Errors of Estimating Near-Surface Q-A statistical Approach

ABSTRACT

Although various estimating methods have been developed for measuring Q from near-surface seismic data, less thought has been given to the accuracy of Q obtained. The errors of Q depend on the ways of measuring Q and the computation techniques used in estimating. The main purpose of this paper is to give a compre- hensive evaluation for the accuracy of measuring near-surface Q. We discuss the possible origins from which errors may develop, and provide a statistical guide to the accuracy that can be expected. A set of real data based on the improved spectral ratio method for near-surface Q was used as an example of validation and sensitivity analysis. The Bonferroni procedure was adopted for deriving the joint confidence intervals for k and n of the power law model. The same approach with modest modification may be applied to analyze the accuracy of Q estimated by other methods.

Although various estimating methods have been developed for measuring Q from near-surface seismic data, less thought has been given to the accuracy of Q obtained. The errors of Q depend on the ways of measuring Q and the computation techniques used in estimating. The main purpose of this paper is to give a compre- hensive evaluation for the accuracy of measuring near-surface Q. We discuss the possible origins from which errors may develop, and provide a statistical guide to the accuracy that can be expected. A set of real data based on the improved spectral ratio method for near-surface Q was used as an example of validation and sensitivity analysis. The Bonferroni procedure was adopted for deriving the joint confidence intervals for k and n of the power law model. The same approach with modest modification may be applied to analyze the accuracy of Q estimated by other methods.

Cite this paper

nullC. Chen and Y. Jeng, "Errors of Estimating Near-Surface Q-A statistical Approach,"*International Journal of Geosciences*, Vol. 2 No. 2, 2011, pp. 164-171. doi: 10.4236/ijg.2011.22017.

nullC. Chen and Y. Jeng, "Errors of Estimating Near-Surface Q-A statistical Approach,"

References

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[2] A. I. Best, J. Sothcott and C. McCann, “A Laboratory Study of Seismic Velocity and Attenuation Anisotropy in Near-Surface Sedimentary Rocks,” Geophysical Prospecting, Vol. 55, No. 5, September 2007, pp. 609-625. doi:10.1111/j.1365-2478.2007.00642.x

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[4] A. I. Best, “Introduction to Special Section – Seismic Quality Factor,” Geophysical Prospecting, Vol. 55, No. 5, September 2007, pp. 607-608.

[5] J. E. White, “Computed Seismic Speeds and Attenuation in Rocks with Partial Gas Saturation,” Geophysics, Vol. 40, No. 2, April 1975, pp. 224-232. doi:10.1190/1.1440520

[6] R. J. O'Connell and B. Budiansky, “Viscoelastic Pro- perties of Fluid-Saturated Cracked Solid,” Journal of Ge- ophysical Research, Vol. 82, No. 36, December 1977, pp. 5719-5735. doi:10.1029/JB082i036p05719

[7] Y. Jeng, J. Y. Tsai and S. H. Chen, “An Improved Method of Determining Near-Surface Q,” Geophysics, Vol. 64, No. 6, September-October 1999, pp. 1608-1617. doi:10.1190/1.1444665

[8] Q. Li, W. S. D. Wilcock, T. L. Pratt, C. M. Snelson and T. M. Brocher, “Seismic Attenuation Structure of the Seattle Basin, Washington State, from Explosive-Source Refrac- tion Data,” Bulletin of the Seismological Society of Ame- rica, Vol. 96, No. 2, April 2006, pp. 553-571. doi:10.1785/0120040164

[9] Y. Jeng, “Shallow Seismic Investigation of a Site with Poor Reflection Quality,” Geophysics, Vol. 60, No. 6, November-December 1995, pp. 1715-1726. doi:10.1190/1.1443904

[10] Y. Jeng, C.-S. Chen, H.-M. Yu, A. S.-R. Jeng, C.-Y. Tang and M.-J. Lin, “Ultrashallow Seismic Experiment on a Trenched Section of the Chelunpu Fault Zone, Taiwan,” Tectonophysics, Vol. 443, No. 3-4, October 2007, pp. 255-270. doi:10.1016/j.tecto.2007.01.021

[11] Y. Jeng, S. H. Chen and K. J. Chen, “Effects of Uncon- solidated Layers on Shallow Seismic Wave Propagation,” EGS Annales Geophysical, Supplement 1 to Vol. 14, April 1996, p. C168.

[12] S. W. Patton, “Robust and Least-Squares Estimation of Acoustic Attenuation from Well-Log Data,” Geophysics, Vol. 53, No. 9, September 1988, pp. 1225-1232. doi:10.1190/1.1442563

[13] M. Sams and D. Goldberg, “The Validity of Q Estimates from Borehole Data Using Spectral Ratios,” Geophysics, Vol. 55, No. 1, January 1990, pp. 97-101. doi:10.1190/1.1442776

[14] R. E. White, “The Accuracy of Estimating Q from Seismic Data,” Geophysics, Vol. 57, No. 11, November 1992, pp. 1508-1511. doi:10.1190/1.1443218

[15] D. H. Johnston and M. N. Toks?z, “Definitions and Ter- minology,” In: M. N. Toks?z and D. H. Johnston, Eds, Seismic Wave Attenuation, Geophysics Reprints Series, Society of Exploration Geophysics, Tulsa, 1981, pp. 1-5.

[16] E. L. Hamilton, “Compressional-Wave Attenuation in Ma- rine Sediments,” Geophysics, Vol. 37, No. 4, August 1972, pp. 620-646. doi:10.1190/1.1440287

[17] S. C. Constable, R. L. Parker and C. G. Constable, “Oc- cam’s Inversion: A Practical Algorithm for Generating Smooth Models from Electromagnetic Sounding Data,” Geophysics, Vol. 52, No. 3, March 1987, pp. 289-300. doi:10.1190/1.1442303

[18] F. D. Stacey, “Physics of the Earth,” John Wiley & Sons, Inc., Hoboken, 1977.

[19] D. Rees, “Foundations of Statistics,” Chapman and Hall, 1987.

[20] J. F. Gibbs and E. F. Roth, “Seismic Velocities and Attenuation from Borehole Measurements near the Parkfield Prediction Zone, Central California,” Earthquake Spectral, Vol. 5, No. 3, August 1989, pp. 513-537. doi:10.1193/1.1585538

[21] R. H. Myers, “Classical and Modern Regression with Ap- plications,” PWS-KENT Publishing Company, Boston, 1990.

[22] J. Y. Tsai, “Analysis of Shallow 3-Component Q Values,” Master’s Thesis, National Taiwan Normal University, Taiwan (China), 1994.

[23] R. Dasgupta and R. A. Clark, “Estimation of Q from Sur- face Seismic Reflection Data,” Geophysics, Vol. 63, No. 6, November-December 1998, pp. 2120-2128. doi:10.1190/1.1444505

[24] I. Lerche and W. Menke, “An Inversion Method for Separating Apparent and Intrinsic Attenuation in Layered Media,” Geophysical Journal of the Royal Astronomical Society, Vol. 87, No. 2, November 1986, pp. 333-347.

[25] J. P. Neep, M. S. Sams, M. H. Worthington and K. A. O’Hara-Dhand, “Measurement of Seismic Attenuation from High-Resolution Crosshole Data,” Geophysics, Vol. 61, No. 4, July-August 1996, pp. 1175-1188. doi:10.1190/1.1444037

[1] Y. H. Wang, “Inverse Q-Filter for Seismic Resolution Enhancement,” Geophysics, Vol. 71, No. 3, May-June 2006, pp. V51-V60. doi:10.1190/1.2192912

[2] A. I. Best, J. Sothcott and C. McCann, “A Laboratory Study of Seismic Velocity and Attenuation Anisotropy in Near-Surface Sedimentary Rocks,” Geophysical Prospecting, Vol. 55, No. 5, September 2007, pp. 609-625. doi:10.1111/j.1365-2478.2007.00642.x

[3] J. H. Xia, R. D. Miller, C. B. Parka and G. Tian, “Deter- mining Q of Near-Surface Materials from Rayleigh Waves,” Journal of Applied Geophysics, Vol. 51, No. 2-4, December 2002, pp. 121-129. doi:10.1016/S0926-9851(02)00228-8

[4] A. I. Best, “Introduction to Special Section – Seismic Quality Factor,” Geophysical Prospecting, Vol. 55, No. 5, September 2007, pp. 607-608.

[5] J. E. White, “Computed Seismic Speeds and Attenuation in Rocks with Partial Gas Saturation,” Geophysics, Vol. 40, No. 2, April 1975, pp. 224-232. doi:10.1190/1.1440520

[6] R. J. O'Connell and B. Budiansky, “Viscoelastic Pro- perties of Fluid-Saturated Cracked Solid,” Journal of Ge- ophysical Research, Vol. 82, No. 36, December 1977, pp. 5719-5735. doi:10.1029/JB082i036p05719

[7] Y. Jeng, J. Y. Tsai and S. H. Chen, “An Improved Method of Determining Near-Surface Q,” Geophysics, Vol. 64, No. 6, September-October 1999, pp. 1608-1617. doi:10.1190/1.1444665

[8] Q. Li, W. S. D. Wilcock, T. L. Pratt, C. M. Snelson and T. M. Brocher, “Seismic Attenuation Structure of the Seattle Basin, Washington State, from Explosive-Source Refrac- tion Data,” Bulletin of the Seismological Society of Ame- rica, Vol. 96, No. 2, April 2006, pp. 553-571. doi:10.1785/0120040164

[9] Y. Jeng, “Shallow Seismic Investigation of a Site with Poor Reflection Quality,” Geophysics, Vol. 60, No. 6, November-December 1995, pp. 1715-1726. doi:10.1190/1.1443904

[10] Y. Jeng, C.-S. Chen, H.-M. Yu, A. S.-R. Jeng, C.-Y. Tang and M.-J. Lin, “Ultrashallow Seismic Experiment on a Trenched Section of the Chelunpu Fault Zone, Taiwan,” Tectonophysics, Vol. 443, No. 3-4, October 2007, pp. 255-270. doi:10.1016/j.tecto.2007.01.021

[11] Y. Jeng, S. H. Chen and K. J. Chen, “Effects of Uncon- solidated Layers on Shallow Seismic Wave Propagation,” EGS Annales Geophysical, Supplement 1 to Vol. 14, April 1996, p. C168.

[12] S. W. Patton, “Robust and Least-Squares Estimation of Acoustic Attenuation from Well-Log Data,” Geophysics, Vol. 53, No. 9, September 1988, pp. 1225-1232. doi:10.1190/1.1442563

[13] M. Sams and D. Goldberg, “The Validity of Q Estimates from Borehole Data Using Spectral Ratios,” Geophysics, Vol. 55, No. 1, January 1990, pp. 97-101. doi:10.1190/1.1442776

[14] R. E. White, “The Accuracy of Estimating Q from Seismic Data,” Geophysics, Vol. 57, No. 11, November 1992, pp. 1508-1511. doi:10.1190/1.1443218

[15] D. H. Johnston and M. N. Toks?z, “Definitions and Ter- minology,” In: M. N. Toks?z and D. H. Johnston, Eds, Seismic Wave Attenuation, Geophysics Reprints Series, Society of Exploration Geophysics, Tulsa, 1981, pp. 1-5.

[16] E. L. Hamilton, “Compressional-Wave Attenuation in Ma- rine Sediments,” Geophysics, Vol. 37, No. 4, August 1972, pp. 620-646. doi:10.1190/1.1440287

[17] S. C. Constable, R. L. Parker and C. G. Constable, “Oc- cam’s Inversion: A Practical Algorithm for Generating Smooth Models from Electromagnetic Sounding Data,” Geophysics, Vol. 52, No. 3, March 1987, pp. 289-300. doi:10.1190/1.1442303

[18] F. D. Stacey, “Physics of the Earth,” John Wiley & Sons, Inc., Hoboken, 1977.

[19] D. Rees, “Foundations of Statistics,” Chapman and Hall, 1987.

[20] J. F. Gibbs and E. F. Roth, “Seismic Velocities and Attenuation from Borehole Measurements near the Parkfield Prediction Zone, Central California,” Earthquake Spectral, Vol. 5, No. 3, August 1989, pp. 513-537. doi:10.1193/1.1585538

[21] R. H. Myers, “Classical and Modern Regression with Ap- plications,” PWS-KENT Publishing Company, Boston, 1990.

[22] J. Y. Tsai, “Analysis of Shallow 3-Component Q Values,” Master’s Thesis, National Taiwan Normal University, Taiwan (China), 1994.

[23] R. Dasgupta and R. A. Clark, “Estimation of Q from Sur- face Seismic Reflection Data,” Geophysics, Vol. 63, No. 6, November-December 1998, pp. 2120-2128. doi:10.1190/1.1444505

[24] I. Lerche and W. Menke, “An Inversion Method for Separating Apparent and Intrinsic Attenuation in Layered Media,” Geophysical Journal of the Royal Astronomical Society, Vol. 87, No. 2, November 1986, pp. 333-347.

[25] J. P. Neep, M. S. Sams, M. H. Worthington and K. A. O’Hara-Dhand, “Measurement of Seismic Attenuation from High-Resolution Crosshole Data,” Geophysics, Vol. 61, No. 4, July-August 1996, pp. 1175-1188. doi:10.1190/1.1444037