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I believe Seismometers record ground displacement. However, I have also read in certain articles that this can be ground displacement or acceleration depending on the frequency of the seismometer. Could someone kindly elaborate on how a seismometer works.

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A geophone (type of seismometer) contains a coil of wire, wrapped on a mass, surrounded by a magnet. As the Earth moves we assume the mass stays still due to inertia and this changing magnetic field will produce a current in the coil of wire. This current is measured as a voltage and relates to the rate of change of displacement of the Earth with respect to time or:

$$ v \propto \frac{dx}{dt} $$

Where v is voltage, and $\frac{dx}{dt}$ is the velocity of ground motion. Correct me if I'm wrong but the difference in seismometers eg. MEMS accelerometers (acceleration) vs geophone (velocity) is their frequency response.

https://www.crewes.org/ResearchLinks/GraduateTheses/2008/Hons-MSc-2008.pdf

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Neither displacement nor acceleration; most seismometers measure velocity. If you want displacement, you integrate the output over time, and if you want acceleration, you differentiate the output over time. Check the datasheet for the instrument you are interested in. For example, the Guralp 3T datasheet says that it outputs 1500V m/s, so for each meter per second of ground velocity the output increases by 1500V. (It also says it only outputs from +20V to -20V, so this means ground velocities greater than 20/1500 = 0.013 m/s will be "off the chart" i.e. saturate the instrument).

Actually, the voltage output from a seismometer is not exactly proportional to displacement, velocity, OR acceleration. The actual output is the input displacement convolved with the impulse response of the seismometer. It's just that the impulse response is designed such that it will have an approximately linear response to ground velocity within the corner frequencies. In the 3T datasheet we were looking at, they say it's within -3 dB of linear as long as it's measuring ground that's not oscillating faster than 50Hz or slower than 0.0083Hz for one version of the instrument.

Measuring displacement directly is known as geodesy (as opposed to seismometry) and the tools used for those measurements include GPS, lidar, and radar.

To measure acceleration (strong motion), as Jay says, you can use an accelerometer. Or, precariously balanced rocks for the palaeo case!

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