The Projected Gradient Method for the Recovery Research of Sub-surface Rock Density

Abstract

With the development of the measuring instruments of Earth’s gravity gradient tensor, the full tensor gravity (FTG) data can be obtained validly and accurately. Their high data resolution induces their application in many research domains. With the improvement of the instrument manufacturing capability, the FTG data can be acquired on the satellite, airborne, vehicle, marine and submarine. And, three dimension data inversion is an effective and significant method for the quantitative interpretation of FTG data. The inversion of large scale data may consume large number of time with the increasing of the data and model parameters. Therefore, in the future development of data processing, researchers not only pay attention to the improvement of inversion method precision, but also pay attention to the improvement of the calculation efficiency. Therefore, a fast and effectively numerical algorithm to improve the inversion efficiency is more meaningful. Accordingly, an improved gradient method with projections onto convex set is used to accelerate the recovery rate of the sub-surface rock density. This gradient method can obtain an optimal gradient direction to give the fastest descent speed of the target function. This new efficient algorithm can make good use of the mass FTG data.