Flexure of the Lithosphere

These lecture notes are basically a supplement to Turcotte and Schubert, Chapter 3. The results of the first derivation are the same as equation 3-130 in T&S but rather than guessing the general solution, the solution is developed using fourier transforms. The approach is similar to the solutions of the marine magnetic anomaly problem, the lithospheric heat conduction problem, the strike-slip fault flexure problem and the flat-earth gravity problem. In all these cases, we use the Cauchy integral theorem to perform the inverse fourier transform. Later we'll combine this flexure solution with the gravity solution to develop the gravity-to-topography transfer function. Moreover, one can take this approach further to develop a Green's function relating temperature, heat flow, topography and gravity to a point heat source (e.g., Sandwell, Thermal Isostasy: response of a Moving Lithosphere to a Distributed Heat Source, In addition to the constant flexural rigidity solution found in the literature, we develop an iterative solution to flexure with spatially-variable rigidity. Before going over these notes, please re-read section 3-9 in Turcotte and Schubert on the development of moment versus curvature for a thin elastic plate. q(x) x w(x) F