Large-scale inversion of gravity gradiometry with differential equations

With recent advances in technology, geophysicists are able to acquire large-scale airborne gravity gradiometry data sets for oil and gas, and mineral exploration. The inversion of these data are advantageous by giving the interpreter a 3D model to interpret. The number of data and model parameters associated with these data sets make an inversion difficult to carry out without substantial computational resources. In this work, we present a finite-volume, differential-equation method for gravity gradiometry data inversion. The computation of the sensitivity times a vector and its adjoint is done by solving a fourth-order Poisson equation using a multigrid method. The forward modeling is set up as a solution of a linear inverse problem so that the sensitivities are never explicitly formed. This allows us to dramatically increase the storage capacity of the problem and invert regional problems. To demonstrate the effectiveness of our method, we present an inversion of the Bathurst Mining Camp region on a personal computer that consists of 1.4 million data and a mesh of 24 million cells.