Geophys. J. Int. (2007) 169, 789–794 doi: 10.1111/j.1365-246X.2007.3396.x GJI Geodesy, potential field and applied geophysics FAST TRACK PAPER A new analytical solution estimating the flexural rigidity in the Central Andes S. Wienecke, 1, ∗,† C. Braitenberg 2 and H.-J. G¨ otze 3, ∗ 1 Geological Survey of Norway, Leiv Eirikssons vei 39, 7491 Trondheim, Norway 2 Department of Earth Sciences, University Trieste, Via Weiss 1, 34100 Trieste, Italy 3 Institut f ¨ ur Geowissenschaften, Abtl. Geophysik, CAU Kiel, Otto Hahn Platz 1, 24118 Kiel, Germany Accepted 2007 February 9. Received 2007 February 7; in original form 2006 May 23 SUMMARY We present a new 2-D analytical solution of the fourth-order differential equation, which describes the flexure of a thin elastic plate. The new analytical solution allows the differential equation for an elastic plate to be solved for any irregular shaped topography with a high spatial resolution. We apply the new method to the Central Andes. The flexural rigidity distribution calculated by this technique correlates well with tectonic units and the location of fault zones, for example, the Central Andean Gravity High correlates with the presence of a rigid, high-density body. Key words: crust, depth of compensation, gravity, isostasy, Moho discontinuity. 1 INTRODUCTION The integration of geophysical, petrophysical and geological data allows the investigation of key processes of mountain building, the location of fault zones and the deformation processes within the crust. The spatial distribution of flexural rigidity indicates significant structural units of the crust as a function of their isostatic response. The flexural rigidity of the elastic lithosphere can be estimated us- ing a fourth-order differential equation describing the flexure of a thin elastic plate (Turcotte & Schubert 1982; G¨ oldner 1988). Hertz (1884) proposed three different solutions for the simple case of an ice plate floating on water. The deflection was calculated for a point load without taking the gravity into account. However, applied to geological problems the flexural values (in range of μm) were too small compared with the expected depths for a crust–mantle inter- face. For this reason spectral methods (coherence and admittance) have been preferred for the solution of the differential equation in the frequency space (Watts 1988). For continents, the reliability of the spectral technique has been questioned, because of drawbacks connected to the spectral approach (Braitenberg et al. 2002). The first drawback for the inverse calculation of the flexure from gravity observations is that the admittance method becomes unstable in the case of small topographic heights. Secondly, a large spatial window ∗ Formerly at: Institut f¨ ur Geologische Wissenschaften, Fachbereich: Geophysik, Freie Universit¨ at Berlin, Malteserstr. 74–100, 12449 Berlin, Germany. †Now at: Statoil Research Centre, Arkitekt Ebbellsvei 10, Rotvoll, N-7005 Trondheim, Norway. E-mail: suw@statoil.com. (at least 375-km side length) is required for the analysis (Macario et al. 1995). Even with new wavelet transform techniques using Forsyth’s method (Swain & Kirby 2006) or methods which use a combination of admittance and coherence (Daly et al. 2004) such a side length is still necessary for higher flexural rigidity values. Ac- cordingly the flexural rigidity distribution is estimated only roughly and correlation with smaller tectonic features not possible. Some of the disadvantages of the spectral methods were overcome by the convolution approach developed by Braitenberg et al. (2002). Al- though much work has been done to date, it is still questionable from the physical point of view, if it is sufficient to calculate the rigidity over an area of a side length lower than 375 km. The purpose of this study is to present a new analytical solution for an elastic plate (ASEP), making use of three solutions proposed by Hertz (1884). We evaluate all three solutions for their feasibility. The ASEP will be compared with the inverse Fourier transform of the transfer func- tion of the spectral methods (Watts 2001), as both solve the same differential equation. As a case example for the application of the ASEP, we calculate the flexural rigidity distribution for the Central Andes, where an extensive database is available to us. We aim to establish our new method for calculating the flexural rigidity distri- bution with a high spatial resolution in order to compare the results with geological information. 2 METHOD The new analytical solution solves the differential equation of the fourth order for any irregular shape of the topography. The equation, which was analytical solved, calculates the flexure w of a thin elastic plate: C  2007 The Authors 789 Journal compilation C  2007 RAS