Quantification of Uncertainty in Velocity Log Upscaling using Reversible Jump MCMC

The motivation for generating upscaled velocity models includes practical goals such as reducing the computational cost of modeling or data processing. Existing 1-D effective medium solutions such as Backus averaging pose challenges as they can smooth sharp contacts like unconformities without careful application and therefore cannot reproduce the seismic response of the fine scale medium. In this paper, we apply Bayesian inversion, with reversible jump Markov Chain Monte Carlo (rjMCMC) sampling, to implement upscaling velocity logs as an inverse problem. The inversion minimizes the misfit between reference seismograms computed from the original well log and the seismic response of the coarse, upscaled velocity model. The results include an ensemble of upscaled models from which information such as the optimal coarse model and the upscaling uncertainty can be estimated. With this method, we are able to compare upscaling uncertainty when using single-offset and multi-offset seismograms as reference signals. The uncertainty of upscaled models generated using multi-offset seismograms as reference signals is lower than the value obtained using only a zero-offset seismogram as a reference.