Uncertainty of 1-D Fracture Intensity Measurements

Abstract

This paper presents an analytical solution for quantifying the uncertainty of a one-dimensional (1-D) fracture intensity (P10) measurement, which counts fracture number per sampling length. The analytical solution is derived based upon P10 measurements in a wide range of scenarios from a single fracture to multiple fractures and from finite length of the scan line to infinite length of the scan line. The results show that the uncertainty of a P10 measurement can be expressed through the variance of a Poisson distribution. Furthermore, the analytical solution is verified via numerical simulation. This is carried out by generating a three-dimensional (3-D) fracture model that was sampled by scan lines considering the associated uncertainties. The results of the numerical simulation agree well with the analytical solution. Examples of possible applications are then provided.