Abstract
In this paper, we developed one waveform tomography method for P velocity and density inversion in elastic media. Starting from the elastic wave equation, we derived one P wave equation which includes the scattered terms of P-wave to P-wave conversion and S-wave to P-wave conversion. By discretizing the scattering integral equation corresponding to this equation directly, we can obtain one equation corresponding to each point on the waveform. The result of this formulation is a very large system of algebraic equations that is solved using ART and SIRT. The results of computational simulation applied to cross-hole geometry show that our method is valid when the velocity and density perturbation is not very large. Next we will extend this method to heterogeneous media and apply it to real field data.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
Chen, J.C. and Y. Wei, Inversion of two-dimensional elastic wave equation with two-variables within Born approximation, Apllied Sciencese(China),1988.
Harris, J. M. and G. Wang, Diffraction tomography for inhomogeneities in a layered background medium, Sixty-Third Annual Meeting and International Exposition of Society of Exploration Geophysicists, Expanded Abstracts, 49–52, 1993.
Hooshyar, M.A. and A.B. Weglein, Inversion of the two-dimensional SH elastic wave equation for the density and shear modulus, J. Acoust. Soc.Am., 78, 1280, 1986.
Norton, S.J. and L.R; Testard, Reconstruction of one-dimensional inhomogeneneities in elastic modulus and density using acoustical dimensional resonances, J. Acousti. Soc. Am., 79(4),932–942,1988.
Miller, D., M. Oristaglio, and G. Beylkin, A new slant on seismic imaging: Migration and integral geometry, Geophysics, 57,7, 943–946, 1984.
Mora, P., Elastic wavefield inversion and adjoin operator for the elastic wave equation, in: Mathematical Geophysics, p. 117–137, Edited by N. J. Valaar, G. Nolet, MJ.R. Wortel & S.A.P.L. Cloetingh, 1988 by P. Reidel Publishing Company.
Tarantola, A., 1984, The seismic reflection inverse, problem, Inverse Problems of Acoustic and Elastic waves, edited by F. Santosa, Y.H.Dao, W.Symes and Ch. Holland, SIAM, Philadelplia.
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 1995 Springer Science+Business Media New York
About this chapter
Cite this chapter
Yin, F., Harris, J.M. (1995). Waveform Tomography for Two Parameters in Elastic Media Applied to Cross-Well Geophysics. In: Jones, J.P. (eds) Acoustical Imaging. Acoustical Imaging, vol 21. Springer, Boston, MA. https://doi.org/10.1007/978-1-4615-1943-0_77
Download citation
DOI: https://doi.org/10.1007/978-1-4615-1943-0_77
Publisher Name: Springer, Boston, MA
Print ISBN: 978-1-4613-5797-1
Online ISBN: 978-1-4615-1943-0
eBook Packages: Springer Book Archive