Causal Instrument Corrections for Short‐Period and Broadband Seismometers

Online Material: Matlab codes and data example of instrument corrections. Of all the filters applied to recordings of seismic waves, which include source, path, and site effects, the one we know most precisely is the instrument filter. Therefore, it behooves seismologists to accurately remove the effect of the instrument from raw seismograms. Applying instrument corrections allows analysis of the seismogram in terms of physical units (e.g., displacement or particle velocity of the Earth’s surface) instead of the output of the instrument (e.g., digital counts). The instrument correction can be considered the most fundamental processing step in seismology since it relates the raw data to an observable quantity of interest to seismologists. Complicating matters is the fact that, in practice, the term “instrument correction” refers to more than simply the seismometer. The instrument correction compensates for the complete recording system including the seismometer, telemetry, digitizer, and any anti‐alias filters. Knowledge of all these components is necessary to perform an accurate instrument correction. The subject of instrument corrections has been covered extensively in the literature (Seidl, 1980; Scherbaum, 1996). However, the prospect of applying instrument corrections still evokes angst among many seismologists—the authors of this paper included. There may be several reasons for this. For instance, the seminal paper by Seidl (1980) exists in a journal that is not currently available in electronic format and cannot be accessed online. Also, a standard method for applying instrument corrections involves the programs TRANSFER and EVALRESP in the Seismic Analysis Code (SAC) package (Goldstein et al. , 2003). The exact mathematical methods implemented in these codes are not thoroughly described in the documentation accompanying SAC. We describe a general method for causal instrument correction that is applicable to data from a wide range of seismometers and present a set of codes for implementing the …