Abstract
1. Acoustic waves types
2. General principles of the device functioning
3. Results of the research
Conclusion
References
Coal is one of the most important energy resources in Ukraine, it's a base raw material for chemical and metallurgical industries and completely irreplaceable energy source for electric power stations. However, coal mining is still one of the most dangerous brunches of industry in Ukraine, so all reasonable demands of safety and stability must be completely fulfilled for all used equipment and accomplished technological processes. One of the ways to increase a coal mining safety is to provide constant prospection of the coal layer been processed using different seismo-acoustic methods
Scientific research essence.
Nowadays a coal-plough speed is controlled manually relying on the prospection data and miner's own experience. In some cases speed is controlled by monitoring a current load of a coal-plough engine, so, if it rises, it means there are a hard stratum on the track and speed should be decreased to avoid a coal-plough damage and eliminate any danger for human lifes.
The graduate work purpose
To find a way of detecting heterogeneity areas of coal layer to automatically control a coal-plough speed.
The main idea of the work
To develop a method for determining the heterogeneity areas of the coal layer.
The theory of seismography is based on fundamental solutions of Lame equations, they describe all types of waves in general way. They can't be solved clearly because there are many side conditions for real tasks: all types of waves should be considered, their reflections and distortions by heterogeneous areas must be taken into account. Lame equations can be solved only for some ideal theoretical cases when all those mentioned above complexities can be simplified.
First of all the coordinate axes are selected in such a way that X axe is pointed on the seismic signal source and Z axe is normal to the researched layer, so we can assume that it's parameters change only along Z axe as described on figure 1.
Figure 1 - Coordinate axes direction
Direct waves
The most simple solution is for the isotropic environment conditions. The system of Lame equations for this case:
(1)
where u, v, w- transference vector components.
These are general wave equations, if following values are considered as the spread of disturbances:
, 
The solution of these equations are two independent waves: longitudinal and transverse one, they are present in all types of solutions for environments of any complexity. Let's find continuous differentiable solutions of Lame equations in general form:
(2.1)
(2.2)
where φ- scalar transference potential, 
-vector transference potential , the vector of mass forces is presented as the sum of two components potential and solenoidal).
Then, to determine potentials we can write the following equation:
(3.1)
(3.2)
In the case of massive force absence:
(4.1)
(4.2)
These equations are ordinary wave equations, and we can conclude that part of the solution, corresponding to the scalar potential φ is moving with speed Vp. This process is accompanied by environment volume changes.
Surface waves
In the limited isotropic environment a division of shear waves and waves of compression is getting complex because boundary conditions must be assumed. For a limited environment among the wave equations solutions an important one are surface waves described by Relay - waves, spread along the border of the environment and exponentially decaying when moving away from it. When the location of the border is at z = 0 it may be written as :
(5)
where w- oscillations frequency, ki—wave vector components, à - the rate of decay of spatial waves.
The depth of penetration of such waves inside the reservoir (or rocks) is the proportion of the wavelength. The speed of propagation of surface waves in the theory lies in the range of 0874 to 0955 the value of Vs
Channel wave
A wave, initiated by a real source of hesitation can be considered a spherical wave, let's factor it at the plane components using double Fourier integral:
(6)
where 
,
,
.
Figure 2 - Vector k position
Plane wave in an arbitrary point can be represented as a sum of direct wave and reflected waves (from the layer border). Each of these multiple reflected waves can be represented as a wave spreading from "imaginary" source. As a result, we get:
(7)
where
h – width of the layer, Z0 - Z coordinate of the source, V, and Ê2 -reflection ratios on the borders of the layer.
Previous equation will be true for Lave waves if we use the Henkel's function:
(8)
(9)
(10)
So, we can make some conclusions: amplitude of the channel wave decreases extremely slowly:
(11)
channel wave propagation velocity can be defined as follows:
(12)
where c - the speed of propagation of waves in the layer (Vs - for Lave waves).
Dispersion equation in the simplest case of one layer Lave waves has following form:
(13)
Side waves
A field of reflected waves can be presented by equation:
(14)
where the first term is a reflected wave and the second one is so-called side wave:
(15)
, 
Figure 3 - An explanation of the nature of the side wave
Sensors are located along the shtrek at the same distance on from each other. Seismic waves caused by working coal-plough are registered with sensors. Obtained results are preprocessed to filter out noise and distortion caused by coal-plough, then signal is analised to figure out huge heterogeneities of the coal seam. A simplified scheme of seismic waves spreading and location of the sensors is shown in figure 4.
Figure 4 - Simplified model of seismic waves spreading in a coal seam
(animation: 76K, 20 frames, 5 cycles; refresh a page to start)
For more accurate analysis, data from sensors is obtained in different positions of a coal-plough.
At the moment, seismic waves passing in a homogeneous coal seams are researched. As a result, of mathematical modeling we can obtain a seismic wave response at any point of a coal seam for the case of homogeneous environment without any defects (fractures,, etc.). This model is built with software package Lab View (figure 5).
Figure 5 - An example of seismogram at one point of the model
Detection of heterogeneity of a coal seam and correspondent response to it's presence would improve safety and increase overall productivity of the coal-plough machine. Also, it can make a contribution to the development of automated coal-mining systems.
- Ñòàíäàðò GSM06.10 Ñïîñîá äîñòóïà: URL: http://pda.etsi.org/pda/
- John Wiley GSM Switching Services and Protocols: ISBN 0-471-49903-X . –338 pages
- Gunnar Heine GSM networks: protocols, terminology, and implementation : ISBN 0-89006-471-7 – 417 pages
The graduate work is currently under development. It'll be complete till december 2008.
© DonNTU, Kirichenko Max Alex, 2008
