Singular Points of the Tremor of the Earth’s Surface

Abstract

A method for studying properties of the Earth’s surface tremor, measured by means of GPS, is proposed. The following tremor characteristics are considered: the entropy of wavelet coefficients, the Donoho–Johnston wavelet index, and two estimates of the spectral slope. The anomalous areas of tremor are determined by estimating the probability densities of extreme values of the studied properties. The criteria for abnormal tremor behavior are based on the proximity to, or the difference between, tremor properties and white noise. The greatest deviation from the properties of white noise is characterized by entropy minima and spectral slope and DJ index maxima. This behavior of the tremor is called “active”. The “passive” tremor behavior is characterized by the maximum proximity to the properties of white noise. The principal components approach provides weighted averaged density maps of these two variants of extreme distributions of parameters in a moving time window of 3 years. Singular points are the points of maximum average densities. The method is applied to the analysis of daily time series from a GPS network in California during the period 2009–2022. Singular points of tremor form well-defined clusters were found. The passive tremor could be caused by the activation of movement in fragments of the San Andreas fault.

Keywords

• GPS tremor singular points
• entropy
• spectral slope
• probability density
• principal components