CN113126147A - Detection method for determining spatial form of hidden collapse column of rock roadway floor - Google Patents

Detection method for determining spatial form of hidden collapse column of rock roadway floor Download PDF

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CN113126147A
CN113126147A CN202110229051.1A CN202110229051A CN113126147A CN 113126147 A CN113126147 A CN 113126147A CN 202110229051 A CN202110229051 A CN 202110229051A CN 113126147 A CN113126147 A CN 113126147A
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diffracted wave
seismic
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黄兰英
王勃
刘盛东
王圣程
宋雪娟
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Xuzhou University of Technology
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    • GPHYSICS
    • G01MEASURING; TESTING
    • G01VGEOPHYSICS; GRAVITATIONAL MEASUREMENTS; DETECTING MASSES OR OBJECTS; TAGS
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    • G01V1/28Processing seismic data, e.g. for interpretation or for event detection
    • G01V1/30Analysis
    • G01V1/301Analysis for determining seismic cross-sections or geostructures
    • GPHYSICS
    • G01MEASURING; TESTING
    • G01VGEOPHYSICS; GRAVITATIONAL MEASUREMENTS; DETECTING MASSES OR OBJECTS; TAGS
    • G01V1/00Seismology; Seismic or acoustic prospecting or detecting
    • G01V1/22Transmitting seismic signals to recording or processing apparatus
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    • GPHYSICS
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    • G01V1/00Seismology; Seismic or acoustic prospecting or detecting
    • G01V1/28Processing seismic data, e.g. for interpretation or for event detection
    • GPHYSICS
    • G01MEASURING; TESTING
    • G01VGEOPHYSICS; GRAVITATIONAL MEASUREMENTS; DETECTING MASSES OR OBJECTS; TAGS
    • G01V1/00Seismology; Seismic or acoustic prospecting or detecting
    • G01V1/28Processing seismic data, e.g. for interpretation or for event detection
    • G01V1/282Application of seismic models, synthetic seismograms
    • GPHYSICS
    • G01MEASURING; TESTING
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    • G01V1/00Seismology; Seismic or acoustic prospecting or detecting
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Abstract

A detection method for determining the spatial form of a hidden sinking column of a rock roadway bottom plate comprises the steps that excitation points and wave detection points are respectively arranged at the middle position of a rubber belt main roadway bottom plate, the left side position of a rail main roadway bottom plate and the right side position of a return air main roadway bottom plate, after earthquake is excited by the excitation points, an earthquake host can receive a top point diffracted wave signal of the sinking column, the intersection point of the top point diffracted wave signal positions received each time is taken, and the final top point position of the sinking column can be determined; the earthquake host receives the diffracted wave signals of the broken trapping points a, b, c and d, calculates the diffracted wave signals of the broken trapping points a, b, c and d, determines the positions of the broken trapping points a, b, c and d, finally connects the determined positions of the top points of the trapping columns, the positions of the broken trapping points a, b and c and the broken trapping point d, and finally determines the space form of the hidden trapping column under the bottom plate of the rock roadway; the method is simple in construction and convenient and fast to use, can accurately detect the sinking column hidden below the bottom plate of the rock roadway and can determine the space form of the sinking column.

Description

Detection method for determining spatial form of hidden collapse column of rock roadway floor
Technical Field
The invention relates to a method for detecting a subsided column, in particular to a method for detecting the spatial form of the subsided column on a bottom plate of a rock roadway, and belongs to the technical field of coal mine roadway safety production.
Background
The collapse column is an irregular collapse body formed by collapse of overlying rocks at the top of a karst cave in coal-series underburden limestone, belongs to a hidden vertical structure, has the characteristics of concealment, outburst, conduction of abundant karst underground water and the like, and is extremely harmful to safe production of coal mines, environment and local people life. Since 2010 camel mountain extra-large AoHui water inrush accidents, AoHui rock collapse column water inrush flooding accidents present new characteristics, and water inrush channels are collapse columns hidden under roadway bottom plates, so that the water inrush channels are more concealed, and the danger to coal mine safety production is higher.
The characteristics of the space form and the like of the trapping column are basic elements for describing the trapping column and are also the basis for estimating the mechanism of the cause, judging the water conductivity of the trapping column and predicting water inrush.
The existing research results are more, but unfortunately, most of the results are obtained by taking the sinking column which is locally exposed in the field or exposed on the ground as a research object, and the research reports on the space form of the sinking column hidden under the roadway bottom plate are few.
As is well known, mine roadways can be classified into three major categories, i.e., development roadways, preparation roadways and mining roadways, according to the purpose and service range. The rock lanes during development comprise a return air large lane, a rubber belt large lane, a track large lane and the like, and disastrous accidents such as water inrush and the like are easy to happen when the sinking pillars hidden below the bottom plate of the rock lane are encountered by mistake in the process of tunneling the rock lane.
Therefore, how to detect the collapse column and the space form thereof by using the existing rock roadway position condition is a problem worthy of innovative thinking.
Disclosure of Invention
The invention aims to provide a detection method for determining the spatial form of the hidden collapse column on the bottom plate of the rock roadway, which is simple in construction and convenient and fast to use, can accurately detect the hidden collapse column below the bottom plate of the rock roadway and determine the spatial form of the hidden collapse column, and provides guidance for subsequent safe tunneling of the rock roadway.
In order to achieve the purpose, the invention provides a detection method for determining the spatial form of a hidden sinking column on a bottom plate of a rock roadway, which comprises the following steps:
the method comprises the following steps: arranging n excitation points I and m detection points I in the middle of a bottom plate of a large rubber belt roadway, wherein the excitation points I are used for exciting seismic waves, the excitation points I emit seismic waves and then reach an underlying collapse column, and diffracted wave signals fed back by the excitation points I are received by the detection points I and transmitted to a seismic host through a wireless network;
secondly, seismic waves are excited through the excitation point I, when the seismic waves reach the underlying collapse column, seismic wave signals are received by the detection point I and are transmitted to the seismic host, and due to the existence of the fault point a and the fault point b, the wave impedances at the fault point a and the fault point b are obviously different from those at the four circles, so that when the excited seismic waves meet the underlying collapse column, the seismic host receives vertex diffracted wave signals of the underlying collapse column, diffracted wave signals of the fault point a and delayed diffracted wave signals of the fault point b;
thirdly, calculating the vertex diffracted wave signals in the first step and the second step to determine the main energy direction alpha of the vertex diffracted wavex,y(x-1 … n, y-1 … m), by αx,y(x 1 … n, y 1 … m) determining the position of the vertex; calculating diffracted wave signals of the trap breaking point a and delayed diffracted wave signals of the trap breaking point b in the first step through a polarization analysis method based on generalized S transformation, and determining the main energy direction alpha of the diffracted wave of the trap breaking point ax,y,z(x is 1 … n, y is 1 … m, and z is a), the main energy direction α of the delayed diffracted wave at the trap point bx,y,z(x-1 … n, y-1 … m, z-b); by alphax,y,a(x is 1 … n, y is 1 … m, and z is a) determining the position of the fracture point a by alphax,y,b(x 1 … n, y 1 … m, and z b) determining the position of the fracture point b;
step two: i excitation points II and j detection points II are arranged at the left side of a bottom plate of a large track roadway and are used for exciting seismic waves, the excitation points II emit seismic waves and then reach an underlying collapse column, and diffracted wave signals fed back by the excitation points II are received by the detection points II and are transmitted to a seismic host through a wireless network;
secondly, seismic waves are excited through the excitation point II, when the seismic waves reach the underlying collapse column, seismic wave signals are received by the detection point II and transmitted to the seismic host, the seismic host receives the top diffracted wave signals of the underlying collapse column, and the seismic host can receive diffracted wave signals of the fracture point c of the underlying collapse column according to the shortest time principle;
thirdly, the vertex diffracted wave signals in the second step are calculated to determine the main energy direction alpha of the vertex diffracted wavex,y(x-1 … i, y-1 … j), by αx,y(x-1 … i, y-1 … j) determining the location of the vertex; calculating the diffracted wave signal of the fault point c in the second step through a polarization analysis method based on generalized S transformation, and determining the main energy direction alpha of the diffracted wave of the fault point cx,y,z(x-1 … i, y-1 … j, z-c); by alphax,y,z(x-1 … i, y-1 … j, z-c) determining the position of the fracture point c;
step three: arranging k excitation points III and h detection points III at the right position of a bottom plate of a return air main roadway, wherein the excitation points III are used for exciting seismic waves, the excitation points III emit seismic waves and then reach an underlying collapse column, and diffracted wave signals fed back by the excitation points III are received by the detection points III and are transmitted to a seismic host through a wireless network;
secondly, seismic waves are excited through the excitation point III, when the seismic waves reach the underlying collapse column, a seismic wave signal is received by the detection point III and transmitted to the seismic host, the seismic host receives a top diffracted wave signal of the underlying collapse column, and according to the shortest time principle, the seismic host can receive a diffracted wave signal of the fracture point d of the underlying collapse column;
thirdly, calculating the vertex diffracted wave signals in the third step and determining the main energy direction alpha of the vertex diffracted wavex,y(x-1 … k, y-1 … h), by αx,y(x 1 … k, y 1 … h) determining the position of the vertex; calculating the diffracted wave signal of the fault point d in the third step through a polarization analysis method based on generalized S transformation, and determining the main energy direction alpha of the diffracted wave of the fault point dx,y,z(x-1 … k, y-1 … h, z-d); by alphax,y,z(x is 1 … k, y is 1 … h, and z is d) determining the position of the fracture point d;
step four: after the rubber belt main lane, the track main lane and the return air main lane excite the earthquake waves, the earthquake host can receive the top point diffracted wave signals of the collapse column, and the final top point position of the collapse column can be determined by taking the intersection point of the top point diffracted wave signal positions received each time;
step five: and (4) connecting the top point position of the sinking column determined in the fourth step, the positions of the breaking point a and the breaking point b determined in the first step, the position of the breaking point c determined in the second step and the position of the breaking point d determined in the third step, and finally determining the space form of the hidden sinking column below the bottom plate of the rock roadway.
Further, the calculation process of the main energy direction of the delayed diffraction wave of the interrupted trap point b is as follows:
the method comprises the following steps: calculating the three-component x, y and z diffraction wave time spectrum to obtain a cross energy matrix MS as follows:
Figure BDA0002958177070000031
wherein, IxxRepresents the cross amplitude between the x component and the x component at time t at frequency f;
Ixyrepresents the cross amplitude between the x and y components at time t at frequency f;
Ixzrepresents the cross amplitude between the x and z components at time t at frequency f;
Iyyrepresents the cross amplitude between the y component and the y component at time t at frequency f;
Iyzrepresents the cross amplitude between the y component and the z component at time t at frequency f;
Izzrepresents the cross amplitude between the z component and the z component at time t at frequency f;
step two: performing eigenvalue analysis on the matrix MS (t, f), wherein the eigenvector corresponding to the maximum eigenvalue is V (V)x,Vy,Vz) The main energy direction of the diffracted wave can be represented by the formula
Figure BDA0002958177070000032
And (4) determining.
Compared with the prior art, the excitation point I and the wave detection point I are arranged in the middle of the rubber belt main roadway bottom plate, the excitation point II and the wave detection point II are arranged at the left side of the rail main roadway bottom plate, the excitation point III and the wave detection point III are arranged at the right side of the air return main roadway bottom plate, after the earthquake is excited through the excitation point I, the excitation point II and the excitation point III respectively, the earthquake host can receive the top point diffracted wave signal of the collapse column, the intersection point of the top point diffracted wave signal positions received each time is taken, and the final top point position of the collapse column can be determined; the earthquake host can receive the diffracted wave signal of the trap breaking point a, the diffracted wave signal of the trap breaking point b, the diffracted wave signal of the trap breaking point c and the diffracted wave signal of the trap breaking point d, calculate the diffracted wave signal of the trap breaking point a, the diffracted wave signal of the trap breaking point b, the diffracted wave signal of the trap breaking point c and the diffracted wave signal of the trap breaking point d, determine the positions of the trap breaking point a, the trap breaking point b, the trap breaking point c and the trap breaking point d, and finally connect the determined vertex position of the trap column, the positions of the trap breaking point a, the trap breaking point b, the trap breaking point c and the trap breaking point d, namely finally determine the spatial form of the trap column under the rock roadway floor; the method is simple in construction and convenient and fast to use, can accurately detect the collapse columns hidden below the bottom plate of the rock roadway, can determine the space forms of the collapse columns, and provides guidance for subsequent safe tunneling of the rock roadway.
Drawings
FIG. 1 is a schematic structural view of the present invention;
fig. 2 is a top view of fig. 1.
In the figure: 1. the rubber belt main roadway floor comprises 1.1 parts of excitation points I and 1.2 parts of wave detection points I and 2 parts of rail main roadway floor, 2.1 parts of excitation points II and 2.2 parts of wave detection points II and 3 parts of return air main roadway floor, 3.1 parts of excitation points III and 3.2 parts of wave detection points III.
Detailed Description
The invention will be further explained with reference to the accompanying drawings, and the invention will be described with reference to the rock drivage direction in fig. 2 as the front.
As shown in fig. 1 and fig. 2, a detection method for determining the spatial form of a hidden sinking column on a bottom plate of a rock roadway comprises the following steps:
the method comprises the following steps: arranging n excitation points I1.1 and m demodulator probes I1.2 in the middle of a rubber belt roadway bottom plate 1, wherein the excitation points I1.1 and the demodulator probes I1.2 are connected with a seismic host through a wireless network; the excitation point I1.1 is used for exciting seismic waves, the excitation point I1.1 emits the seismic waves and then reaches the underlying collapse column, and diffracted wave signals fed back by the excitation point I1.1 are received by the detection point I2 and transmitted to the seismic host through a wireless network;
secondly, seismic waves are excited through the excitation point I1.1, when the seismic waves reach the underlying collapse column, seismic wave signals are received by the detection point I1.2 and transmitted to the seismic host, and due to the existence of the fault point a and the fault point b, the wave impedances at the fault point a and the fault point b are obviously different from those at four weeks, so that when the excited seismic waves encounter the underlying collapse column, the seismic host receives top diffracted wave signals of the underlying collapse column, diffracted wave signals of the fault point a and delayed diffracted wave signals of the fault point b;
thirdly, calculating the vertex diffracted wave signals in the first step and the second step to determine the main energy direction alpha of the vertex diffracted wavex,y(x-1 … n, y-1 … m), by αx,y(x 1 … n, y 1 … m) determining the position of the vertex; calculating diffracted wave signals of the trap breaking point a and delayed diffracted wave signals of the trap breaking point b in the first step through a polarization analysis method based on generalized S transformation, and determining the main energy direction alpha of the diffracted wave of the trap breaking point ax,y,z(x is 1 … n, y is 1 … m, and z is a), the main energy direction α of the delayed diffracted wave at the trap point bx,y,z(x-1 … n, y-1 … m, z-b); by alphax,y,a(x is 1 … n, y is 1 … m, and z is a) determining the position of the fracture point a by alphax,y,b(x 1 … n, y 1 … m, and z b) determining the position of the fracture point b;
step two: arranging i excitation points II 2.1 and j detection points II 2.2 at the left side of a track main roadway bottom plate 2, wherein the excitation points II 2.1 and the detection points II 2.2 are connected with an earthquake host through a wireless network;
secondly, seismic waves are excited through the excitation point II 2.1, when the seismic waves reach the underlying collapse column, seismic wave signals are received by the detection point II 2.2 and transmitted to the seismic host, the seismic host receives the top diffracted wave signals of the underlying collapse column, and the seismic host can receive diffracted wave signals of the fracture point c of the underlying collapse column according to the shortest time principle;
thirdly, the vertex diffracted wave signals in the second step are calculated to determine the main energy direction alpha of the vertex diffracted wavex,y(x-1 … i, y-1 … j), by αx,y(x-1 … i, y-1 … j) determining the location of the vertex; calculating the diffracted wave signal of the fault point c in the second step through a polarization analysis method based on generalized S transformation, and determining the main energy direction alpha of the diffracted wave of the fault point cx,y,z(x-1 … i, y-1 … j, z-c); by alphax,y,z(x-1 … i, y-1 … j, z-c) determining the position of the fracture point c;
step three: arranging k excitation points III 3.1 and h wave detection points III 3.2 at the right position of a bottom plate 3 of the air return large roadway, wherein the excitation points III 3.1 are used for exciting seismic waves, the excitation points III 3.1 emit seismic waves and then reach a lower-base subsidence column, and diffracted wave signals fed back by the excitation points III 3.2 are received by the wave detection points III.2 and are transmitted to a seismic host through a wireless network;
secondly, seismic waves are excited through the excitation point III 3.1, when the seismic waves reach the underlying collapse column, seismic wave signals are received by the detection point III 3.2 and transmitted to the seismic host, the seismic host receives the top diffracted wave signals of the underlying collapse column, and the seismic host can receive diffracted wave signals of the fracture point c of the underlying collapse column according to the shortest time principle;
thirdly, calculating the vertex diffracted wave signals in the third step and determining the main energy direction alpha of the vertex diffracted wavex,y(x-1 … k, y-1 … h), by αx,y(x 1 … k, y 1 … h) determining the position of the vertex; calculating the diffracted wave signal of the fault point d in the third step through a polarization analysis method based on generalized S transformation, and determining the main energy direction alpha of the diffracted wave of the fault point dx,y,z(x-1 … k, y-1 … h, z-d); by alphax,y,z(x is 1 … k, y is 1 … h, and z is d) determining the position of the fracture point d;
step four: after the rubber belt main lane, the track main lane and the return air main lane excite the earthquake waves, the earthquake host can receive the top point diffracted wave signals of the collapse column, and the final top point position of the collapse column can be determined by taking the intersection point of the top point diffracted wave signal positions received each time;
step five: and (4) connecting the top point position of the sinking column determined in the fourth step, the positions of the breaking point a and the breaking point b determined in the first step, the position of the breaking point c determined in the second step and the position of the breaking point d determined in the third step, and finally determining the space form of the hidden sinking column below the bottom plate of the rock roadway.
The calculation process of the main energy direction of the delayed diffraction wave of the interrupted trap point b is as follows:
the method comprises the following steps: calculating the three-component x, y and z diffraction wave time spectrum to obtain a cross energy matrix MS as follows:
Figure BDA0002958177070000061
wherein, IxxRepresents the cross amplitude between the x component and the x component at time t at frequency f;
Ixyrepresents the cross amplitude between the x and y components at time t at frequency f;
Ixzrepresents the cross amplitude between the x and z components at time t at frequency f;
Iyyrepresents the cross amplitude between the y component and the y component at time t at frequency f;
Iyzrepresents the cross amplitude between the y component and the z component at time t at frequency f;
Izzrepresents the cross amplitude between the z component and the z component at time t at frequency f;
step two: performing eigenvalue analysis on the matrix MS (t, f), wherein the eigenvector corresponding to the maximum eigenvalue is V (V)x,Vy,Vz) The main energy direction of the diffracted wave can be represented by the formula
Figure BDA0002958177070000062
And (4) determining.

Claims (2)

1. A detection method for determining the spatial form of a hidden sinking column of a rock roadway floor is characterized by comprising the following steps:
the method comprises the following steps: arranging n excitation points I (1.1) and m detection points I (1.2) in the middle of a rubber belt roadway bottom plate (1), wherein the excitation points I (1.1) are used for exciting seismic waves, the excitation points I (1.1) emit seismic waves and then reach a underlying collapse column, and diffracted wave signals fed back by the excitation points I (1.2) are received by the detection points I (1.2) and transmitted to a seismic host through a wireless network;
secondly, seismic waves are excited through the excitation point I (1.1), seismic wave signals are received by the detection point I (1.2) and transmitted to the seismic host, and due to the existence of the trap breaking point a and the trap breaking point b, wave impedances at the trap breaking point a and the trap breaking point b are obviously different from those at the four weeks, so that when the excited seismic waves encounter the underlying trapping column, the seismic host receives vertex diffracted wave signals of the underlying trapping column, diffracted wave signals of the trap breaking point a and delayed diffracted wave signals of the trap breaking point b;
thirdly, calculating the vertex diffracted wave signals in the first step and the second step to determine the main energy direction alpha of the vertex diffracted wavex,y(x-1 … n, y-1 … m), by αx,y(x 1 … n, y 1 … m) determining the position of the vertex; calculating diffracted wave signals of the trap breaking point a and delayed diffracted wave signals of the trap breaking point b in the first step through a polarization analysis method based on generalized S transformation, and determining the main energy direction alpha of the diffracted wave of the trap breaking point ax,y,z(x is 1 … n, y is 1 … m, and z is a), the main energy direction α of the delayed diffracted wave at the trap point bx,y,z(x-1 … n, y-1 … m, z-b); by alphax,y,a(x is 1 … n, y is 1 … m, and z is a) determining the position of the fracture point a by alphax,y,b(x 1 … n, y 1 … m, and z b) determining the position of the fracture point b;
step two: i excitation points II (2.1) and j detection points II (2.2) are arranged at the left side of a track main roadway bottom plate (2), the excitation points II (2.1) are used for exciting seismic waves, the excitation points II (2.1) emit seismic waves and then reach a lower foundation collapse column, and diffracted wave signals fed back by the excitation points II (2.2) are received by a detection point II (2.2) and transmitted to a seismic host through a wireless network;
secondly, seismic waves are excited through an excitation point II (2.1), seismic wave signals are received by a detection point II (2.2) and transmitted to a seismic host, the seismic host receives the top diffracted wave signals of the underlying collapse column, and the seismic host can receive the diffracted wave signals of the fracture point c of the underlying collapse column according to the shortest time principle;
thirdly, the vertex diffracted wave signals in the second step are calculated to determine the main energy direction alpha of the vertex diffracted wavex,y(x-1 … i, y-1 … j), by αx,y(x-1 … i, y-1 … j) determining the location of the vertex; calculating the diffracted wave signal of the fault point c in the second step through a polarization analysis method based on generalized S transformation, and determining the main energy direction alpha of the diffracted wave of the fault point cx,y,z(x-1 … i, y-1 … j, z-c); by alphax,y,z(x-1 … i, y-1 … j, z-c) determining the position of the fracture point c;
step three: arranging k excitation points III (3.1) and h wave detection points III (3.2) at the right position of a bottom plate (3) of an air return main roadway, wherein the excitation points III (3.1) are used for exciting seismic waves, the excitation points III (3.1) emit seismic waves and then reach a underlying collapse column, and diffracted wave signals fed back by the excitation points III (3.2) are received by a detection point III (3.2) and transmitted to a seismic host through a wireless network;
secondly, seismic waves are excited through an excitation point III (3.1), when the seismic waves reach the underlying collapse column, the seismic host receives the top diffracted wave signal of the underlying collapse column, and according to the shortest time principle, the seismic host can receive the diffracted wave signal of the fracture point d of the underlying collapse column;
thirdly, calculating the vertex diffracted wave signals in the third step and determining the main energy direction alpha of the vertex diffracted wavex,y(x-1 … k, y-1 … h), by αx,y(x 1 … k, y 1 … h) determining the position of the vertex; calculating the diffracted wave signal of the fault point d in the third step through a polarization analysis method based on generalized S transformation, and determining the main energy direction alpha of the diffracted wave of the fault point dx,y,z(x-1 … k, y-1 … h, z-d); by alphax,y,z(x is 1 … k, y is 1 … h, and z is d) determining the position of the fracture point d;
step four: after the rubber belt main lane, the track main lane and the return air main lane excite the earthquake waves, the earthquake host can receive the top point diffracted wave signals of the collapse column, and the final top point position of the collapse column can be determined by taking the intersection point of the top point diffracted wave signal positions received each time;
step five: and (4) connecting the top point position of the sinking column determined in the fourth step, the positions of the breaking point a and the breaking point b determined in the first step, the position of the breaking point c determined in the second step and the position of the breaking point d determined in the third step, and finally determining the space form of the hidden sinking column below the bottom plate of the rock roadway.
2. The method for detecting the spatial configuration of the hidden sinking column on the bottom plate of the rock roadway according to claim 1, wherein the step one, the calculation process of the main energy direction of the delayed diffracted wave of the interrupted sinking point b is as follows:
the method comprises the following steps: calculating the three-component x, y and z diffraction wave time spectrum to obtain a cross energy matrix MS as follows:
Figure FDA0002958177060000021
wherein, IxxRepresents the cross amplitude between the x component and the x component at time t at frequency f;
Ixyrepresents the cross amplitude between the x and y components at time t at frequency f;
Ixzrepresents the cross amplitude between the x and z components at time t at frequency f;
Iyyrepresents the cross amplitude between the y component and the y component at time t at frequency f;
Iyzrepresents the cross amplitude between the y component and the z component at time t at frequency f;
Izzrepresents the cross amplitude between the z component and the z component at time t at frequency f;
step two: performing eigenvalue analysis on the matrix MS (t, f), wherein the eigenvector corresponding to the maximum eigenvalue is V (V)x,Vy,Vz) The main energy direction of the diffracted wave can be represented by the formula
Figure FDA0002958177060000031
And (4) determining.
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* Cited by examiner, † Cited by third party
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