HR: 17:00h
AN: S34B-05    [Abstracts]
TI: On Characterization of Elasticity Parameters in Context of Measurement Errors
AU: * Slawinski, M A
EM: mslawins@mun.ca
AF: Memorial University of Newfoundland, Dept. of Earth Sciences, St. John's, NF A1B 3X5, Canada
AB: In this presentation, we discuss the one-to-one relation between the elasticity parameters and the traveltime and polarization of a propagating signal in the context of the measurement errors. The one-to-one relationship between seismic measurements and a model postulated in the realm of the constitutive equation of an elastic continuum provides the link between the observational and theoretical aspects of seismic tomography [1]. The existence of this link encourages us to develop methods of inferring the elasticity parameters from measurements. However, a consideration of required accuracy and the analysis of error sensitivity suggest that the pragmatic application of this one-to-one relationship might be a difficult task indeed [4]. There are eight symmetry classes of an elastic continuum whose properties are contained in the density-scaled elasticity tensor [6]. Given this tensor in an arbitrary coordinate system, we can identify to which symmetry class it belongs, as well as obtain the orientation of its symmetry axes and planes, and hence the elasticity parameters in a natural coordinate system [2]. To obtain the tensor to be studied, we consider either ray velocities and polarizations [1] or wavefront slownesses and polarizations [5]. For the former, we assume that the medium is homogeneous in order to invoke the straightness of rays to calculate ray velocity given the source and receiver position; for the latter, we assume that the medium is homogeneous in at least one direction in order to invoke the ray parameter. In spite of the limitations due to homogeneities, both approaches are sensitive to measurement errors, which are not negligible. In view of these observational concerns [4], we consider several weaker objectives based on the theoretical formulation. Rather than distinguishing among eight symmetry classes and obtaining the corresponding elasticity parameters, we might be able to distinguish among a few groups that contain several classes within them and are characterized by ranges of parameters. Such an approach takes advantage of similarities among several eigenproperties that distinguish a given group from the others. Furthermore, we might not require to measure the traveltime of the three waves --- the quasishear wave being more difficult to observe. Also, we might not require to measure polarizations, which, in general, exhibit a larger measurement error than do the traveltimes. (To obtain a complete elasticity tensor we need both polarizations and traveltimes for the three waves [3].) 1. Bóna, A., Bucataru, I., Slawinski, M.A. (2007) Elasticity parameters from traveltime and polarization measurements. Journal of Applied Geophysics (accepted) 2. Bóna, A., Bucataru, I., Slawinski, M.A. (2007) Coordinate-free characterization of elasticity tensor. Journal of Elasticity 87(2-3), 109--132 3. Bóna, A., Bucataru, I., Slawinski, M.A. (2007) Material symmetries versus wavefront symmetries. Q. Jl Mech. appl. Math 60(2), 73--8 4. Bóna, A., Slawinski, M.A. (2007) Comparison of two inversions for elasticity tensor. Journal of Applied Geophysics (submitted) 5. Dewangan, P., Grechka, V. (2003) Inversion of multicomponent, multiazimuth, walkaway VSP data for the stiffness tensor. Geophysics 68(3), 1022--1031 6. Ting, T.C.T. (2003) Generalized Cowin-Mehrabadi theorems and a direct proof that the number of linear elastic symmetries is eight. Internat. J. of Solids and Structures 40, 7129--7142
DE: 3260 Inverse theory
DE: 3275 Uncertainty quantification (1873)
DE: 7200 SEISMOLOGY
DE: 7203 Body waves
SC: Seismology [S]
MN: 2007 Fall Meeting