Mathematics – Probability
Scientific paper
Apr 2008
adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=2008geoji.173..265e&link_type=abstract
Geophysical Journal International, Volume 173, Issue 1, pp. 265-280.
Mathematics
Probability
2
Inverse Theory, Spatial Analysis, Probability Distributions, Acoustic Properties
Scientific paper
Inversion of seismic reflection coefficients is formulated in a Bayesian framework. Measured reflection coefficients and model parameters are assigned statistical distributions based on information known prior to the inversion, and together with the forward model uncertainties are propagated into the final result. This enables a quantification of the reliability of the inversion. Quadratic approximations to the Zoeppritz equations are used as the forward model. Compared with the linear approximations the bias is reduced and the uncertainty estimate is more reliable. The differences when using the quadratic approximations and the exact expressions are minor. The solution algorithm is sampling based, and because of the non-linear forward model, the Metropolis-Hastings algorithm is used. To achieve convergence it is important to keep strict control of the acceptance probability in the algorithm. Joint inversion using information from both reflected PP waves and converted PS waves yields smaller bias and reduced uncertainty compared to using only reflected PP waves.
Erik Rabben Tor
Tjelmeland Håkon
Ursin Bjørn
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