Facies uncertainty in petrophysical forward function: A West Africa offshore field example

In the context of geophysical inversion, a petrophysical forward function provides the link between properties that are directly geophysically detectable {left parenthesis, less than bracket}e.g., seismic velocities and attenuation{right parenthesis, greater than bracket} and rock and fluid properties. Due to heterogeneity of rock properties uncertainty of the petrophysical forward function can be high. Uncertainty in the petrophysical forward function comes from two different sources: {left parenthesis, less than bracket}1{right parenthesis, greater than bracket} measurement uncertainty, and {left parenthesis, less than bracket}2{right parenthesis, greater than bracket} theoretical uncertainty. Measurement uncertainty accounts for errors in the acquisition and processing of data. Theoretical uncertainty on the other hand accounts for lack of knowledge about the rock type and appropriate physical theory to describe its elastic behavior. We present a method to construct the petrophysical forward function with its associated uncertainty from the both sources indicated above. The uncertainty of the petrophysical forward function is represented by a weighted sum of Gaussian distributions. Each Gaussian represents the measurement uncertainty of one facies, and the weight of the Gaussian represents the probability of the associated facies being the correct rock type to model the elastic behavior of samples. We first apply the method by assuming no theoretical uncertainty and show that the predictions of the petrophysical forward function are biased under this assumption. Then we apply the method by considering theoretical uncertainty about the type of the facies. The results show that introducing uncertainty in the facies reduces uncertainty in the final probabilistic petrophysical forward function and removes biases from its predictions.