Transdimensional change-point modeling as a tool to investigate uncertainty in applied geophysical inference: An example using borehole geophysical logs

Abstract

Recently developed methods for inferring abrupt changes in data series enable such change points in time or space to be identified, and also allow us to estimate noise levels of the observed data. The inferred probability distributions of these parameters provide insights into the capacity of the observed data to constrain the geophysical analysis and hence the magnitudes, and likely sources, of uncertainty. We carry out a change-point analysis of sections of four borehole geophysical logs (density, neutron absorption, sonic interval time, and electrical resistivity) using transdimensional Bayesian Markov chain Monte Carlo to sample a model parameter space. The output is an ensemble of values which approximate the posterior distribution of model parameters. We compare the modeled change points, borehole log parameters, and the variance of the noise distribution of each log with the observed lithology classes down the borehole to make an appraisal of the uncertainty characteristics inherent in the data. Our two examples, one with well-defined lithology changes and one with more subtle contrasts, show quantitatively the nature of the lithology contrasts for which the geophysical borehole log data will produce a detectable response in terms of inferred change points. We highlight the different components of variation in the observed data: due to the geologic process (dominant lithology changes) that we hope to be able to infer, geologic noise due to variability within each lithology, and analytical noise due to the measurement process. This inference process will be a practical addition to the analytical tool box for borehole and other geophysical data series. It reveals the level of uncertainties in the relationships between the data and the observed lithologies and would be of great use in planning and interpreting the results of subsequent routine processing.