Evaluating the utility of gravity gradient tensor components

Abstract

Gravity gradiometry allows individual components and combinations of components to be used in interpretation. Knowledge of the information content of different components and their combinations is therefore crucial to their effectiveness, and a quantitative rating of information level is needed to guide the choice. To this end, I use linear inverse theory to examine the relationship between the different tensor components and combinations thereof and the model parameters to be determined. The model used is a rectangular prism, characterized by seven parameters: the prism location [Formula: see text], [Formula: see text]; its width [Formula: see text] and breadth [Formula: see text]; the density [Formula: see text]; the depth to top [Formula: see text]; and thickness [Formula: see text]. Varying these values allows a variety of body shapes, e.g., blocks, plates, dykes, and rods, to be considered. The Jacobian matrix, which relates parameters and their associated gravity response, clarifies the importance and stability of model parameters in the presence of data errors. In general, for single tensor components and combinations, the progression from well to poorly determined parameters follows the trend of [Formula: see text], [Formula: see text], [Formula: see text], [Formula: see text], [Formula: see text], [Formula: see text], to [Formula: see text]. Ranking the estimated model errors from a range of models showed that data sets consisting of concatenated components produced the smallest parameter errors. For data sets comprising combined tensor components, the invariants of the tensor produced the smallest parameter errors. Of the single tensor components, [Formula: see text] gave the best performance overall, but those single components with strong directional sensitivity can produce some individual parameters with smaller estimated errors (e.g., [Formula: see text] and [Formula: see text] estimated from [Formula: see text]).