistics., 2nd edn. Springer-Verlag, New York (2004)
Rodi, W.: Grid-search event location with non-Gaussian error models. Phys. Earth Planet. Inter. 158(1), 55–66 (2006). https://doi.org/10.1016/j.pepi.2006.03.010
Ross, Z.E., Meier, M.A., Hauksson, E.: P wave arrival picking and first-motion polarity determination with deep learning. J. Geophys. Res. 123(6), 5120–5129 (2018). https://doi.org/10.1029/2017JB015251
Sambridge, M.: Geophysical inversion with a neighborhood algorithm-II: appraising the ensemble. Geophys. J. Int. 138(3), 727–746 (1999). https://doi.org/10.1046/j.1365-246x.1999.00900.x
Sambridge, M., Drijkoningen, G.: Genetic algorithms in seismic waveform inversion. Geophys. J. Int. 109(2), 323–342 (1992). https://doi.org/10.1111/j.1365-246X.1992.tb00100.x
Sambridge, M., Gallagher, K.: Earthquake hypocenter location using genetic algorithms. Bull. Seismol. Soc. Am. 83(5), 1467–1491 (1993)
Sambridge, M., Kennett, B.: Seismic event location: nonlinear inversion using a neighborhood algorithm. Pure Appl. Geophys. 158(1), 241–257 (2001). https://doi.org/10.1007/PL00001158
Schweitzer, J.: HYPOSAT—an enhanced routine to locate seismic events. Pure Appl. Geophys. 158(1), 277–289 (2001)
Shearer, P.M.: Improving local earthquake locations using the \(l_1\) norm and waveform cross correlation: application to the Whittier Narrows, California, aftershock sequence. J. Geophys. Res. Solid Earth 102(B4), 8269–8283 (1997). https://doi.org/10.1029/96JB03228
Tarantola, A., Valette, B.: Inverse problems—quest for information. J. Geophys. pp. 159–170 (1982)
Tarantola, A.: Inverse Problem Theory and Methods for Model Parameter Estimation. Society for Industrial and Applied Mathematics. Philadelphia, PA, USA (2004)
Trugman, D.T., Shearer, P.M.: Growclust: a hierarchical clustering algorithm for relative earthquake relocation, with application to the Spanish Springs and Sheldon, Nevada, earthquake sequences. Seismol. Res. Lett. 88(2A), 379–391 (2017). https://doi.org/10.1785/0220160188
Waldhauser, F.: HypoDD: a computer program to compute doubledifference earthquake locations (2001)
Waldhauser, F., Ellsworth, W.L.: A double-difference earthquake location algorithm: method and application to the Northern Hayward Fault, California. Bull. Seismol. Soc. Am. 90(6), 1353 (2000). https://doi.org/10.1785/0120000006
Walker, R.T., Bergman, E.A., Szeliga, W., Fielding, E.J.: Insights into the 1968–1997 Dasht-e-Bayaz and Zirkuh earthquake sequences, eastern Iran, from calibrated relocations, InSAR and high-resolution satellite imagery. Geophys. J. Int. 187, 1577–1603 (2011)
Walker, R.T., Bergman, E.A., Elliott, J.R., Fielding, E.J., Ghods, A.R., Ghoraishi, M., Jackson, J., Nazari, H., Nemati, M., Oveisi, B., Talebian, M., Walters, R.J.: The 2010–2011 South Rigan (Baluchestan) earthquake sequence and its implications for distributed deformation and earthquake hazard in southeast Iran. Geophys. J. Int. 193, 349–374 (2013). https://doi.org/10.1093/gji/ggs109
Wolfe, C.J.: On the mathematics of using difference operators to relocate earthquakes. Bull. Seismol. Soc. Am. 92(8), 2879 (2002). https://doi.org/10.1785/0120010189
Acknowledgements
Both authors thank Eric Bergman for his constructive comments and suggestions about this review article. The first author is especially much thankful to him for teaching and sharing this fascinating research field of earthquake location.
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Karasözen, E., Karasözen, B. Earthquake location methods. Int J Geomath 11, 13 (2020). https://doi.org/10.1007/s13137-020-00149-9
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DOI: https://doi.org/10.1007/s13137-020-00149-9
Keywords
- Inverse problems
- Computational seismology
- Error estimation
- Probabilistic methods
- Earthquake location
- Multiple-event