Fast Forward Mapping And Fast Inversion For Gravity Gradiometer Data

Compared with traditional airborne gravimetry, airborne gravity gradientmeasurements in addition to a fast, economical and flexible features, moreimportantly, the gravity gradient data for geological bodies have higher resolution. Inrecent decades airborne gravity gradient measurements in foreign countries has beenrapidly developed, airborne gravity gradient measurement systems and inversioninterpretation methods have made great progress. In contrast, the domestic research inthis area has just begun.The thesis present an algorithm for inverting single gravity gradiometer data torecover three-dimensional (3-D) distributions of density contrast for the undergroundgeological body. The theory is based upon a regularized inversion that constructs adensity contrast distribution having minimum structure, and the inverse solution isobtained by minimizing a model objective function subject to the data and boundconstraints on the model. For practical application, wavelet transforms and aninterior-point method are applied to the inversion of gravity gradient data. The fastwavelet transform is used, along with thresholding the small wavelet coefficients, toform a sparse representation of the sensitivity matrix. The compressed matrix is usedto carry out fast forward modelling by performing matrix-vector multiplications in thewavelet domain. The reduction in CPU time is directly proportional to thecompression ratio of the matrix. A second important feature of the algorithm used hereis the use of an interior-point method of optimization to enforce positivity constraints.In this approach, the positivity is incorporated into the inversion by a sequence ofnon-linear optimizations approximated by truncated Newton steps. At the heart of thealgorithm, a linear system of equations is solved. The conjugate gradient techniquehas been used as the basic solver to take the advantage of the efficient forwardmodelling offered by the sparse matrix representation.Numerical simulations show that the three-dimensional (3-D) gravity gradientforward in using sensitivity matrix of wavelet compression can reduce the forward calculation of matrix-vector multiplication time of more than50%; numericalinversion used preconditioned conjugate gradient method and the improvedconvergence criteria, the entire inversion time reduced by more than90%; addingdepth weighting function to some extent, improved the depth resolution of theinversion problem, however, due to the inherent lack of depth information in fielddata, the inversion results in shallow part still better than in deep part, the other apriori information necessary to introduce further improvements.