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Analysis Methods to Identify the Instrument Response Function (IRF) for De-convolution


c.       Analysis Methods to Identify the Instrument Response Function (IRF) for De-convolution

The recorded trace on a seismometer is the incident ground motion convolved with the response function of the sensor and data acquisition system.  It is necessary to remove the response function from the data in order to obtain the true measured time history of ground motion.  Methods of removing the response function exist if it is known [1, 2].  However, for a signal recorded from a legacy instrument, the amplitude and phase response of the instrument may not have been preserved.  Many of these legacy instruments no longer exist and records of calibrations performed during their lifetime may be missing or incomplete.


The challenge is to conduct research to devise methods of analyzing the waveform time series represented in the legacy data to estimate the sensor and data acquisition instrument response function (IRF).  The frequency passband required for seismic waveform analysis is primarily over the operational monitoring band of 0.02 to 20 Hz, but also of interest are methods applicable at lower frequencies down to 0.0083 Hz (120-second periods).  Possible approaches can include, but not limited to, analysis of the microseism and other background noise [3], analysis of recorded events in the historical archive with known signal characteristics (such as large magnitude earthquakes), and comparison of the legacy IRF to other nearby seismometers with known response functions that may have been operating during overlapping time periods.


A potential approach is to develop a signal analysis algorithm to identify the amplitude of the first and subsequent peaks, and to derive the uncertainty in these values, given an IRF and a noise spectrum model, or in a self-consistent analysis in which the full trace constrains how significant the IRF and noise are in modifying the size of the largest peaks and features. An outcome of interest is to generate such a self-consistent analysis from a legacy recording trace, and deduce limits on how much influence the IRF or noise would have on the amplitude of the major peaks (primarily the first one), to produce the “true amplitude” and its uncertainty.  There might be analogous applications in medical record analyses (e.g., elucidating relative size of s- vs. t- waves vs. other elements of electrocardiogram traces) [4].


Questions – Contact: Thomas Kiess,

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