The moment method used to infer stress from fault/slip data in sigma space: invalidity and modification

The moment method has recently been used to infer stress in sigma space from fault/slip data. However, if these data are distributed along a hyperplane having a smaller dimension than that of the space minus one, due to limited fault/slip population or biased sampling of it, the best solution of stress vector is not in most cases, as expected, the eigenvector of the datum matrix relating to the smallest eigenvalue. The solution lies within the subspace composed of the eigenvectors relating to the small eigenvalues, for which some auxiliary constraints need to be included. Shear sense constraint alone is adopted, and incorporated by way of grid search, which gives rise to a range of accepted stress vectors in the subspace. Examples from the Chelungpu fault, Taiwan, illustrate the feasibility of the proposed scheme.