RESTORATION OF CROSS-SECTIONS THROUGH UNFAULTED, VARIABLY STRAINED STRATA

Data on the dip of bedding and the state of strain at specific locatio ns within a cross-section constrain the restoration of unfaulted, two- dimensional, variably strained strata. There are two major categories for restoration of such strata. The first is one-step restoration, whi ch involves retro-deforming the strain ellipses into their correspondi ng unit circles while simultaneously removing dips from associated bed s. This procedure is appropriate if strain indicators record the trans formation of the strata from the undeformed state to present deformati on. The second category pertains to situations in which strain indicat ors record the transformation of the present deformed state from an in termediate, deformed state. The second category requires multiple step restoration. For the one-step restoration procedure presented in this paper, the first task is to determine the transformation constants th at describe development of observed strain and bedding for each locati on. The next task is to determine the retro-deformation constants whic h relate points in their present deformed state to their locations in the undeformed state. Retro-deformation constants are related to the s patial derivatives of the Cartesian retrodeformation displacements fun ctions, U(x,y) and V*(x,y) (for movements in the x and y directions, respectively). The spatial derivatives of these functions at locations of observed strain and the displacements of selected points about the se sites are the basis for constructing continuous, retro-deformation displacements functions for the deformed section as a whole. The retro -deformation displacements functions are then invoked to restore the c ross-section. This procedure is illustrated with an example cross-sect ion from the Appalachian Fold Belt, and the example shows that the sec tion may be satisfactorily restored in this way. It is just as likely, however, that the strain indicators for the example section are a mea sure of the transformation of the cross-section from a prior, deformed state to the present deformation. Accordingly, multiple-step restorat ion is required, first to an intermediate, less deformed state and the n to the undeformed state. Two sets of retro-deformation displacement functions are then needed, i.e. one set for transformation to an inter mediate state followed by a second to the undeformed state. This proce dure was done for the Appalachian fold-thrust belt example, restoring first the present deformed section to an intermediate state derived fr om the regional fold history. In turn, intermediate state points were transformed to an undeformed state assuming knowledge of an undeformed stratal thickness and assuming that cross-sectional area has been pre served. This procedure is technically different to that used in the on e-step procedure, but conceptually similar. The objective, once again, is to discover appropriate retro-deformation displacements functions.