GEOPHYSICAL RESEARCH LETTERS, VOL. 25, NO. 20, PAGES 3903-3906, OCTOBER 15, 1998 The effect of inplane force variations on a faulted elastic thin-plate, implications for rifted sedimentary basins Ronald T. van Balen Fac, der Aardwetenschappen, Vrije Universiteit, Amsterdam, The Netherlands Yury Y. Podladchikov Department of Earth Sciences, ETH-Zentrum, Ziirich, Switzerland Abstract. Studies of flexural motions of lithosphere commonly apply a differential equation based on the Lhin-plate approach. 111 this approximation, thc flcxural response to a changing horizontal inplane force depends only on the curvature of the midplane of the thin-plate representing the mechanical behaviour of the lithosphere. However, in cases where an abrupt change of the geomctry of the lithosphere occurs the midplane of the thin-plate is offset. We demonstrate that the combinddun uf lhcufrhel with an inplane horizontal force produces an additional, rheology independent moment at the psi ti or^ ollhe gronrtly change. This cffcct has been overlooked by previous studies of lithosphere deflections, and thin-plate prohlems in general. In the presented analysis, the thin-plate with an abrupt change in plate geometry represents lithopshere with a mechanically healed, inactive fault. However, the derived analytical solutions are general and can be used to study problems with similar ahrupt geometry changes. cause abrupt changes in the geometry of the midplane of the adopted thin-plate. This has not been taken into account in the existing studies. Below, we apply the derived analytical solutions to typical settings in rifted sedimentary basins. In our denvation oC the analytical solutions a vertical fault is assumed, which cuts the entire thin-plate. Such a configuration is a good representation for the situation in rifted sedimentary basins as scisn~otcctur~ic and dccy sdhnlic rcflcctioi~ data suggest that fundamental faults in the basement of rifted sedimentary basins art. plarlar and arc restricted to the brittle, cold, topmost part of the lithosphere, corresponding to the upper crust [King el a/., 1988; K~~szniretnf., 19911. Furthemre, the results offinite element modelling demonstrate that the assumption of a vertical fault plane does not significantly influence the predictions of deflections, as long as the fault dip is equal to or more than 63" [Van Rnlen eta/., 19981. The fundamental planar basement faults must have thc largest effect on the deflection, as they cause most of the pre-existing deformation of the uppercrustal competent laycr in rifted basins. However, elastic solutions for faults not - -- -- - - - - - - - -- cutting the entire upper crust also exist [Savage and Guohua, A horizontal inplane force acting on a thin-plate causes 19851 and possibly can be extended to include variations in vertical deflection. For a thin-plate with acontinuou~ midplane, innlane force levels. In addition. in this naner onlv flexural ,~~r , the effect of a changing inplane force on the deflection depends rnitions of lithosphere for cases in which its behaviour can on the curvature of the plate's midplane [Timoshenko and described by a single elastic thin-plate are considered. The Woinowsliv-Krieger, 19591. The deflections of such a thin-plate generalimtion to multiple-layer thin-plate systems [ ~c~utt et al., due to changing inplane forces can be determined by applying a 1988: Burov and Diamenr.19951 is the subject of another paper differential equalion [e.g. Timoslrenko atd Woinowchy-Krieger, [van ~~l~~ et al., 19981. 19591. However. if the thin-plate has an abrupt geometrical change, its midplane is discontinuous. Therefore, in such a case the differential equation can not he applied. In this paper Derivation of analytical solutions of deflections analytical solutions for this situation are presented. Here, the caused a abrupt change in plate geometry represents a prc-existing, Faulting of a thin-plate causes an offset of the plate's mid- mechanically healed and inactive fault in the lithosphere. But, the plane ( ~ i ~ ~ ~ ~ 1). qIe of ail inplane force to a thin- applied method and the derived analytical solutions can be used in similar thin-plate flexural problems. In lithospheric flexurc studies, the differentialelastic thinplate equation is used to determine the flexural response of the subsidence ...... lithosphere to vertical loads and inplane forces [e.g. Cloriingh et ......... _ .... :..:. ......... al., 1985; Karner, 19861. In these studies, the elastic thin-plate represents the mechanical behaviour of the rheologically ..... complicated lithosphere (see Disc~ssion) The application ofthe differential equation implies that the midplane of the thin-plate is ......... continuous. However, in many cases, especially in rifted ......... ......... ......... ......... ......... sedimentary basins, the lithosphere is deformed by faults, which . ......... ......... . , , . . , . . ......... flexed faulted flexed Copyright 1998 by the American Geophysical Union. thin-plate area thin-plate Paper number GRL-1998900005. Figure 1. Moment occuring at the fault due to application of an 0094-8276198lGRL-1998900005$05.00 inplance force to a thin-plate with a displaced midplane. 3903