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ABSTRACT: Here we present a new mathematical tool, the localized Hartley (HL) transform (Hartley, 1942; Bracewell, 1990), that allows for the filtering of 1-D time series through the identification of the power at various spatial and temporal
wavelengths. Its application to and the associated results are presented from its application to continuous Global Positioning
System (GPS) data from southern California for the time period 1994 through 2006. The HL transform filter removes the high-frequency
components of the data and effectively isolates the longer period signal. This long-period signal is modeled as time-dependent
postseismic deformation using the viscoelastic-gravitational model of Fernández and Rundle (2004) for six stations selected for their proximity to the Northridge earthquake. The x-, y-, and z-components of the postseismic
deformation are compared to the filtered data. Results suggest that this long-period deformation is a result of postseismic
relaxation and that the HL transform filter provides an important new technique for the filtering of geophysical data consisting
of the superposition of the effects of numerous complex sources at a variety of spatial and temporal scales.
Pure and Applied Geophysics 07/2008; 165(8):1577-1602. · 1.79 Impact Factor
