The relationship between strain rates, crustal thickening, palaeomagnetism, finite strain and fault movements within a deforming zone

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The deformation of continental lithosphere generally does not occur on a single fault, but is distributed over a zone up to a few hundred kilometers wide. If the deformation rate is constant throughout the zone, and if the velocity is continuous everywhere and does not change with time, the deformation gradient tensor can be obtained analytically. This tensor directly determines the amount of crustal thickening, and is related in a complicated manner to the finite strain tensor. The declination of remnant magnetization, measured within the zone, can also be rotated by the deformation. Because palaeomagnetic measurements are generally made on rigid blocks which have not been deformed, there is no simple relationship between such rotations and the finite strain. Expressions for all these quantities are obtained in terms of the velocity gradients, which are taken to be constant. The history of western North America is used to illustrate the relationship between the present deformation by strike slip and thrust motions, the rotations of the remnant magnetization vectors and the shape of accreted terranes.
At the surface distributed deformation is taken up by motion on faults which separate the zone into blocks. The displacement rate on the faults, their strike and the finite rotations of the blocks are all controlled by the velocity gradients. Analytic expressions relating these quantities are obtained. A deforming zone containing normal faults which crosses Central Greece takes up both strike slip and extension, and illustrates the relationship between the structures within and the motion across the zone. A similar, but more complicated, zone in northeastern Iran involves both strike slip and shortening.

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