Average regional strain due to slip on numerous faults of different orientations

If a region is cut by faults with different orientations and if the faults intersect the boundaries of the region of interest, then the average finite (rotational) strain, , is given by where μ is the shear modulus, V is the volume of the region, and represents the sum of asymmetric moment tensors, . For each fault, , where M 0 is the scalar seismic moment and û and are the unit vectors parallel to the slip vector and perpendicular to the fault plane. This result is applicable when the average regional strain occurs primarily by displacements of essentially rigid blocks that together compose the region of interest and hence when both elastic strains and inelastic strains due to folding and bending are small.