The effect of the topography on Magnetic Resonance Tomography (MRT) Diplomarbeit Ines Rommel Technical University Berlin Institute of Applied Geoscience Department of Applied Geophysics October 2006 Hiermit versichere ich, die vor- liegende Arbeit selbstst¨andig, ohne unerlaubte fremde Hilfe und nur mit den angegebenen Hilfsmitteln angefertigt zu haben. Berlin, den 6. Oktober 2006 Ines Rommel I II Zusammenfassung Der Einfluss der Topographie auf die Magnetische Resonanz Tomographie (MRT) Die Magnetische Resonanz Sondierung (MRS) ist eine geophysikalische Methode um Grund- wasser direkt von der Oberfl¨ache aus zu detektieren und zu untersuchen. Mittlerweile ist es m¨oglich in der Anwendung der MRS mit getrennter Sende- und Emp- fangsspule zu messen. Diese Messungen eignen sich fur¨ hochaufl¨osende 2D-Untersuchungen der oberfl¨achennahen Wassergehaltsverteilung, da sie eine erh¨ohte r¨aumliche Aufl¨osung und zuverl¨assige Signalamplituden liefern. In bisherigen Modellierungen fur¨ gleiche und getrennte Sende- und Empfangsspulen wurde die Topographie vernachl¨assigt. Diese Arbeit untersucht und bewertet den Einfluss der Topographie auf MRS Messungen und stellt den Vergleich zur flach modellierten Erde mit horizontaler Oberfl¨ache her. Zus¨atzlich dazu wurden die Spulenseparation, die Profil- richtung und der Neigungswinkel der Spulen mit in Betracht gezogen. Die 2D Modellierung einer Dunenstruktur¨ mit Hilfe der Finiten Elementen Methode zeigt durch Ver¨anderungen in der Neigung der Dune¨ und die damit einhergehende relative Ver¨anderung der Spulen- lage, Einflusse¨ des zus¨atzlichen oder reduzierten Untersuchungsvolumens und des Winkels zwischen den Spulen. Die Abweichung der Amplituden zur flach modellierten Erde steigt mit zunehmender Spulenseparation und steigender Neigung der Dune.¨ Zus¨atzlich zu den 2D Modellierungen wird eine 2D Inversion fur¨ Messungen mit getren- nten Spulen unter Berucksichtigung¨ der Topographie durchgefuhrt.¨ Die Inversion spiegelt das Modell wieder und gibt zuverl¨assige Ergebnisse. Die Inversion einfacher Wassermod- elle mit vernachl¨assigter Topographie liefert offensichtlich falsche Ergebnisse. Trotzdem der invertierte Wassergehalt vertikal zur wahren Topographie hin verschoben wird, bleiben große Abweichungen zum Modell erhalten. Um die Verbesserung durch die Einbeziehung der Topographie in der Dateninterpretation zu zeigen, wurden MRS Messungen uber¨ eine Dune¨ im Nordosten Deutschlands durchge- fuhrt.¨ Ein detailliertes und plausibles Modell einer 2D Wassergehaltsverteilung wurde er- mittelt, das durch gleichstromgeoelektrische und induzierte Polarisationsmessungen best¨arkt werden kann. Die Betrachtung der Topographie verbessert die Inversionsergebnisse und eine bessere Anpassung an die Daten wird erzielt. Als Ergebnis dieser Arbeit ist zu sagen, dass es nicht vertretbar ist, bei Untersuchungen mit getrennten Spulen die Topographie in der Modellierung und der Inversion zu vernach- l¨assigen. III IV Abstract The effect of the topography on Magnetic Resonance Tomography (MRT) Magnetic Resonance Sounding (MRS) is a geophysical method to detect and explore groundwater directly from the surface. Recently, in the application of the MRS, it is possible to measure with separated trans- mitter and receiver loops. This measurement provides enhanced spatial resolution and sufficient signal amplitudes to perform high resolution 2D surveys to obtain the water content distribution of the shallow subsurface. So far, the topography is neglected in conventional modeling of coincident and separated loop measurements. This study investigates and assesses the effect of the topography on the MRS measurements in comparison to the flat modeled earth with a horizontal surface. In addition, the loop separation, the profile direction and the tilt angle of the loop are taken into account. The 2D modeling of a dune structure, using the finite element method, shows through the changes of the slope of the dune and the associated relative changes in the orientation of the loops, the effects of the additional or reduced investigated volume and of the angle between the loops. The deviation of the amplitude to the flat modeled earth increases with increasing separation of the loops and increasing slope of the dune. In addition to the 2D modeling, a 2D inversion for separated loop surveys is performed, which takes the topography into account. The inversion reflects the model and gives reliable results. The inversion of water models neglecting the topography provides obviously wrong inversion results. Despite shifting the inverted water content vertically to the real topography, high deviations to the model remain. To show the improvements of incorporating the topography into the data interpretation a MRS survey across a dune in the northeast of Germany has been realized. A detailed and reasonable model of a 2D water content distribution, which can be encouraged by the measured geoelectrical and IP data was determined using the inversion scheme. The consideration of the topography improves the inversion results and thus a better adaptation to the data is achieved. As the result of this thesis, it is not justifiable to neglect the topography in the modeling and the inversion for separated loop surveys. V VI Contents 1 Introduction 1 2 Theory 3 2.1 The basics of Magnetic Resonance Sounding (MRS) ............. 3 2.2 The Finite Element Method (FEM) ...................... 13 3 Synthetic Data 17 3.1 Comparison of a modeling with a square and a circular loop and different separations ................................... 17 3.2 Modeling with coincident and separated loop configuration ......... 21 3.2.1 Modeling with COMSOL ........................ 22 3.3 Homogeneous half space ............................ 24 3.3.1 Coincident soundings .......................... 29 3.3.2 Edge-to-edge measurements ...................... 34 3.4 Three layer model ................................ 38 3.5 Comparison between north-south and east-west profile ........... 41 3.6 Inversion of synthetic data ........................... 45 4 Field data set 53 4.1 Geophysical measurements ........................... 55 4.2 Data processing ................................. 57 4.3 Modeling of the dune .............................. 61 4.4 2D inversion ................................... 66 5 Conclusions 71 Bibliography 73 A Appendix 75 A.1 Appendix to Chapter 2 ............................. 77 A.2 Appendix to Chapter 3 ............................. 80 VII Contents VIII 1 Introduction The Magnetic Resonance Sounding (MRS), also known as Surface Nuclear Magnetic Reso- nance (SNMR), is a relatively new geophysical method to assess groundwater. It is the only geophysical method that allows the direct detection of water and a reliable estimation of the water content from the surface. The connection of the measured signal and the amount of the water results in a very high potential of this method in environmental, engineering and geophysical questions. The measured transient signal also contains information about the pore structure and the hydraulic conductivity. In 1946, the Nuclear Magnetic Resonance was discovered by Bloch [1946] and Purcell et al. [1946], and became an established tool in physics, medicine and chemistry. The initial idea of using this technique for the exploration of groundwater was developed in the early 1960s. Only in the 1980s the equipment was designed by Russian scientists. The applications and results of the surveys for water prospecting was first published by Semenov [1987]. In 2000, new and improved equipment was designed by Iris Instruments with increasing power and the possibility for measuring with separated transmitter and receiver loops. The extended formulation of the theory for different transmitter and receiver loop was developed by Weichman et al. [1999; 2000]. In 2003, first measurements and the first assessment of the properties of separated loop measurements were published by Hertrich and Yaramanci [2003]. A detailed physical description of separated loop measurements and their contribution to high resolution two dimensional water content distribution mapping is studied in the PhD thesis of Hertrich [2005]. The high potential of the measurement with separated transmitter and receiver lies in the investigation of 2D structures. For the interpretation of the MRS data, the loop separation, separation direction and separation orientation have to be taken into account for each individual sounding of the survey. In conventional modeling of 2D separated loop measurements, flat and horizontally strat- ified earth is assumed, but for the extension to arbitrary field applications, the effect of topography has to be considered. If the loops are located on the same plane, the apparent inclination angle can simply be changed as a sum of the true inclination of the Earth’s magnetic field and the tilt angle of the loop. As soon as the loops are not on one plane this simplification is not valid. The numerical computation of the magnetic field is demonstrated with the help of the Finite Element Method (FEM) in three dimensions. It is possible to model and calculate any arbitrary topography and internal subsurface conductivity, as well as every wanted 2D or 3D water content distribution. The advantage of this method is the use of the unstructured tetrahedron mesh with local mesh refinement and the flexible description of arbitrary geometry. 1 1 Introduction Chapter 2 gives a general introduction into the theory of the Magnetic Resonance Sound- ing including the properties of the magnetic