Open AccessNon‐linear Bayesian joint inversion of seismic reflection coefficients
Author(s) -
Erik Rabben Tor,
Tjelmeland Håkon,
Ursin Bjørn
Publication year - 2008
Publication title -
geophysical journal international
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.302
H-Index - 168
eISSN - 1365-246X
pISSN - 0956-540X
DOI - 10.1111/j.1365-246x.2007.03710.x
Subject(s) - inversion (geology) , bayesian probability , quadratic equation , reflection (computer programming) , inverse problem , seismic inversion , mathematics , algorithm , computer science , statistics , geology , mathematical analysis , seismology , geometry , azimuth , tectonics , programming language
SUMMARY 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.