All celestial mass bodies have the ability to generate quakes, even the Earth's Moon. The larger the mass body, the greater the chance for quakes. The Earth alone averages tens of thousands of earthquakes, of varying intensities, each year. These quakes are the result of its consistent force of gravitational acceleration on the mass, whose intensity is based on its mass density. The greatest gravitational force is expressed from within the center of mass, where the density is the greatest. Increase the density of a mass and you increase the probability for quakes. A spinning mass provides for an even greater probability of quakes, as the varying stratified layers of the mass are massaged into place as the mass body attempts to adapt to the gravitational forces being applied to it. Mars is no different in any of these respects relevant to its gravitational center of mass.
As a side note, the architectural design for a martian research station takes advantage of the spherical shape. The spherical design results in highly efficient and effective air circulation when either facing towards or away from the sun. Less surface area makes these buildings less susceptible to temperature changes, and thus, inexpensive to heat and cool as compared to rectangular structures. Per the NASA paper 'The Second Conference on Lunar Bases and Space Activities of the 21st Century, volume 1', the structural integrity of this spherical design increases in a low gravity environment. This is a great advantage for surviving martian quakes may be rhythmically longer in duration than earthquakes.
As science fiction imitates science fact, you can gain a greater appreciation of what it would be like to build and live on the moon through reading the epic novel, ‘Shadow-Forge Revelations’.