Theoretical and observed noise in a high-sensitivity long-period seismograph

Theoretical expressions for the spectra of the noise in a galvanometer, a seismometer, and a seismometer-galvanometer seismograph are derived from electrical analog circuits and from the Johnson noise of the resistive elements in these circuits. The contributions of the internal damping of the seismometer and of the galvanometer, and of the series resistor to the total potential energy of the thermal noise in a high-sensitivity long-period seismograph are explicit in the expressions. The theoretical thermal spectra agree with observations made at Las Cruces, New Mexico (LC-NM), and at Queen Creek, Arizona (QC-AZ). At LC-NM, the outputs from two matched vertical seismographs were subtracted to obtain estimates of the individual seismograph noise at periods from 4 to 800 sec. Additional experiments demonstrated that the seismograph noise between 10 and 1,000 sec could be estimated equally well by replacing the seismometer: (1) with a resistor, (2) with a coil and magnet oriented vertically or north-south, or by (3) rigidly blocking the seismometer mass. The observed spectra from LC-NM indicate an excess noise in the electronics of the galvanometer phototube amplifier (GPTA) having a one-over-f character at periods longer than 300 sec. At QC-AZ, seismograph noise was recorded with a resistor substituted for the seismometer. The observed noise spectra agree identically with the theoretical noise spectra at periods from 25 to 60 sec and with theoretical noise spectra plus a 1/f noise in the GPTA electronics at periods out to 2,560 sec. The QC-AZ observed and theoretical noise spectra are plotted from 3 to 2,560 sec as the mean-square voltage at the seismograph output and as the root-mean-square displacement of the ground that would produce the same signal as the noise. Typical minimum vertical amplitude spectra of the microseismic background are above the instrument noise spectra in the period range from 3 to 2,560 sec. The agreement between the theoretical thermal noise spectra and the two sets of observational spectra confirms the validity both of the theoretical expressions and of the experimental procedures.