A method for quickly and accurately calculating the true thickness of rock layers based on a solid geometric model

Abstract

The present invention discloses a method for quickly and accurately solving the true thickness of rock formations based on a three-dimensional geometric model. It includes the following steps: step one, obtaining basic data; obtaining the coordinates and elevation of any point on the top and bottom of the rock formation; measuring the occurrence of the rock layer surface; step two, establishing a three-dimensional geometric model; setting the top and bottom surfaces of the rock formation to be planes and parallel; making the top and bottom surfaces of the rock formation in a rectangular parallelepiped, and marking the top and bottom points of the rock formation; making line segments representing the true thickness of the rock formation through a series of auxiliary lines and points, and establishing a three-dimensional geometric model; step three, based on the three-dimensional geometric model, deriving the solution formula for the true thickness of the rock formation under various circumstances; step four, establishing a general formula for the true thickness of the rock formation; step five, substituting the basic data into the general formula for the true thickness of the rock formation to calculate the true thickness of the rock formation. The present invention has the advantages of high work efficiency, small error in acquired data, small calculation error, simple solution and high accuracy.

Description

Technical Field

[0001] The present invention relates to the field of geological exploration technology, and more specifically, it is a simple method for quickly and accurately solving the true thickness of rock layers by using interface point measurement data based on a three-dimensional geometric model. More specifically, it is a simple method for quickly and accurately solving the true thickness of rock layers by using interface point measurement data based on a three-dimensional geometric model. Background Art

[0002] The main method for solving the true thickness of rock formations is the "wire method". The "wire method" is the Leontovsky formula, and the method based on the improved formula later on the basis of this formula. It uses wires connected to the top and bottom surfaces as auxiliary tools in the field to measure the length, azimuth, inclination and other parameters of the wires to calculate the true thickness of the rock formation. This method has great disadvantages in application. For example, it is restricted by topographic and geological conditions and requires continuous layered measurements, layered calculation of the true thickness of the rock formation, and finally accumulation. The field workload is large and cumbersome, and accumulating the layered calculation values ​​will increase the calculation error; when the bedrock outcrop is not good, it is necessary to find multiple bedrock outcrops for measurement, and it is also necessary to determine whether the bedrock outcrops measured in layers have repeated and missed rock formations, which is cumbersome in the field; the stretching and bending characteristics of the wire will cause large errors, affecting the accuracy of the solution. These shortcomings lead to a large workload and cumbersome work in obtaining the basic data in the field of this solution method, large errors in the acquired data, large calculation errors, complex solutions and low accuracy.

[0003] Therefore, it is necessary to develop a method for calculating the true thickness of rock layers with high working efficiency, small error in acquired data, small error in calculation, simple solution and high accuracy. Summary of the invention

[0004] The purpose of the present invention is to provide a method for quickly and accurately solving the true thickness of rock formations based on a three-dimensional geometric model. The method is a simple method for quickly and accurately solving the true thickness of rock formations based on a three-dimensional geometric model using interface point measurement data. The method has the characteristics of high work efficiency, small error in acquired data, small error in calculation, simple solution and high accuracy. It solves the problems of large workload and cumbersome work in acquiring on-site basic data, large error in acquired data, large error in calculation, complex solution and low accuracy caused by the constraints of conditions such as terrain, bedrock outcrop conditions and poor characteristics of measuring tools in traditional methods.

[0005] In order to achieve the above object, the technical solution of the present invention is: a method for quickly and accurately solving the true thickness of rock formations based on a three-dimensional geometric model, which is different in that it includes the following steps:

[0006] Step 1: Obtain basic data;

[0007] Obtain the coordinates and elevation of any point on the top and bottom of the rock layer; measure the occurrence of the rock layer;

[0008] Step 2: Establish a three-dimensional geometric model;

[0009] Assume that the top and bottom surfaces of the rock layer are both flat and parallel;

[0010] In a rectangular parallelepiped, according to certain feasible settings (e.g., setting the top and bottom surfaces of the rock layer as planes and parallel, setting point d as the projection point of point a on the horizontal plane passing through point b, etc.), draw the top and bottom surfaces of the rock layer, and mark the top and bottom points of the rock layer; through a series of auxiliary lines and points, draw line segments representing the true thickness of the rock layer, and establish a three-dimensional geometric model;

[0011] The establishment of a three-dimensional geometric model is divided into three major situations: (1) the rock layer is inclined, (2) the rock layer is horizontal, and (3) the rock layer is vertical. According to the elevation relationship between the top point and the bottom point, the major situation of the rock layer inclination is further divided into: 1) the top point elevation is greater than the bottom point elevation, 2) the top point elevation is equal to the bottom point elevation, and 3) the top point elevation is less than the bottom point elevation. According to the needs of the solution, the situation where the top point elevation is greater than the bottom point elevation when the rock layer is inclined is further divided into three sub-situations.

[0012] Step 3: Based on the three-dimensional geometric model, derive the solution formula for the true thickness of the rock layer in the above-mentioned various situations;

[0013] Step 4: Establish a general formula for true thickness of rock formations;

[0014] Assume that the top and bottom surfaces of the rock layer are plane and parallel; the general formula for the true thickness of the rock layer is: H = (h1-h2) × cosα-η × ((x1-x2) 2 +(y1-y2) 2 ) 0.5 ×sinβsinα

[0015] Among them: β value is obtained by graphing method or trigonometric function method, η is obtained by graphing method;

[0016] x1, y1, and h1 are the horizontal and vertical coordinates and elevation of point a on the top surface of the rock layer, respectively; x2, y2, and h2 are the horizontal and vertical coordinates and elevation of point b on the bottom surface of the rock layer, respectively, and the units are all meters;

[0017] α is the inclination angle of the rock layer, in degrees;

[0018] β is the angle between the azimuth line of straight line ab and the strike line of the bottom of the rock layer, in degrees;

[0019] η is the relative position coefficient of the foot of the vertical; when the rock layer is inclined and point d is located on the opposite side of the rock layer inclination of the straight line m, η = 1; in other cases (such as horizontal and vertical rock layers), η = -1;

[0020] Step 5: Substitute the basic data in step 1 into the general formula of true thickness of rock formation in step 4 to calculate the true thickness of rock formation.

[0021] In the above technical solution, in step 1, the basic data includes the coordinates of the measurement points, elevation, inclination and dip angle of the rock formation;

[0022] The specific method of obtaining basic data is: select a point at any convenient position on the top and bottom of the rock layer, respectively named point a and point b, and use appropriate professional measurement equipment (optional Rtk, prism-free total station, conventional total station, etc.) to measure the coordinates and elevation of point a and point b; or use other technical means to obtain the measurement data of the interface point, such as reading the coordinates and elevation of point a and point b from the plane geological survey map;

[0023] Let the horizontal coordinate of point a be x1, the vertical coordinate be y1, and the elevation be h1; let the horizontal coordinate of point b be x2, the vertical coordinate be y2, and the elevation be h2;

[0024] Geological professionals measure the occurrence of rock formations, assuming that the dip is δ and the inclination is α.

[0025] In the above technical solution, the establishment of the three-dimensional geometric model is divided into three major situations: rock layer tilt, rock layer horizontal and rock layer vertical;

[0026] According to the elevation relationship between the top point and the bottom point, the rock layer inclination is divided into three situations: the top point elevation is greater than the bottom point elevation, the top point elevation is equal to the bottom point elevation, and the top point elevation is less than the bottom point elevation.

[0027] When the rock layer is inclined, point d is set as the projection point of point a on the horizontal plane passing through point b, and straight line m is set as the rock layer strike line passing through point b (i.e., the intersection line of the bottom of the rock layer and the horizontal plane);

[0028] According to the needs of the solution, the situation where the elevation of the top point is greater than the elevation of the bottom point when the rock layer is inclined is divided into three subdivisions: point d is located on the right side of the straight line m, point d is located on the straight line m, and point d is located on the left side of the straight line m.

[0029] In the above technical solution, in step 2, the top and bottom surfaces of the rock layer are set to be plane and parallel;

[0030] When the rock layer is tilted, such as Figure 2 As shown in the figure, the specific method of establishing a solid geometric model is:

[0031] Step S211: draw a horizontal plane k passing through point b; suppose the strike lines of the top and bottom of the rock layer on plane k are straight lines l and m respectively, the projection point of point a on plane k is point d, connect ad, then l∥m, line segment ad⊥plane k;

[0032] Step S212: Make a cuboid so that the bottom surface ABCD of the cuboid coincides with the plane k; the left and right edges of the bottom surface of the cuboid are parallel to the strike line of the rock formation, that is, the straight line AD||l||m||BC;

[0033] Step S213: Draw the top surface (intersection points with the edges are E, F, G, H) and bottom surface (intersection points with the edges are I, J, K, L) of the rock layer in the cuboid using auxiliary lines; assume that face CDMP of the cuboid is the front face;

[0034] Step S214: draw a surface afd⊥ lines l and m, and intersect at points f and e respectively, connect af and df, then af⊥ lines l and m, df⊥ lines l and m;

[0035] Step S215: Assume that the intersection of the straight line ad and the bottom of the rock layer is point c, connect ce, then ∠ced and ∠afd are the true inclination angle α of the rock layer surface, that is, ∠ced=∠afd=α;

[0036] Step S216: connect cb and db, then ∠cbd is the apparent inclination angle γ of the rock layer on the vertical plane cbd, that is, ∠cbd = γ;

[0037] Step S217: ∠dbe is the angle β between the azimuth line bd of the straight line ab and the strike line m of the bottom surface of the rock layer, then ∠dbe=β (β can be obtained by drawing the azimuth line bd of the straight line ab and the strike line of the rock layer surface in the same horizontal plane using drawing software such as CAD, and then measuring the angle between the two straight lines; or firstly calculating the azimuth of ab from the ordinate and abscissa coordinates of point a and point b, and then calculating based on the azimuth of ab and the strike line of the rock layer surface);

[0038] Step S218: Draw a line segment cj⊥af and intersect it at point j, then ∠acj=α, the line segment cj is a common perpendicular line segment between the top and bottom surfaces of the rock formation, and its length is the true thickness of the rock formation;

[0039] The formula for calculating the true thickness of the rock layer is: H = (h1-h2) × cosα-η × ((x1-x2) 2 +(y1-y2) 2 ) 0.5 ×sinβsinα.

[0040] In the above technical solution, when the rock layer is horizontal, Figure 3 As shown in the figure, the specific method of establishing a solid geometric model is:

[0041] Step S221: Make a cuboid so that the bottom surface ABCD of the cuboid coincides with the bottom surface of the rock layer. Since the bottom surface of the rock layer is a horizontal plane, the bottom surface ABCD of the cuboid is also a horizontal plane. The intersection points of the top surface of the rock layer and the edges of the cuboid are set as points E, F, G, and H respectively, and the surface MPCD is set as the front surface.

[0042] Step S222: Let the projection point of point a on plane ABCD be point d, connect ad, then line segment ad⊥plane ABCD;

[0043] Step S223: The top and bottom surfaces of the rock formation are parallel, that is, the surface EFGH∥the surface ABCD, then the line segment ad⊥the surface EFGH, then the line segment ad is the common perpendicular line segment of the top and bottom surfaces of the rock formation, and its length is the true thickness H of the rock formation;

[0044] The formula for calculating the true thickness of the rock layer is: H = h1-h2.

[0045] In the above technical solution, when the rock layer is vertical, Figure 4 As shown in the figure, the specific method of establishing a solid geometric model is:

[0046] Step S231: draw a horizontal plane k passing through point b; let the strike lines of the top and bottom of the rock layer on plane k be straight lines l and m respectively, the projection point of point a on plane k is point d, connect ad, then l∥m, point d is on straight line l, line segment ad⊥plane k and⊥straight line l;

[0047] Step S232: Make a cuboid so that the bottom surface ABCD of the cuboid coincides with the plane k; the left and right edges of the bottom surface of the cuboid are parallel to the strike line of the rock formation, that is, the straight line AD∥l∥m;

[0048] Step S233: Draw the top surface (intersection points with the edges are E, F, G, H) and bottom surface (intersection points with the edges are I, J, K, L) of the rock layer in the cuboid using auxiliary lines; set the surface MPCD as the front surface;

[0049] Step S234: connect ab and db, then the straight line db is the azimuth line of the straight line ab on the horizontal plane k, ∠dbf is the angle β between the azimuth line bd of the straight line ab and the strike line m of the bottom surface of the rock layer, then ∠dbf=β (β can be obtained by drawing the azimuth line bd of the straight line ab and the strike line of the rock layer surface in the same horizontal plane through drawing software such as CAD, and then measuring the angle between the two straight lines; or first calculate the azimuth angle of ab from the ordinate and abscissa coordinates of point a and point b, and then calculate it according to the azimuth angle of ab and the strike line of the rock layer surface);

[0050] Step S235: Let the projection point of point d on plane IJKL (i.e., the bottom surface of the rock formation) be point f, and connect df. Then point f is on straight line IJ, and line segment df⊥plane IJKL. Then line segment df is a common perpendicular line segment between the top and bottom surfaces of the rock formation, and its length is the true thickness H of the rock formation;

[0051] The formula for calculating the true thickness of the rock layer is: H = ((x1-x2) 2 +(y1-y2) 2 ) 0.5 ×sinβ.

[0052] In the above technical solution, in step 3, when the elevation of the top point a is greater than the elevation of the bottom point b when the rock layer is inclined, and point d is located on the right side of the straight line m (that is, point d is located on the side opposite to the rock layer inclination of the straight line m), the true thickness of the rock layer H = (h1-h2) × cosα-((x1-x2) 2 +(y1-y2) 2 ) 0.5 ×sinβsinα;

[0053] When the rock layer is inclined, the elevation of the top point a is greater than the elevation of the bottom point b, and point d is located on the straight line m, the true thickness of the rock layer H = (h1-h2) × cosα;

[0054] When the rock layer is inclined, the elevation of the top point a is greater than the elevation of the bottom point b, and point d is located on the left side of the straight line m, the true thickness of the rock layer H = (h1-h2) × cosα + ((x1-x2) 2 +(y1-y2) 2 ) 0.5 ×sinβsinα.

[0055] When the rock layer is inclined, the elevation of the top point a is equal to the elevation of the bottom point b, the true thickness of the rock layer H = ((x1-x2) 2 +(y1-y2) 2 ) 0.5 ×sinβsinα;

[0056] When the elevation of the top point a is less than the elevation of the bottom point b when the rock layer is inclined, the true thickness of the rock layer H = (h1-h2) × cosα + ((x1-x2) 2 +(y1-y2) 2 ) 0.5 ×sinβsin.

[0057] The rock layer in the present invention patent refers to a rock layer in an ideal situation: the top and bottom surfaces of the rock layer are both plane and parallel. The true thickness of the rock layer refers to the vertical thickness between the top and bottom surfaces of the rock layer.

[0058] Compared with the prior art, the present invention has the following advantages:

[0059] (1) In the field, only one point is selected on the top and bottom of the rock layer, a total of two points, and their coordinates and elevations are measured to obtain measurement data conveniently and quickly; therefore, the field geological surveying and mapping work to obtain basic data is simple and convenient, with small workload and high work efficiency;

[0060] (2) According to the outcrop conditions of the bedrock on site, appropriate professional measuring tools can be selected to measure the coordinates and elevations of the measuring points. For places that are difficult for personnel to reach (such as steep slopes, cliffs, the other side of the river, etc.), a prism-free total station can be easily used for measurement; therefore, the basic data acquisition is easy, the working method is flexible, and the applicability is strong; other technical means can also be used, such as reading the coordinates and elevations of any point on the top and bottom of the rock layer from a plane geological survey map. This data acquisition method is also simple, convenient, and fast;

[0061] (3) The errors in the field basic data acquisition and calculation processes are greatly reduced, and the accuracy of the solution results is significantly improved;

[0062] (4) Based on the derivation of the solid geometry model, a general solution formula is established. The solution is very intuitive and easy to understand. After the general formula is derived, the solution is simple and fast. BRIEF DESCRIPTION OF THE DRAWINGS

[0063] Figure 1 The figure is a flow chart for solving the true thickness of rock formations according to the present invention.

[0064] Figure 2 This is a three-dimensional geometric model diagram established by the present invention when the rock layer is inclined.

[0065] Figure 3 This is a three-dimensional geometric model diagram established by the present invention when the rock layer is horizontal.

[0066] Figure 4 It is a three-dimensional geometric model diagram established by the present invention when the rock layer is vertical. DETAILED DESCRIPTION

[0067] The following is a detailed description of the implementation of the present invention in conjunction with the accompanying drawings, but they do not constitute a limitation of the present invention and are only given as examples. At the same time, the advantages of the present invention are made clearer and easier to understand through the description.

[0068] Referring to the attached figure, it can be seen that a method for quickly and accurately solving the true thickness of rock formations based on a three-dimensional geometric model is as follows: Figure 1 As shown, the following steps are included:

[0069] Step 1: Obtain basic data

[0070] Choose appropriate professional measuring equipment (optional: Rtk, prism-free total station, conventional total station, etc.), select a point on the top and bottom of the rock layer (named as point a and point b respectively) at a convenient location, and measure its coordinates and elevation; or use other technical means to obtain the measurement data of the interface point, such as reading from a plane geological survey map. Set the horizontal coordinate of point a to x1, the vertical coordinate to y1, and the elevation to h1; the horizontal coordinate of point b to x2, the vertical coordinate to y2, and the elevation to h2; geological professionals measure the occurrence of the rock layer (set the dip to δ and the dip angle to α).

[0071] Step 2: Establish a three-dimensional geometric model of the true thickness of the rock layer and derive the solution formula

[0072] The establishment of three-dimensional geometric models is divided into three major situations: inclined rock layers, horizontal and vertical.

[0073] When the rock layer is inclined, the three-dimensional geometric model is established as follows:

[0074] (1) Draw a horizontal plane k through point b. Suppose the top and bottom strike lines of the rock layer on plane k are straight lines l and m respectively (e.g. Figure 2 As shown), the projection point of point a on plane k is point d, connect ad, then l∥m, line segment ad⊥plane k;

[0075] (2) Construct a cuboid so that its bottom surface ABCD coincides with plane k; the left and right edges of the bottom surface of the cuboid are parallel to the strike line of the rock formation, that is, straight line AD∥l∥m∥BC;

[0076] (3) Use auxiliary lines to draw the top surface (intersection points with the edges are E, F, G, H) and bottom surface (intersection points with the edges are I, J, K, L) of the rock layer in the cuboid. Let the face CDMP of the cuboid be the front face;

[0077] (4) Construct a plane afd that is ⊥ to the lines l and m and intersects them at points f and e respectively. Connect af and df. Then af ​​is ⊥ to the lines l and m, and df is ⊥ to the lines l and m.

[0078] (5) Let the intersection of straight line ad and the bottom of the rock layer be point c, and connect ce. Then ∠ced and ∠afd are the true inclination angle α of the rock layer, that is, ∠ced = ∠afd = α;

[0079] (6) Connect cb and db, then ∠cbd is the apparent inclination angle γ of the rock layer on the vertical plane cbd, that is, ∠cbd = γ;

[0080] (7) ∠dbe is the angle β between the azimuth line bd of the straight line ab and the strike line m of the bottom surface of the rock layer, then ∠dbe = β (β can be obtained by drawing the azimuth line bd of the straight line ab and the strike line of the rock layer surface in the same horizontal plane using drawing software such as CAD, and then measuring the angle between the two straight lines; or firstly calculate the azimuth of ab from the ordinate and abscissa coordinates of points a and b, and then calculate it based on the azimuth of ab and the strike line of the rock layer surface);

[0081] (8) Draw a line segment cj⊥af and intersect it at point j, then ∠acj=α, and the line segment cj is the common perpendicular segment of the top and bottom surfaces of the rock layer, and its length is the true thickness of the rock layer.

[0082] When the rock layer is inclined, the formula for calculating the true thickness of the rock layer is derived as follows:

[0083] According to the elevation relationship between point a and point b, there are three cases. The three cases are: the first case: the elevation of point a is greater than the elevation of point b, that is, point a is above plane k; the second case: the elevation of point a is equal to the elevation of point b, that is, point a is in plane k; the third case: the elevation of point a is less than the elevation of point b, that is, point a is below plane k. According to the relative position of point d, the first case is further subdivided into three subdivisions: the first subdivision: point d is located on the right side of line m, that is, point d is located on the opposite side of the rock formation inclination of line m; the second subdivision: point d is on line m; the third subdivision: point d is located on the left side of line m, that is, point d is located on the side of the rock formation inclination of line m.

[0084] (1) When the elevation relationship between point a and point b is the first subdivision of the first case (point d is on the right side of line m);

[0085] Point d is located on the right side of line m, that is, point d is located on the opposite side of the rock formation inclination of line m, such as Figure 2 shown.

[0086] Using geometric relationships, we know that tanγ=sinβtanα

[0087] Line segment cd = line segment bd × tanγ = line segment bd × sinβtanα

[0088] And line segment bd = ((x1-x2) 2 +(y1-y2) 2 ) 0.5 , line segment ad = h1 - h2

[0089] Then the true thickness of the rock layer H = the length of the line segment cj = (line segment ad - line segment cd) × cosα The true thickness of the rock layer H = ((h1-h2)-((x1-x2) 2 +(y1-y2) 2 ) 0.5 ×sinβtanα)×cosα

[0090] True thickness of rock layer H = (h1-h2) × cosα-((x1-x2) 2 +(y1-y2) 2 ) 0.5 ×sinβsinα

[0091] In order to demonstrate the general formula for solving the true thickness of the rock layer later, the above formula is written as the following equivalent formula:

[0092] True thickness of rock layer H = (h1-h2) × cosα-η × ((x1-x2) 2 +(y1-y2) 2 )0.5 ×sinβsinα①

[0093] Where: η is the relative position coefficient of the foot of the vertical. When the rock layer is inclined and point d is located on the opposite side of the rock layer of the straight line m, η = 1; in other cases, η = -1.

[0094] When the elevation relationship between point a and point b is the second subdivision of the first case (i.e. the elevation of point a is greater than the elevation of point b) (point d is on line m);

[0095] Using the three-dimensional geometric model in the first subdivision case, point d is moved to the left (i.e., the direction of rock formation inclination) along straight line ef until it coincides with point e, and the corresponding auxiliary lines and points are also moved synchronously, then the three-dimensional geometric model in the second subdivision case is obtained.

[0096] Using geometric relationships, we know that the true thickness of the rock layer H = (h1-h2) × cosα②

[0097] The applicability of formula ① for solving the true thickness of rock formations in the second subdivision case is verified below:

[0098] Since point d is on line m, point d coincides with point e (that is, β = 0, or x1 = x2, y1 = y2)

[0099] ((x1-x2) 2 +(y1-y2) 2 ) 0.5 ×sinβsinα=0, substitute into formula ①

[0100] H=(h1-h2)×cosα, which is formula ②

[0101] It can be seen from this that the true thickness of the rock layer in the second subdivision case can be solved using formula ①.

[0102] When the elevation relationship between point a and point b is the third subdivision of the first case (point a’s elevation is greater than point b’s elevation) (point d is on the left side of line m);

[0103] Using the three-dimensional geometric model in the first subdivision case, point d moves to the left (in the direction of rock formation inclination) along straight line ef, passes through point e, and moves to the left side of straight line m. The corresponding auxiliary lines and points also move synchronously, and the three-dimensional geometric model in the third subdivision case is obtained.

[0104] Point d is located on the left side of line m, that is, point d is located on the side of the rock formation inclination of line m η = -1

[0105] Referring to the solution method of the first subdivision case, the true thickness of the rock layer in the third subdivision case is calculated in the same way:

[0106] True thickness of rock layer H = (h1-h2) × cosα + ((x1-x2) 2 +(y1-y2) 2 ) 0.5 ×sinβsinα③

[0107] Substituting η=-1 into formula ①, we can get formula ③

[0108] It can be seen from this that the true thickness of the rock layer in the third subdivision case can be solved using formula ①.

[0109] (2) When the elevation relationship between point a and point b is the second case (i.e. the elevation of point a is equal to the elevation of point b),

[0110] Using the three-dimensional geometric model of the first subdivision case in the first case, point d is moved to the left (in the direction of the rock formation inclination) along the straight line ef until it coincides with point f, and the corresponding auxiliary lines and points are also moved synchronously, then the three-dimensional geometric model of the second case is obtained.

[0111] Using geometric relationships, we can know that the true thickness of the rock layer H = ((x1-x2) 2 +(y1-y2) 2 ) 0.5 ×sinβsinα④

[0112] The applicability of formula ① for calculating the true thickness of rock formations in this case is verified below:

[0113] The elevation of point a is equal to the elevation of point b, that is, point a is on line l, that is, point d is on the side of the rock layer that is inclined to line m.

[0114] h1-h2=0,η=-1Substitute into formula①

[0115] H=((x1-x2) 2 +(y1-y2) 2 ) 0.5 ×sinβsinα, which is formula ④.

[0116] It can be seen from this that the true thickness of the rock layer in the second case can be solved using formula ①.

[0117] (3) When the elevation relationship between point a and point b is the third case (i.e. the elevation of point a is less than the elevation of point b),

[0118] Using the three-dimensional geometric model of the first subdivision case in the first case, point d is moved to the left (in the direction of rock formation inclination) along straight line ef and passes through point f. The corresponding auxiliary lines and points also move synchronously, and the three-dimensional geometric model of the third case is obtained.

[0119] Referring to the solution method of the first subdivision of the first case, the true thickness of the rock layer in the third case can be obtained in the same way:

[0120] True thickness of rock layer H = (h1-h2) × cosα + ((x1-x2) 2 +(y1-y2) 2 ) 0.5 ×sinβsinα⑤

[0121] The elevation of point a is less than that of point b, that is, point d is located on the left side of line l, that is, point d is located on the side of the rock formation inclination of line m;

[0122] η=-1,

[0123] Substituting η=-1 into formula ①, we can obtain formula ⑤.

[0124] It can be seen from this that the true thickness of the rock layer in the third case can be solved using formula ①.

[0125] In summary, the true thickness of the rock layer in various cases when the rock layer is inclined can be solved using formula ①.

[0126] When the rock layer is horizontal, the three-dimensional geometric model is established as follows:

[0127] (1) Construct a cuboid so that its bottom surface ABCD coincides with the bottom surface of the rock layer. Since the bottom surface of the rock layer is a horizontal plane, the bottom surface ABCD of the cuboid is also a horizontal plane. The intersection points of the top surface of the rock layer and the edges of the cuboid are E, F, G, and H respectively. Let the plane MPCD be the front face (e.g. Figure 3 shown).

[0128] (2) Let the projection point of point a on plane ABCD be point d, and connect ad. Then line segment ad⊥plane ABCD;

[0129] (3) The top and bottom surfaces of the rock formation are parallel, that is, plane EFGH∥plane ABCD, then line segment ad⊥plane EFGH, then line segment ad is the common perpendicular line segment of the top and bottom surfaces of the rock formation, and its length is the true thickness H of the rock formation.

[0130] When the rock layer is horizontal, the formula for calculating the true thickness of the rock layer is derived as follows:

[0131] Using geometric relationships, we know that the true thickness of the rock layer is H = h1-h2⑥

[0132] The applicability of formula ① for calculating the true thickness of rock formations in this case is verified below:

[0133] The rock layer is horizontal, then the rock layer inclination angle α=0, cosα=1, sinα=0, substitute into formula ①

[0134] H=h1-h2, which is formula ⑥,

[0135] It can be seen from this that the true thickness of the rock layer when it is horizontal can be solved using formula ①.

[0136] When the rock layer is vertical, the three-dimensional geometric model is established as follows:

[0137] (1) Draw a horizontal plane k passing through point b. Let the top and bottom of the rock layer on plane k be straight lines l and m respectively, and the projection point of point a on plane k be point d. Connect ad, then l∥m, point d is on straight line l, line segment ad⊥plane k and ⊥ straight line l (such as Figure 4 shown);

[0138] (2) Construct a cuboid so that its bottom surface ABCD coincides with plane k; the left and right edges of the bottom surface of the cuboid are parallel to the strike line of the rock formation, that is, straight line AD∥l∥m;

[0139] (3) Use auxiliary lines to draw the top surface (intersection points with the edges are E, F, G, H) and bottom surface (intersection points with the edges are I, J, K, L) of the rock layer in the cuboid; let surface MPCD be the front surface;

[0140] (4) Connect ab and db, then the straight line db is the azimuth line of the straight line ab on the horizontal plane k, ∠dbf is the angle β between the azimuth line bd of the straight line ab and the strike line m of the bottom surface of the rock layer, then ∠dbf = β (β can be obtained by drawing the azimuth line bd of the straight line ab and the strike line of the rock layer surface in the same horizontal plane using drawing software such as CAD, and then measuring the angle between the two straight lines; or first calculate the azimuth angle of ab from the ordinate and abscissa coordinates of points a and b, and then calculate it based on the azimuth angle of ab and the strike line of the rock layer surface);

[0141] (5) Let the projection point of point d on plane IJKL (bottom of rock layer) be point f. Connect df, then point f is on straight line IJ. Line segment df⊥plane IJKL. Then line segment df is the common perpendicular line segment between the top and bottom of rock layer, and its length is the true thickness H of rock layer.

[0142] When the rock layer is vertical, the formula for calculating the true thickness of the rock layer is derived as follows:

[0143] Using the relationship between geometry and trigonometric functions, we know that the perpendicular line segment df = line segment db × sinβ

[0144] And line segment db=((x1-x2) 2 +(y1-y2) 2 ) 0.5

[0145] Perpendicular line segment df = line segment db × sinβ = ((x1-x2) 2 +(y1-y2) 2 ) 0.5 ×sinβ

[0146] True thickness of rock layer H = ((x1-x2) 2 +(y1-y2) 2 ) 0.5 ×sinβ⑦

[0147] The applicability of formula ① for calculating the true thickness of rock formations in this case is verified below:

[0148] The rock layer is vertical, then α=90°, η=-1, substitute into formula ①:

[0149] True thickness of rock layer H = ((x1-x2) 2 +(y1-y2) 2 ) 0.5 × sinβ,

[0150] It can be seen from this that the true thickness of the rock layer when the rock surface is vertical can be solved using formula ①.

[0151] Step 3: Establish a general formula for true thickness of rock formations;

[0152] Through induction and summary, the general formula for the true thickness of rock formations is formula ①, which is:

[0153] True thickness of rock layer H = (h1-h2) × cosα-η × ((x1-x2) 2 +(y1-y2) 2 ) 0.5 ×sinβsinα①

[0154] In formula ①: the top and bottom surfaces of the rock formation are assumed to be planes and parallel; x1, y1, and h1 are the horizontal and vertical coordinates and elevation of point a on the top surface of the rock formation, respectively; x2, y2, and h2 are the horizontal and vertical coordinates and elevation of point b on the bottom surface of the rock formation, respectively, and the units are all in meters; point d is assumed to be the projection point of point a on the horizontal plane passing through point b; when the rock formation is inclined, straight line m is assumed to be the strike line of the rock formation passing through point b (i.e., the intersection of the bottom surface of the rock formation and the horizontal plane); α is the inclination angle of the rock formation surface, in degrees; β is the angle between the azimuth line of straight line ab and the strike line of the bottom surface of the rock formation, in degrees; η is the relative position coefficient of the foot of the perpendicular. When the rock formation surface is inclined and point d is located on the opposite side of the rock formation inclination of straight line m, η = 1; in other cases (e.g., the rock formation is horizontal and the rock formation is vertical), η = -1.

[0155] Step 4: Calculation of true thickness of rock layer

[0156] The method for calculating the true thickness of rock formations specifically includes the following steps:

[0157] (1) The measurement data (x1, y1, h1) of point a on the top surface of the rock layer and the measurement data (x2, y2, h2) of point b on the bottom surface of the rock layer can be obtained through on-site professional measurement or other technical means;

[0158] (2) Use geological tools and methods to measure the occurrence of the rock layer (i.e., measure the dip δ and inclination α of the rock layer);

[0159] The β value is obtained by graphing or trigonometric method, and η is obtained by graphing;

[0160] (3) Substituting the basic data into formula ①, the true thickness of the rock layer can be calculated.

[0161] Other parts not described belong to the prior art.

Claims

1. A method for quickly and accurately calculating the true thickness of rock formations based on a three-dimensional geometric model, characterized in that: The following steps are included: Step 1: Obtain basic data; Obtain the coordinates and elevation of any point on the top and bottom of the rock layer; measure the occurrence of the rock layer; The basic data include the coordinates of the measurement points, elevation, inclination and dip angle of the rock formation; The specific method of obtaining basic data is: select a point at any position on the top and bottom of the rock layer, respectively named point a and point b, and use measuring equipment such as Rtk, prism-free total station, and conventional total station to measure the coordinates and elevations of point a and point b; or read the coordinates and elevations of point a and point b from the plane geological survey map; Let the horizontal coordinate of point a be x1, the vertical coordinate be y1, and the elevation be h1; let the horizontal coordinate of point b be x2, the vertical coordinate be y2, and the elevation be h2; To measure the occurrence of rock formations, let the dip be δ and the inclination be α; Step 2: Establish a three-dimensional geometric model; Assume that the top and bottom surfaces of the rock layer are both flat and parallel; In a rectangular parallelepiped, according to certain feasible settings, the top and bottom surfaces of the rock layer are drawn, and the top and bottom points of the rock layer are marked; through a series of auxiliary lines and points, line segments representing the true thickness of the rock layer are drawn to establish a three-dimensional geometric model; Step 3: Based on the three-dimensional geometric model, derive the solution formula for the true thickness of the rock layer; Step 4: Establish a general formula for true thickness of rock formations; The general formula for the true thickness of a rock formation is: H=(h1-h2)×cosα-η×((x1-x2) 2 +(y1-y2) 2 ) 0.5 ×sinβsinα Among them: β value is obtained by graphing method or trigonometric function method, η is obtained by graphing method; x1, y1, and h1 are the horizontal and vertical coordinates and elevation of point a on the top surface of the rock layer, respectively; x2, y2, and h2 are the horizontal and vertical coordinates and elevation of point b on the bottom surface of the rock layer, respectively, and the units are all meters; α is the inclination angle of the rock layer, in degrees; β is the angle between the azimuth line of straight line ab and the strike line of the bottom of the rock layer, in degrees; η is the relative position coefficient of the vertical foot; Step 5: Substitute the basic data in step 1 into the general formula of true thickness of rock formation in step 4 to calculate the true thickness of rock formation; The establishment of the three-dimensional geometric model is divided into three major situations: rock layer tilt, rock layer horizontal and rock layer vertical; According to the elevation relationship between the top point and the bottom point, the rock layer inclination is divided into three situations: the top point elevation is greater than the bottom point elevation, the top point elevation is equal to the bottom point elevation, and the top point elevation is less than the bottom point elevation. When the rock formation is inclined, point d is set as the projection point of point a on the horizontal plane passing through point b, and straight line m is set as the rock formation strike line passing through point b; The situation where the elevation of the top point is greater than the elevation of the bottom point when the rock layer is inclined is divided into three subdivisions: point d is located on the right side of the straight line m, point d is located on the straight line m, and point d is located on the left side of the straight line m.

2. The method for quickly and accurately calculating the true thickness of rock formations based on a three-dimensional geometric model according to claim 1 is characterized in that: In step 2, When the rock layer is inclined, the specific method of establishing a three-dimensional geometric model is: Step S211: draw a horizontal plane k passing through point b; suppose the strike lines of the top and bottom of the rock layer on plane k are straight lines l and m respectively, the projection point of point a on plane k is point d, connect ad, then l∥m, line segment ad⊥plane k; Step S212: Make a cuboid so that the bottom surface ABCD of the cuboid coincides with the plane k; the left and right edges of the bottom surface of the cuboid are parallel to the strike line of the rock formation, that is, the straight line AD||l||m||BC; Step S213: Draw the top and bottom surfaces of the rock layer in the cuboid using auxiliary lines; set the surface CDMP of the cuboid as the front surface; Step S214: draw a surface afd⊥ lines l and m, and intersect at points f and e respectively, connect af and df, then af⊥ lines l and m, df⊥ lines l and m; Step S215: Assume that the intersection of the straight line ad and the bottom of the rock layer is point c, connect ce, then ∠ced and ∠afd are the true inclination angle α of the rock layer surface, that is, ∠ced=∠afd=α; Step S216: connect cb and db, then ∠cbd is the apparent inclination angle γ of the rock layer on the vertical plane cbd, that is, ∠cbd=γ; Step S217: ∠dbe is the angle β between the azimuth line bd of the straight line ab and the strike line m of the bottom of the rock layer, then ∠dbe=β; Step S218: Draw a line segment cj⊥af and intersect it at point j, then ∠acj=α, the line segment cj is a common perpendicular line segment between the top and bottom surfaces of the rock layer, and its length is the true thickness of the rock layer; The formula for calculating the true thickness of the rock layer is: H = (h1-h2) × cosα-η × ((x1-x2) 2 +(y1-y2) 2 ) 0.5 ×sinβsinα.

3. The method for quickly and accurately calculating the true thickness of rock formations based on a three-dimensional geometric model according to claim 1 is characterized in that: When the rock layer is horizontal, the specific method of establishing a three-dimensional geometric model is: Step S221: Make a cuboid so that the bottom surface ABCD of the cuboid coincides with the bottom surface of the rock layer. Since the bottom surface of the rock layer is a horizontal plane, the bottom surface ABCD of the cuboid is also a horizontal plane. The intersection points of the top surface of the rock layer and the edges of the cuboid are set as points E, F, G, and H respectively, and the surface MPCD is set as the front surface. Step S222: Let the projection point of point a on plane ABCD be point d, connect ad, then line segment ad⊥plane ABCD; Step S223: The top and bottom surfaces of the rock formation are parallel, that is, the surface EFGH∥the surface ABCD, then the line segment ad⊥the surface EFGH, then the line segment ad is the common perpendicular line segment of the top and bottom surfaces of the rock formation, and its length is the true thickness H of the rock formation; The formula for calculating the true thickness of the rock layer is: H=h1-h2.

4. The method for quickly and accurately calculating the true thickness of rock formations based on a three-dimensional geometric model according to claim 1 is characterized in that: When the rock layer is vertical, the specific method of establishing a three-dimensional geometric model is: Step S231: draw a horizontal plane k passing through point b; let the strike lines of the top and bottom of the rock layer on plane k be straight lines l and m respectively, the projection point of point a on plane k is point d, connect ad, then l∥m, point d is on straight line l, line segment ad⊥plane k and⊥straight line l; Step S232: Make a cuboid so that the bottom surface ABCD of the cuboid coincides with the plane k; the left and right edges of the bottom surface of the cuboid are parallel to the strike line of the rock formation, that is, the straight line AD∥l∥m; Step S233: Draw the top and bottom surfaces of the rock layer in the cuboid using auxiliary lines; set the surface MPCD as the front surface; Step S234: connect ab and db, then the straight line db is the azimuth line of the straight line ab on the horizontal plane k, ∠dbf is the angle β between the azimuth line bd of the straight line ab and the strike line m of the bottom of the rock layer, then ∠dbf=β; Step S235: Let the projection point of point d on plane IJKL be point f, connect df, then point f is on straight line IJ, line segment df⊥plane IJKL, then line segment df is the common perpendicular line segment of the top and bottom surfaces of the rock layer, and its length is the true thickness H of the rock layer; The formula for calculating the true thickness of the rock layer is: H = ((x1-x2) 2 +(y1-y2) 2 ) 0.5 ×sinβ.

5. The method for quickly and accurately calculating the true thickness of rock formations based on a three-dimensional geometric model according to claim 2 is characterized in that: In step 3, when the elevation of the top point a is greater than the elevation of the bottom point b when the rock layer is inclined, and point d is located on the right side of the straight line m, the true thickness of the rock layer H = (h1-h2) × cosα-((x1-x2) 2 +(y1-y2) 2 ) 0.5 ×sinβsinα; When the rock layer is inclined, the elevation of the top point a is greater than the elevation of the bottom point b, and point d is located on the straight line m, the true thickness of the rock layer H = (h1-h2) × cosα; When the rock layer is inclined, the elevation of the top point a is greater than the elevation of the bottom point b, and point d is located on the left side of the straight line m, the true thickness of the rock layer H = (h1-h2) × cosα + ((x1-x2) 2 +(y1-y2) 2 ) 0.5 ×sinβsinα; When the elevation of the top point a is equal to the elevation of the bottom point b when the rock layer is inclined, the true thickness of the rock layer H = ((x1-x2) 2 +(y1-y2) 2 ) 0.5 ×sinβsinα; When the rock layer is inclined, the elevation of the top point a is less than the elevation of the bottom point b, the true thickness of the rock layer H = (h1-h2) × cosα + ((x1-x2) 2 +(y1-y2) 2 ) 0.5 ×sinβsin.

Images