Register      Login
Exploration Geophysics Exploration Geophysics Society
Journal of the Australian Society of Exploration Geophysicists
RESEARCH ARTICLE (Open Access)

Development and numerical tests of a Bayesian approach to inferring shallow velocity structures using microtremor arrays

Ikuo Cho 1 4 Takaki Iwata 2 3
+ Author Affiliations
- Author Affiliations

1 Geological Survey of Japan, AIST, 1-1-1 Higashi, Tsukuba, Ibaraki 305-8567, Japan.

2 College of Community Development, Tokiwa University, 1-430-1 Miwa, Mito, Ibaraki 310-8585, Japan.

3 Institute of Statistical Mathematics, 10-3 Midori-cho, Tachikawa, Tokyo 190-8562, Japan.

4 Corresponding author. Email: ikuo-chou@aist.go.jp

Exploration Geophysics 49(6) 881-890 https://doi.org/10.1071/EG18011
Submitted: 17 January 2018  Accepted: 19 January 2018   Published: 19 March 2018
Originally submitted to SEGJ 1 June 2017, accepted 22 October 2017  

Journal compilation © ASEG 2018 Open Access CC BY-NC-ND

Abstract

We propose an empirical Bayesian approach to inferring shallow (depth ranges from a few to several tens of metres) S-wave velocity structures using microtremor arrays and execute numerical tests to assess the feasibility of this approach. In our approach, the estimate of the S-wave structure (posterior) is derived from an empirical S-wave structure model (prior) and phase velocities of Rayleigh waves obtained with microtremor arrays. In other words, we aim to find a model that is close to the empirical model and is able to explain phase velocities with a 1D surface-wave theory. The inversion is stabilised by the constraints from the prior model so that model parameterisation with many thin layers can be adopted. The velocity structure is individually estimated for each of two cases (assumptions): the case where we assume fundamental-mode dominance and the case where we take into account the higher modes. Optimal values of the model parameters (e.g. a thickness parameter) are found, based on Akaike’s Bayesian Information Criterion (ABIC), and the choice of the better assumption of the surface-wave theory is also based on ABIC. Numerical tests, where synthetic data is generated from a horizontally stratified two-layer model, indicate that the relative weight between a prior model and the observed data is appropriately adjusted by ABIC. It is revealed that a value of the thickness parameter required to reproduce the given two-layer model is successfully found by ABIC. We also suggest that we can make a plausible choice of the assumption of the surface-wave theory with ABIC, unless observation error is extremely large.

Key words: arrays, inversion, modelling, passive, shallow, surface wave, velocity.


References

Akaike, H., 1980, Likelihood and Bayes procedure, in J. M. Bernard, M. H. De Groot, D. U. Lindley, and A. F. M. Smith, eds., Bayesian statistics: University Press, Valencia, Spain, 143–203.

Aki, K., 1957, Space and time spectra of stationary stochastic waves, with special reference to microtremors: Bulletin of the Earthquake Research Institute, University of Tokyo, 35, 415–457

Arai, H., and Tokimatsu, K., 2005, S-wave velocity profiling by joint inversion of microtremor dispersion curve and Horizontal-to-Vertical (H/V) spectrum: Bulletin of the Seismological Society of America, 95, 1766–1778
S-wave velocity profiling by joint inversion of microtremor dispersion curve and Horizontal-to-Vertical (H/V) spectrum:Crossref | GoogleScholarGoogle Scholar |

Ballard, R. F., Jr, 1964, Determination of soil shear moduli at depths by in-situ vibratory techniques: Misc. Pap. No. 4–691, U.S. Army Engineer Waterways Experiment Station, Vicksburg, Miss.

Chimoto, K., Yamanaka, H., Tsuno, S., Miyake, H., and Yamada, N., 2016, Estimation of shallow S-wave velocity structure using microtremor array exploration at temporary strong motion observation stations for aftershocks of the 2016 Kumamoto earthquake: Earth, Planets, and Space, 68, 206
Estimation of shallow S-wave velocity structure using microtremor array exploration at temporary strong motion observation stations for aftershocks of the 2016 Kumamoto earthquake:Crossref | GoogleScholarGoogle Scholar |

Cho, I., and Senna, S., 2016, Constructing a system to explore shallow velocity structures using a miniature microtremor array: accumulating and utilizing large microtremor database: Synthesiology, 9, 86–96
Constructing a system to explore shallow velocity structures using a miniature microtremor array: accumulating and utilizing large microtremor database:Crossref | GoogleScholarGoogle Scholar |

Cho, I., Nakanishi, I., Ling, S., and Okada, H., 1999, Application of forking genetic algorithm fGA to an exploration method using microtremors: Butsuri Tansa, 52, 227–246

Cho, I., Tada, T., and Shinozaki, Y., 2004, A new method to determine phase velocities of Rayleigh waves from microseisms: Geophysics, 69, 1535–1551
A new method to determine phase velocities of Rayleigh waves from microseisms:Crossref | GoogleScholarGoogle Scholar |

Cho, I., Tsurugi, M., Kagawa, T., and Iwata, T., 2006, Modelling of deep sedimentary velocity structure for evaluation of broadband strong ground motions: site-amplification spectra in Osaka sedimentary basin: Journal of Japan Association for Earthquake Engineering, 6, 113–132
Modelling of deep sedimentary velocity structure for evaluation of broadband strong ground motions: site-amplification spectra in Osaka sedimentary basin:Crossref | GoogleScholarGoogle Scholar |

Cho, I., Senna, S., and Fujiwara, H., 2013, Miniature array analysis of microtremors: Geophysics, 78, KS13–KS23
Miniature array analysis of microtremors:Crossref | GoogleScholarGoogle Scholar |

Cuéllar, V., 1994, Determination of the dynamic behaviour of soils using surface waves: Spanish experiences: Proceedings of the 10th World Conference on Earthquake Engineering, Balkema, Rotterdam, 6725–6734.

Fukahata, Y., 2009, Development of study of inversion analyses using ABIC in seismology: Zisin, 61, S103–S113
Development of study of inversion analyses using ABIC in seismology:Crossref | GoogleScholarGoogle Scholar |

Fukahata, Y., and Wright, T. J., 2008, A non-linear geodetic data inversion using ABIC for slip distribution on a fault with an unknown dip angle: Geophysical Journal International, 173, 353–364
A non-linear geodetic data inversion using ABIC for slip distribution on a fault with an unknown dip angle:Crossref | GoogleScholarGoogle Scholar |

Gazetas, G., 1982, Vibrational characteristics of soil deposits with variable wave velocity: International Journal for Numerical and Analytical Methods in Geomechanics, 6, 1–20
Vibrational characteristics of soil deposits with variable wave velocity:Crossref | GoogleScholarGoogle Scholar |

Goto, H., Mitsunaga, H., Inatani, M., Iiyama, K., Hada, K., Ikeda, K., Takaya, T., Kimura, S., Akiyama, R., Sawada, S., and Morikawa, H., 2017, Shallow subsurface structure estimated from dense aftershock records and microtremor observation in Furukawa district, Miyagi, Japan: Exploration Geophysics, 48, 16–27
Shallow subsurface structure estimated from dense aftershock records and microtremor observation in Furukawa district, Miyagi, Japan:Crossref | GoogleScholarGoogle Scholar |

Heukelom, W., and Foster, C. R., 1960, Dynamic testing of pavements: Journal of Structural Division (ASCE), 86, 1–28

Hisada, Y., 1994, An efficient method for computing Green’s functions for a layered half-space with sources and receivers at close depths: Bulletin of the Seismological Society of America, 84, 1456–1472

Hisada, Y., 1995, An efficient method for computing Green’s functions for a layered half-space with sources and receivers at close depths (Part 2): Bulletin of the Seismological Society of America, 85, 1080–1093

Ikeda, T., Matsuoka, T., Tsuji, T., and Hayashi, K., 2012, Multimode inversion with amplitude response of surface waves in the spatial autocorrelation method: Geophysical Journal International, 190, 541–552
Multimode inversion with amplitude response of surface waves in the spatial autocorrelation method:Crossref | GoogleScholarGoogle Scholar |

Iwata, T., 2013, Estimation of completeness magnitude considering daily variation in earthquake detection capability: Geophysical Journal International, 194, 1909–1919
Estimation of completeness magnitude considering daily variation in earthquake detection capability:Crossref | GoogleScholarGoogle Scholar |

Iwata, T., 2014, Decomposition of seasonality and long-term trend in seismological data: a Bayesian modelling of earthquake detection capability: Australian & New Zealand Journal of Statistics, 56, 201–215
Decomposition of seasonality and long-term trend in seismological data: a Bayesian modelling of earthquake detection capability:Crossref | GoogleScholarGoogle Scholar |

Kass, R. E., and Raftery, A. E., 1995, Bayes factors: Journal of the American Statistical Association, 90, 773–795
Bayes factors:Crossref | GoogleScholarGoogle Scholar |

Koketsu, K., and Higashi, S., 1992, Three-dimensional topography of the sediment/basement interface in the Tokyo metropolitan area, central Japan: Bulletin of the Seismological Society of America, 82, 2328–2349

Ludwig, W. J., Nafe, J. E., and Drake, C. L., 1970, Seismic refraction, in A. E. Maxwell, ed., The sea: Wiley Interscience, 4, 53–84.

MacKay, D. J. C., 1995, Probable networks and plausible predictions: a review of practical Bayesian methods for supervised neural networks: Network: Computation in Neural Systems, 6, 469–505
Probable networks and plausible predictions: a review of practical Bayesian methods for supervised neural networks:Crossref | GoogleScholarGoogle Scholar |

Matsu’ura, M., Noda, A., and Fukahata, Y., 2007, Geodetic data inversion based on Bayesian formulation with direct and indirect prior information: Geophysical Journal International, 171, 1342–1351
Geodetic data inversion based on Bayesian formulation with direct and indirect prior information:Crossref | GoogleScholarGoogle Scholar |

Ogata, Y., Imoto, M., and Katsura, K., 1991, 3-D spatial variation of b-values of magnitude-frequency distribution beneath the Kanto District, Japan: Geophysical Journal International, 104, 135–146
3-D spatial variation of b-values of magnitude-frequency distribution beneath the Kanto District, Japan:Crossref | GoogleScholarGoogle Scholar |

Okada, H., 2003, The microtremor survey method: Society of Exploration Geophysicists, Geophysical Monograph Series 12.

Pelekis, P. C., and Athanasopoulos, G. A., 2011, An overview of surface wave methods and a reliability study of a simplified inversion technique: Soil Dynamics and Earthquake Engineering, 31, 1654–1668
An overview of surface wave methods and a reliability study of a simplified inversion technique:Crossref | GoogleScholarGoogle Scholar |

Poggi, V., Fäh, D., Burjanek, J., and Giardini, D., 2012, The use of Rayleigh-wave ellipticity for site-specific hazard assessment and microzonation: application to the city of Lucerne, Switzerland: Geophysical Journal International, 188, 1154–1172
The use of Rayleigh-wave ellipticity for site-specific hazard assessment and microzonation: application to the city of Lucerne, Switzerland:Crossref | GoogleScholarGoogle Scholar |

Press, W. H., Teukolsky, S. A., Vetterling, W. T., and Flannery, B. P., 2007, Numerical recipes: the art of scientific computing (3rd edition): Cambridge University Press.

Sekiguchi, H., Irikura, K., and Iwata, T., 2000, Fault geometry at the rupture termination of the 1995 Hyogo-ken Nanbu Earthquake: Bulletin of the Seismological Society of America, 90, 117–133
Fault geometry at the rupture termination of the 1995 Hyogo-ken Nanbu Earthquake:Crossref | GoogleScholarGoogle Scholar |

Society of Exploration Geophysicists of Japan Standardisation Committee, 2008, Applications manual of geophysical methods to engineering and environmental problems: Society of Exploration Geophysicists of Japan, 111–126 [in Japanese].

Tada, T., Cho, I., and Shinozaki, Y., 2007, Beyond the SPAC method: exploiting the wealth of circular-array methods for microtremor exploration: Bulletin of the Seismological Society of America, 97, 2080–2095
Beyond the SPAC method: exploiting the wealth of circular-array methods for microtremor exploration:Crossref | GoogleScholarGoogle Scholar |

Tierney, L., and Kadane, J. B., 1986, Accurate approximation for posterior moments and marginal densities: Journal of the American Statistical Association, 81, 82–86
Accurate approximation for posterior moments and marginal densities:Crossref | GoogleScholarGoogle Scholar |

Tokimatsu, K., Tamura, S., and Kojima, H., 1992, Effects of multiple modes on Rayleigh wave dispersion characteristics: Journal of Geotechnical Engineering, 118, 1529–1543
Effects of multiple modes on Rayleigh wave dispersion characteristics:Crossref | GoogleScholarGoogle Scholar |

Wakai, A., Senna, S., Jin, K., Cho, I., Matsuyama, H., and Fujiwara, H., 2017, A method for setting engineering bedrock using records of miniature array microtremor observation in Kanto Area: JpGU-AGU Joint Meeting, 2017, SSS15-P19.