A method for rebalancing a group of accelerometers in a gravity gradiometer instrument (GGI) includes the steps of defining and implementing a number of groupwise actuation constrainment modes based on a design of the gravity gradiometer instrument and its accelerometers. Implementing one constrainment mode comprises differentially scaling and distributing a single electrical current to multiple accelerometers' rebalance circuitry to cancel a specific acceleration effect experienced by the group of accelerometers or gradiometer as a whole. Superposition of a number of such modes enables rebalancing the full acceleration environment experienced by the group of accelerometers, given negligible local differential acceleration effects specific to, say, an individual accelerometer of the assembly. Mathematically, the multiple of constrainment modes are encapsulated by an actuation or constrainment modal influence matrix, arranged one mode per column of the matrix, and the electrical currents of respective modes are encapsulated in a vector listing of currents.