Determination and sensitivity analysis of the seismic velocity of a shallow layer from refraction traveltimes measures
DOI:
https://doi.org/10.1260/1750-9548.2.4.437Abstract
In this paper, we are interested in determining the seismic velocity of a shallow under-ground layer from refraction traveltimes measures. We present a study case taken from an experimental seismic survey. The study case is a wide-angle seismic inversion using experimental traveltimes measures and based on ray tracing technique and genetic algorithms. The hypothesis on the velocity distribution, coming from the seismic experiment, makes the computation of some seismic rays expensive in time. We propose to reduce the computations time by introducing a formulation of the inverse problem that avoids such costly rays, hence the inversion becomes feasible. Also we present a sensitivity analysis based on a singular value decomposition of the jacobian of the traveltimes with respect to velocity. We give the relationship between the traveltimes measure errors and the velocity estimation error. We discuss the advantages of this method over the classical one based on the resolution matrix.
References
A. Tarantola, “Inverse Problem Theory And Methods For Model Parameter Estimation”, siam, 2005.
R. Snieder, and J. Trampert, “Inverse problems in geophysics”, in Wavedistribution inversion, Springer Verlag, 1999.
K. Mosegaard and M. Sambridge “Monte Carlo Methods in Geophysical Inverse Problems”, Reviews of Geophysics, 2002. https://doi.org/10.1029/2000rg000089
N. Rawlinson and M. Sambridge “Seismic Traveltime Tomography of The Crust and Lithosphere” Advances in Geophysics, 46, 81-197. https://doi.org/10.1016/s0065-2687(03)46002-0
G. Drakatosa, V. Karastathisa, J. Makrisb, J. Papouliac, G. Stavrakakisa “3D Crustal Structure In The Neotectonic Basin Of The Gulf Of Saronikos (Greece)”, Tectonophysics, 2005. https://doi.org/10.1016/j.tecto.2005.02.004
A. M. Asad, S. K. Pullammanappallil, R. Anooshehpoor, and J. N. Louie, “Inversion Of Travel Time Data For Earthquake Locations And Three-Dimensional Velocity Structure In The Eureka Valley Area, Eastern California”, Bulletin of the Seismological Society of America, 1999.
Y. Wang, R. G. Pratt. “Sensitivities Of Seismic Traveltimes And Amplitudes In Refkection Tomography”, Geophysical journal international, 1997, vol. 131, no 3, pp. 618-642. https://doi.org/10.1111/j.1365-246x.1997.tb06603.x
P. Al Khoury, G. Chavant, F. Clément and P. Hervé, “Inversion of spectroscopic data of CO2”, Inverse Problems in Engineering, 2005.
V. Cerveny, “Seismic Ray Theory”, Cambridge, 2001.
Fomel S. et Sethian J. A., “Fast-Phase Space Computation Of Multiple Arrivals”, Proceedings of the National Academy of Sciences of the United States of America, vol. 99, no. 11, pp. 7329-7334 2002. https://doi.org/10.1073/pnas.102476599
F. Delprat-Jannaud, and P. Lailly, “Ill-Posed And Well-Posed Formulations Of The Reflection Tomography Problem”, Journal of Geophysical Research, 1993. https://doi.org/10.1190/1.1888774
J. Ivanov, R. D. Miller, J. Xia and D. Steepless “The inverse problem of Refraction travel times, part I: Types of Geophysical Nonuniqueness through minimization”, Pure and Applied Geophysics, 2005, vol. 162, no 3, pp. 447-459. https://doi.org/10.1007/s00024-004-2615-1
J. Ivanov, R. D. Miller, J. Xia and D. Steepless “The inverse problem of refraction travel times, part II: Quantifying Refraction Nonuniqueness using a three-layer model”, Pure and Applied Geophysics, 2005, vol. 162, no3, pp. 461-477. https://doi.org/10.1007/s00024-004-2616-0
F. Delbos, J. Gilbert, R. Glowinski and D. Sinoquet, “Constrained Optimisation In Seismic Reflection Tomography: An SQP Augmented Lagrangian Approach”, Geophysical Journal International, 2006. https://doi.org/10.1111/j.1365-246x.2005.02729.x
L. D'Auria, P. Gasparini, A. Herrero, R. De Matteis, J. Virieux and A. Zollo “Bayesian Estimation Of 2-D P-Velocity Models From Active Seismic Arrival Time Data: Imaging Of The Shallow Structure Of MT Vesuvius (Southern Italy)”, Geophys. J. Int. (2002) 151, 566-582. https://doi.org/10.1046/j.1365-246x.2002.01795.x
T. Back, “Evolutionary Algorithms in Theory and Practice”, Oxford University Press, 1996.
D. E. Goldberg, “Genetic Algorithms in Search. Optimisation and Machine Learning”, Addison-Wesley Pub. Co. 1989.
Published
How to Cite
Issue
Section
Copyright (c) 2008 S Zein, E Canot, J Erhel, N Nassif
This work is licensed under a Creative Commons Attribution 4.0 International License.