АППРОКСИМАЦИЯ ГРАВИТИРУЮЩЕГО ВЛИЯНИЯ УСЕЧЕННОГО КОНУСА

• Main Author: Мазуров, Б.
• Format: Text
• Language: unknown
• Published: Государственное образовательное учреждение высшего профессионального образования Сибирская государственная геодезическая академия 2008
• Subjects: Yakutia
• Online Access: http://cyberleninka.ru/article/n/approksimatsiya-gravitiruyuschego-vliyaniya-usechennogo-konusa; http://cyberleninka.ru/article_covers/14352776.png

In his last publications the author presents solutions of inverse problems, in which the results of simultaneous mathematical treatment of multiple geodetic and gravimetric observations on the earth's surface are the estimates of not only the points coordinates and displacements, but also of gravitating bodies masses and their variations. These examples deal with the volcanic eruptions and preparation for them. The spherical deep-seated magma bed of the volcano and its conical surface are presented as changing gravitating bodies. For the earth's surface relief the cone is rather a typical elementary shape of the body. More common is a truncated cone. Apart from volcanoes, in natural environment these may be some components of mountains peaks. In technogenic sphere we deal with not only cone-shaped rises, but also with conical depressions. In opencast mining the sites of exhausted rocks are conical too. For example kimberlite deposits are also cone-shaped. Development of Mir tube (Yakutia) resulted in a conical quarry of 520 m depth. Ore wastes dumps often look like truncated cones. By far the author approximated conical gravitating bodies to a sphere (one-point mass). It would be quite reasonable to define the approximating cone model more exactly by increasing the number of point masses. In this case it is desirable that the number of parameters to be estimated was as small as possible. Thus, the requirement for a greater redundancy of measurements necessary for mathematical treatment will be met. For example, with the substance of a cone being homogeneous, the parameter to be estimated is its total mass which is dispersed in a certain way throughout the area (in five points). The present paper shows a five-points model of a gravitating truncated cone, whose substance density is considered to be the same for any of its parts. To calculate the coordinates of the gravity centres of five masses with equal volumes rigorous mathematical formulae have been derived analytically. Using these formulae for approximating cone-shaped bodies of the earth's relief (opencast mining, waste dumps, volcanoes, etc) we can see more exactly their gravitational effect by means of simultaneous mathematical treatment of the repeat geodetic and gravimetric observations. For a still greater detalization of a gravitating cone these formulae can also be used. In his last publications the author presents solutions of inverse problems, in which the results of simultaneous mathematical treatment of multiple geodetic and gravimetric observations on the earth's surface are the estimates of not only the points coordinates and displacements, but also of gravitating bodies masses and their variations. These examples deal with the volcanic eruptions and preparation for them. The spherical deep-seated magma bed of the volcano and its conical surface are presented as changing gravitating bodies. For the earth's surface relief the cone is rather a typical elementary shape of the body. More common is a truncated cone. Apart from volcanoes, in natural environment these may be some components of mountains peaks. In technogenic sphere we deal with not only cone-shaped rises, but also with conical depressions. In opencast mining the sites of exhausted rocks are conical too. For example kimberlite deposits are also cone-shaped. Development of Mir tube (Yakutia) resulted in a conical quarry of 520 m depth. Ore wastes dumps often look like truncated cones. By far the author approximated conical gravitating bodies to a sphere (one-point mass). It would be quite reasonable to define the approximating cone model more exactly by increasing the number of point masses. In this case it is desirable that the number of parameters to be estimated was as small as possible. Thus, the requirement for a greater redundancy of measurements necessary for mathematical treatment will be met. For example, with the substance of a cone being homogeneous, the parameter to be estimated is its total mass which is dispersed in a certain way throughout the area (in five points). The present paper shows a five-points model of a gravitating truncated cone, whose substance density is considered to be the same for any of its parts. To calculate the coordinates of the gravity centres of five masses with equal volumes rigorous mathematical formulae have been derived analytically. Using these formulae for approximating cone-shaped bodies of the earth's relief (opencast mining, waste dumps, volcanoes, etc) we can see more exactly their gravitational effect by means of simultaneous mathematical treatment of the repeat geodetic and gravimetric observations. For a still greater detalization of a gravitating cone these formulae can also be used.