Method for calculating self-noise spectra and operating ranges for seismographic inertial sensors and recorders

Understanding the performance of sensors and recorders is prerequisite to making appropriate use of them in seismology and earthquake engineering. This paper explores a critical aspect of instrument performance, the “self” noise level of the device and the amplitude range it can usefully record. Self noise limits the smallest signals, while instrument clipping level creates the upper limit (above which it either cannot produce signals or becomes unacceptably nonlinear). Where these levels fall, and the “operating range” between them, determines much of the instrument's viability and the applications for which it is appropriate. The representation of seismic-instrument self-noise levels and their effective operating ranges (cf., dynamic range) for seismological inertial sensors, recorders (data acquisition units, or DAUs), and integrated systems of sensors and recorders (data acquisition systems, or DASs) forces one to address an unnatural comparison between transient finite-bandwidth signals, such as earthquake records, and the instrument's self noise, an effectively stationary signal of infinite duration. In addition to being transient, earthquakes and other records of interest are characterized by a peak amplitude and generally a narrow, peaked spectral shape. Unfortunately, any power spectrum computed for such transient signals is ill defined, since the maximum of that spectrum depends strongly upon signal and record durations. In contrast, the noise floor of an instrument is approximately stationary and properly described by a power spectral density (PSD) or its root (rPSD). Put another way, earthquake records have units of amplitude (e.g., m/s²) while PSDs have units of amplitude-squared per hertz (e.g., (m/s²)²/Hz) and the rPSD has units of amplitude per root of hertz (e.g., (m/s²)/Hz^1/2). Thus, this incompatability is a conflict between earthquake (amplitude) and PSD (spectral density) units that requires one to make various assumptions before they can be compared. For purposes of instrument operational performance, we provide a means of evaluating signal and noise and the range between them in a manner representative of time-domain instrument performance. We call these “operating range diagrams” (ORDs), plots of instrument self noise and clipping level; the “operating range” is the range between these values. For frequency-domain performance we elect to show self noise as an rPSD that may be compared to another instrument's noise or to ambient Earth noise (e.g., Peterson 1993); however, to limit the number of arbitrary choices required to merge transient and stationary signals we do not compare the rPSD to transient signals in the frequency domain. Our solution for a time-domain comparison is not new but rather builds upon the consensus of the first and second Guidelines for Seismometer Testing workshops (Hutt et al. 2009) and long established practice in acoustics. We propose this method as a standard for characterizing seismic instruments, and it has been endorsed by the second workshop (Hutt et al. 2009, 2010) and the Advanced National Seismic System (ANSS) Working Group (2008) and recent ANSS procurement specifications.