What is "modern seismometer"
The principle of a "modern seismometer" is still the same: a mass on a spring. What makes a seismometer "modern", is the careful mechanical design, accurate method of detection of the test mass motion (coil in magnetic field, sometime capacitive method), and, in some wideband sensors, feedback applied to the test mass which allowing to avoid the resonance of the mass and to extend sensitivity to lower frequency range.
Hopefully, the reader would not be satisfied with such a short description. See the following pages for a very thorough review of seismometers and seismic observations in general:
Seismic Sensors and their Calibration, by Erhard Wielandt, Institute of Geophysics, University of Stuttgart
You may also check the following links