Introduction

Flexural isostasy is the deflection of Earth's lithosphere in response to topographic loading and unloading. When a topographic load is generated by motion along a thrust fault, for example, the lithosphere subsides beneath the load. The width of this zone of subsidence varies from place to place depending on the thickness of the lithosphere, but it is generally within the range of 100 to 300 km. Conversely, a reduction in topographic load causes the lithosphere to rebound, driving rock uplift. Flexural-isostatic uplift in response to erosion replaces approximately 80% of the eroded rock mass, thereby lengthening the time scale of mountain-belt denudation by a factor of approximately five because erosion must remove all of the rock that makes up the topographic load and the crustal root beneath it in order to erode the mountain down to sea level. Given the ubiquity of erosion in mountain belts, it is reasonable to assume that flexural-isostasy plays a key role in nearly all examples of large-scale landform evolution. Flexural isostasy also plays an important role in the evolution of ice sheets because the topographic load of the ice sheet causes lithospheric subsidence, thereby influencing rates of accumulation and ablation on the ice sheet. In this chapter, we will discuss three broadly-applicable methods (series and integral solutions, Fourier filtering, and the Alternating- Direction Implicit (ADI) method) for solving the flexural-isostatic equation in geomorphic applications.