MODELS OF HORIZONTAL MOVEMENT AND DEFORMATION OF EARTH'S SURFACE BLOCKS

Abstract

Theoretical provisions in the field of construction and
analytical formation of functional factor models that
display horizontal displacement and deformation of
blocks of the earth's surface on the mined or preserved
mineral deposits are presented. The models were
created based on representations of blocks based on
spatial restrictions of their horizontal dimensions and
elastic properties in the hierarchical mosaic structure
of rocks. They consider the rotational and translational
vector movement of points on the earth's surface of one
or two adjacent blocks.
The travel-time attributes of the block movement were
calculated with the methods of approximating the
parabolic vertex and the least square sum of residuals
with experimentally determined marker moving
vectors. Based on the rating formulas and model
correlations the connection of kinematic parameters of
rotation and translator motion has been established.
In the binary model of adjacent blocks, the contribution
of their separate movement is regulated by quazi-step
weighting function with given dimension of block
contact zone. Based on moving data differencing, the
analytical expressions for linear and angular area
deformations are obtained. After analysis of the total
deformation, the regularities of its area distribution,
localized mainly in the block contact zone. The paper
contains rules and quantitative criteria, according to
which the following deformation state is to note at the
medial point of the contact zone line: pressure,
compensation or extension. Examples of movement and
deformation modelling are given, on which we can see
the possibility of its use for the interpretation of the
moving of the earth’s surface markers, noticed due the
GPS satellite navigation data. Recommendations for
practical application of the models are given.