Building a seismometer from scratch which produces verifiable data is going to be quite hard. But not impossible. I don’t know of an open source project, but here are my thoughts on how you would go about designing one if you choose to. I apologise if I am just telling you things you know.
Disclaimer I am no expert on seismometers, but I have some experience working with people who used seismometers to measure ground tremors in our labs so that we could correlate bad data from precision experiments with seismic events. The most useful part of this is we had a very expensive seismometer partially dissembled in my office.
The basic principle of a seismometer is a heavy mass on a spring, and a way to read out where the mass is. As the earth shakes the heavy and resists motion, so there is relative motion between the mass and the earth. However, if you built this very simple version any small kick would make the mass start swinging like a pendulum for ages making it very hard to get meaningful data.
What you first need to do is build a single degree of freedom oscillator (i.e. something that can move up and down but not in any other direction, or in any other single direction you choose). Harold’s suggestion of a speaker is an example.
What a lot of seismometers do is they have the mass attached to a flexure mechanism with two three-fold-symmetric planes of flexures (such as the triangle flexure in this paper https://aip.scitation.org/doi/pdf/10.1063/1.4707036) above each-other rigidly connected in the centre and connected to the mass, this constrains the motion to only move up and down (there will be slight rotation, this cab be fixed with a more complicated design but this is not necessary). This flexure mechanism is often too weak to support the mass so it is then supported by a bigger spring. [If you are interested in this I can try and sketch a clearer diagram.]
Once you have a single degree of freedom oscillator you must have to play with the design to get something with a low resonant resonant frequency as you can only measure above this. This tends to mean having a heavy mass, which makes the single flexure mechanism harder to build (and easier to break so you often need a locking mechanism for transport if it is too heavy). You also need to have damping to take energy out of the system so it doesn’t vibrate for ages when disturbed, this is probably best done with eddy current damping (copper plates on the mass which move through a magnetic field).
Once the physical design is good you need a way to record motion. This is normally done with a permanent magnet and a coil of wire (again Harrold’s suggestion of a speaker is a good example of this). This turns the motion into a voltage, but you still need to play with a low-pass filter to cut out the high frequency noise. The issue here is if you put the filter cut off too high you get too much noise, but if it is too low you cut off your signal. You would probably want to look into a higher order filter to have quite a sharp cut off. You can also do some of the filtering in electronics (everything close to half your data collection sample rate should be removed in electronics) and then build an IIR filter into your data collection to further remove high frequency noise.
The final step which I think is the hardest step is turning your signal into meaningful data, for this you need a way to convert the voltage into a velocity. To calibrate this you could wobble the device at a known speed at lots of different frequencies so you can measure the frequency response of the seismometer. This is not that easy to do, but without this calibration it is hard to get people to trust your data. This step is going to be the hardest step if you build your own, what you want is a graph like on the top right of the last page of the data-sheet of the product that Harold linked to (http://cdn.sparkfun.com/datasheets/Sensors/Accelerometers/SM-24%20Brochure.pdf).