Estimating Autocovariance of In‐Situ Soil Properties

TLDR

Soil property spatial variability is typically modeled by trend surfaces with residuals, and computer-aided design now routinely applies statistical procedures to estimate these trends and residuals. The authors propose a maximum likelihood method to jointly estimate spatial trends, measurement noise, and the autocovariance of residuals. The method is validated through simulation experiments that assess small‑sample performance and optimal boring layouts, and applied to field vane strength data, comparing results to traditional moment estimators. The maximum likelihood approach demonstrates superior statistical properties over traditional procedures, achieves asymptotic behavior even with modest sample sizes, and yields comparable or improved results in field vane strength analyses.

Abstract

The spatial variability of soil properties in situ is often modeled by trend surfaces and residual variations about trend. With the advent of computer‐aided design, statistical procedures are now routinely applied to trend and residual estimation. A maximum likelihood (ML) technique is presented for simultaneously estimating spatial trends, measurement noise, and the autocovariance structure of residuals about spatial trends. This technique has more favorable statistical properties than traditional procedures, and these properties have an important practical advantage in that they lend themselves to incorporation in computerized data‐analysis systems. Simulation experiments are used to verify small‐sample‐size properties of ML estimation and to draw conclusions on optimal boring layouts. The experiments show that analytical asymptotic properties of maximum likelihood estimators are approached even at the modest sample sizes common in geotechnical site investigations. Field vane strengths from a site‐exploration program are analyzed using the maximum likelihood technique and comparisons are made with results obtained using traditional moment estimators.