Three-dimensional modeling and correlation tomography of gravity gradiometry

Abstract

 In analysis of airborne gravity gradiometry, both the simulation that can calculate precise gravity gradient using subsurface density distribution and the inversion that can estimate subsurface density using observed data are necessary. Both the new simulation method that can treat complex density anomalies ant the new inversion method that is not based on the least-squares method were proposed in this paper.
 Most of three dimensional (3-D) gravity calculations depend on the calculation method using cuboids or rectangular prisms in previous researches. However it is slightly difficult to approximate 3-D terrains and anomalous bodies with complex figure using superposition of cuboids or prisms. For example, it is difficult for the traditional method to construct smooth inclination surface in case of an inclined dyke because an inclined dyke is often approximated by the step-like anomalous body using a lot of cuboids. The new technique to calculate gravity anomaly that is suitable for 3-D terrain and anomalous body with complex figure is proposed in this paper. This technique uses numerical integration using hexahedral element in order to calculate gravity gradiometry anomaly. As the result of numerical simulation using the new 3-D program, it is found that the boundary of density anomaly can be estimated by the distribution of gravity gradient of z-direction (g_zz). And horizontally changed density anomaly can be selectively extracted by using gravity gradient of x-direction and y-direction (g_xx and g_yy). In the simulation of airborne gravity gradiometry, it is found that the peak values of gravity gradient are influenced by the flight height. But the distribution shapes of gravity gradient are not influenced by the flight height. As the result of simulation using the inclined bodies, it is found that inclination angle might be estimated quantitatively from the profile of gravity gradient.
 In addition to the new 3-D simulation method, gravity gradiometry correlation tomography that can estimate 3-D density contrast is proposed in this paper. The correlation tomography can rapidly calculate 3-D correlation factor that reflects relative density distribution although it cannot calculate density distribution directly. As the result of correlation tomography using two density anomalies that have high and low densities, it is confirmed that positive and negative anomalies appeared around the center of high and low density anomalies respectively. The correlation tomography of gravity gradiometry will become a useful tool to analyze gravity gradiometry data as a simplified or auxiliary method for 3-D inversion.