1. A method for estimating stress characteristics of formations, the method comprising the steps of: a) acquiring one of sonic anisotropy data, image data or both associated with one or more borehole wherein the one or more borehole is one of vertical, deviated or both; b) employing the sonic anisotropy data to estimate fast shear direction (FSA) so as to extract FSA observed data; c) computing the FSA from forward modeling, wherein the forward modeling utilizes a first deviatoric stress tensor to extract FSA predicted data; d) computing FSA misfit from the difference between the FSA observed data and the FSA predicted data to obtain a computed FSA misfit that relates to the first deviatoric stress tensor; e) if the computed FSA misfit is equal to or less than a defined value, then store the computed FSA misfit; f) repeat steps (c) thru (e) using another deviatoric stress tensor such that a different deviatoric stress tensor is used for each repeat, until one of all or multiple predefined deviatoric stress tensors have been applied in step (c); and g) selecting the smallest stored computed misfit from the group consisting of the stored computed FSA misfit, one or more other stored computed misfit or some combination thereof, to determine a final estimated deviatoric stress tensor whereby the final estimated deviatoric stress tensor is used for reservoir activities.