A Short Note on the Selection of the Fault Plane, the Seismic Moment Tensor, the Strain and Rotational Tensors, and the Gradient of Displacement

The gradient of displacement of the ground produced by a dislocation (at a point or finite) is the sum of a deformation part and a rotational part. The deformation part, which is symmetric, is usually deduced from seismology via the seismic moment tensor, which is also symmetric. The rotational part, which is antisymmetric, is usually deduced from paleomagnetism. It can not be deduced from the symmetric seismic moment tensor Mij . Nevertheless, if the selection of the fault plane is possible, the rotational tensor can be calculated from the asymmetric tensor Cij = vinj where ni and vi are the components of the normal vector to the fault and the slip vector on this fault, respectively. When the selection of the fault plane is possible, the seismic moment tensor Mij is not so appropriate to describe the source because of its intrinsic symmetric character. The tensor Cij may be better, and the gradient of displacement itself could be used instead of the strain tensor.