Continuous Parameter Nonhomogeneous Semi-Markov Model for Stratigraphic Analyses from Well Log Data

Well log data are a common source of information for characterizing subsurface environments. A statistical methodology is developed and applied for the interpretation of such data in terms of a multi-state depositional sequence. The well log data is classified into a discrete set of states (e.g., sand, silt, clay) and stratigraphic transitions between these states are described as a continuous parameter, nonhomogeneous semi-Markov process. The state by state transitions at any vertical horizon are modeled using a transition intensity matrix. Transition intensity is defined as the number of transitions from one state to another per unit depth. This procedure does not require a discretization of the deposition axis as is done with a Markov Chain model. The transition intensities are allowed to vary by position in the stratigraphic sequence to account for nonstationarities in the deposition process. A kernel estimator is used to estimate the transition intensity at any depth as a weighted moving average of the number of transitions from one soil type to another and of the associated bed thicknesses. A simulation strategy for simulating pseudo-well logs that have the same statistical properties as the sampled well logs is also developed. An application of the methodology to data from Lake Bonneville sediments in Utah is provided.