Summary
An algorithm for the optimum distribution of any number of regional seismic stations is formulated. The information needed from a given region is the relative distribution of seismic intensity and the travel times of seismic waves used in earthquake location procedure. To define the optimum distribution of a regional network, some generalization of D-planning (minimization of the ellipsoid volume of earthquake location errors) was applied. The D-optimum criterion is generalized for a case where equations describing the process are nonlinear and when the most probable values of the sought parameters (origin time and earthquake focus coordinates) are not known.
As an example of the algorithm application, the optimum distribution of seismic stations in the central district of the Lublin Coal Basin in Poland is given.
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References
Atkinson, A. C., Hunter, W. G. (1968),The design of experiments for parameter estimation, Technometries,10, 271–289.
Atwood, C. L. (1973),Sequences converging to D-optimal designs of experiments, Annals of Statist.,1, 342–352.
Azbiel, J. Ya., Kylis-Borok, V. V., Yanovskaya, T. B. (1966),Mietodika sovmiestnoy interprietacji y godografov i amplitudnykh krivykh pri izuchenii vierchniej mantii, Vychislitelnaja siejsmologia, Vyp.2, 3–46.
Box, G. E. P., Lucas, H. L. (1959),Design of experiments in non-linear situations, Biometrika,46, 77–90.
Box, G. E. P., Hunter, W. G. (1965),Sequential design of experiments for non-linear models. IBM Scientific Computing Symposium in Statist., 113–137.
Box, M. J., Draper, N. R. (1971),Factorial designs, the |XX|criterion and some related matters, Technometrics,13, 731–742.
Chernoff, H. (1953),Locally optimum designs for estimating parameters, Ann. Math. Statist.,24, 586–602.
Dembowski, Z., Porzycki, J. (1967),Wyniki prac geologiczno-posukiwawczych prowadzonych na nowo odkrytym Lubelskim Zag-Tebiu Weglowym., Prz. Geol.15, 4–10.
Dembowski, Z. (1974),Warunki geologiczono-górnicze w Lubelskim Zaglebiu Weglowym., Kwart. Geol.18, 459–474.
Douglas, A. (1967),Joint epicentre determination, Nature215, 47–48.
Douglas, A., Lil-wall, R. C. (1972),Methods of estimating travel times and epicentres, Geoph. J. Roy. Astr. Soc.30, 187–197.
Draper, N. R., Smith, H.,Applied regression analysis (John Wiley and Sons, Inc., New York, London, Sydney, 1966).
Draper, N. R., Hunter, W. G. (1967a),The use of prior distributions in the design of experiments for parameter estimation in nonlinear situations, Biometrica54, 147–153.
Draper, N. R., Hunter, W. G. (1967b),The Use of prior distributions in the design of experiments for parameter estimation in nonlinear situations — multiresponse case, Biometrica54, 662–665.
Dykstra, Otto, Jr. (1971),The augmentation of experimental data to maxime |X X|. Technometrics13, 682–688.
Fedorov, V. V.,Theory of optimal experiments (Academic Press, New York, 1972).
Flinn, E. A. (1965),Confidence regions and error determinations for seismic event location, Rev. Geophys.3, 157–185.
Hill, W. J., Hunter, W. G. (1974),Design of experiments for subsets of parameters, Technometrics16, 425–434.
John, R. C. St., Draper, N. R. (1975),D-optimality for regression designs: a review, Technometers17, 15–23.
Kiefer, J. (1959),Optimum experimental designs, J. Roy. Statist., Soc.B 21, 272–319.
Kiefer, J., Wolfowitz, J. (1959),Optimum designs in regression problems, Ann. Math. Statist.30, 271–294.
Kijko, A. (1975a),Methods for determining positions of very near earthquakes, Publs. Inst. Geophys. Pol. Ac. Sci. 84.
Kijko, A. (1975b),An analysis of optimal configuration of seismic stations in mines in a locally inhomogeneous medium, Acta Geoph. Pol.XXIII, 319–325.
Kijko, A. (1975c),On optimal extensions of regional networks of seismic stations, Publs. Inst. Geoph. Pol. Ac. Sci.96, 57–119.
Kijko, A. (1976a),An analysis of optimal recording of mine shocks in anisotropic media. I: An analysis of an optimal configuration of seismic stations in anisotropic-homogeneous media, Acta Geoph. Pol. (in print).
Kijko, A. (1976b),An analysis of optimal recording of mine shocks in anisotropic media. II: An analysis of optimal configuration of seismic stations in anisotropic-statistically perturbed media, Acta Geoph. Pol. (in print).
Kijko, A. (1976c),An analysis of the extension of the regional seismic network in Upper Silesia, Acta Geoph. Pol.XXIV, 205–215.
Kijko, A. (1977),Optimum seismic network in the Ostrava Coal Basin, Czechoslovakia, Acta Geophys. Pol.XXV (in print).
Kondorskaya, N. V., Zelankina, T. S., Mebel, S. S., Vartanova, L. Yu. (1966)Nekotrye rezultaty primienieniya elektronnoy vychislitelnoy mashiny pri obobshchenii seysmicheskikh nablyudenly. Vychislitelnaya seysmologia1, 31–53.
Lilwall, R. C., Douglas, A. (1970),Estimation of P-wave travel times using the joint epicentre method, Geophys. J. Roy. Astr. Soc.19, 165–181.
Papoulis, A.,Probability, random variables, and stochastic processes (McGraw-Hill, Inc, 1965).
Porzycki, J. (1970),Lubelskie Zagłębie Węglowe, Przewodnik XLII Zjazdu Pol. Tow. Geol., 33–55.
Slavina, L. B. (1971),O zavisimosti opredielenya połozenya epicentra zemletryaseniya of raspolozenya stancij i ot osobennostey vremion probega P-voln, AN SSSR, Fiz. Zemli,2, 77–87.
Veith, K. F. (1975),Refined hypocenters and accurate reliability estimates, Bull. Seism. Soc. Am.,65, 1199–1222.
Wald, A. (1943),On the efficient design of statistical investigations, Ann. Math. Statist14, 134–140.
Wynn, H. P. (1970),The sequential generation of D-optimum experimental designs, Ann. Math. Statist.41, 1655–1664.
Wynn, H. P. (1972),Results in the theory and construction of D-optimum experimental designs (with discussion). J. R. Statist. Soc.B34, 133–147; 170–186.
Zelichowski, A. M. (1972),Rozwój budowy geologicznej obszaru miedzy górami Swietokrzyskimi i Bugiem, Biul. Inst. Geol. 263.
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Kijko, A. An algorithm for the optimum distribution of a regional seismic network—I. PAGEOPH 115, 999–1009 (1977). https://doi.org/10.1007/BF00881222
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DOI: https://doi.org/10.1007/BF00881222