Quantum gravity-gradient sensing technology exhibits unique advantages and significant application potential in geophysical research and practical scenarios. We present a free-fall vertical gravity gradiometer based on cold-atom interferometry. Phase-difference extraction employs an elliptical-fitting method that is simple to implement and responds rapidly to gravitational variations. A detailed analysis is conducted on the noise associated with this method and corresponding optimizations are carried out. The device achieves a performance with a sensitivity of 52.9 $\mathrm{E}/\sqrt{\mathrm{Hz}}$ and a stability better than 0.5 E over $7\times {10}^4$ s ($1\mathrm{E}=1\times {10}^{-9}{\mathrm{s}}^{-2}$). Based on this performance, we initially completed the application simulation of resource exploration scenarios in the laboratory and evaluated its accuracy and sensitivity in the exploration field. This research work provides support for future geophysical research and applications.

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• Atom interferometry
• Cold atoms & matter waves
• Geophysics
• Laboratory studies of gravity
• Noise
• Quantum sensing
• Alkali metals
• Ultracold gases