Methods for Local Recovery of Tectonic Stresses Based on Kinematic Data: Physical Inconsistency and False Objectives. Part I

This work criticizes the entrenched views according to which the orientation of the principal tectonic stress axes can be determined from local (in time and space) observations of the kinematic indicators which jointly allow estimating the strain rate of a crustal block under study. The criticized approach ignores or replaces by subjective assumptions the following factors: (1) The block’s interaction with a hosting medium expressed in terms of the equilibrium conditions of the block; (2) The stress rate which (in addition to stresses) can affect the strain rate; (3)The specific macroscopic mechanical properties of the block’s material under the unknown sought stresses, including the ratio of the stress relaxation time to the period of observations. This approach, which is developed in some Solid Earth sciences and mainly in tectonophysics, is referred to in our paper as the method of local kinematic reconstruction (MLKR) of stresses. After briefly surveying the concept of forces and stresses and discussing the importance of studying the tectonic stresses, this paper refutes the MLKR notions based on general arguments and by the example of certain thought experiments. It is shown that the use of the MLKR for the conditions of the Earth’s interior does not guarantee against obtaining the results that fundamentally and drastically differ from the true tectonic stresses. In the studied rock block, depending on the factors ignored in the MLKR, the principal axes of the strain rate tensor, on one hand, and the principal stress axes, on the other hand, can be oriented discordantly in any arbitrary given fashion. In particular, in the processes accompanied by the release of elastic energy, the maximal rate of elongation can be oriented along the axis of maximal compression, whereas the maximal rate of shortening can be aligned with the axis of the maximal tension. In this paper, the deformation processes that are most detrimental to the results of stress reconstruction by the MLKR are revealed. We introduce the notion of the inherited stress-state regime in which the orientation of the axes of principal stresses during the observation period does not depend on the deformation process and, hence, cannot be in principle determined by the MLKR. An attempt to directly locally recover the stress axes from the kinematic data is a false objective because neither the physical meaning of the stress tensor nor the way it is introduced has anything to do with strains. It is concluded that the MLKR is physically inadequate and that the tectonophysical concept of locality should be abandoned in favor of returning to the notions of classical physics, namely, to using the conservation laws. By the example of several guides on tectonophysics, this paper exposes typical errors in understanding the stress reconstruction problem.