Three-dimensional shear wave velocity imaging by ambient seismic noise tomography

SUMMARY 3-D shear wave velocity images are of particular interest for engineering seismology. To obtain information about the local subsoil structure, we present a one-step inversion procedure based on the computation of high-frequency correlation functions between stations of a small-scale array deployed for recording ambient seismic noise. The calculation of Rayleigh wave phase velocities is based on the frequency-domain SPatial AutoCorrelation technique. Constitutively, a tomographic inversion of the traveltimes estimated for each frequency is performed, allowing the laterally varying 3-D surface wave velocity structure below the array to be retrieved. We test our technique by using simulations of seismic noise for a simple realistic site and by using real-world recordings from a small-scale array performed at the Nauen test site (Germany). The results imply that the cross-sections from passive seismic interferometry provide a clear image of the local structural heterogeneities and the shear wave velocities are satisfactorily reproduced. The velocity structure is also found to be in good agreement with the results of geoelectrical measurements, indicating the potential of the method to be easily applied for deriving the shallow 3-D velocity structure in urban areas and for monitoring purposes.

[1]  Kenneth Levenberg A METHOD FOR THE SOLUTION OF CERTAIN NON – LINEAR PROBLEMS IN LEAST SQUARES , 1944 .

[2]  Evert Slob,et al.  A Comparison of Strategies for Seismic Interferometry , 2009 .

[3]  Yingjie Yang,et al.  Processing seismic ambient noise data to obtain reliable broad-band surface wave dispersion measurements , 2007 .

[4]  Morgan P. Moschetti,et al.  Surface wave tomography of the western United States from ambient seismic noise: Rayleigh wave group velocity maps , 2007 .

[5]  Stephen Bannister,et al.  Ambient noise Rayleigh wave tomography of New Zealand , 2007 .

[6]  David Halliday,et al.  Seismic interferometry of scattered surface waves in attenuative media , 2009 .

[7]  Surface-Wave Group-Velocity Tomography for Shallow Structures , 2001 .

[8]  Donat Fäh,et al.  A theoretical investigation of average H/V ratios , 2001 .

[9]  Dino Bindi,et al.  Characterization of shallow geology by high‐frequency seismic noise tomography , 2009 .

[10]  Gregory C. Beroza,et al.  Anelastic Earth structure from the coherency of the ambient seismic field , 2008 .

[11]  Michel Campillo,et al.  3‐D surface wave tomography of the Piton de la Fournaise volcano using seismic noise correlations , 2007 .

[12]  H. Cox Spatial Correlation in Arbitrary Noise Fields , 1974 .

[13]  R. Weaver,et al.  On the emergence of the Green's function in the correlations of a diffuse field: pulse-echo using thermal phonons. , 2001, Ultrasonics.

[14]  Ezio Faccioli,et al.  2d and 3D elastic wave propagation by a pseudo-spectral domain decomposition method , 1997 .

[15]  Ugur Yaramanci,et al.  Aquifer characterisation using Surface NMR jointly with other geophysical techniques at the Nauen/Berlin test site , 2002 .

[16]  T. Yokoi,et al.  Consistency of the spatial autocorrelation method with seismic interferometry and its consequence , 2008 .

[17]  Coherent pressure fluctuations observed at two sites on the deep sea floor , 1986 .

[18]  Frank Scherbaum,et al.  Determination of shallow shear wave velocity profiles in the Cologne, Germany area using ambient vibrations , 2003 .

[19]  Jin Soo Shin,et al.  Surface‐wave tomography from ambient seismic noise of accelerograph networks in southern Korea , 2006 .

[20]  Peter Gerstoft,et al.  Surface wave tomography from microseisms in Southern California , 2005 .

[21]  J. Henstridge A signal processing method for circular arrays , 1979 .

[22]  Peter Gerstoft,et al.  Extracting time‐domain Green's function estimates from ambient seismic noise , 2005 .

[23]  Anatoli L. Levshin,et al.  Ambient noise Rayleigh wave tomography across Europe , 2007 .

[24]  Kohji Tokimatsu,et al.  S-Wave Velocity Profiling by Inversion of Microtremor H/V Spectrum , 2004 .

[25]  Morgan P. Moschetti,et al.  An explicit relationship between time‐domain noise correlation and spatial autocorrelation (SPAC) results , 2010 .

[26]  J. Claerbout,et al.  Acoustic daylight imaging via spectral factorization: helioseismology and reservoir monitoring , 1999 .

[27]  David Halliday,et al.  Seismic interferometry, surface waves and source distribution , 2008 .

[28]  F. Kruger,et al.  Influence of the seismic noise characteristics on noise correlations , 2005 .

[29]  David R. O'Hallaron,et al.  Large-scale simulation of elastic wave propagation in heterogeneous media on parallel computers , 1998 .

[30]  Pierre-Yves Bard,et al.  Numerical and Theoretical Investigations on the Possibilities and Limitations of Nakamura's Technique , 1994 .

[31]  Michael Asten,et al.  On bias and noise in passive seismic data from finite circular array data processed using SPAC methods , 2006 .

[32]  Nolet,et al.  Seismic Tomography || Seismic wave propagation and seismic tomography , 1987 .

[33]  Glenn J. Rix,et al.  Accuracy and Resolution of Surface Wave Inversion , 1991 .

[34]  R. Weaver,et al.  Ultrasonics without a source: thermal fluctuation correlations at MHz frequencies. , 2001, Physical review letters.

[35]  B. Efron Bootstrap Methods: Another Look at the Jackknife , 1979 .

[36]  K. Stokoe,et al.  Liquefaction resistance of soils from shear-wave velocity , 2000 .

[37]  Kees Wapenaar,et al.  Seismic interferometry : history and present status , 2008 .

[38]  William T. Holmes,et al.  The 1997 NEHRP Recommended Provisions for Seismic Regulations for New Buildings and Other Structures , 2000 .

[39]  Maarten V. de Hoop,et al.  Surface-wave array tomography in SE Tibet from ambient seismic noise and two-station analysis: I - Phase velocity maps , 2006 .

[40]  T. Bohlen,et al.  Scholte-wave tomography for shallow-water marine sediments , 2007 .

[41]  G. Prieto,et al.  Earthquake ground motion prediction using the ambient seismic field , 2008 .

[42]  G. Prieto,et al.  Attenuation tomography of the western United States from ambient seismic noise , 2011 .

[43]  Michel Campillo,et al.  High-Resolution Surface-Wave Tomography from Ambient Seismic Noise , 2005, Science.

[44]  J. M. Roesset,et al.  Characterization of geotechical sites by SASW method , 1994 .

[45]  S. Parolai,et al.  S-wave Velocity Profiles for Earthquake Engineering Purposes for the Cologne Area (Germany) , 2006 .

[46]  M. Koch Bootstrap inversion for vertical and lateral variations of the S wave structure and the υp/υs-ratio from shallow earthquakes in the Rhinegraben seismic zone, Germany , 1992 .

[47]  W. B. Joyner,et al.  Equations for Estimating Horizontal Response Spectra and Peak Acceleration from Western North American Earthquakes: A Summary of Recent Work , 1997 .

[48]  Keiiti Aki,et al.  Space and Time Spectra of Stationary Stochastic Waves, with Special Reference to Microtremors , 1957 .

[49]  Bo Holm Jacobsen,et al.  Sensitivity Kernels for Time-Distance Inversion , 2000 .

[50]  K. Wapenaar Retrieving the elastodynamic Green's function of an arbitrary inhomogeneous medium by cross correlation. , 2004, Physical review letters.

[51]  S. Foti,et al.  Multi-Offset Phase Analysis of Surface Wave Data (MOPA) , 2006 .

[52]  Michel Campillo,et al.  Phase and Correlation in `Random' Seismic Fields and the Reconstruction of the Green Function , 2004 .

[53]  Francisco Luzón,et al.  On the correlation of seismic microtremors , 2005 .

[54]  Francisco J. Sánchez-Sesma,et al.  Retrieval of the Green’s Function from Cross Correlation: The Canonical Elastic Problem , 2006 .

[55]  G. D. Bensen,et al.  Broadband ambient noise surface wave tomography across the United States , 2008 .

[56]  David P. Hill,et al.  Surface-wave potential for triggering tectonic (nonvolcanic) tremor , 2010 .

[57]  R. Snieder Extracting the Green's function from the correlation of coda waves: a derivation based on stationary phase. , 2004, Physical review. E, Statistical, nonlinear, and soft matter physics.

[58]  Kojiro Irikura,et al.  Three-dimensional simulation of the near-fault ground motion for the 1995 Hyogo-Ken Nanbu (Kobe), Japan, earthquake , 1998, Bulletin of the Seismological Society of America.

[59]  Mickael Tanter,et al.  Recovering the Green's function from field-field correlations in an open scattering medium. , 2003, The Journal of the Acoustical Society of America.

[60]  P. Mora,et al.  Simulation-based comparison of four site-response estimation techniques , 1998, Bulletin of the Seismological Society of America.

[61]  Árpád Elbert,et al.  Some recent results on the zeros of Bessel functions and orthogonal polynomials , 2001 .

[62]  Edi Kissling,et al.  Geotomography with local earthquake data , 1988 .

[63]  Chih-Ping Lin,et al.  Effect of lateral heterogeneity on surface wave testing: Numerical simulations and a countermeasure , 2007 .

[64]  Guust Nolet,et al.  Three-dimensional sensitivity kernels for finite-frequency traveltimes: the banana–doughnut paradox , 1999 .

[65]  John W. Tukey,et al.  CRITICAL EVALUATION OF CHEMICAL AND PHYSICAL STRUCTURAL INFORMATION. , 1800 .

[66]  Rongjiang Wang,et al.  Shear wave velocity model of the Santiago de Chile basin derived from ambient noise measurements: a comparison of proxies for seismic site conditions and amplification , 2010 .

[67]  Jianghai Xia,et al.  Estimation of near‐surface shear‐wave velocity by inversion of Rayleigh waves , 1999 .

[68]  D. Fäh,et al.  Inversion of local S-wave velocity structures from average H/V ratios, and their use for the estimation of site-effects , 2003 .

[69]  B. Kennett,et al.  A reappraisal of regional surface wave tomography , 2002 .

[70]  J. Vidale,et al.  Tomography without rays , 1993, Bulletin of the Seismological Society of America.

[71]  Michel Campillo,et al.  Emergence of broadband Rayleigh waves from correlations of the ambient seismic noise , 2004 .

[72]  Göran Ekström,et al.  Determination of surface‐wave phase velocities across USArray from noise and Aki's spectral formulation , 2009 .

[73]  Keiiti Aki,et al.  A NOTE ON THE USE OF MICROSEISMS IN DETERMINING THE SHALLOW STRUCTURES OF THE EARTH’S CRUST , 1965 .

[74]  Peter Gerstoft,et al.  Seismic interferometry-turning noise into signal , 2006 .

[75]  G. Nolet,et al.  Seismic wave propagation and seismic tomography , 1987 .

[76]  M. Rodriguez,et al.  An Alternative Approach to the spac Analysis of Microtremors: Exploiting Stationarity of Noise , 2005 .

[77]  Kenneth H. Stokoe,et al.  Use of Rayleigh Waves in Liquefaction Studies , 1985 .

[78]  Gene H. Golub,et al.  Singular value decomposition and least squares solutions , 1970, Milestones in Matrix Computation.

[79]  D. Marquardt An Algorithm for Least-Squares Estimation of Nonlinear Parameters , 1963 .

[80]  Richard L. Weaver,et al.  Diffuse fields in open systems and the emergence of the Green’s function (L) , 2004 .

[81]  T. Lay,et al.  Modern Global Seismology , 1995 .

[82]  P. Gerstoft,et al.  Distribution of noise sources for seismic interferometry , 2010 .

[83]  A. Morelli Inverse Problem Theory , 2010 .

[84]  M. Longuet-Higgins A theory of the origin of microseisms , 1950, Philosophical Transactions of the Royal Society of London. Series A, Mathematical and Physical Sciences.

[85]  S. Parolai,et al.  Modelling basin effects on earthquake ground motion in the Santiago de Chile basin by a spectral element code , 2011 .

[86]  Roel Snieder,et al.  Retrieving the Green's function of the diffusion equation from the response to a random forcing. , 2006, Physical review. E, Statistical, nonlinear, and soft matter physics.

[87]  David Hinkley,et al.  Bootstrap Methods: Another Look at the Jackknife , 2008 .

[88]  P. Ditmar,et al.  Smoothness criteria in surface wave tomography , 1990 .

[89]  A. Paul,et al.  Long-Range Correlations in the Diffuse Seismic Coda , 2003, Science.

[90]  P. Bard,et al.  Shear wave velocity imaging of the Avignonet landslide (France) using ambient noise cross correlation , 2010 .

[92]  K. E. Bullen,et al.  An Introduction to the Theory of Seismology , 1964 .