Sample Size Automation in a Pseudo-random Model Uncertainty Workflow

Abstract

Velocity model building (VMB) using tomography produces one credible realization of an earth model, which, in turn, generates one conceivable subsurface image. The inversion, by its nature, is highly non-linear, and can lead to uncertainty with a single model and image approach. Uncertainty can be quantified by using a model population, rather than a single realization. In this scenario, all models must equally explain the data by producing flat gathers from the inversion. Defining what is an appropriate sample size for a nonlinear system using a pseudo-random approach to model uncertainty is critical for cost and turnaround. We automate a real-time constraint on the expanding model population using statistical relevance to the attributes produced through the uncertainty process. Analysis using cumulative distribution functions (CDFs) of the deviation in the model population define an automated threshold. The sample size threshold is met when there is no additional statistical relevance for the output attributes; the process stops and the model uncertainty metrics defining spatial reliability of the data are output. We demonstrate this method on data from the North Sea.