A Finite‐Difference Technique to Incorporate Spatial Variations In Rigidity and Planar Faults Into 3‐D Models For Lithospheric Flexure

Abstract

We present a finite‐difference formulation for 3‐D elastic flexure of the lithosphere, which is solved by a direct‐matrix method. to incorporate the effect of spatial variations in rigidity, additional terms for the bi‐harmonic 3‐D flexure equation have been derived from a variational displacement formulation as used in finite‐element methods. Additionally, planar faults are treated as discontinuities. These are implemented by an additional degree of freedom for fault heave, and a coupled continuum equation for zero‐differential tilting across the fault. the 3‐D finite‐difference results have been tested for line loads, point loads and disc loads by analytical solutions, and for spatial variation in effective elastic thickness (EET) by 2‐D finite‐difference solutions. Fault‐related flexure patterns are compared to the 2‐D analytical broken‐plate model developed by Vening‐Meinesz (1950). We subsequently apply the 3‐D fault model to investigate fault controlled 3‐D basement geometries in Lake Tanganyika (East Africa). We show that our model is capable of predicting 3‐D basement geometries, characteristically observed in rifted basins. the modelling results indicate that fault‐controlled upper crustal flexure patterns are associated with low values for EET. A comparison with regional scale‐model studies, showing a superposition of high EET flexure effects, supports a multilayered rheological control on continental rifting. Copyright © 1994, Wiley Blackwell. All rights reserved