Isomorphic geodetic and electrical networks: An application to the analysis of airborne gravity gradiometer survey data

Abstract

Early in 1987, the Bell Aerospace/Textron Gravity Gradiometer Survey System (GGSS) will be tested by the Air Force Geophysics Laboratory in an airborne survey of a 300 × 300 km region of Oklahoma and Texas. The survey pattern will be a grid with a 5 km separation between adjacent tracks, both north‐south and east‐west. One way to process the GGSS survey data is to analyze an electrical network that is isomorphic to the survey network. The integrated gradients between the nodes where the survey lines cross correspond to the applied voltages between the nodes of the electrical network; the gradient variances correspond to the internodal resistances; the elements of the adjusted gravity vector correspond to the nodal voltages; and the solution variances correspond to the resistances to ground. An error analysis is performed by calculating the resistance to ground of the electrical network; a technique for making the calculations in large networks is explored in detail. For sample survey scenarios with one ground‐truth control point near each corner of the survey square and with realistic values for the survey parameters, the standard deviation in the gravity disturbance is less than 1 mGal and the deflection of the vertical standard deviation is less than 0.25 arc-s at all nodes. With no ground truth, but with a gravimeter on the aircraft that can independently determine gravity to 10 mGal at all nodes, the adjusted standard deviation in gravity disturbance is less than 1 mGal.