Estimation of paleostress orientation within deformation zones between two mobile plates RUUD WEIJERMARS* Hans Ramberg Tectonic Laboratory, Geological Institute, University of Uppsala, Bcac 555, S-751 22 Uppsala, Sweden ABSTRACT collision zone where part of the differential motion between the Eurasian and African plates is accommodated by strike-slip faults. The orientation of the principal stress axes within deformation zones between two mobile plates is modeled here analytically, using a INTRODUCTION thin-plate theory. The simple analytical approach helps to explain why plates cease to move after collision. Orogenic periods last only several Geologists have pieced together a picture which suggests that the tens of million years because the stress associated with a particular con- process of breakup, dispersal, and renewed aggregation of supercon- stant driving force (causing a constant strain rate) is no longer able to tinents is one of the key features of plate-tectonic evolution on Earth. maintain a significant horizontal displacement. In contrast, the uplift The mechanics of plate tectonics are complex, but the major forces rate increases rapidly as the horizontal velocity decreases, and this may acting on the lithosphere are due to slab-pull and ridge-push associ- explain why the termination of orogenic epochs are usually heralded by ated with the density variations due to surface cooling and various the rapid deposition of thick sequences of immature sedimentary rocks types of viscous forces and chemical differentiation in the mantle. The or flysch. fact that the surface plates of the Earth are in stress remains invisible The analytical model also elaborates the relationship between ho- unless leading to permanent distortion by brittle failure or ductile de- mogeneous bulk deformations driven by a constant stress orientation formation. Large deformations of the lithosphere are principally con- and those due to a fixed displacement direction of physical boundaries fined to plate boundaries, where large deviatoric stresses may accu- of the deformation zone. Two major kinematic possibilities are consid- mulate as manifested by a high earthquake frequency. Working out ered: (1) plates converging either orthogonally or obliquely, making the the physics and reconstructing the history of this concentrated de- deformation zone an analogue for orogenic collision; and (2) plates di- formation is a major research task. verging either orthogonally or obliquely, so that the deformation zone is Reconstructing the history of deformation structures is compli- dynamically similar to initiating rift basins. The theoretical investigation cated, because the deformation path followed depends principally led to the formulation of the following rules. Deformation zones between upon (1) the orientation of the stress field, (2) the rheology of the converging plates have the major axis of bulk deviatoric stress coinciding rocks, and (3) boundary conditions prevailing during the deformation. with the bisector of the acute angle between the relative plate velocity These three parameters may have been either constant or unsteady in vector and the normal to the deformation-zone boundary. In case of time. Despite all of these uncertainties, a significant amount of the- extension within a deformation or riftzon e separating diverging plates, oretical work and some practical methods have been developed for the bisector will outline the minor axis of the bulk deviatoric stress. inferring paleostress orientations from natural fault patterns (for ex- The deformation tensor of the analytical model yields a new ample, Anderson, 1951; Arthaud and Mattauer, 1969; Angelier, 1979). method for estimating the orientation of paleostress in natural examples, What has remained relatively unexplored is the relationship between here applied to the deformed wall rock of the Moroccan Border fault. stress and large finite deformations of more penetrative character. The marker used is a competent sequence of Devonian sandstone and Penetrative deformation is meant here to include creep either by crys- limestone asymmetrically folded adjacent to the dextral Border fault. talline flow or microfracturing and pressure solution, on a regional The steeply plunging Z-folds of the marker beds suggest that the prin- scale. cipal deviatoric paleostress, rv was oriented 37°-44° to the fault trace. The approach advocated here to understand better the mechan- Hie age of the Moroccan Border fault is poorly constrained and may be ics and history of large penetrative deformations involves two rigid Variscan or younger. The T1 orientation implies a major component of plates, separated by a deformation zone, with free-slip conditions at simple shear parallel to the strike-slip fault and a minor component of the top and the bottom surface (Fig. 1). Thin-plate approaches have extension perpendicular to the fault trace. The implied crustal move- been previously used both in analytical models (Stevenson and ment is compatible with the modern tectonics of the Eurasian-African Turner, 1975; McKenzie and Jackson, 1983; England and others, 1985; Wdowinski and others, 1989) and in numerical simulations of continental deformation (Vilotte and others, 1982; England and Mc- Kenzie, 1982, 1983; Sonder and England, 1986). Assumptions are 'Present address (leave of absence from Uppsala University): Earth Sci- ence Department, King Fahd University of Petroleum and Minerals, 31261 made to simplify the natural prototypes to the most essential features Dhahran, Saudi Arabia. so that the fundamental aspects of the mechanics are preserved. The Data Repository item 9329 contains additional material related to this article. Geological Society of America Bulletin, v. 105, p. 1491-1510, 18 figs., 2 tables, November 1993. 1491 Downloaded from http://pubs.geoscienceworld.org/gsa/gsabulletin/article-pdf/105/11/1491/3381722/i0016-7606-105-11-1491.pdf by guest on 27 September 2021 R. WEIJERMARS Figure 1. Definition sketch of the thin- plate concept used in the analytical modeling. x3=-O1/2 The deformation is restricted to a zone sepa- rated by subvertical walls of differential slip from the adjacent rigid plates. The principal orientations of the total stress, or, are related to the relative movement direction of the plates, Vr, indicated by the arrows. The condition of plane strain implies that the intermediate de- viatone stress, T2 = 0, which in turn implies that the tectonic contribution to the confining a2=P=01/2 pressure P = TJ/2. Other cases are discussed T2=0 (plane strain) below. analytical model developed here investigates the systematic relation- tion gradients. In nature, localized slip on narrow subvertical faults ship between plate motion, principal deviatoric stress direction, total bounding the foothills of an orogen may be accommodated either by stress, and confining pressure. This is valuable because experienced the development of mylonite zones (below ~7-km depth and typically field geologists commonly resort to mental models, invoking mech- strain-rate softening) or by weathering of the walls of brittle faults. anisms that could have led to the structures observed in the field. Bird (1984) has provided experimental support for the idea that major These models usually prompt allegations about the orientation of the brittle faults, weathered by hydrothermal circulation, develop ex- principal stresses. The accuracy of such mental models may benefit tremely low frictional resistance due to the hydration of clay minerals. from investigating and quantifying the relationship between stress, For mechanical modeling of deformation with negligible dilation progressive deformation, and tectonics. (no volume change), it is theoretically convenient and sufficient to Rather than forward modeling, finite deformation patterns in na- consider only deviatoric stresses. When this deviatoric stress is ture require inversion; that is, the final deformation stage is preserved, caused by lateral movements of plates adjacent to the deformation and the stress orientation is one of the unknown quantities. Estima- zone, however, these plates exert a total stress which may include tion of the orientation of paleostress is therefore only potentially both a deviatoric and confining component. Excluded from this anal- possible after determining how elements of the original deformation ysis is the obvious contribution to confining pressure arising from the tensor relate to normalized physical dimensions. The method is illus- lithostatic load. A tectonically induced confining component of stress, trated by application to fold structures adjacent to the Moroccan Bor- however, which would reduce or increase the actual confining pres- der fault, a strike-slip fault near the Eurasian-African plate boundary. sure at depth due to plate-tectonic forces, is carefully separated here Additionally, the critical parameters controlling the deformation pat- from the total tectonic stress. This approach not only helps to under- terns in the analytical model are suitable for determining paleostress stand variations in metamorphic gradients, a subsidiary interest of the orientation in a natural prototype only if the underlying assumptions present work, but is essential in coupling plate movements directly to hold for both. The analytical theory used here assumes (1) a constant deviatoric stresses. stress orientation, (2) an isotropic rheology, and (3) boundary condi- tions warranting homogeneous plane deformation without volume Deviatoric