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Book review: Dekorrelative Gravimetrie

Fig. 1. Willi Freeden, Mathias Bauer assisted by Christian Blick, Erdenebaatar Byamba, Thomas Degro, Zita Hauler, Bernd Jakobs, Laura Mailänder, Thomas Neu and Helga Nutz: Dekorrelative Gravimetrie. 393 pages, 2020, Springer Spektrum, ISBN 978-3-662-61907-0, eBook 54.99 €, Hard cover 69.99 €

Apart from a complete formulation of the necessary geoscientific framework, this book focuses on the geoscientific context of issues and problems that occur in gravitative exploration (Figure 1). In addition, an insight into the current status of the research is provided, by reducing gravimetry to calculable (decorrelated) models. The various unsolved questions and problems of gravimetry should be made known to a wide circle of scientists, the exploration industry, raw material extraction and other professional colleagues. The mathematics are used here as a key technology for modelling and simulation interests based on the analysis and interpretation according to density and precise gravitative measurements.

The bridging function is characteristic in order to create a cycle from the potential measurements by geophysicists, to the cleansing of data by geophysicists, to a subsequent theory formation and modelling with implementation and numerical calculation through to the interpretation by geologists and raw materials engineers. The book covers the entire range from geological engineering, geodesy (parts II and III in particular), mine surveying to geophysics through to geomathematics and delivers groundbreaking and innovative mathematical knowledge as transfer methodology from gravitative measurements to mathematical-numerical modelling structures as well as solutions for the deposit discourse with new geological areas of application.

Up to now for the successful use of gravimetric research methods it was necessary that the geological structures to be detected had clear density contrasts, such as with a salt dome. As the density in the salt dome clearly stands out from that of surrounding rocks, a characteristic contour diagram of a minimum in the centre of the salt dome is revealed in the gravimetric signals. So far such structures can be characterised and analysed more precisely with known gravimetric exploration methods so that appropriate conclusions about the salt dome are possible from the gravimetric signals. The methodology presented in this book claims to also be able to detect the less distinctive geological formations, e. g., outside the salt dome, in contrast to each other. A crucial aid is a wavelet decorrelation, i. e. a multiscale decomposition of gravitative signatures, so that layer boundaries of geological formations become visible.

For global analyses the solution using the non-spatial spherical harmonics, the frequency, has been the standard in geo-desy since P. S. de Laplace, A. M. Legendre and C. F. Gauss. This book, with whose help it is possible to detect in particular local structures for exploration, therefore deals to a large extent with the ideal spatial method by means of local-compact cores with fixed – in the case of splines – and variable widths – in the case of wavelets. However, frequency-based modelling can be used in an initial step as eligible preliminary information.

The integral equation inherent in Newton’s law implies that no sharp contours of the gravitation potential can normally be obtained in the survey area from gravimetric information. A wavelet decorrelation opens up the possibility of dismantling the signal into different signature bands in order to obtain finer structures through “band specification”. However, an appropriate redistribution of the mass leaves the resulting potential unchanged. This uniqueness problem insists on a certain degree of preliminary information in the survey area for the gravimetric practical application. A complete reconstruction of the density only from terrestrial gravimetric measurements is generally not possible even in combination with satellite data. For this reason, seismic information, e. g., about the geology of the survey area, should always be included in the modelling. Two different methodological approaches are used to solve this inverse gravimetry problem. Firstly, the Mollifier-Newton-Wavelet Inversion, a discreet inversion method that creates an underground model from gravitation data and includes information already known about the exploration area, which should reduce or overcome the uncertainties by the mathematical-related situation of the ill-posed gravimetry problem. The Mollifier-Newton-Wavelet functions with their spherical beams are used as components of a non-linear system of equations in order to create a density model locally on the inside from the gravitation anomalies on the surface. This method is understood as a discreet expression, which uses the already known continuous Mollifier-Newton-Wavelet accesses in combination with a new “smoothing idea”. Secondly, the Mollifier-Newton-Spline Inversion, which is essentially a discreet non-linear minimisation problem and involves the Newton potential operator on the core function generated by the Newton core.

Using the example of the region of Saarland, important applications, particularly for areas with mining-related voids or dense building developments, are shown. The wavelet decorrelation of geological structures successful in seismology should also be developed for the potential method of gravimetry in order to validate its effectiveness in areas heavily impacted by mining. The research project sponsored by the BMWi “Satellite-assisted potential method for geothermal exploration” was used for this purpose. In this project the concepts for the use of potential methods of the gravimetry were developed for the initial assessment in the planning and implementation of geothermal projects. The increasingly efficient gravimeters with significantly improved measuring accuracy, as well as the rapid development of the computers, lead to new methods of data decomposition, which are used as approximative geomathematical methods, and show that in future weaker anomalies can be recorded and modelled. This means that the geological structure of an area can be better interpreted and modelled by the gravimetry. The information already known in the test area serves to eliminate any problems with regard to clarity and stability in the inversion process in order to get as close as possible to the existing geological structure with the calculated result.

From the reviewer’s point of view, the book is a scientific set of rules for modern geoengineering. It can serve as a rich source of information to colleagues in applied maths, geophysics, geodesy or raw materials extraction, who deal with the various questions of inverse gravimetry, in order to go beyond the traditional limits of the geophysical exploration and also certain geodetic questions. For this, an insight into the current status of the gravimetric multiscale research is provided and proven that the gravimetry can be reduced to easily accessible and thus calculable decorrelation models and permits the use of potential methods in the exploration. The decorrelative gravimetry is thus a new exploration technology, which as a canonical innovation results from the combination of new measuring and modelling techniques.

Prof. Dr.-Ing. em. Bertold Witte, Aachen/Germany