A Refined Least Squares Collocation Method Based on Multiquadric Function

Trend removal is the most common approach in conventional least squares collocation (LSC) to deal with nonstationarity. Due to the inaccuracy of the trend model, conventional LSC can barely eliminate the drift component of the data that results in estimation bias of the local covariance function and error of the interpolation values. Here we present a refined LSC method to estimate the drift component of the field and compensate the residualfrom LSC. The refined method employs the mulitiquadric function to approach the drift and the collocation to estimate signals. We apply the refined method to a synthetic data set and coseismic displacement data from the 2009 L'Aquila, Italy earthquake, and compare the results of refined method with conventional methods. The statistical results of residuals indicate that the refined method can achieve a more accurate result than conventional methods and is affected less by the observation distribution.