Evaluating the utility of gravity gradient tensor components

Abstract

Gravity gradiometry offers multiple single components and possible combinations of components to be used in interpretation. Knowledge of the information content of components and their combinations is therefore crucial to their effectiveness and so a quantitative rating of information level is needed to guide the choice. To this end we 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 simple prism, characterized by seven parameters: the prism location, xc, yc, its width w and breadth b, the density I?, the depth to top z, and thickness t. Varying these values allows a wide variety of body shapes, e.g., blocks, plates, dykes, 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 I?, xc, yc, w, b, z to t. Ranking the estimated model errors from a range of models shows that data sets consisting of concatenated components produce the smallest parameter errors. For data sets comprising combined tensor components, the invariants I1 and I2 produce the smallest model errors. Of the single tensor components, Tzz gives the best performance overall, but those single components with strong directional sensitivity can produce some individual parameters with smaller estimated errors (e.g., w and xc estimated from Txz).