The improvement of sparsity gravity inversion using an adaptive lanczos bidiagonalization method

Abstract

Inversion of gravity data is one the important steps in the interpretation of practical data. The detection of sharp boundaries between anomalous bodies and host rocks is an interesting point in the geological frameworks. The gravity inversion with sparsity constraint is a useful method to recover block subsurface density distribution, which is efficiently used for the quantitative interpretation of gravity data. The reweighted regularized method is a useful method to solve the inverse problem. However, in this type, we must face the updating gravity forward matrix and large matrix operation. The application of Lanczos bidiagonalization method can reduce the size of data and matrix in the inversion to resolve the large scale inversion problem. However, a very important problem is not resolved, which is update of reweighted forward matrix and new Lanczos bidiagonalization matrix. Here, an adaptive Lanczos bidiagonalization method is studied to select the Lanczos bidiagonalization factor. And a new projected method with adaptive Lanczos bidiagonalization method is study to avoid the updating sparsity reweighted function. We calculate the reweighted forward matrix and Lanczos bidiagonalization matrix only one time, which can essentially reduce the computational complexity. The inversion results of synthetic data show that the new improved method is faster and better than common reweight regularized Lanczos bidiagonalization method to produce an acceptable solution for focusing inverse problem. The improvement of adaptive Lanczos bidiagonalization in sparsity gravity inversion is also tested on gravity data collected over the Mobrun massive sulfide ore body in Noranda, Quebec, Canada. The inversion results indicate a remarkable correlation with true structure of the ore body that is achieved from drilling data.