We present a method dedicated to the interpretation of full tensor ͑gravity͒ gradiometry ͑FTG͒ data called tensor decon-volution. It is especially designed to benefit from the simultaneous use of all the FTG components and of the gravity field. In particular, it uses tensor scalar invariants as a basis for source location. The invariant expressions involve all of the independent components of the tensor. This method is a ten-sor analog of Euler deconvolution, but has the following advantages compared to the conventional Euler deconvolution method: ͑1͒ It provides a solution at every observation point, without the use of a sliding window. ͑2͒ It determines the structural index automatically; as a consequence, the structural index follows the variations of the field morphology. ͑3͒ It uses all components of the measured full gradient tensor and gravity field, thus reducing errors caused by random noise. It is based on scalar invariants that are by nature insensitive to the orientation of the measuring device. We tested our method on both noise-free and noise-contaminated data. These tests show that tensor solutions cluster in the vicinity of the center of causative bodies, whereas Euler solutions better outline their edges. Hence, these methods should be combined for improved contouring and depth estimation. In addition , we use a clustering method to improve the selection of solutions, which proves advantageous when data are noisy or when signals from close causative bodies interfere.