640 Seismological Research Letters Volume 81, Number 4 July/August 2010 doi: 10.1785/gssrl.81.4.640 E Method for Calculating Self-Noise Spectra and Operating Ranges for Seismographic Inertial Sensors and Recorders J. R. Evans, F. Followill, C. R. Hutt, R. P. Kromer, R. L. Nigbor, A. T. Ringler, J. M. Steim, and E. Wielandt J. R. Evans, 1 F. Followill, 2 C. R. Hutt, 3 R. P. Kromer, 4 R. L. Nigbor, 5 A. T. Ringler, 3 J. M. Steim, 6 and E. Wielandt 7 Online Material: MatLab scripts, guidance, and supporting material. INTRODUCTION Understanding the performance of sensors and recorders is pre- requisite to making appropriate use of them in seismology and earthquake engineering. Tis 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 lim- its 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. Te representation of seismic-instrument self-noise lev- els and their efective operating ranges (cf., dynamic range) for seismological inertial sensors, recorders (data acquisition units, or DAUs), and integrated systems of sensors and record- ers (data acquisition systems, or DASs) forces one to address an unnatural comparison between transient fnite-bandwidth signals, such as earthquake records, and the instrument’s self noise, an efectively stationary signal of infnite 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 defned, since the maximum of that spectrum depends strongly upon signal and record durations. In contrast, the noise foor 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/s 2 ) while PSDs have units of amplitude-squared per hertz ( e.g., (m/s 2 ) 2 /Hz) and the rPSD has units of amplitude per root of hertz ( e.g., (m/s 2 )/Hz 1/2 ). Tus, this incompatability is a confict 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 dia- grams” (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 frst 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 instru- ments, 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 procure- ment specifcations. BACKGROUND Drawing upon work in acoustics, Steim (1986) introduced the notion of an operating range to seismology, comparing fractional-octave rms (root mean square) self-noise amplitudes to the rms of a just-clipping sine wave. Note that by virtue of integrating the self noise over half octaves, both values now have units of simple amplitude ( e.g., m/s 2 ), although their magnitudes typically vary with frequency. Tus, this representation is a com- parison for the time domain between instrument self noise and band-limited transient reference signals refective of just-clip- ping seismic records. (Notwithstanding that operating range is 1. U.S. Geological Survey, Menlo Park, CA 2. Lawrence Livermore National Laboratories (retired), Livermore, CA 3. U.S. Geological Survey, Albuquerque, NM 4. Sandia National Laboratories (retired), Albuquerque, NM 5. University of California, Los Angeles, CA 6. Quanterra, Harvard, MA 7. Universität Stuttgart (emeritus), Stuttgart, Germany