In the context of inverse problems of mathematical geodesy, the calculation of the gravitational potential at the Earth's surface from its Hesse tensor at satellite's height turns out to be exponentially ill-posed. In fact, it requires specific tensorial procedures for its solution. This paper proposes a wavelet-based regularization method to overcome the calamities of the ill-posedness, thereby providing a "zooming-in" technique of modeling the gravitational potential from global to local scale. As a particularly remarkable ingredient the paper offers a new procedure of multiscale regularization by use of locally adapted regularization parameters.

Measuring techniques for the very high cycle fatigue behaviour of high strength steel at ultrasonic frequencies Dedicated to Prof. Dr.-Ing. Christina Berger on the occasion of her 65 th birthday To analyse the fatigue behaviour of steels in the very high cycle fatigue regime, an ultrasonic testing facility was developed that allows describing the cyclic deformation behaviour at ultrasonic frequencies by measuring characteristic fatigue data at a sufficiently high frequency. In correlation with scanning electron micrographs, fatigue tests prove that the sensitive measuring techniques indicate fatigue induced microstructural changes by a significant rise in the process parameters more than 10 6 cycles before final failure occurs. By further analysis of the attenuation behaviour of the ultrasonic resonance system, the logarithmic decrement can be used as a reasonable physical value to indicate changes in the microstructure with a very high sensitivity. This allows an improved understanding of the fatigue mechanisms in the very high cycle fatigue regime.

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