by A.F. Shakal and J.T. Ragsdale
Shakal, A.F. and J.T. Ragsdale (1984). Acceleration, Velocity and Displacement Noise Analysis for the CSMIP Accelerogram Digitization System, from Proc. Eighth World Conf. Earthq. Enginrg., San Francisco, May 1984.
Click on the link below for the full text:
Introduction
A series of tests were undertaken to establish the level and characteristics of processing noise associated with a scanning digitizer used by the California Strong-Motion Instrumentation Program (CSMIP). Digitizations of straight-line traces were used to determine the peak values of acceleration, velocity and displacement to be expected from intrinsic processing noise. The noise-level peak acceleration is about .0015 g, as expected from the digitizer step-size. This value is a constant and does not change with the cut-off period used in the long-period filtering. The peak velocity and displacement values increase as a function of increasing filter cut-off period. For 1-second period, peak velocity has approximately a 0.1 cm/sec uncertainty, and peak displacement has a 0.01 cm uncertainty. For a 5-second filter cut-off, these values increase to about 0.5 cm/sec and 0.5 cm, respectively. The velocity response (PSV) and Fourier (FS) spectra for straight-line digitizations increase linearly with period (decrease with frequency as ω-1), passing through approximately 1 cm/sec at 1 Hz (5% damping). Equivalently, the pseudo-acceleration (PSA) spectrum is approximately constant at a value of .003 g.
Digitization tests were also made using synthetic (tapered-sinusoid) accelerograms. These records were used to study the characteristics and noise levels of standard processing within selected frequency bands. These tests indicate that for certain accelerograms, the decimation (spectral folding) associated with the low-pass filtering can introduce spurious long-period energy into the data. Adequate filtering prior to decimation removes the effect, though it tends not to be severe for most earthquake accelerograms because of their spectral width. The correction can be achieved through a relatively minor modification of the original code. An additional minor modification can approximately correct the recently noted high-frequency inaccuracy of the standard instrument-correction algorithm.
