A slow shake carries the mass along
Picture a box containing a mass held by a horizontal spring. Push the box along a table. As the box starts to accelerate, the mass lags and the spring stretches or compresses. That changing gap gives the instrument something to measure. Inertia is the tendency of an object to resist changes in its motion.
Now move the box slowly back and forth. The spring has time to pull the mass into each new position. Mass and box travel almost together, leaving a small change in their separation. A mass fixed in space is a useful limiting picture for rapid shaking; the distance between the actual mass and the case is what the pickup sees.
Sources: [1]
The rate of shaking changes the response
The spring and mass have a preferred rhythm. Their natural frequency is the oscillation frequency they would have without damping. A damper gradually reduces the free motion and changes its frequency. It also restrains the large response, called resonance, that can appear when ground motion approaches a strongly responding part of the instrument’s range.
Consider a teaching example with a natural frequency of one cycle per second and moderate damping, described here by a damping ratio of 0.7. Keep the base amplitude at 0.8 millimetres. One shake every four seconds produces a relative-displacement amplitude of about 0.05 millimetres. Four shakes per second produce about 0.8 millimetres. The same input amplitude has produced internal motions differing by more than a factor of ten.
A moving-coil pickup adds another conversion. In one arrangement the magnet is fixed to the case and the coil moves with the mass. Their relative motion generates a voltage proportional to their relative speed. At a turning point relative to the case, the coil briefly stops and its voltage passes through zero. It moves faster near the middle of that relative swing and produces more voltage there. Manufacturer sensitivity therefore includes a velocity unit: volts for each metre per second of relative motion. Interpreting the voltage requires both the mechanical response and this electrical conversion.
Feedback holds the mass near its centre
A different design measures how far the mass has moved from its equilibrium position inside the case and uses a separate coil to pull it back. The circuit repeats this correction continuously. This is force feedback. The gap becomes small, and the force needed to keep it small becomes a useful output.
Where the loop responds quickly enough, has sufficient gain and stays within its force range, the mass nearly follows the case’s acceleration. Actual actuator force divided by mass then approximates ground acceleration. Further circuitry can transform the response to provide a velocity output. The output designation and its calibration tell the user which quantity a recorded curve represents.
Detection and actuation take time. Increasing feedback gain also requires control of the delays, or an attempted correction can drive a new oscillation. The Güralp manual describes position sensing, loop compensation and the different outputs separately. Following these steps explains how a small internal displacement can accompany a clear signal from the ground.
Sources: [2]
Calibration still leaves a useful frequency band
Calibration supplies a known motion or force and measures the voltage amplitude and how far its peaks lead or lag the reference motion. Repeating this over different rates gives the instrument response: the conversion from each kind of ground oscillation to an electrical signal. Processing can reverse that conversion to recover ground displacement within a useful frequency band.
Compensation amplifies noise too. A very slow oscillation may produce a tiny voltage; multiplying it several hundred times also multiplies the small unwanted voltage mixed into the record. Recovery therefore uses a useful frequency band, gradually reduces the response at its edges and limits amplification where the instrument is weak. Read the recovered curve together with that band. It describes the ground motion the instrument can distinguish over those rates of shaking.