The seismometers of the SIL array can be used as accelerometers by modifying the transfer function slightly. The frequency response described by equation 29 and shown in Figure 4 is proportional to the velocity of the ground motion at the geophone site. Acceleration is the time derivative of velocity. In the frequency domain this corresponds to multiplying the input signal (i.e. ground velocity) by s. To find the response of the SIL system to ground acceleration the velocity proportional transfer function is divided by frequency, i.e. one extra pole is added at (0.0, 0.0). Equation 29 then becomes:
To obtain the acceleration at the recording station, the spectra of the seismograms are divided by . Figure 5 shows a plot of versus frequency for the six types of geophones used in the SIL system. For the two short period instruments, the response has a peak at their respective eigen frequencies. For the broadband instruments the acceleration response is flat from about 0.2 Hz (determined by the digitizer) down to the respective eigen frequency of each geophone type.
The ground displacement at the geophone sites can be obtained from the velocity proportional seismograms by integration. In the frequency domain this corresponds to dividing the input of the system by s or, equivalently, multiplying the transfer function by s. This implies adding one zero at (0.0, 0.0). Equation 29 then gives the displacement proportional transfer function as:
To obtain the ground motion, the spectra of the seismograms are divided by . Figure 6 shows as a function of frequency for the six seismometer types.