Bayesian inversion of microtremor array dispersion data in southwestern British Columbia

Geophysical Journal International

Volumn 183, Issue 2, 2010, Pages 923-940

  Molnar, Sheri ^a,b   Dosso, Stan E ^a   Cassidy, John F ^a,b  

^a UNIVERSITY OF VICTORIA   (Canada)

^b NATURAL RESOURCES CANADA   (Canada)

Author keywords

Downhole methods; Inverse theory; Probability distributions; Site effects; Surface waves and free oscillations

Indexed keywords

APPROPRIATE MODELS; BAYESIAN; BAYESIAN FORMULATION; BAYESIAN INFORMATION CRITERION; BAYESIAN INVERSION; BRITISH COLUMBIA; COMPRESSIONAL; CONE PENETRATION TESTING; CONFIDENCE INTERVAL; DATA ERRORS; DISPERSION CURVES; DISPERSION DATA; DOWNHOLES; EFFICIENT IMPLEMENTATION; FRASER RIVER; GAUSSIAN ERRORS; GEOLOGICAL SETTING; GEOPHYSICAL MODELS; INTER-RELATIONSHIPS; INVERSE THEORY; INVERSION RESULTS; LINEAR GRADIENTS; MARKOV CHAIN MONTE CARLO; METROPOLIS-HASTINGS SAMPLINGS; MICROTREMOR ARRAY; MICROTREMORS; NON LINEAR INVERSION; NON-PARAMETRIC ESTIMATIONS; NONLINEAR PROBLEMS; NUMBER OF LAYERS; PARAMETER UNCERTAINTY; PARAMETRIZATIONS; POSTERIOR PROBABILITY; POSTERIORI; POWER-LAW; RAYLEIGH SURFACE WAVES; RESIDUAL ANALYSIS; RESOLVING POWER; SEISMIC RISK; SHEAR-WAVE VELOCITY; SITE EFFECTS; SITE RESPONSE; UNCERTAINTY ESTIMATES; UNCERTAINTY ESTIMATION; URBAN NOISE; VELOCITY DISPERSION; WAVE VELOCITY;

ACOUSTIC WAVE VELOCITY; BAYESIAN NETWORKS; COVARIANCE MATRIX; DISPERSION (WAVES); DISPERSIONS; ERROR STATISTICS; ESTIMATION; INVERSE PROBLEMS; MONTE CARLO METHODS; PROBABILITY DENSITY FUNCTION; SEISMOLOGY; SHEAR FLOW; SHEAR WAVES; STATISTICAL TESTS; STREAM FLOW; SURFACE TESTING; SURFACE WAVES; SURFACES; UNCERTAINTY ANALYSIS; WAVE PROPAGATION;

PROBABILITY DISTRIBUTIONS;

BAYESIAN ANALYSIS; DATA INVERSION; MARKOV CHAIN; MICROTREMOR; MONTE CARLO ANALYSIS; PARAMETERIZATION; RAYLEIGH WAVE; S-WAVE; SEISMIC DATA; SEISMIC NOISE; SITE EFFECT; VELOCITY PROFILE; WAVE VELOCITY;

BRITISH COLUMBIA; CANADA; FRASER DELTA; VANCOUVER;

EID: 77958544942     PISSN: 0956540X     EISSN: 1365246X     Source Type: Journal    
DOI: 10.1111/j.1365-246X.2010.04761.x     Document Type: Article

References (69)

1. Aki, K., 1957. Space and time spectra of stationary stochastic waves, with special reference to microtremors, Bull. Earthq. Res. Inst., 35, 415-456.
2. Asten, M.W. & Henstridge, J.D., 1984. Array estimators and use of microseisms for reconnaissance of sedimentary basins, Geophysics, 49, 1828-1837.
3. Aster, R.C., Borcher, B. & Thurber, C.H., 2005. Parameter Estimation and Inverse Problems, Elsevier, Amsterdam
4. Baki{dotless}r, B.S., Sucuoǧlu, H. & Yi{dotless}lmaz, T., 1999. An overview of local site effects and the associated building damage in Adapazari{dotless} during the 17 August 1999 İzmit earthquake, Bull. seism. Soc. Am., 92, 509-526.
5. Bodin, T. & Sambridge, M., 2009. Seismic tomography with the reversible jump algorithm, Geophys. J. Int., 178, 1411-1436.
6. Booth, D.B., Wells, R.E. & Givler, R.W., 2004. Chimney damage in the Greater Seattle area from the Nisqually earthquake of 28 February 2001, Bull. seism. Soc. Am., 94, 1143-1158.
7. Calderón-Macías, C. & Luke, B., 2007. Improved parameterisation to invert Rayleigh-wave data for shallow profiles containing stiff inclusions, Geophysics, 72, U1-U10.
8. Capon, J., 1969. High-resolution frequency-wavenumber spectrum analysis, Proc. IEEE, 57, 1408-1418.
9. Cornou, C., Ohrnberger, M., Boore, D.M., Kudo, K. & Bard, P.-Y., 2006. Derivation of structural models from ambient vibration array recordings: Results from an International blind test, in Proceedings3rd International Symposium on the Effects of Surface Geology on Seismic Motion, Grenoble, France, August 30th to September 1st, 2006.
10. Dalguer, L.A., Irikura, K., Riera, J.D. & Chiu, H.C., 2001. The importance of the dynamic source effects on strong ground motion during the 1999 Chi-Chi, Taiwan, earthquake: brief interpretation of the damage distribution on buildings, Bull. seism. Soc. Am., 91, 1112-1127.
11. Dallimore, S.R., Edwardson, K.A., Hunter, J.A., Clague, J.J., Meldrum, J.L. & Luternauer, J.L., 1995. Composite Geotechnical Logs for Two Deep Boreholes in the Fraser River Delta, British Columbia, Geological Survey of Canada, Open file 3018.
12. Dettmer, J., Dosso, S.E. & Holland, C.W., 2007. Uncertainty estimation in seismo-acoustic reflection travel-time inversion, J. acoust. Soc. Am., 122, 161-176.
13. Dettmer, J., Dosso, S.E. & Holland, C.W., 2009. Model selection and Bayesian inference for high-resolution seabed reflection inversion, J. acoust. Soc. Am., 125, 706-716.
14. Di Giulio, G., Cornou, C., Ohrnberger, M., Wathelet, M. & Rovelli, A., 2006. Deriving wavefield characteristics and shear-velocity profiles from two-dimensional small-aperture arrays analysis of ambient vibrations in a small-size alluvial basin, Colfiorito, Italy, Bull. Seism. Soc. Am., 96, 1915-1933.
15. Dosso, S.E., 2002. Quantifying uncertainties in geoacoustic inversion I: A fast Gibbs sampler approach, J. acoust. Soc. Am., 111, 2166-2177.
16. Dosso, S.E. & Wilmut, M.J., 2008. Uncertainty estimation in simultaneous Bayesian tracking and environmental inversion, J. acoust. Soc. Am., 124, 82-97.
17. Dosso, S.E., Wilmut, M.J. & Lapinski, A.-L., S., 2001. An adaptive-hybrid algorithm for geoacoustic inversion, IEEE J. Ocean. Eng., 26, 324-336.
18. Dosso, S.E., Nielsen, P.L. & Wilmut, M.J., 2006. Data error covariance in matched-field geoacoustic inversion, J. acoust. Soc. Am., 119, 208-219.
19. FEMA, 2003. NEHRP (National Earthquake and Hazards Reduction Program) recommended provisions for seismic regulations for new buildings and other structures, in Building Seismic Safety Council, Washington, DC
20. Foti, S., Comina, C., Boiero, D. & Socco, L.V., 2009. Non-uniqueness in surface-wave inversion and consequences on seismic site analyses, Soil Dyn. Eq. Eng., 29, 982-993.
21. Freund, J. E., 1967. Modern Elementary Statistics, Prentice-Hall, Englewood Cliffs, NJ
22. Gelfand, A.E. & Dey, D.K., 1994. Bayesian model choice: asymptotics and exact calculations, J. R. Stat. Soc. 56, 501-514.
23. Gilks, W.R., Richardson, S. & Spiegelhalter, D.J. (Eds.), 1996. Markov Chain Monte Carlo in Practice, Chapman & Hall, Boca Raton, FL
24. Gouveia, W.P. & Scales, J.A., 1998. Bayesian seismic waveform inversion: parameter estimation and uncertainty analysis, J. geophys. Res., 103, 2759-2779.
25. Haskell, N.A., 1953. The dispersion of surface waves on multilayered media, Bull. seism. Soc. Am., 43, 17-34.
26. Horike, M., 1985. Inversion of phase velocity of long-period microtremors to the S-wave-velocity structure down to the basement in urbanized areas, J. Phys. Earth, 33, 59-96.
27. Hunter, J.A. & Christian, H.A., 2001. Use of shear-wave velocities to estimate thick soil amplification effects in the Fraser River delta, British Columbia, in Symposium Proceedings on the Application of Geophysics to Engineering and Environmental Problems, Environmental and Engineering Geophysical Society, Denver, Colorado
28. Hunter, J.A., Woeller, D.J. & Luternauer, J.L., 1991. Comparison of surface, borehole, and seismic cone penetrometer methods for determining the shallow shear wave velocity structure in the Fraser River delta, British Columbia, in Current Research, Part A, pp. 23-26, Geological Survey of Canada, Paper 91-1A.
29. Hunter, J.A., Burns, R.A., Good, R.L. & Pelletier, C.F., 1998.A Compilation of Shear-Wave Velocities and Borehole Geophysical Logs in Unconsolidated Sediments of the Fraser River delta, British Columbia, Geological Survey of Canada, Open file 3622.
30. Hunter, J.A., Benjumea, B., Harris, J.B., Miller, R.D., Pullan, S.E., Burns, R.A. & Good, R.L., 2002. Surface and downhole shear-wave seismic methods for thick soil site investigations, Soil Dyn. Eq. Eng., 22, 931-941.
31. Ingber, L., 1989. Very fast simulated re-annealing, Math. Comput. Model., 12, 967-973.
32. Jongmans, D., Ohrnberger, M. & Wathelet, M., 2005. Final report WP13: Recommendations for quality array measurements and processing, European Commission-Research General Directorate, Site Effects Assessment Using Ambient Excitiations (SESAME), Deliverable 24.13, March 2005.
33. Kass, R.E. & Raftery, A.E., 1995. Bayes factors, J. Am. Stat. Assoc., 90, 773-795.
34. Kawase, H., 1996. The cause of the damage belt in Kobe: "The basin-edge effect, " constructive interference of the direct S-wave with the basin-induced diffracted/Rayleigh waves, Seism. Res. Lett., 67, 25-34.
35. Kind, F., Fäh, D. & Giardini, D., 2005. Array measurements of S-wave velocities from ambient vibrations, Geophys. J. Int., 160, 114-126.
36. Lacoss, R.T., Kelly, E.J. & Toksoz, M.N., 1969. Estimation of seismic noise structure using arrays, Geophysics, 34, 21-38.
37. Lai, C., Foti, S. & Rix, G., 2005. Propagation of data uncertainty in surface wave inversion, J. Environ. Eng. Geophys., 10, 219-228.
38. Levson, V.M., Monahan, P.A. & Mate, D.J., 1998. Observed relationships between geology and liquefaction/amplification hazards, in Proceedings of the 8th International Congress, pp. 849-855, eds Moore, D. & Hungr, O., International Association for Engineering Geology and the Environment, Vancouver, Canada, September 21-25, 1998.
39. MacKay, D.J.C., 2003. Information Theory, Inference, and Learning Algorithms, Cambridge University Press, Cambridge, UK
40. Malinverno, A., 2002. Parsimonious Bayesian Markov chain Monte Carlo inversion in a nonlinear geophysical problem, Geophys. J. Int., 151, 675-688.
41. Massey, F.J., 1951. The Kolmogorov-Smirnov test for goodness of fit, J. Am. Stat. Assoc., 46, 68-78.
42. Molnar, S., Cassidy, J.F. & Dosso, S.E., 2004. Comparing intensity variation of the 2001 Nisqually earthquake to geology in Victoria, British Columbia, Bull. seism. Soc. Am., 94, 2229-2238.
43. Molnar, S., Cassidy, J.F., Monahan, P.A. & Dosso, S.E., 2007. Comparison of geophysical shear-wave velocity methods, in Proceedings 9th Canadian Conference of Earthquake Engineering, Ottawa, Ontario, June 26-29, 2007, Paper 1173.
44. Monahan, P.A. & Levson, V.M., 1997. Earthquake hazard assessment in greater Victoria, British Columbia: development of a shear-wave velocity model for the Quaternary deposits, in Geological Fieldwork 1996, pp. 467-479, British Columbia Geological Survey, Paper 1997-1.
45. Monahan, P.A. & Levson, V.M., 2000. Quaternary Geological Map of Greater Victoria, British Columbia Geological Survey, Ministry of Energy and Mines, Victoria, BC, Geoscience Map 2000-2002.
46. Monahan, P.A. & Levson, V.M., 2001. Development of a shear-wave velocity model of the near-surface deposits of southwestern British Columbia, Canada, in Proceedings 4th International Conference on Recent Advances in Geotechnical Earthquake Engineering and Soil Dynamics, San Diego, California, March 26-31, 2001, Paper 11.16.
47. Montgomery, D.C. & Peck, E.A., 1992. Introduction to Linear Regression Analysis, Wiley, New York
48. Nelder, J.A. & Mead, R., 1965. A simplex method for function minimization, Comput. J., 7, 308-313.
49. Ohrnberger, M., Schissele, E., Cornou, C., Wathelet, M., Savvaidis, A., Scherbaum, F., Jongmans, D. & Kind, F., 2004. Microtremor array measurements for site effect investigations: comparison of analysis methods for field data crosschecked by simulated wavefields, in Proceedings 13th World Conference on Earthquake Engineering, Vancouver, Canada, August 1-6, 2004, Paper 940.
50. Onur, T., Ventura, C.E. & Finn, W.D.L., 2005. Regional seismic risk in British Columbia-damage and loss distribution in Victoria and Vancouver, Can. J. Civil Eng., 32, 361-371.
51. Parker, R.L., 1994. Geophysical Inverse Theory, Princeton University Press, Princeton, NJ
52. Parolai, S., Mucciarelli, M., Gallipoli, M.R., Richwalski, S.M. & Strollo, A., 2007. Comparison of empirical and numerical site responses at the Tito test site, southern Italy, Bull. seism. Soc. Am., 97, 1413-1431.
53. Picozzi, M., Strollo, A., Parolai, S., Durukal, E., Ozel, O., Karabulut, S., Zschau, J. & Erdik, M., 2009. Site characterisation by seismic noise in Istanbul, Turkey, Soil Dyn. Eq. Eng., 29, 469-482.
54. Renalier, F., Jongmans, D., Wathelet, M., Cornou, C., Endrun, B., Ohrnberger, M. & Savvaidis, A., 2009. Influence of parameterisation on inversion of surface wave dispersion curves and definition of a strategy of inversion, EGU General Assembly, Geophys. Res. Abstr., 11, EGU2009-7799.
55. Roten, D. & Fäh, D., 2007. A combined inversion of Rayleigh wave dispersion and 2-D resonance frequencies, Geophys. J. Int., 168, 1261-1275.
56. Sambridge, M. & Mosegaard, K., 2002. Monte Carlo methods in geophysical inverse problems, Rev. Geophys., 40, 1-29.
57. Sambridge, M., Gallagher, K., Jackson, A. & Rickwood, P., 2006. Trans-dimensional inverse problems, nodel comparision and the evidence. Geophy. J. Int., 167, 528-542.
58. Savvaidis, A., Ohrnberger, M., Wathelet, M., Cornou, C., Bard, P.-Y. & Theodulidis, N., 2009. Variability analysis of shallow shear wave velocity profiles obtained from dispersion curve inversion considering multiple model parametrizations, SSA Meeting, Monterey, CA, Seism. Res. Lett., 80, 354.
59. Schevenels, M., Lombaert, G., Degrande, G. & François, S., 2008. A probabilitistic assessment of resolution in the SASW test and its impact on the prediction of ground vibrations, Geophys. J. Int., 172, 262-275.
60. Schwartz, G., 1978. Estimating the dimension of a model, Ann. Stat., 6, 461-464.
61. Socco, L.V. & Boiero, D., 2008. Improved Monte Carlo inversion of surface wave data, Geophys. Prospect., 56, 357-371.
62. Tarantola, A., 1987. Inverse Problem Theory: Methods for Data Fitting and Model Parameter Estimation, Elsevier, Amsterdam
63. Thomson, W.T., 1950. Transmission of elastic waves through a stratified solid medium, J. appl. Phys., 21, 89-93.
64. S inversion, J. Seism., 12, 1-19.
65. Woeller, D.J., Luternauer, J.L. & Hunter, J.A., 1993. Presentation and Interpretation of Seismic Cone Penetration Test Data, Fraser River Delta, British Columbia, Geological Survey of Canada, Open file 2715.
66. Wuorinen, V., 1974. A preliminary seismic microzonation of Victoria, British Columbia M.A. thesis University of Victoria, Victoria, British Columbia
67. Xia, J., Miller, R.D. & Park, C.B., 1999. Estimation of near-surface shear-wave velocity by inversion of Rayleigh wave. Geophysics, 64, 691-700.
68. Xia, J., Miller, R.D., Park, C.B., Hunter, J.A. & Harris, J.B., 2000. Comparing shear-wave velocity profiles from MASW with borehole measurements in unconsolidated sediments, Fraser River delta, B.C., Canada, J. Environ. Eng. Geophys., 5, 1-13.
69. Xia, J., Miller, R.D., Yixian, X., Yinhe, L., Chao, C., Jiangping, L., Ivanov, J. & Zheng, C., 2009. High-frequency Rayleigh-wave method, J. Earth. Sci., 20, 563-579.