Sensitivity of crustal deformation instruments to changes insecular rate

A variety of instruments (including borehole strainmeters, water wells, creepmeters, laser ranging and differential magnetometers) are used to monitor crustal deformation in areas that are prone to geologic hazards such as earthquakes and volcanic eruptions. In monitoring the deformation, one typically examines the data for either a change in rate, or a simple offset in the record. However, one needs to place a statistical confidence level that the detected signal differs from the background “noise”. Calculation of the statistical confidence level may be done using the formalism of the matched filter, whose output is the signal-to-noise ratio, ρ. Two ingredients are needed to form a matched filter: 1) The power density spectrum of the instrument and 2) the functional form of the signal that we desire to detect. Using the available crustal deformation data from the Parkfield, California network, the background noise for individual instruments as a function of frequency, f, is estimated using the traditional method of the power density spectra. Except for two-color laser distance-ranging data, the power spectra for most of the instruments have a frequency dependence of f⁻ⁿ where 2≤n≤3. The confidence level with which a hypothesized signal is present is determined directly from the signal-to-noise ratio, with the numerator being a function of the signal and the denominator being a function of the power spectrum. Using a creepmeter as an example, a 0.04-mm change occurring over 1 hour, a 0.06-mm occurring over 10 hours, or 0.20-mm over 100 hours are all signals for which ρ=2 and therefore have only a 5% confidence that these signals could be background noise.