f Block inversion of surface NMR date using simulated annealing

Surface nuclear magnetic resonance (SNMR) is a new non-invasive groundwater-exploration method allowing direct determination of the mobile water content using relaxation amplitudes and of the permeability using decay times of excited hydrogen protons [1, 2]. At present inversion of SNMR data is only one dimensional. The currently available inversion schemes are the programs NUMIS [1], using a smooth regularised least-squares inversion and SAINV [2], using smooth-inversion with simulated annealing (SA), an optimised random search algorithm which is largely independent of the starting model and can escape from local minima [3]. The program SAINV allows to choose between two different types of regularisation, being standard ‘‘smooth’’ (type I) and a more ’’blocky’’ regularisation (type II) [2]. So far the inversion is carried out on the basis of a number of predefined inversion layers that have fixed positions and thicknesses. The inversion scheme introduced in the present paper, based on SA as well, uses block-inversion. In analogy to 1D geoelectrics (VES) the inversion tries to fit the water content of each layer as well as the depth of the layer boundary for a given number of inversion layers, e.g. a 3-layer-case. In block-inversion also a regularisation of type II instead of type I may be used, however, with negligible differences in the results except for very high degrees of regularisation. Inversions have been carried out for data obtained from SNMR measurements at the test site Haldensleben [4]. At this site borehole measurements confirmed a 3-layer-case with a single aquifer between 21.7 and 46 m having a sharp upper boundary due to a very small capillary zone as well as a sharp lower boundary to glacial till and about 30% of mobile water. While the smooth inversion type I yields only a rough estimation of the aquifer location the results of the smooth inversion type II are somewhat more realistic, however, only for a high degree of regularisation. The results of the block inversion are in good agreement with the known sharp boundaries of the aquifer and, in contrast to the smooth inversion, prove to be not influenced by the degree of the applied regularisation. For all inversion results the error of the data fit is generally less than 4 % and the water content is slightly underestimated Block-inversion has some significant advantages. There is no limitation due to the use of predefined inversion layers and therefore it allows a more nature like interpretation especially for aquifers with sharp boundaries. Furthermore it is largely independent of the type and the degree of regularisation and so considerably reduces the ambiguity of the inversion of SNMR data.