CN117706643A - Method for dynamically monitoring development height and range of two zones of coal seam roof - Google Patents

Method for dynamically monitoring development height and range of two zones of coal seam roof Download PDF

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CN117706643A
CN117706643A CN202311706886.7A CN202311706886A CN117706643A CN 117706643 A CN117706643 A CN 117706643A CN 202311706886 A CN202311706886 A CN 202311706886A CN 117706643 A CN117706643 A CN 117706643A
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data
data acquisition
coal seam
working face
zones
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李毛飞
肖路平
姜志海
岳建华
窦中浩
王路瑶
孙博洋
陈子良
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China University of Mining and Technology CUMT
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China University of Mining and Technology CUMT
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Abstract

The invention belongs to the technical field of transient electromagnetic monitoring methods, and particularly relates to a method for dynamically monitoring the development heights and the development ranges of two zones of a coal seam roof, which comprises data acquisition and data processing; the data acquisition is carried out through a data acquisition system, and the data acquisition system consists of a central control console, a signal transmission system, a ground emission loop, a three-component magnetic sensor, a data acquisition station and a transmission line; the data acquisition adopts segmented arithmetic dense sampling, and the intervals of sampling points are equal; the data processing further comprises preliminary preparation, preliminary processing, constraint inversion, change rate calculation, diagrammatical display and data interpretation. The invention can monitor the development height of the two zones of the coal seam roof and the continuity of the water-resisting layer with high efficiency and fineness, accurately master the development form of the mining-induced fracture, provide important basis for formulating the mining area water control scheme and ensure the safe production of the coal mine.

Description

Method for dynamically monitoring development height and range of two zones of coal seam roof
Technical Field
The invention belongs to the technical field of transient electromagnetic monitoring methods, and particularly relates to a method for dynamically monitoring the development heights and the development ranges of two zones of a coal seam roof.
Background
Coal is a main basic energy source in China, various water bodies (including surface water, loose layer water, karst-fissure aquifer water, mined (old) goaf water and the like) on a coal seam roof are flushed into an underground mining space through different water guide channels in a burst, slow-release or stagnated-release mode to form coal seam roof water damage accidents, so that the water inflow amount of a tunnel or a working face is increased, even a well is flooded, great loss is caused for lives of people, property and safety of coal enterprises, and healthy development of the coal industry is influenced.
After the coal seam is recovered, a roof management mode of a caving method is adopted, and a caving zone, a water guide crack zone and a bending zone are formed by the coal seam overlying strata. When the roof caving zone and the fracture zone of the coal seam develop to the roof aquifer, serious economic loss and casualties are easily caused to the working face, and the overlying strata are deformed to damage the accurate detection and monitoring of the development height of the two zones, thereby being beneficial to ensuring the safe recovery of the working face.
At present, the technology for detecting the hydrogeology of coal mines in China mainly comprises the following steps of ground surface and underground: the ground mainly comprises a direct current resistivity method, a transient electromagnetic method, a controllable source audio frequency magnetotelluric sounding method and the like; the underground mainly comprises a mine direct current method, a mine transient electromagnetic method, audio frequency electric perspective and the like.
Compared with ground geophysical prospecting, underground geophysical prospecting has the problems of half space, excessive space and full space, and construction environment, an observation system and instrument equipment have special requirements, so that the technical bottleneck of mine geophysical field observation is large, interference factors are many, and the difficulties of data acquisition, physical inversion and geological interpretation are large. The mine direct current method has a large difference from the ground direct current method, and is mainly characterized in the following aspects: (1) in the underground deep detection environment, the construction space is narrow, the interference of metal and the like is large, and the applicability of the equipment is poor. (2) The underground detection has constraints on instrument power, current, response time and the like, and meanwhile, the problems of explosion prevention, safety and the like are related.
The ground hydrographic sounding technology comprises a direct current resistivity method, a transient electromagnetic method, controllable source audio frequency magnetotelluric sounding and the like. However, certain disadvantages exist. For the direct current resistivity method, an intuitive resistivity profile is provided, the distribution of the underground water guide structure and the aquifer can be reflected, and the device and the equipment are simple and relatively simple to operate. However, the method requires a long measurement time, is easily affected by the topography and is not high in resolution.
The controllable source audio magnetotelluric sounding can provide information of shallow and medium deep underground structures, rock-soil layer interfaces, aquifers and the like, the detection depth is large, the working efficiency is high, the influence of terrain is small, the influence of noise is easy, the instrument calibration requirement is high, and the detection depth is limited in a low-resistance area.
Transient electromagnetic methods are methods that use ungrounded return lines or grounded galvanic couple sources to send primary fields into the subsurface and use return lines or galvanic couple to observe secondary vortex fields during the pauses of the primary fields. The method has the advantages of quick construction, large detection depth, strong anti-interference capability, sensitivity to low-resistance body reflection, no shielding by a high-resistance layer and the like, but is sensitive to external interference and noise, and relatively complex in data processing and interpretation.
Disclosure of Invention
The invention aims to provide a method for dynamically monitoring the development height and the development range of two zones of a coal seam roof, which can monitor the development height of the two zones of the coal seam roof and the continuity of a water barrier layer with high efficiency and fineness, accurately master the development form of mining-induced cracks, provide important basis for formulating a mining area water control scheme and ensure the safe production of a coal mine.
The technical scheme adopted by the invention is as follows:
the method for dynamically monitoring the development heights and the development ranges of two zones of the coal seam roof comprises data acquisition and data processing;
the data acquisition is carried out through a data acquisition system, and the data acquisition system consists of a central control console, a signal transmission system, a ground emission loop, a three-component magnetic sensor, a data acquisition station and a transmission line;
the data acquisition adopts segmented arithmetic intensive sampling, and the sampling interval depends on the electrical characteristics of stratum in the monitoring area;
the data processing comprises preliminary preparation, preliminary processing, constraint inversion, change rate calculation, diagrammatical display and data interpretation.
The layout mode of each unit in the data acquisition system is as follows:
s1: layout of ground emission loop: after the primary pressing of the coal face occurs, arranging a long rectangular transmitting loop at the position 200m from the position where the cutting hole is located when the primary pressing is performed in the advancing direction of the working face, wherein the long side of the loop is perpendicular to the trend of the working face, the short side of the loop is parallel to the trend of the working face, the central axis of the loop along the short side direction is consistent with the direction of the central axis of the trend of the working face, the length of the long side is set according to the trend length of the coal face, the distance from an end point to the working face is greater than 150m, the trend length of the working face is 300m, the long side is more than or equal to 600m, and the short side is more than or equal to 300m;
s2: laying a measuring line and a measuring point: the length direction of the measuring line is arranged in the transmitting loop, the center of the measuring line coincides with the geometric center of the transmitting loop, the measuring point distance is 10m, the length of the measuring line is greater than the inclined length of the coal face, the distances from the end points of the measuring line to the boundaries of the two sides of the working face are respectively greater than 30m, namely at least 3 measuring points are respectively arranged outside the two sides of the working face, and the total length of the measuring line is 360m;
s3: data acquisition station and three-component magnetic sensor lay: adopting data acquisition stations with 24 functions, wherein each data acquisition station is connected with 8 three-component magnetic sensors;
s4: and (3) layout of a control system: the central control console is arranged in the coal mine commanding and dispatching control center and is used for transmitting monitoring instructions.
In the data acquisition, multiple measurements are required, and the measurement time is as follows: the first measurement is carried out after the initial pressure is applied, after each unit is arranged, the measurement is ready to be started, in the continuous tunneling process of the working face along the trend, the whole acquisition system is fixed in the measurement process, the system is positioned on an unexplored coal seam at the beginning, the data acquired for the first time are regarded as in-situ stratum data, and each time the working face tunnels for 50m, the measurement is carried out until the working face tunnels for 350m beyond the survey line.
The data processing comprises the following steps:
s21: early preparation: obtaining geological, hydrological and logging data of a mining area through inquiry, performing eight Fourier fitting on resistivity logging data, and constructing a mining area multi-layer ground model according to the rock resistivity parameter difference for analyzing the stratum electrical characteristic distribution;
the inquiry mode is any one or more of reference documents, database retrieval and inquiry to geological exploration units;
s22: preliminary processing of data: converting the data format, eliminating interference distortion points, and storing the data;
the storage sequence adopts any one of the distances between the measuring line and the working surface from large to small according to the measurement date from first to last or during measurement;
s23: transient electromagnetic constraint inversion: performing constraint inversion by using an OCCAM inversion method, taking a model norm as a model smoothness constraint condition, and obtaining an inversion result by iteratively searching a minimum fitting difference;
s24: calculating a calculation formula of the relative change rate of the resistivity:for obtaining a percentage value;
s25: and (3) drawing shows: respectively drawing a resistivity profile under different stoping degrees and a resistivity change rate profile under different stoping degrees according to the relative change rate calculation and constraint inversion results;
s26: data interpretation: analyzing the electrical changes of the low-resistivity layer and the roof rock stratum according to the resistivity change rate profile, and determining a crack development influence area; and determining the development height and range of the roof collapse zone and the water guide fracture zone of the working face coal seam mining according to the detection results of different dates.
The data acquisition and data processing process comprises the following specific implementation steps:
1. a large transmitting loop is paved on the ground above the non-stoping position of the coal mining working face to transmit electromagnetic signals to the underground, a measuring line and a three-component receiving magnetic sensor are arranged in a certain range in the center of the transmitting loop along the trend of the working face, in the stoping process of the working face, an acquisition system is fixed at a preset layout position, the relative position of the working face and the measuring line is changed continuously, and the system measures data once every time the working face is stoped for a certain distance and transmits the data to a master control desk through a ground data acquisition station and a data transmission system;
2. data processing, namely, establishing a rock stratum ground model by means of logging data fitting through preliminary preparation, preliminary processing, constraint inversion, change rate calculation, diagrammatical display and data interpretation; performing multi-layer constraint inversion by using an OCCAM inversion method, and drawing a resistivity profile; taking data obtained by an in-situ stratum as background values and other date data as current data, calculating the relative change rate of resistivity, and drawing a section diagram of the relative change rate;
3. and analyzing the continuity of the low-resistance layer and the change range of the top plate resistivity through the drawing, dividing the low-resistivity layer, delineating a crack development area, delineating the development height and the development range of two zones finally, and realizing dynamic monitoring and early warning and forecasting on the working face stoping process.
The invention has the technical effects that:
the method for dynamically monitoring the development height and the development range of the two zones of the coal seam roof can acquire multidirectional electromagnetic signal characteristics through the arrangement of the ground signal transmission loop and the arrangement of the ground signal three-component magnetic sensor, and then obtains an analysis result through a data processing process, thereby being beneficial to accurately grasping the development form of mining cracks, objectively analyzing the water filling rule of a mine, reasonably evaluating the influence of the mining of the coal seam on the overburden aquifer and being an important basis for making a mine water control scheme.
According to the method for dynamically monitoring the development height and the development range of the two bands of the coal seam roof, the distance between the ground signal three-component magnetic sensors is 10 meters, the sampling rate of the system is changed according to different electrical characteristics of strata in a monitored area, a large amount of data is obtained for constraint inversion, the resolution capability of the two bands of the coal seam roof is greatly improved, and fine exploration is realized.
The method for dynamically monitoring the development heights and the development ranges of the two zones of the coal seam roof is arranged in the acquisition system on the ground above the non-stoping position of the coal seam face, once the arrangement is completed, the movement is not needed in the subsequent measurement, and the stratum electrical information of the coal seam face with different stoping degrees is acquired at different times at the fixed position, so that the time and the labor cost are saved.
According to the method for dynamically monitoring the development heights and the development ranges of the two zones of the roof of the coal seam, the relative change rate profile is drawn by calculating the change rate of the resistivity, so that the change rule of the resistivity of the roof is displayed more intuitively and clearly.
Drawings
FIG. 1 is a schematic top view of a layout of cells according to an embodiment of the present invention;
FIG. 2 is a schematic diagram of the layout and connection of units according to an embodiment of the present invention;
FIG. 3 is a schematic flow chart of data acquisition according to an embodiment of the present invention;
FIG. 4 is a fitted view of log data of an embodiment of the present invention;
FIG. 5 is a flow chart of data processing according to an embodiment of the present invention.
Detailed Description
The present invention will be specifically described with reference to examples below in order to make the objects and advantages of the present invention more apparent. It should be understood that the following text is intended to describe only one or more specific embodiments of the invention and does not limit the scope of the invention strictly as claimed.
1-5, the method for dynamically monitoring the development heights and the development ranges of two zones of the roof of the coal seam comprises data acquisition and data processing;
the data acquisition is carried out through a data acquisition system, and the data acquisition system consists of a central control console, a signal transmission system, a ground emission loop, a three-component magnetic sensor, a data acquisition station and a transmission line;
the data acquisition adopts segmented arithmetic intensive sampling, and the sampling interval depends on the electrical characteristics of stratum in the monitoring area;
specifically, when single-point data is collected, a piecewise arithmetic intensive sampling mode is adopted, sampling intervals are determined according to the formation electrical characteristics of a monitoring area, if conductivity is good, the sampling intervals take larger values, for example, the total sampling duration is 10ms, the sampling frequency is increased to be set to 100ksps per ADC (analog to digital converter), namely, the ADC samples an analog signal 100 times per second, so that a large amount of data can be obtained through each measurement and collection, the arithmetic collection is a linear sampling method, also called equidistant sampling, and in the arithmetic collection, the intervals among sampling points are equal;
the data processing comprises preliminary preparation, preliminary processing, constraint inversion, change rate calculation, diagrammatical display and data interpretation.
As shown in fig. 1 and 2, the layout manner of each unit in the data acquisition is as follows:
s1: layout of ground emission loop: after the primary pressing of the coal face occurs, arranging a long rectangular transmitting loop at the position 200m from the position where the cutting hole is located when the primary pressing is performed in the advancing direction of the working face, wherein the long side of the loop is perpendicular to the trend of the working face, the short side of the loop is parallel to the trend of the working face, the central axis of the loop along the short side direction is consistent with the direction of the central axis of the trend of the working face, the length of the long side is set according to the trend length of the coal face, the distance from an end point to the working face is greater than 150m, the trend length of the working face is 300m, the long side is more than or equal to 600m, and the short side is more than or equal to 300m;
wherein, the high-voltage wire, the telegraph pole, the iron drum and other things influencing the transmitted signal in the process of laying the survey line should record the information such as position and size;
s2: laying a measuring line and a measuring point: the length direction of the measuring line is arranged in the transmitting loop, the center of the measuring line coincides with the geometric center of the transmitting loop, the measuring point distance is 10m, the length of the measuring line is greater than the inclined length of the coal face, the distances from the end points of the measuring line to the boundaries of the two sides of the working face are respectively greater than 30m, namely at least 3 measuring points are respectively arranged outside the two sides of the working face, and the total length of the measuring line is 360m;
s3: data acquisition station and three-component magnetic sensor lay: adopting data acquisition stations with 24 functions, wherein each data acquisition station is connected with 8 three-component magnetic sensors, and the number of the three-component magnetic sensors and the number of the data acquisition stations are determined according to the measurement points;
s4: and (3) layout of a control system: the central control console is arranged in a coal mine command and dispatch control center, is controlled by a special person and is used for transmitting monitoring instructions.
As shown in fig. 3 and 5, in the data acquisition, multiple measurements are required, and the measurement time is as follows: the first measurement is carried out after the initial pressure is applied, after each unit is arranged, the measurement is ready to be started, in the continuous tunneling process of the working face along the trend, the whole acquisition system is fixed in the measurement process, the system is positioned on an unexplored coal seam at the beginning, the data acquired for the first time are regarded as in-situ stratum data, and each time the working face tunnels for 50m, the measurement is carried out until the working face tunnels for 350m beyond the survey line.
As shown in fig. 4 and 5, the data processing includes the steps of:
s21: early preparation: obtaining geological, hydrological and logging data of a mining area through inquiry, performing eight Fourier fitting on resistivity logging data, and constructing a mining area multi-layer ground model according to the rock resistivity parameter difference for analyzing the stratum electrical characteristic distribution;
the inquiry mode is any one or more of reference documents, database retrieval and inquiry to geological exploration units;
s22: preliminary processing of data: converting the data format, eliminating interference distortion points, storing the data, and facilitating the next processing;
the storage sequence adopts any one of the distances between the measuring line and the working surface from large to small according to the measurement date from first to last or during measurement;
s23: transient electromagnetic constraint inversion: performing constraint inversion by using an OCCAM inversion method, taking a model norm as a model smoothness constraint condition, and obtaining an inversion result by iteratively searching a minimum fitting difference;
s24: calculating a calculation formula of the relative change rate of the resistivity:the method is used for obtaining the percentage value, and can be obtained by adopting the formula for better analysis of the resistivity change rule of the coal face;
s25: and (3) drawing shows: respectively drawing a resistivity profile under different stoping degrees and a resistivity change rate profile under different stoping degrees according to the relative change rate calculation and constraint inversion results; the horizontal axes of the two are used for representing the coordinates of the measuring points, and the small-size points are the northwest ends of the measuring lines; the vertical axis represents depth, and the units are m; the numerical values are represented by different color scale values, wherein the warm (yellow) hues are high values and the cool (blue) hues are relatively low values;
s26: data interpretation: observing the resistivity change characteristics through a resistivity section chart, accurately determining the development height and range of the two zones of the top plate of the working surface, analyzing the electrical changes of the low-resistivity layer and the top plate rock stratum according to the resistivity change rate section chart, and determining the crack development influence area; and determining the development height and range of the roof collapse zone and the water guide fracture zone of the working face coal seam mining according to the detection results of different dates.
In the step S23, the OCCAM inversion method is used for fitting observation data, and model smoothness constraint is added in the Z direction;
when the number of the model vectors is N and the number of the data vectors is M, the objective function is:
wherein m= (m 1 ,m 2 ,…,m N ) Represents a model parameter vector, d= (d) 1 ,d 2 ,…,d M ) Representing the vector of data and,is an error weighting matrix, each component is the data error of an observation point, each component is the data error of the observation point, F is a forward algorithm, the inversion process is a process of continuous data fitting on the basis of forward modeling, namely, each calculation of an objective function involves the calculation of the forward modeling>Representing the target fit residual vector,/->Representing a roughness matrix;
in the OCCAM inversion, the first order roughness of the model is used:
model roughness matrix is introduced using first order roughness:
wherein the model first order roughness matrix is expressed asI.e. the expression form of the objective function is met;
the OCCAM inversion algorithm converts the nonlinear problem into a linear problem by continuously iterating and applying the thought of local linearization, and applies the Fourier expansion theorem to one of the model parameters m k And (3) unfolding:
F(m K +Δm)≈F(m k )+J(m k )Δm (4)
wherein J (m) k ) Is a jacobian matrix, also called a sensitivity matrix, calculated using the differential pair equation (5). The matrix may be calculated using a differential approach to obtain:
wherein m is k+1 =m k +Δm,During a single model iteration, J (m k ) And->To be known, the formula is therefore a regularized least squares problem, when the coefficient matrix is full of rank, solving the solution of the system of equations:
the foregoing is merely a preferred embodiment of the present invention and it should be noted that modifications and adaptations to those skilled in the art may be made without departing from the principles of the present invention, which are intended to be comprehended within the scope of the present invention. Structures, devices and methods of operation not specifically described and illustrated herein, unless otherwise indicated and limited, are implemented according to conventional means in the art.

Claims (8)

1. The method for dynamically monitoring the development height and range of two zones of the roof of the coal seam is characterized by comprising the following steps: the method comprises data acquisition and data processing;
the data acquisition is carried out through a data acquisition system, and the data acquisition system consists of a central control console, a signal transmission system, a ground emission loop, a three-component magnetic sensor, a data acquisition station and a transmission line;
the data processing further comprises preliminary preparation, preliminary processing, constraint inversion, change rate calculation, diagrammatical display and data interpretation.
2. The method for dynamically monitoring the development height and range of two zones of a roof of a coal seam according to claim 1, wherein the method comprises the following steps: the layout mode of each unit in the data acquisition system is as follows:
s1: layout of ground emission loop: after the primary pressing of the coal face occurs, arranging a long rectangular transmitting loop at the position 200m from the position where the cutting hole is located when the primary pressing is performed in the advancing direction of the working face, wherein the long side of the loop is perpendicular to the trend of the working face, the short side of the loop is parallel to the trend of the working face, the central axis of the loop along the short side direction is consistent with the direction of the central axis of the trend of the working face, the length of the long side is set according to the trend length of the coal face, the distance from an end point to the working face is greater than 150m, the trend length of the working face is 300m, the long side is more than or equal to 600m, and the short side is more than or equal to 300m;
s2: laying a measuring line and a measuring point: the length direction of the measuring line is arranged in the transmitting loop, the center of the measuring line coincides with the geometric center of the transmitting loop, the measuring point distance is 10m, the length of the measuring line is greater than the inclined length of the coal face, the distances from the end points of the measuring line to the boundaries of the two sides of the working face are respectively greater than 30m, namely at least 3 measuring points are respectively arranged outside the two sides of the working face, and the total length of the measuring line is 360m;
s3: data acquisition station and three-component magnetic sensor lay: adopting data acquisition stations with 24 functions, wherein each data acquisition station is connected with 8 three-component magnetic sensors;
s4: and (3) layout of a control system: the central control console is arranged in the coal mine commanding and dispatching control center and is used for transmitting monitoring instructions.
3. The method for dynamically monitoring the development height and range of two zones of a roof of a coal seam according to claim 1, wherein the method comprises the following steps: the data acquisition adopts segmented arithmetic dense sampling, and the sampling interval depends on the electrical characteristics of stratum in the monitored area.
4. The method for dynamically monitoring the development height and range of two zones of a roof of a coal seam according to claim 1, wherein the method comprises the following steps: in the data acquisition, multiple measurements are required, and the measurement time is as follows: the first measurement is carried out after the initial pressure is applied, after each unit is arranged, the measurement is ready to be started, in the continuous tunneling process of the working face along the trend, the whole acquisition system is fixed in the measurement process, the system is positioned on an unexplored coal seam at the beginning, the data acquired for the first time are regarded as in-situ stratum data, and each time the working face tunnels for 50m, the measurement is carried out until the working face tunnels for 350m beyond the survey line.
5. The method for dynamically monitoring the development height and range of two zones of a roof of a coal seam according to claim 1, wherein the method comprises the following steps: the data processing comprises the following steps:
s21: early preparation: obtaining geological, hydrological and logging data of a mining area through inquiry, performing eight Fourier fitting on resistivity logging data, and constructing a mining area multi-layer ground model according to the rock resistivity parameter difference for analyzing the stratum electrical characteristic distribution;
s22: preliminary processing of data: converting the data format, eliminating interference distortion points, and storing the data;
s23: transient electromagnetic constraint inversion: performing constraint inversion by using an OCCAM inversion method, taking a model norm as a model smoothness constraint condition, and obtaining an inversion result by iteratively searching a minimum fitting difference;
s24: calculating a calculation formula of the relative change rate of the resistivity:for obtaining a percentage value;
s25: and (3) drawing shows: respectively drawing a resistivity profile under different stoping degrees and a resistivity change rate profile under different stoping degrees according to the relative change rate calculation and constraint inversion results;
s26: data interpretation: analyzing the electrical changes of the low-resistivity layer and the roof rock stratum according to the resistivity change rate profile, and determining a crack development influence area; and determining the development height and range of the roof collapse zone and the water guide fracture zone of the working face coal seam mining according to the detection results of different dates.
6. The method for dynamically monitoring the development height and range of two zones of a roof of a coal seam according to claim 5, wherein: in S21, the query mode is any one or more of reference, database search, and query to the geological exploration unit.
7. The method for dynamically monitoring the development height and range of two zones of a roof of a coal seam according to claim 1, wherein the method comprises the following steps: in the step S22, the storage sequence is any one of the distances between the measuring line and the working surface from the first to the last or the measuring time according to the measuring date.
8. The method for dynamically monitoring the development height and range of two zones of a roof of a coal seam according to claim 1, wherein the method comprises the following steps: in the step S23, the OCCAM inversion method is used for fitting observation data, and model smoothness constraint is added in the Z direction;
when the number of the model vectors is N and the number of the data vectors is M, the objective function is:
wherein m= (m 1 ,m 2 ,…,m N ) Represents a model parameter vector, d= (d) 1 ,d 2 ,…,d M ) Representing the vector of data and,is an error weighting matrix, each component is the data error of the observation point, F is a forward algorithm, the inversion process is a continuous data fitting process based on forward algorithm, and the error weighting matrix is a block of the data error of the observation point>Representing the target fit residual vector,/->Representing a roughness matrix;
in the OCCAM inversion, the first order roughness of the model is used:
model roughness matrix is introduced using first order roughness:
wherein the model first order roughness matrix is expressed as
Through continuous iteration, the nonlinear problem is converted into a linear problem, and one model parameter m is subjected to Fourier expansion theorem k And (3) unfolding:
F(m K +Δm)≈F(m k )+J(m k )Δm (4)
wherein J (m) k ) Is a jacobian matrix, calculated by using a differential pair formula (5), and obtained:
wherein m is k+1 =m k +Δm,During a single model iteration, J (m k ) Andas is known, when the coefficient matrix is full rank, the solution of the system of equations is found:
CN202311706886.7A 2023-12-13 2023-12-13 Method for dynamically monitoring development height and range of two zones of coal seam roof Pending CN117706643A (en)

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Application Number Priority Date Filing Date Title
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