Temperature sensitivity analysis on mass-spring potential with electrostatic frequency reduction for lunar seismometers

A broadband seismometer has been identified as an important scientific instrument that can be deployed on the surface of Earth’s Moon in the near future. To achieve the goals of the International Lunar Network, this next generation of seismometers is required to achieve at least 2 × 10−10 ms−2 Hz−1/2 at 1 mHz, which are several orders of magnitude more sensitive at the same frequency than the ones deployed during the Apollo program; their goal is to capture the lunar seismic noise floor, observe the lunar normal modes, and record distant teleseisms from all over the Moon. The Electrostatic Frequency Reduction (EFR) technique has been employed in a seismometer design in our laboratory and can enhance the Moonquake measurement sensitivity covering a longer period down to 1 mHz. EFR has advantages over the traditional frequency reduction techniques since it can be autonomously tuned and lowers the resonance frequency without modifying the mechanical design of a capacitive readout seismometer, an approach desirable for spaceflight-qualified instrumentation. A drawback is that we have also found that the EFR as well as other frequency reduction techniques amplify the temperature sensitivity of a seismometer beyond the limit of a conventional temperature control system. Here, we describe quantitatively and analytically the temperature dependence of a spring suspended mass model of a seismometer and provide practical solutions to minimize the thermal effects on a lunar seismometer using the EFR technique. By choosing the materials for the seismometer housing and the spring suspension that could balance the shear modulus and thermal expansion coefficients, one could mitigate the thermal sensitivity of the seismometer using the EFR technique. These modifications allow us to approach the stringent requirements for instrument self-noise necessary for the science objective.