A Method to Estimate Spatial Resolution in 2-D Seismic Surface Wave Tomographic Problems

Jorge L. de Souza

Coordena??o de Geofísica, MCTI/Observatório Nacional, Rio de Janeiro, Brazil.

DOI: 10.4236/ijg.2014.58068                

Abstract

A novel methodology to quantify the spatial resolution in 2-D seismic surface wave tomographic problems is proposed in this study. It is based on both the resolving kernels computed via full resolution matrix and the concept of Full Width at Half Maximum (FWHM) of a Gaussian function. This method allows estimating quantitatively the spatial resolution at any cell of a gridded area. It was applied in the northeastern Brazil and the estimated spatial resolution range is in agreement with all previous surface wave investigations in the South America continent.

Keywords

Surface Waves, Seismic Tomography, Wave Propagation, Spatial Resolution, Northeastern Brazil

Conflicts of Interest

The authors declare no conflicts of interest.

References

[1]	van der Lee, S., James, D. and Silver, P. (2001) Upper Mantle S Velocity Structure of Central and Western South America. Journal of Geophysical Research, 106, 30821-30834. http://dx.doi.org/10.1029/2001JB000338
[2]	Feng, M., Assumpcao, M. and van der Lee, S. (2004) Group-Velocity Tomography and Lithospheric S-Velocity Structure of the South American Continent. Physics of the Earth and Planetary Interiors, 147, 315-331. http://dx.doi.org/10.1016/j.pepi.2004.07.008
[3]	Feng, M., van der Lee, S. and Assumpcao, M. (2007) Upper Mantle Structure of South America from Joint Inversion of Waveforms and Fundamental Mode Group Velocities of Rayleigh Waves. Journal of Geophysical Research, 112, B04312. http://dx.doi.org/10.1029/2006JB004449
[4]	Corchete, V. (2011) Shear-Wave Velocity Structure of South America from Rayleigh-Wave Analysis. Terra Nova, 24, 87-104. http://dx.doi.org/10.1111/j.1365-3121.2011.01042.x.
[5]	Feng, C.-C. and Teng, T.-L. (1983) Three-Dimensional Crust and Upper Mantle Structure of the Eurasian Continent. Journal of Geophysical Research, 88, 2261-2272. http://dx.doi.org/10.1029/JB088iB03p02261
[6]	Aki, K. and Richards, P.G. (1980) Quantitative Seismology. 1st Edition, Freeman, San Francisco, 932.
[7]	Lines, L.R. and Treitel, S. (1984) Tutorial: A Review of Least-Squares Inversion and Its Application to Geophysical Problems. Geophysical Prospecting, 32, 159-186. http://dx.doi.org/10.1111/j.1365-2478.1984.tb00726.x
[8]	Cloetingh, S., Nolet, G. and Wortel, R. (1979) On the Use of Rayleigh Wave Group Velocities for the Analysis of Continental Margins. Tectonophysics, 59, 335-346. http://dx.doi.org/10.1016/0040-1951(79)90054-4
[9]	Lévêque, J.-J., Rivera, L. and Wittlinger, G. (1993) On the Use of the Checker-Board Test to Assess the Resolution of Tomographic Inversions. Geophysical Journal International, 115, 313-318. http://dx.doi.org/10.1111/j.1365-246X.1993.tb05605.x
[10]	Dos Santos, N.P. and de Souza, J.L. (2005) Aplicacao de eficientes técnicas computacionais a problemas de tomografia sísmica com ondas superficiais. Revista Brasileira de Geofísica, 23, 285-294.
[11]	Menke, W. (1989) Geophysical Data Analysis: Discrete Inverse Theory. 1st Edition, Academic Press, San Diego, 289.
[12]	Wikipedia. Full Width at Half Maximum. http://en.wikipedia.org/wiki/Full_width_at_half_maximum.
[13]	Herbert, C.G. and Johnstone, R.A.W. (2002) Mass Spectrometry Basics. 1st Edition, CRC Press, Boca Raton, 453.
[14]	De Hoffmann, E. and Stroobant, V. (2007) Mass Spectrometry: Principles and Applications. 1st Edition, John Wiley & Sons, England, 489.
[15]	Weisstein, E. (2014) Wolfram Math World, Gaussian Function. http://mathworld.wolfram.com/GaussianFunction.html
[16]	Vilar, C.S. (2004) Estrutura tridimensional da onda S na litosfera do nordeste brasileiro. Ph.D. Thesis, MCTI/ Observatório Nacional, Rio de Janeiro, Brazil.
[17]	Butler, R., Lay, T., Creager, K., Earl, P., Fischer, K., Gaherty, J., Laske, G., Leith, B., Park, J., Ritzwoller, M., Tromp, J. and Wen, L. (2004) The Global Seismographic Network Surpasses Its Design Goal. Eos, Transactions American Geophysical Union, 85, 225-229. http://dx.doi.org/10.1029/2004EO230001
[18]	Goldstein, P., Dodge, D., Firpo, M. and Minner, L. (2003) SAC2000: Signal Processing and Analysis Tools for Seismologists and Engineers. In: Lee, W.H.K., Kanamori, H., Jennings, P.C. and Kisslinger, C., Eds., The IASPEI International Handbook of Earthquake and Engineering Seismology, Academic Press, London, 1613-1614. http://dx.doi.org/10.1016/S0074-6142(03)80284-X
[19]	Levshin, A.L., Ritzwoller, M.H. and Resovsky, J.S. (1999) Source Effects on Surface Wave Group Travel Times and Group Velocity Maps. Physics of the Earth and Planetary Interiors, 115, 293-312. http://dx.doi.org/10.1016/S0031-9201(99)00113-2
[20]	Dziewonski, A., Bloch, S. and Landisman, M. (1969) A Technique for the Analysis of Transient Seismic Signals. Bulletin of the Seismological Society of America, 59, 427-444.
[21]	Silveira, G., Stutzmann, E., Griot, D.-A., Montagner, J.-P. and Victor, L.M. (1998) Anisotropy Tomography of the Atlantic Ocean from Rayleigh Surface Waves. Physics of the Earth and Planetary Interiors, 106, 257-273. http://dx.doi.org/10.1016/S0031-9201(98)00079-X
[22]	Vdovin, O., Rial, J.A., Levshin, A.L. and Ritzwoller, M.H. (1999) Group-Velocity Tomography of South America and the Surrounding Oceans. Geophysical Journal International, 136, 324-340. http://dx.doi.org/10.1046/j.1365-246X.1999.00727.x
[23]	Silveira, G. and Stutzmann, E. (2002) Anisotropic Tomography of the Atlantic Ocean. Physics of the Earth and Planetary Interiors, 132, 237-248. http://dx.doi.org/10.1016/S0031-9201(02)00076-6
[24]	Wessel, P. and Smith, W.H.F. (1998) New, Improved Version of the Generic Mapping Tools Released. Eos, Transactions American Geophysical Union, 79, 579. http://dx.doi.org/10.1029/98EO00426