Parametric Analysis and Calibration of the STS-1 Seismometer of the IRIS/IDA Seismographic Network

We have estimated the observed system response of STS-1 sensors installed at stations of the IRIS/IDA Seismographic Network using cross-spectral analysis of random binary calibration signals. Systematic deviations of up to 1% in amplitude and 1 ° in phase between the measured and the manufacturers "nominal" responses are observed in the range 0.2 to 100 mHz and up to 12% in amplitude and 5 ° in phase for frequencies above 5 Hz. A parametric analysis of the STS-1 seismometer is developed that leads to a more complete pole and zero model of the sensor, accounting accurately both for small changes in individual instrument parameters and for the effects of an incomplete compensation of the mechanical response by the feedback circuit. This model is then used to fit the observed responses with a precision of 0.2% for the amplitude and 0.1 ° for the phase over the entire useful bandwidth of the instrument. Introduction The development of the STS1 seismometers around 1980 (Wielandt and Strekeisen, 1982; Wielandt and Steim, 1986) marked a significant step in the progress of seismometry. In particular, it greatly expanded the bandwidth and dynamic range that could be recorded by single sensor. The parallel developments of high dynamic range and low-noise analog-to-digital converters led to the implementation of the systems now being deployed in the new global seismographic networks. In order to capitalize upon the increased bandwidth and dynamic range, the response of the system must be known with commensurate precision. Traditionally, the STS-1 sensors are closely adjusted at the factory to a simple, approximate model response--the "nominal model'--which is assumed to be stable in time. Our experience based on the IRIS/IDA Network instruments shows that the actual responses are indeed in agreement with this model to within a few percent in the range 0.02 to 100 mHz and are stable under normal conditions. However, when examined in detail, using the technique of random binary calibration and cross-spectral analysis (Berger et al., 1979), systematic differences between the nominal and the observed responses are seen, particularly at frequencies above 5 Hz. A more detailed parametric analysis of the feedback system developed in this article provides a model of the transfer function that better predicts the observed behavior of the system. The results presented constitute a relative calibration, describing the shape of the frequency response but not the absolute values of the sensitivity. For several reasons, explained later, the calibration of the whole frequency range of the sensor response requires two procedures, with random signal of different characteristics and time series sampled at different rates: a calibration of the low-frequency range, below 100 mHz, and a calibration of the high-frequency range, above 100 mHz. Parametric Analysis and Model of the STS-1 Transfer Function The seismometer can be described as a mechanical pendulum equipped with a displacement transducer and two parallel control loops that produce feedback forces that are proportional to the relative displacement, its integral, and its derivative, and whose sum is approximately proportional to ground acceleration. The system, illustrated in Figure 1, is divided into six subsystems. The input is the ground acceleration ag, and there are two outputs: the broadband output, providing the signal ebb, and the long-period output, providing the signal elp (from which the mass position output em is derived). Since the sensors are used in the very broadband configuration (low-frequency comer of the response located at 360 sec), we focus the present analysis on the broadband output, as this signal contains the whole teleseismic frequency range and the long-period signal becomes secondary. According to the signal flow-graph (Balabanian and Bickart, 1969) of Figure 1, in the Fourier domain the system loop gain is L = T, T2(T3T4 + TsT6) (1) and the transfer function of the broadband output system: