Higher-order gravitational potential gradients for geoscientific applications

Gravity data have been applied for modelling and interpretation studies in geosciences. This contribution reviews currently observable and foreseen gravity data represented by gradients of the gravitational potential. Functional models linking 3-D mass density distribution functions to potential gradients of up to the third order are formulated using volume integrals of the Newtonian type with unitless kernel functions expressed both analytically and using infinite series of associated Legendre functions. Spatial and spectral properties of the kernel functions are analysed and sensitivity of the gradients to particular mass density distributions is studied. Two particular mass density distribution models are used in numerical experiments: a local 3-D mass density model representing shallow mass density variations and a global mass model represented by Earth's upper sediments with lateral mass density variations. Computed values of the gradients demonstrate their different sensitivities to particular mass density distributions which change with an increasing distance of the gradients from gravitating masses. Third-order gradients are particularly useful for studying near subsurface or shallow density structures such as caves, caverns, salt domes, sediment basement morphology, continental margins or buried fault systems that could be identified spatially more closely. Thus, higher-order gradients would offer an interesting tool for mass density mapping once their observability with the sufficient accuracy and resolution is realized.