Abstract: |
A challenge in seismic amplitude versus angle (AVA) inversion to elastic parameters is inclusion of prior information from geology, geophysical relations, well logs and other sources. In a recent publication, Lindgren et al. developed the necessary background for using linear stochastic partial differential equations (SPDEs) as prior fields in latent Gaussian models and highlighted the link between such representations and Matérn covariance functions. This approach allows for flexible incorporation of nonstationarity and anisotropy in the prior model. Another advantage is that the prior field is Markovian and therefore the precision matrix is very sparse, introducing huge computational and memory benefits. The seismic AVA inversion problem is essentially a trivariate random field inversion problem and the extension of the univariate SPDE approach entails using a system of SPDEs as priors. This allows us to control stationarity, anisotropy and smoothness of the individual elastic parameters as well as for the link between them through the cross-covariance SPDEs and therefore allows us to make more realistic prior models. We incorporate this approach in seismic AVA inversion, trying to improve inversion results.
Reference: Lindgren, F. Lindstrøm, J. and Rue, H. (2011) An explicit link between Gaussian fields and Gaussian Markov random fields: The SPDE approach. Journal of the Royal Statistical Society, Series B, vol 5, to appear |
