A more accurate way to measure spatial correlation length from CPT data – ARMA models

ABSTRACT: Spatial variability is one of the largest sources of uncertainty in geotechnical applications. This variability is primarily characterized by the spatial correlation length, a parameter that describes the distance over which the parameters of a material are similar. Spatial variability is generally described with traditional methods of time series analysis. In statistics, the Auto-Regressive Moving Average (ARMA) model is commonly used to describe the relationship between two points in time. Instead of assuming an autocorrelation model, the ARMA model calculates the necessary auto-regressive components (AR), as well as a decaying mean structure (MA). The advantage of this method is that it is calculated for each specific field study, so that the data is not forced to fit into a fixed autocorrelation model (e.g. Markovian, Gaussian, etc.). Additionally, a very simple and fast algorithm is needed to calculate the necessary AR, and MA estimates. In this study, the ARMA model is introduced as a means of measuring correlation length, and two case studies and a simulation are used to compare the correlation length values from the ARMA model to the other estimates. The ARMA model was able to find correlation length estimates that were very similar to other methods in the case study values, and much more accurate values in the simulation, compared to other methods.